Table

best variational

-0.4341237

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4341237exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.4341237best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.4341229	8.0e-7	1.7e-7	variational	VMC (RNN)	Wu et al. (2024)	run script	2024
-0.4340889	3.5e-5	2.6e-6	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4336375	4.9e-4	3.9e-6	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-0.4452193

best variational

-0.4452193

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4452193exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.4452193best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.4452189	4.5e-7	5.7e-8	variational	VMC (RNN)	Wu et al. (2024)	run script	2024
-0.4452186	7.1e-7	9.0e-8	variational	VMC (RNN)	Wu et al. (2024)	run script	2024
-0.4451815	3.8e-5	4.1e-6	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.4450490	1.7e-4	5.1e-6	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4443974	8.2e-4	6.1e-6	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

QMBL check, checks/bethe-heisenberg-chain/

exact

-0.4422078

Exact solution

best variational

-0.4422078

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4422078exact	0	n/a	exact	Exact solution	QMBL check, checks/bethe-heisenberg-chain/	QMBL code	n/a
-0.4422078best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.4378396	4.4e-3	5.0e-6	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4324019	9.8e-3	5.5e-6	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

QMBL check, checks/bethe-heisenberg-chain/

exact

-0.4431678

Exact solution

best variational

-0.4431678

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4431678exact	0	n/a	exact	Exact solution	QMBL check, checks/bethe-heisenberg-chain/	QMBL code	n/a
-0.4431678best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.4430967	7.1e-5	1.6e-6	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.4391762	4.0e-3	4.6e-6	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4334590	9.7e-3	5.6e-6	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-0.513442(1)

variational wave function

best extrapolated

-0.5132(2)

DMRG

best approximate

-0.5138(2)

NLCE

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.513442best variational	0	1.0e-6	variational	variational wave function	Schäfer et al. (2023)	2023
-0.5132best extrapolated	0	2.0e-4	extrapolated	DMRG	Schäfer et al. (2023)	2023
-0.5138best approximate	0	2.0e-4	approximate	NLCE	Schäfer et al. (2023)	2023
-0.5000	1.4e-2	n/a	approximate	NLCE	Schäfer et al. (2023)	2023

best variational

-1.5339(5)

variational wave function

best extrapolated

-1.532(1)

DMRG

best approximate

-1.533(2)

NLCE

E/N (S.S)	σ	bound type	method	source	year
-1.5339best variational	5.0e-4	variational	variational wave function	Schäfer et al. (2023)	2023
-1.532best extrapolated	1.0e-3	extrapolated	DMRG	Schäfer et al. (2023)	2023
-1.533best approximate	2.0e-3	approximate	NLCE	Schäfer et al. (2023)	2023

best variational

-0.48946(5)

variational wave function

best extrapolated

-0.4865(7)

DMRG

best approximate

-0.492(1)

NLCE

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.48946best variational	0	5.0e-5	variational	variational wave function	Schäfer et al. (2023)	2023
-0.4865best extrapolated	0	7.0e-4	extrapolated	DMRG	Schäfer et al. (2023)	2023
-0.492best approximate	0	1.0e-3	approximate	NLCE	Schäfer et al. (2023)	2023
-0.467	2.5e-2	n/a	approximate	NLCE	Schäfer et al. (2023)	2023

best variational

-1.490(1)

variational wave function

best extrapolated

-1.4764(5)

DMRG

best approximate

-1.489(5)

NLCE

E/N (S.S)	σ	bound type	method	source	year
-1.490best variational	1.0e-3	variational	variational wave function	Schäfer et al. (2023)	2023
-1.4764best extrapolated	5.0e-4	extrapolated	DMRG	Schäfer et al. (2023)	2023
-1.489best approximate	5.0e-3	approximate	NLCE	Schäfer et al. (2023)	2023

best variational

-0.5421(4)

VMC (LCN)

Fu et al. (2022)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5421best variational	0	4.0e-4	variational	VMC (LCN)	Fu et al. (2022)		2022

best extrapolated

-0.4386(5)

DMRG

Depenbrock et al. (2012)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.4386best extrapolated	0	5.0e-4	extrapolated	DMRG	Depenbrock et al. (2012)	2012
-0.4379tied with best extrapolated at 2σ	7.0e-4	3.0e-4	extrapolated	DMRG	Yan et al. (2011)	2011
-0.4375tied with best extrapolated at 2σ	1.1e-3	6.0e-5	extrapolated	iPESS	Liao et al. (2017)	2017

exact

-0.4412486

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4412486exact	0	n/a	exact	ED	Läuchli et al. (2011)		2011

exact

-0.4537396

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4537396exact	0	n/a	exact	ED	Läuchli et al. (2011)		2011

exact

-0.4471262

best variational

-0.4471262

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4471262exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.4471262best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.4467304	4.0e-4	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.4376736	9.5e-3	3.3e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4043250	4.3e-2	4.4e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-0.4384773

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4384773exact	0	n/a	exact	ED	Läuchli et al. (2011)		2011

exact

-0.4385521

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4385521exact	0	n/a	exact	ED	Läuchli et al. (2011)		2011

exact

-0.4390813

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4390813exact	0	n/a	exact	ED	Läuchli et al. (2011)		2011

exact

-0.4392871

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4392871exact	0	n/a	exact	ED	Läuchli et al. (2011)		2011

exact

-0.4383765

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4383765exact	0	n/a	exact	ED	Läuchli et al. (2011)		2011

exact

-0.437999

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.437999exact	0	n/a	exact	ED	Läuchli et al. (2011)		2011

exact

-0.4381426

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4381426exact	0	n/a	exact	ED	Läuchli et al. (2011)		2011

exact

-0.4387039

best variational

-0.4375(2)

VMC (GCNN)

Đurić et al. (2024)

uses NetKet

best extrapolated

-0.4383(2)

DMRG

Depenbrock et al. (2012)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4387039exact	0	n/a	exact	ED	Wietek & Läuchli (2018)		2018
-0.4375best variational	0	2.1e-4	variational	VMC (GCNN)	Đurić et al. (2024)	uses NetKet	2024
-0.4304	7.1e-3	2.6e-5	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.4383best extrapolated	0	2.0e-4	extrapolated	DMRG	Depenbrock et al. (2012)		2012

best extrapolated

-0.4383(3)

DMRG

Depenbrock et al. (2012)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4461111	n/a	n/a	variational non-ergodic sampling	VMC (GCNN)	Đurić et al. (2024)	uses NetKet	2024
-0.4383best extrapolated	0	3.0e-4	extrapolated	DMRG	Depenbrock et al. (2012)		2012

best variational

-0.42987(1)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.42987best variational	0	1.4e-5	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.42868	1.2e-3	3.0e-5	variational	VMC (Gutzwiller)	He et al. (2024)		2024
-0.42866	1.2e-3	2.0e-5	variational	VMC (Gutzwiller)	Ran et al. (2007)		2007
-0.42724	2.6e-3	3.0e-5	variational	VMC (Gutzwiller)	He et al. (2024)		2024

best variational

-0.489472(8)

variational wave function

best extrapolated

-0.490(6)

DMRG

Hagymási et al. (2020)

best approximate

-0.49(1)

NLCE

Hagymási et al. (2020)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.489472best variational	0	8.0e-6	variational	variational wave function	Schäfer et al. (2023)	2023
-0.490best extrapolated	0	6.0e-3	extrapolated	DMRG	Hagymási et al. (2020)	2020
-0.49best approximate	0	1.5e-2	approximate	NLCE	Hagymási et al. (2020)	2020
-0.49tied with best approximate at 2σ	<1e-2	n/a	approximate	NLCE	Schäfer et al. (2023)	2023
-0.49tied with best approximate at 2σ	<1e-2	5.0e-4	approximate	NLCE	Schäfer et al. (2023)	2023
-0.47tied with best approximate at 2σ	2.8e-2	n/a	approximate	NLCE	Schäfer et al. (2023)	2023

best variational

-1.490(1)

variational wave function

best approximate

-1.489(5)

NLCE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-1.490best variational	0	1.0e-3	variational	variational wave function	Schäfer et al. (2023)		2023
-1.489best approximate	0	5.0e-3	approximate	NLCE	Schäfer et al. (2023)		2023

QMBL check, checks/pyrochlore-32-ed/

exact

-0.5168588

best variational

-0.5162(1)

VMC (PP)

uses mVMC

best extrapolated

-0.5168

DMRG

Hagymási et al. (2020)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5168588exact	0	n/a	exact	ED	QMBL check, checks/pyrochlore-32-ed/	QMBL code	n/a
-0.5162best variational	0	1.0e-4	variational	VMC (PP)	Astrakhantsev et al. (2021)	uses mVMC	2021
-0.5152	9.7e-4	2.3e-5	variational	VMC (RBM)	Wu et al. (2024)	uses NetKet	2024
-0.5128	3.4e-3	1.0e-4	variational	VMC (CNN)	Astrakhantsev et al. (2021)	uses NetKet	2021
-0.5168best extrapolated	0	n/a	extrapolated	DMRG	Hagymási et al. (2020)		2020

best variational

-0.49229(7)

VMC (PP + RBM)

uses mVMC

best extrapolated

-0.49434(5)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.49229best variational	0	7.0e-5	variational	VMC (PP + RBM)	Pohle et al. (2023)	uses mVMC	2023
-0.49098	1.3e-3	1.0e-5	variational	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023
-0.49033	2.0e-3	5.0e-6	variational	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023
-0.48909	3.2e-3	2.0e-6	variational	VMC (PP + RBM)	Pohle et al. (2023)	uses mVMC	2023
-0.48602	6.3e-3	3.0e-6	variational	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023
-0.48545	6.8e-3	3.0e-6	variational	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023
-0.49434best extrapolated	0	5.0e-5	extrapolated	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023
-0.49280tied with best extrapolated at 2σ	1.5e-3	1.0e-3	extrapolated	DMRG	Hagymási et al. (2020)		2020

best variational

-0.5028(2)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5028best variational	0	2.0e-4	variational	VMC (PP)	Astrakhantsev et al. (2021)	uses mVMC	2021

best variational

-0.4924(2)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4924best variational	0	2.0e-4	variational	VMC (PP)	Astrakhantsev et al. (2021)	uses mVMC	2021
-0.4908	1.6e-3	2.0e-4	variational	VMC (CNN)	Astrakhantsev et al. (2021)	uses NetKet	2021

best variational

-0.4917(4)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4917best variational	0	4.0e-4	variational	VMC (PP)	Astrakhantsev et al. (2021)	uses mVMC	2021
-0.4900tied with best variational at 2σ	1.7e-3	1.0e-3	variational	VMC (CNN)	Astrakhantsev et al. (2021)	uses NetKet	2021

best variational

-0.4915(2)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4915best variational	0	2.0e-4	variational	VMC (PP)	Astrakhantsev et al. (2021)	uses mVMC	2021

best variational

-0.4871(1)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4871best variational	0	1.0e-4	variational	VMC (PP)	Astrakhantsev et al. (2021)	uses mVMC	2021
-0.4851	2.0e-3	n/a	variational	DMRG	Hagymási et al. (2020)		2020
-0.4826	4.5e-3	2.0e-4	variational	VMC (CNN)	Astrakhantsev et al. (2021)	uses NetKet	2021

best variational

-0.48851(3)

VMC (PP)

uses mVMC

best extrapolated

-0.4924(2)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.48851best variational	0	3.0e-5	variational	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023
-0.48530	3.2e-3	8.0e-6	variational	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023
-0.48524	3.3e-3	7.0e-6	variational	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023
-0.4924best extrapolated	0	2.0e-4	extrapolated	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023
-0.4923tied with best extrapolated at 2σ	1.0e-4	2.0e-4	extrapolated	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023

best variational

-0.485584(3)

VMC (RVB)

Cheng & Li (2026)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.485584best variational	0	2.9e-6	variational	VMC (RVB)	Cheng & Li (2026)		2026
-0.483100	2.5e-3	1.0e-4	variational	VMC (PP)	Astrakhantsev et al. (2021)	uses mVMC	2021

best variational

-0.48800(1)

VMC (PP)

best extrapolated

-0.4921(2)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.48800best variational	0	1.2e-5	variational	VMC (PP)	Pohle et al. (2023)	run script	2023
-0.48537	2.6e-3	1.0e-5	variational	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023
-0.4921best extrapolated	0	2.0e-4	extrapolated	VMC (PP)	Pohle et al. (2023)	uses mVMC	2023

exact (stochastic)

-0.6599522(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6599522exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6612549(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6612549exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6622809(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6622809exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6630939(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6630939exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6637496(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6637496exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6642865(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6642865exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6651098(6)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6651098exact (stochastic)	0	5.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6661668(6)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6661668exact (stochastic)	0	6.0e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6672462(6)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6672462exact (stochastic)	0	6.0e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6623181(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6623181exact (stochastic)	0	3.8e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6677918(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6677918exact (stochastic)	0	4.0e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6570101(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6570101exact (stochastic)	0	3.8e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact

-0.6759867

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6759867exact	0	n/a	exact	ED	Wietek & Läuchli (2018)		2018

exact (stochastic)

-0.6583592(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6583592exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact

-0.4483291

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4483291exact	0	n/a	exact	ED	Astrakhantsev et al. (2021)		2021

best variational

-0.43826(1)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.43826best variational	0	1.2e-5	variational	VMC (PP)	Wu et al. (2024)	uses mVMC	2024

best variational

-0.4376(1)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4376best variational	0	1.0e-4	variational	VMC (PP)	Wu et al. (2024)	uses mVMC	2024

best variational

-0.4371(1)

VMC (PP)

uses mVMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4371best variational	0	1.0e-4	variational	VMC (PP)	Wu et al. (2024)	uses mVMC	2024

exact

-0.7017802

best variational

-0.7017449

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.7017802exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.7017449best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.7017252	2.0e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.6035218

best variational

-0.6035218

DMRG

Huang et al. (2016)

best extrapolated

-0.60351496(1)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6035222	−3.3e-7	1.7e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.6035218exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.603535	n/a	1.0e-6	variational below exact energy	PEPS	Liu et al. (2016)		2016
-0.603523	n/a	1.0e-6	variational below exact energy	PEPS	Liu et al. (2016)		2016
-0.6035218best variational	0	n/a	variational	DMRG	Huang et al. (2016)		2016
-0.6035218	<1e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.6035190tied with best variational at 2σ	2.8e-6	2.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026
-0.6035170tied with best variational at 2σ	4.8e-6	6.0e-6	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.6035160	5.8e-6	1.0e-6	variational	VMC (RNN)	Hibat-Allah et al. (2022)	mhibatallah/RNNWavefunctions	2022
-0.6034969	2.5e-5	2.2e-6	variational	VMC (Adaptive RNN)	McNaughton & Hibat-Allah (2026)	jakemcnaughton/AdaptiveRNNWaveFunctions	2026
-0.6034864	3.5e-5	2.5e-6	variational	VMC (Adaptive RNN)	McNaughton & Hibat-Allah (2026)	jakemcnaughton/AdaptiveRNNWaveFunctions	2026
-0.6034833	3.8e-5	2.8e-6	variational	VMC (RNN)	McNaughton & Hibat-Allah (2026)	jakemcnaughton/AdaptiveRNNWaveFunctions	2026
-0.6034170	1.0e-4	n/a	variational	VMC (LSTM)	Roth (2020)	chrisrothUT/Iterative-Retraining	2020
-0.5948382	8.7e-3	2.5e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.5936507	9.9e-3	2.4e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.60351496best extrapolated	0	1.0e-8	extrapolated	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact

-0.6788721

Richter et al. (2004)

best variational

-0.678871(3)

VMC (CNN BF + RBM)

Hendry et al. (2025)

uses NetKet

best extrapolated

-0.67887177(7)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6788722	−<1e-7	2.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.6788721exact	0	n/a	exact	ED	Richter et al. (2004)		2004
-0.6788721	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.678871best variational	0	3.0e-6	variational	VMC (CNN BF + RBM)	Hendry et al. (2025)	uses NetKet	2025
-0.678870tied with best variational at 2σ	1.0e-6	2.0e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.678870tied with best variational at 2σ	1.0e-6	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.678868tied with best variational at 2σ	3.0e-6	2.0e-6	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.678820	5.1e-5	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.678800	7.1e-5	n/a	variational	VMC (CNN)	Ou et al. (2025)		2025
-0.678622	2.5e-4	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.678500tied with best variational at 2σ	3.7e-4	2.0e-4	variational	VMC (EPS)	Mezzacapo et al. (2009)		2009
-0.669741	9.1e-3	2.6e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.668543	1.0e-2	2.6e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.67887177best extrapolated	0	7.0e-8	extrapolated	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact

-0.6779156

Richter et al. (2004)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6779156exact	0	n/a	exact	ED	Richter et al. (2004)		2004

exact

-0.6773713

Richter et al. (2004)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6773713exact	0	n/a	exact	ED	Richter et al. (2004)		2004
-0.6773713	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

exact

-0.675102

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.675102exact	0	n/a	exact	ED	Wietek & Läuchli (2018)		2018

exact (stochastic)

-0.6190371(2)

SSE QMC

best variational

-0.619034(6)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6190371exact (stochastic)	0	1.7e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.619034best variational	0	5.8e-6	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.619033tied with best variational at 2σ	1.5e-6	3.0e-6	variational	PEPS	Liu et al. (2016)		2016
-0.619025tied with best variational at 2σ	9.5e-6	5.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026
-0.619013	2.1e-5	2.0e-6	variational	PEPS	Liu et al. (2016)		2016

exact (stochastic)

-0.67349005(2)

SSE QMC

best variational

-0.6735

VMC (HQT)

Guo et al. (2026)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.67349005exact (stochastic)	0	2.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.6735best variational	0	n/a	variational	VMC (HQT)	Guo et al. (2026)	uses NetKet	2026
-0.6735	<1e-4	3.0e-6	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.6735tied with best variational at 2σ	<1e-4	2.3e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.6734	<1e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.6735047	n/a	2.0e-7	extrapolated below exact by > 2σ	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact (stochastic)

-0.6286561(2)

SSE QMC

best variational

-0.628656(9)

VMC (2D RNN)

best extrapolated

-0.628657(5)

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6286562	−<1e-7	2.0e-6	exact (stochastic)	QMC	Lubasch et al. (2014)	uses ALPS	2014
-0.6286561exact (stochastic)	0	1.8e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.628656best variational	0	9.0e-6	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.628649tied with best variational at 2σ	7.3e-6	1.7e-6	variational	VMC (RNN)	Wu et al. (2024)	run script	2024
-0.628638tied with best variational at 2σ	1.8e-5	1.1e-6	variational	VMC (2D RNN)	Hibat-Allah et al. (2022)	run script	2022
-0.628637tied with best variational at 2σ	1.9e-5	4.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026
-0.628633	2.3e-5	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.628627	2.9e-5	1.0e-6	variational	VMC (NAQS)	Sharir et al. (2019)	uses FlowKet	2019
-0.628607	4.8e-5	2.5e-6	variational	VMC (RNN)	Wu et al. (2024)	run script	2024
-0.628605	5.1e-5	6.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026
-0.628601	5.5e-5	2.0e-6	variational	PEPS	Liu et al. (2017)		2017
-0.628528	1.3e-4	3.8e-6	variational	VMC (Tensor-RNN)	Wu et al. (2024)	cqsl/mps-rnn	2024
-0.628507	1.5e-4	1.0e-6	variational	PEPS	Liu et al. (2016)		2016
-0.628486	1.7e-4	6.0e-6	variational	VMC (pRNN)	Attar et al. (2026)	werro40/RNN-Natural-Gradients	2026
-0.628400	2.6e-4	2.0e-5	variational	VMC (pRNN)	Attar et al. (2026)	werro40/RNN-Natural-Gradients	2026
-0.627697	9.6e-4	5.5e-6	variational	VMC (2D MPS-RNN)	Wu et al. (2023)	cqsl/mps-rnn	2023
-0.626110	2.5e-3	1.0e-5	variational	PEPS	Liu et al. (2016)		2016
-0.625865	2.8e-3	1.0e-5	variational	VMC (1D MPS-RNN)	Wu et al. (2023)	cqsl/mps-rnn	2023
-0.622758	5.9e-3	1.3e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.620268	8.4e-3	1.4e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.628657best extrapolated	0	4.8e-6	extrapolated	DMRG	Wu et al. (2024)	run script	2024
-0.628641	1.6e-5	5.0e-8	extrapolated	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact (stochastic)

-0.67155266(2)

SSE QMC

best variational

-0.67155260(3)

VMC (ResNet)

Chen & Heyl (2023)

ChenAo-Phys/MinSR

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.67155266exact (stochastic)	0	2.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.67155260best variational	0	3.0e-8	variational	VMC (ResNet)	Chen & Heyl (2023)	ChenAo-Phys/MinSR	2023
-0.67154400	8.6e-6	4.0e-6	variational	VMC (CNN BF + RBM)	Hendry et al. (2025)	uses NetKet	2025
-0.67151900	3.4e-5	4.0e-6	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.67151000	4.3e-5	2.0e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.67147600	7.7e-5	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.67143100	1.2e-4	2.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.67140000	1.5e-4	1.3e-5	variational	VMC (RNN)	Wu et al. (2024)	run script	2024
-0.67135000	2.0e-4	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.67113450	4.2e-4	1.3e-6	variational	VMC (RNN)	Wu et al. (2024)	run script	2024
-0.66935250	2.2e-3	1.0e-5	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.66485616	6.7e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.66443150	7.1e-3	1.5e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.66421150	7.3e-3	1.4e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.6715950	n/a	5.0e-7	extrapolated below exact by > 2σ	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact (stochastic)

-0.6352007(2)

SSE QMC

best variational

-0.635201(7)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6352007exact (stochastic)	0	1.8e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.635201best variational	0	6.9e-6	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.635127	7.4e-5	7.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.67068192(2)

SSE QMC

best variational

-0.67062(2)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.67068192exact (stochastic)	0	2.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.67062best variational	0	2.3e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.6707008	n/a	1.0e-7	extrapolated below exact by > 2σ	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact (stochastic)

-0.6399410(2)

SSE QMC

best variational

-0.639929(6)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6399410exact (stochastic)	0	1.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.639929best variational	0	5.7e-6	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.639842	8.7e-5	6.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.67023225(2)

SSE QMC

best variational

-0.67014(2)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.67023225exact (stochastic)	0	2.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.67014best variational	0	2.1e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.66835	1.8e-3	7.7e-6	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.66381	6.3e-3	1.0e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.66256	7.6e-3	1.0e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.65866	1.1e-2	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.6703092	n/a	5.0e-7	extrapolated below exact by > 2σ	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact (stochastic)

-0.6435317(2)

SSE QMC

best variational

-0.643522(7)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6435317exact (stochastic)	0	1.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.643522best variational	0	7.2e-6	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.643504tied with best variational at 2σ	1.8e-5	3.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026
-0.643448	7.4e-5	1.0e-6	variational	VMC (NAQS)	Sharir et al. (2019)	uses FlowKet	2019
-0.643396	1.3e-4	6.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026
-0.643391	1.3e-4	3.0e-6	variational	PEPS	Liu et al. (2017)		2017

exact (stochastic)

-0.66997660(2)

SSE QMC

best variational

-0.66987(2)

VMC (2D RNN)

best extrapolated

-0.6699687(9)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.66997660exact (stochastic)	0	2.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.66987best variational	0	2.1e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.66972	1.5e-4	1.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.6699687best extrapolated	0	9.0e-7	extrapolated	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact (stochastic)

-0.6463451(4)

SSE QMC

best variational

-0.646337(5)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6463451exact (stochastic)	0	3.8e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.646337best variational	0	5.1e-6	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.646186	1.5e-4	6.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66982043(2)

SSE QMC

best variational

-0.66968(2)

VMC (2D RNN)

best extrapolated

-0.6697819(5)

VMC (2D RNN)

E/N (S.S)	σ	bound type	method	source	code	year
-0.66982043exact (stochastic)	2.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.66968best variational	1.7e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.6697819best extrapolated	5.0e-7	extrapolated	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact (stochastic)

-0.6486091(4)

SSE QMC

best variational

-0.648590(5)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6486091exact (stochastic)	0	3.8e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.648590best variational	0	5.0e-6	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.648401	1.9e-4	5.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66971967(2)

SSE QMC

best variational

-0.66959(1)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.66971967exact (stochastic)	0	2.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.66959best variational	0	1.5e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.6697420	n/a	6.0e-7	extrapolated below exact by > 2σ	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact (stochastic)

-0.6504689(4)

SSE QMC

best variational

-0.650253(5)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6504689exact (stochastic)	0	3.8e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.650253best variational	0	5.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66965176(2)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66965176exact (stochastic)	0	2.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6520251(4)

SSE QMC

best variational

-0.651982(7)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6520251exact (stochastic)	0	3.8e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.651982best variational	0	6.8e-6	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.651812	1.7e-4	5.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66960434(2)

SSE QMC

best variational

-0.66944(2)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.66960434exact (stochastic)	0	2.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.66944best variational	0	1.5e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.66924	2.0e-4	2.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.6696127	n/a	5.0e-7	extrapolated below exact by > 2σ	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

exact (stochastic)

-0.6533456(4)

SSE QMC

best variational

-0.653129(5)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6533456exact (stochastic)	0	3.8e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.653129best variational	0	5.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66957017(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66957017exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6544806(4)

SSE QMC

best variational

-0.654261(4)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6544806exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.654261best variational	0	4.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66954496(3)

SSE QMC

best variational

-0.66937(1)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.66954496exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.66937best variational	0	1.3e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.6695580	n/a	4.0e-7	extrapolated below exact by > 2σ	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

best variational

-0.655241(4)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.655241best variational	0	4.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66952595(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66952595exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6563289(4)

SSE QMC

best variational

-0.656089(4)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6563289exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.656089best variational	0	4.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66951133(3)

SSE QMC

best variational

-0.66930(1)

VMC (2D RNN)

best extrapolated

-0.6694877(4)

VMC (2D RNN)

E/N (S.S)	σ	bound type	method	source	code	year
-0.66951133exact (stochastic)	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.66930best variational	1.3e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.6694877best extrapolated	4.0e-7	extrapolated	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025

best variational

-0.657523(4)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.657523best variational	0	4.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66949091(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66949091exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

best variational

-0.658657(4)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.658657best variational	0	4.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66947776(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66947776exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

best variational

-0.659565(4)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.659565best variational	0	4.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66946889(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66946889exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

best variational

-0.659941(4)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.659941best variational	0	4.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.6606690(4)

SSE QMC

best variational

-0.660323(4)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6606690exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026
-0.660323best variational	0	4.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66946274(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66946274exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

best variational

-0.660649(3)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.660649best variational	0	3.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

best variational

-0.660967(4)

VMC (minGRU)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.660967best variational	0	4.0e-6	variational	VMC (minGRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026

exact (stochastic)

-0.66945833(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66945833exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.66945502(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66945502exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.66945260(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66945260exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6628515(4)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6628515exact (stochastic)	0	3.9e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.66945072(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66945072exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.66944815(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66944815exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.66944645(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66944645exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.66944530(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66944530exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6650415(2)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6650415exact (stochastic)	0	1.6e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.66944454(3)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.66944454exact (stochastic)	0	3.0e-8	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

exact (stochastic)

-0.6661389(2)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6661389exact (stochastic)	0	1.8e-7	exact (stochastic)	SSE QMC	Sandvik (2026)		2026

best variational

-0.6693781

iPEPS

Rader & Läuchli (2018)

best extrapolated

-0.669441878(9)

SSE QMC

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.6693781best variational	0	n/a	variational	iPEPS	Rader & Läuchli (2018)	2018
-0.6690838	2.9e-4	n/a	variational	iPEPS	Rader & Läuchli (2018)	2018
-0.6679742	1.4e-3	n/a	variational	iPEPS	Rader & Läuchli (2018)	2018
-0.6602311	9.1e-3	n/a	variational	iPEPS	Rader & Läuchli (2018)	2018
-0.669441878best extrapolated	0	9.0e-9	extrapolated	SSE QMC	Sandvik (2026)	2026
-0.669441866tied with best extrapolated at 2σ	1.2e-8	1.0e-8	extrapolated	SSE QMC	Sandvik (2026)	2026
-0.669441865tied with best extrapolated at 2σ	1.3e-8	1.1e-8	extrapolated	SSE QMC	Sandvik (2026)	2026
-0.669441861tied with best extrapolated at 2σ	1.7e-8	6.0e-9	extrapolated	SSE QMC	Sandvik (2026)	2026
-0.669441857tied with best extrapolated at 2σ	2.1e-8	7.0e-9	extrapolated	SSE QMC	Sandvik (2026)	2026
-0.669437000tied with best extrapolated at 2σ	4.9e-6	5.0e-6	extrapolated	SSE QMC	Sandvik (1997)	1997
-0.669436000tied with best extrapolated at 2σ	5.9e-6	5.0e-6	extrapolated	SSE QMC	Sandvik (1997)	1997
-0.669430000tied with best extrapolated at 2σ	1.2e-5	2.0e-5	extrapolated	SSE QMC	Sandvik (1997)	1997
-0.669420000tied with best extrapolated at 2σ	2.2e-5	2.0e-5	extrapolated	iPEPS	Rader & Läuchli (2018)	2018
-0.668938000	5.0e-4	6.0e-6	extrapolated	2D minGRU, 3 layers, c4v symmetry, iterative retraining (PSR-NQS)	Merali et al. (2026)	2026

exact

-0.5347197

best variational

-0.5347197

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5347197exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5347197best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.5340324	6.9e-4	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5241703	1.1e-2	5.3e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.5171016	1.8e-2	4.2e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-0.5603734

best variational

-0.560313(3)

VMC (GCNN)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5603734exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.560313best variational	0	3.0e-6	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.560100tied with best variational at 2σ	2.1e-4	4.0e-4	variational	VMC (LCN)	Fu et al. (2022)		2022
-0.559220	1.1e-3	n/a	variational	VMC (GCNN)	Roth & MacDonald (2021)		2021
-0.559214	1.1e-3	6.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.558740	1.6e-3	4.4e-5	variational	VMC (GCNN)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.558102	2.2e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.558008	2.3e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.556200	4.1e-3	2.0e-4	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.555494	4.8e-3	4.7e-5	variational	VMC (ViT)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.555190	5.1e-3	4.0e-5	variational	VMC (PP)	Kaneko et al. (2014), quoted in Iqbal et al. (2016)		2014
-0.555045	5.3e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.554200	6.1e-3	5.0e-5	variational	VMC (EPS)	Mezzacapo & Cirac (2010)		2010
-0.553	n/a	n/a	variational quote-not-in-primary	VMC (Neural Gutzwiller)	Ferrari et al. (2019)		2019
-0.551480	8.8e-3	5.0e-5	variational	VMC (Gutzwiller)	Heidarian et al. (2009)		2009
-0.550088	1.0e-2	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.548025	1.2e-2	3.0e-6	variational	VMC (Gutzwiller)	Iqbal et al. (2016)		2016
-0.543000	1.7e-2	1.0e-3	variational	VMC (Gutzwiller)	Weber et al. (2006)		2006
-0.531981	2.8e-2	1.2e-4	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.510044	5.0e-2	1.7e-4	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.491608	6.9e-2	4.5e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.486783	7.4e-2	4.2e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-0.558603

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.558603exact	0	n/a	exact	ED	Wietek & Läuchli (2018)		2018

best variational

-0.5147668

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5147668best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.5138630	9.0e-4	8.8e-6	variational	VMC (Tensor-RNN)	Wu et al. (2023)	cqsl/mps-rnn	2023
-0.5080270	6.7e-3	1.3e-5	variational	VMC (2D MPS-RNN)	Wu et al. (2023)	cqsl/mps-rnn	2023
-0.5006900	1.4e-2	1.0e-5	variational	VMC (RNN)	Wu et al. (2024)	run script	2024
-0.4896430	2.5e-2	2.2e-5	variational	VMC (1D MPS-RNN)	Wu et al. (2023)	cqsl/mps-rnn	2023
-0.4845483	3.0e-2	2.1e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4767457	3.8e-2	2.3e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-0.55315(3)

VMC (GCNN)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.55315best variational	0	3.0e-5	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.55190	1.2e-3	4.0e-4	variational	VMC (GNN)	Kochkov et al. (2021)		2021

best variational

-0.5150648

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5150648best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.5119722	3.1e-3	1.0e-4	variational	VMC (2D RNN)	Wu et al. (2024)	run script	2024
-0.5114972	3.6e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.4835200	3.2e-2	1.6e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4759670	3.9e-2	1.9e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-0.5493(1)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5493best variational	0	9.8e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.5470	2.3e-3	8.0e-5	variational	VMC (EPS)	Mezzacapo & Cirac (2010)		2010
-0.5462	3.1e-3	2.3e-5	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.5199	2.9e-2	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.4897	6.0e-2	2.3e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4855	6.4e-2	2.1e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-0.5138(1)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5138best variational	0	9.7e-5	variational	VMC (2D RNN)	Wu et al. (2024)	run script	2024
-0.5108	3.0e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.5105	3.3e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.4779	3.6e-2	1.9e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4764	3.7e-2	1.7e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-0.51668(9)

VMC (2D RNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.51668best variational	0	8.6e-5	variational	VMC (2D RNN)	Wu et al. (2024)	run script	2024
-0.50797	8.7e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.47747	3.9e-2	1.8e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.47581	4.1e-2	1.5e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-0.551703(1)

VMC (ViT)

best extrapolated

-0.55200(1)

VMC (ViT)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.551703best variational	0	1.0e-6	variational	VMC (ViT)	Viteritti et al. (2026)		2026
-0.548612	3.1e-3	6.8e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.547160	4.5e-3	3.0e-5	variational	VMC (RVB)	Heidarian et al. (2009)		2009
-0.545900	5.8e-3	1.0e-4	variational	VMC (EPS)	Mezzacapo & Cirac (2010)		2010
-0.545420	6.3e-3	1.0e-5	variational	VMC (Gutzwiller)	Ghorbani et al. (2015)		2015
-0.535700	1.6e-2	1.0e-5	variational	VMC (Gutzwiller)	Ghorbani et al. (2015)		2015
-0.535650	1.6e-2	2.0e-5	variational	VMC (Gutzwiller)	Ghorbani et al. (2015)		2015
-0.55200best extrapolated	0	1.0e-5	extrapolated	VMC (ViT)	Viteritti et al. (2026)		2026

best variational

-0.551602(1)

VMC (ViT)

best extrapolated

-0.55189(1)

VMC (ViT)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.551602best variational	0	1.0e-6	variational	VMC (ViT)	Viteritti et al. (2026)		2026
-0.548105	3.5e-3	5.6e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.55189best extrapolated	0	1.0e-5	extrapolated	VMC (ViT)	Viteritti et al. (2026)		2026

best variational

-0.551528(1)

VMC (ViT)

best extrapolated

-0.55180(1)

VMC (ViT)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.551528best variational	0	1.0e-6	variational	VMC (ViT)	Viteritti et al. (2026)		2026
-0.547934	3.6e-3	4.5e-5	variational	VMC (2D RNN)	Moss et al. (2025)	mschuylermoss/HeisenbergRNN	2025
-0.545348	6.2e-3	n/a	variational	VMC (Gutzwiller)	Iqbal et al. (2016)		2016
-0.55180best extrapolated	0	1.0e-5	extrapolated	VMC (ViT)	Viteritti et al. (2026)		2026

best variational

-0.551429(1)

VMC (ViT)

best extrapolated

-0.55171(1)

VMC (ViT)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.551429best variational	0	1.0e-6	variational	VMC (ViT)	Viteritti et al. (2026)		2026
-0.55171best extrapolated	0	1.0e-5	extrapolated	VMC (ViT)	Viteritti et al. (2026)		2026

J1-J2#

113 instances, energies as E/N (S.S)

lattice size

instance

value

energy

method

source

code

energies

best variational

-0.4538(4)

VMC (LCN)

Fu et al. (2022)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.4538best variational	0	4.0e-4	variational	VMC (LCN)	Fu et al. (2022)	2022
-0.4536tied with best variational at 2σ	2.0e-4	5.0e-4	variational	VMC (GNN)	Kochkov et al. (2021)	2021
-0.4528tied with best variational at 2σ	1.0e-3	2.0e-4	variational	VMC (GNN)	Kochkov et al. (2021)	2021
-0.4496	4.2e-3	4.0e-4	variational	VMC (ResNet)	Kochkov et al. (2021)	2021

exact

-0.5225249

best variational

-0.5225249

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5225249exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5225249best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.5218948	6.3e-4	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5218026	7.2e-4	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5132604	9.3e-3	3.2e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.5069396	1.6e-2	2.7e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-0.68059

best variational

-0.6805657

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.68059exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.6805657best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.6804795	8.6e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.6598172

best variational

-0.6597832

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6598172exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.6597832best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.6597647	1.9e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.6395429

best variational

-0.6395107

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6395429exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.6395107best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.6395066	4.1e-6	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.6198739

best variational

-0.6198639

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6198739exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.6198639best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.6198018	6.2e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.6009545

best variational

-0.6009332

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6009545exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.6009332best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.6009187	1.5e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.5829838

best variational

-0.5829522

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5829838exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5829522best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5829420	1.0e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.5662448

best variational

-0.5662285

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5662448exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5662285best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5662099	1.9e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.5511478

best variational

-0.5511135

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5511478exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5511135best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5511033	1.0e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.5382998

best variational

-0.5382766

VQE

best extrapolated

-0.5370(4)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5382998exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5382766best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5382744	2.2e-6	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5370best extrapolated	0	4.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

exact

-0.5286202

best variational

-0.5286202

DMRG

best extrapolated

-0.5268(4)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5286202exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5286202best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.5286173	2.9e-6	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5286100	1.0e-5	4.8e-6	variational	VMC (ClebschTree)	Wu et al. (2024)	uses NetKet	2024
-0.5285589	6.1e-5	1.1e-5	variational	VMC (GCNN)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.5261135	2.5e-3	1.5e-5	variational	VMC (ViT)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.5236726	4.9e-3	1.0e-4	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.5159672	1.3e-2	5.6e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.5149170	1.4e-2	1.1e-4	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.5079781	2.1e-2	2.3e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.5268best extrapolated	0	4.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

exact

-0.5258958

best variational

-0.5258158

VQE

best extrapolated

-0.518(2)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5258958exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5258158best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5257913	2.5e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.518best extrapolated	0	1.5e-3	extrapolated	TPS	Wang et al. (2011)		2011

exact

-0.5393825

best variational

-0.5393444

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5393825exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5393444best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5390826	2.6e-4	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.5638581

best variational

-0.5637716

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5638581exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5637716best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5637643	7.2e-6	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.5942731

best variational

-0.5942152

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5942731exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.5942152best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.5941871	2.8e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.6273351

best variational

-0.6273137

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6273351exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.6273137best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.6272153	9.8e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.6617197

best variational

-0.6617069

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6617197exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.6617069best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.6615474	1.6e-4	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.6968656

best variational

-0.6967967

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.6968656exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.6967967best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.6967130	8.4e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.7324989

best variational

-0.7324804

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.7324989exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.7324804best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.7324222	5.8e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.7684681

best variational

-0.7684501

VQE

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.7684681exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.7684501best variational	0	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-0.7683608	8.9e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024

exact

-0.638096

best variational

-0.638078

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.638096exact	0	n/a	exact	ED	Schulz et al. (1996)		1996
-0.638078best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

exact

-0.5990463

best variational

-0.599044

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5990463exact	0	n/a	exact	ED	Schulz et al. (1996)		1996
-0.599044best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.599044tied with best variational at 2σ	<1e-6	3.0e-6	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.598950	9.4e-5	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019

exact

-0.5624595

best variational

-0.562453

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5624595exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.562453best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.561888	5.7e-4	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.554997	7.5e-3	2.4e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.550038	1.2e-2	2.9e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-0.529745

best variational

-0.529744

DMRG

best extrapolated

-0.529747(1)

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.529745exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.529744best variational	0	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.529742	2.0e-6	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.529734	1.0e-5	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.529726	1.8e-5	1.0e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.529687	5.7e-5	7.0e-6	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.529570	1.7e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.529547	2.0e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.529360	3.8e-4	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.529280	4.6e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.528919	8.3e-4	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.527150	2.6e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.519531	1.0e-2	2.6e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.513208	1.7e-2	3.2e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.529747best extrapolated	0	1.0e-6	extrapolated	DMRG	Gong et al. (2013)		2013
-0.529720	2.7e-5	1.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013

QMBL check, checks/exact-recompute-2026-09/

exact

-0.5156574

best variational

-0.515655

DMRG

best extrapolated

-0.51566(1)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5156574exact	0	n/a	exact	ED	QMBL check, checks/exact-recompute-2026-09/	QMBL code	2026
-0.515655best variational	0	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.515652	3.0e-6	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.515637	1.8e-5	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.515633	2.2e-5	1.0e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.515580	7.5e-5	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.515520	1.4e-4	1.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.515380	2.8e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.515281	3.7e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.514520	1.1e-3	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.513640	2.0e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.51566	<1e-5	1.0e-6	extrapolated below exact by > 2σ	DMRG	Gong et al. (2013)		2013
-0.51566best extrapolated	0	1.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.51510	5.6e-4	1.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

exact

-0.5038097

best variational

-0.503805

DMRG

best projected

-0.5033(4)

FN-GFMC (PEPS)

best extrapolated

-0.50382(1)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5038097exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.503805best variational	0	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.503800	4.9e-6	1.1e-6	variational	VMC (RBM + PP)	Wu et al. (2024)	uses mVMC	2024
-0.503797	8.0e-6	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.503780tied with best variational at 2σ	2.5e-5	4.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.503771	3.4e-5	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.503765	4.0e-5	1.0e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.503760tied with best variational at 2σ	4.5e-5	3.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.503760	4.5e-5	6.3e-7	variational	VMC (RBM)	Wu et al. (2024)		2024
-0.503640	1.7e-4	2.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.503571	2.3e-4	3.0e-6	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.503258	5.5e-4	4.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.503243	5.6e-4	9.0e-6	variational	VMC (ViT)	Rende & Viteritti (2024)	model code	2024
-0.503230	5.8e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.503216	5.9e-4	8.0e-6	variational	VMC (ViT)	Rende & Viteritti (2024)	model code	2024
-0.503182	6.2e-4	9.0e-6	variational	VMC (ViT)	Rende & Viteritti (2024)	model code	2024
-0.503178	6.3e-4	4.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.503119	6.9e-4	4.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.503052	7.5e-4	3.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.503049	7.6e-4	n/a	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.502970	8.4e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.502942	8.6e-4	2.6e-5	variational	VMC (GCNN)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.502918	8.9e-4	n/a	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.502597	1.2e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.502494	1.3e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.502300	1.5e-3	5.0e-4	variational	VMC (GNN)	Kochkov et al. (2021)		2021
-0.502200	1.6e-3	4.0e-4	variational	VMC (GNN)	Kochkov et al. (2021)		2021
-0.502184	1.6e-3	2.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.502034	1.8e-3	4.0e-5	variational	VMC (ViT)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.501850	2.0e-3	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.501338	2.5e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.501170	2.6e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.501160	2.6e-3	2.1e-5	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.500400	3.4e-3	n/a	variational	VMC (CNN)	Ou et al. (2025)		2025
-0.499962	3.8e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.498500	5.3e-3	2.0e-4	variational	VMC (EPS)	Mezzacapo et al. (2009)		2009
-0.496102	7.7e-3	6.9e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.494700	9.1e-3	4.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.491900	1.2e-2	3.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.488300	1.6e-2	2.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.486928	1.7e-2	2.4e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.484780	1.9e-2	2.5e-4	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.481900	2.2e-2	2.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.481700	2.2e-2	3.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.478197	2.6e-2	3.6e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.5033best projected	0	4.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.5029tied with best projected at 2σ	4.0e-4	1.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.5021	1.2e-3	7.0e-5	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.4978	5.5e-3	3.0e-5	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.4828	2.1e-2	2.0e-5	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.50382best extrapolated	0	1.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.50381tied with best extrapolated at 2σ	1.2e-5	1.0e-6	extrapolated	DMRG	Gong et al. (2013)		2013
-0.50340tied with best extrapolated at 2σ	4.2e-4	3.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

exact

-0.4951777

best variational

-0.495167

DMRG

best projected

-0.4939(5)

FN-GFMC (PEPS)

best extrapolated

-0.49521(7)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4951777exact	0	n/a	exact	ED	Schulz et al. (1996)		1996
-0.495167best variational	0	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.495150	1.7e-5	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.495140tied with best variational at 2σ	2.7e-5	4.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.495120tied with best variational at 2σ	4.7e-5	4.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.495096	7.1e-5	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.495075	9.2e-5	1.0e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.495010	1.6e-4	1.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.493990	1.2e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.493676	1.5e-3	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.493471	1.7e-3	5.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.493357	1.8e-3	5.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.493300	1.9e-3	2.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.493142	2.0e-3	5.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.493030	2.1e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.492900	2.3e-3	5.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.492820	2.3e-3	n/a	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.492535	2.6e-3	n/a	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.492500	2.7e-3	4.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.492000	3.2e-3	1.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.490953	4.2e-3	3.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.490670	4.5e-3	2.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.489920	5.2e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.485700	9.5e-3	2.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.463800	3.1e-2	3.0e-4	variational	PEPS	Lin et al. (2024)		2024
-0.4939best projected	0	5.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.4934tied with best projected at 2σ	5.0e-4	6.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.4931tied with best projected at 2σ	8.0e-4	3.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.4926	1.3e-3	1.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.4883	5.6e-3	1.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.4712	2.3e-2	1.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.49521best extrapolated	0	7.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.49519	2.4e-5	1.0e-6	extrapolated below exact by > 2σ	DMRG	Gong et al. (2013)		2013
-0.49330	1.9e-3	5.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

exact

-0.4932386

best variational

-0.49318(5)

VMC (RBM)

best extrapolated

-0.488(1)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4932386exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.49318best variational	0	5.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.49313tied with best variational at 2σ	5.0e-5	5.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.49298	2.0e-4	5.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.49270	4.8e-4	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.49075	2.4e-3	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.49023	3.0e-3	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.48880	4.4e-3	7.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.48857	4.6e-3	7.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.48802	5.2e-3	7.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.48713	6.1e-3	n/a	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.48640	6.8e-3	n/a	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.48227	1.1e-2	4.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.48067	1.3e-2	1.5e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.47381	1.9e-2	4.5e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.488best extrapolated	0	1.1e-3	extrapolated	TPS	Wang et al. (2011)		2011

exact

-0.5065879

best variational

-0.506299

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5065879exact	0	n/a	exact	ED	Schulz et al. (1996)		1996
-0.506299best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

exact

-0.5300012

best variational

-0.5299243

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5300012exact	0	n/a	exact	ED	Schulz et al. (1996)	run script	1996
-0.5299243best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.5299210tied with best variational at 2σ	3.3e-6	8.0e-6	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.5298840	4.0e-5	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.5275917	2.3e-3	1.9e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4831243	4.7e-2	5.8e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-0.5864866

best variational

-0.586411(9)

VMC (RBM)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5864866exact	0	n/a	exact	ED	Schulz et al. (1996)	run script	1996
-0.586411best variational	0	9.0e-6	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.585900	5.1e-4	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.585784	6.3e-4	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.585780	6.3e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.584215	2.2e-3	1.8e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.576501	9.9e-3	2.9e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-0.649052

best variational

-0.6478705

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.649052exact	0	n/a	exact	ED	Schulz et al. (1996)	run script	1996
-0.6478705best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.6473710	5.0e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.6416472	6.2e-3	3.3e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.6370174	1.1e-2	3.2e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-0.7143604

best variational

-0.71429(1)

VMC (RBM)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.7143604exact	0	n/a	exact	ED	Schulz et al. (1996)	run script	1996
-0.71429best variational	0	1.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.71351	7.8e-4	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.71305	1.2e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.71241	1.9e-3	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.70921	5.1e-3	3.1e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.70016	1.4e-2	3.5e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-0.6366151

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6366151exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

exact

-0.5975117

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5975117exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

exact

-0.5606822

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5606822exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

exact

-0.5272092

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5272092exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

exact

-0.4990762

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4990762exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

exact

-0.4879479

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4879479exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

QMBL check, checks/j1j2-40-sector-ed/

exact

-0.4796232

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4796232exact	0	n/a	exact	ED	QMBL check, checks/j1j2-40-sector-ed/	QMBL code	n/a

exact

-0.5011508

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5011508exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

exact

-0.5263826

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5263826exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

exact

-0.5835051

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5835051exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

exact

-0.6459228

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.6459228exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

exact

-0.7109702

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.7109702exact	0	n/a	exact	ED	Richter & Schulenburg (2009)		2009

best variational

-0.633093

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.633093best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

best variational

-0.594508

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.594508best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

best variational

-0.558295

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.558295best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

best variational

-0.525653(1)

VMC (RBM + PP)

Nomura & Imada (2021)

uses mVMC

best extrapolated

-0.5262(1)

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.525653best variational	0	1.0e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.525513	1.4e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.525390	2.6e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.525196	4.6e-4	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.525013	6.4e-4	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.525010	6.4e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.524648	1.0e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.523020	2.6e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.5262best extrapolated	0	1.0e-4	extrapolated	DMRG	Gong et al. (2013)		2013
-0.5256	6.4e-4	1.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013

best variational

-0.511331(1)

VMC (RBM + PP)

Nomura & Imada (2021)

uses mVMC

best extrapolated

-0.5116(1)

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.511331best variational	0	1.0e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.511250	8.1e-5	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.511010	3.2e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.510970	3.6e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.510740	5.9e-4	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.510534	8.0e-4	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.510162	1.2e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.509300	2.0e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.5116best extrapolated	0	1.0e-4	extrapolated	DMRG	Gong et al. (2013)		2013
-0.5114tied with best extrapolated at 2σ	2.0e-4	1.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.5108	8.0e-4	2.0e-5	extrapolated	TPS	Wang et al. (2011)		2011

best extrapolated

-0.5034(4)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5034best extrapolated	0	4.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best variational

-0.498963(2)

VMC (RBM + PP)

uses mVMC

best extrapolated

-0.4992(1)

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.5001	n/a	1.0e-4	variational energy and variance disagree	VMC (HQT)	Guo et al. (2026)	uses NetKet	2026
-0.498963best variational	0	1.9e-6	variational	VMC (RBM + PP)	Wu et al. (2024)	uses mVMC	2024
-0.498886	7.7e-5	1.0e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.498860	1.0e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.498666	3.0e-4	2.3e-6	variational	VMC (RBM)	Wu et al. (2024)		2024
-0.498570	3.9e-4	6.6e-5	variational	VMC (ClebschTree)	Vieijra & Nys (2021)	uses NetKet	2021
-0.498550	4.1e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.498460	5.0e-4	6.0e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.498175	7.9e-4	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.498115	8.5e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.497961	1.0e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.497641	1.3e-3	2.5e-5	variational	VMC (GCNN)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.497598	1.4e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.497423	1.5e-3	1.6e-5	variational	VMC (ViT)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.496560	2.4e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.496543	2.4e-3	1.6e-5	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.495046	3.9e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.494015	4.9e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.493802	5.2e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.492426	6.5e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.491236	7.7e-3	4.7e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.482701	1.6e-2	1.6e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.477875	2.1e-2	8.6e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.474587	2.4e-2	2.6e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.4992best extrapolated	0	1.0e-4	extrapolated	DMRG	Gong et al. (2013)		2013
-0.4991tied with best extrapolated at 2σ	1.4e-4	1.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.4984	8.0e-4	2.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best extrapolated

-0.4941(1)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4941best extrapolated	0	1.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best variational

-0.488820(2)

VMC (RBM + PP)

Nomura & Imada (2021)

uses mVMC

best extrapolated

-0.4891(1)

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.488820best variational	0	2.0e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.488410	4.1e-4	2.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.488350	4.7e-4	8.0e-5	variational	VMC (ClebschTree)	Vieijra & Nys (2021)	uses NetKet	2021
-0.488160	6.6e-4	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.487982	8.4e-4	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.487810	1.0e-3	1.0e-5	variational	VMC (RBM + PP)	Nomura & Imada (2020)	uses mVMC	2020
-0.487770	1.0e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.487685	1.1e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.484870	3.9e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.483143	5.7e-3	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.4891best extrapolated	0	1.0e-4	extrapolated	DMRG	Gong et al. (2013)		2013
-0.4889tied with best extrapolated at 2σ	1.6e-4	3.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.4880	1.1e-3	2.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best variational

-0.481606

VMC (ViT)

uses NetKet

best extrapolated

-0.4808(9)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.481606best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.4808best extrapolated	0	9.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best variational

-0.498312

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.498312best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

best variational

-0.522091

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.522091best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

best variational

-0.57731

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.57731best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

best variational

-0.637518

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.637518best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

best variational

-0.700508

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.700508best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

best variational

-0.631365

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.631365best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

best variational

-0.592982

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.592982best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.592847	1.4e-4	9.0e-6	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.592750	2.3e-4	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019

best variational

-0.556912

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.556912best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.554852	2.1e-3	1.0e-5	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.549089	7.8e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.545994	1.1e-2	1.8e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.545359	1.2e-2	1.7e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-0.524361

VMC (ViT)

uses NetKet

best extrapolated

-0.5253

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.524361best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.524000	3.6e-4	1.0e-4	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.523999	3.6e-4	4.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.523880	4.8e-4	2.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.523872	4.9e-4	4.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.523710	6.5e-4	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.523680	6.8e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.522391	2.0e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.522043	2.3e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.521880	2.5e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.521487	2.9e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.516623	7.7e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.508699	1.6e-2	2.0e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.508571	1.6e-2	1.9e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.5253best extrapolated	0	n/a	extrapolated	DMRG	Gong et al. (2013)		2013
-0.5243	1.0e-3	2.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013

best variational

-0.51273

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.51273best variational	0	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.51001(1)

VMC (Gutzwiller)

best extrapolated

-0.511

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.51001best variational	0	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.50990tied with best variational at 2σ	1.1e-4	5.0e-4	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.50973	2.8e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.50966	3.5e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.50921	8.0e-4	5.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.50916	8.5e-4	2.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.50905	9.6e-4	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.50811	1.9e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.50798	2.0e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.50768	2.3e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.50719	2.8e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.511best extrapolated	0	n/a	extrapolated	DMRG	Gong et al. (2013)		2013
-0.510	<1e-3	2.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013

best variational

-0.50744

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50744best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.50728	1.6e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.50231

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50231best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.50209	2.2e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.4976939(2)

VMC (CNN-MPS)

Fan et al. (2026)

best projected

-0.4957(2)

FN-GFMC (PEPS)

best extrapolated

-0.4988

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.49782	n/a	3.0e-5	variational read off a training trace	VMC (HQT)	Guo et al. (2026)	uses NetKet	2026
-0.4976939best variational	0	2.0e-7	variational	VMC (CNN-MPS)	Fan et al. (2026)		2026
-0.4976923	1.6e-6	2.0e-7	variational	VMC (T-MPS)	Fan et al. (2026)		2026
-0.4976921	1.8e-6	4.0e-7	variational	VMC (ResNet)	Chen & Heyl (2023)	ChenAo-Phys/MinSR	2023
-0.4976790	1.5e-5	n/a	variational	VMC (CTWF)	Chen et al. (2025)	uses Quantax	2025
-0.4976764	1.8e-5	7.0e-7	variational	VMC (ViT)	Viteritti et al. (2024), quoted in Chen et al. (2025)		2024
-0.4976340	6.0e-5	1.0e-6	variational	VMC (ViT)	Rende et al. (2023)		2023
-0.4976293	6.5e-5	1.1e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.4976270	6.7e-5	4.0e-6	variational	VMC (ResNet)	Chen & Heyl (2023)	ChenAo-Phys/MinSR	2023
-0.4975830	1.1e-4	6.0e-6	variational	VMC (ConvNeXt)	Nutakki et al. (2025)	NeuralQXLab/convnextnnqs	2025
-0.4975490	1.4e-4	2.0e-6	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.4974680	2.3e-4	n/a	variational	VMC (CNN)	Liang et al. (2022)		2022
-0.4974370	2.6e-4	7.0e-6	variational	VMC (GCNN)	Roth et al. (2023)	uses NetKet	2023
-0.4974000	2.9e-4	n/a	variational	VMC (HQT)	Guo et al. (2026)	uses NetKet	2026
-0.4971840	5.1e-4	6.0e-6	variational	VMC (ViT)	Rende & Viteritti (2024)	model code	2024
-0.4971800	5.1e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.4971700	5.2e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022
-0.4971080	5.9e-4	6.0e-6	variational	VMC (ViT)	Rende & Viteritti (2024)	model code	2024
-0.4970250	6.7e-4	6.0e-6	variational	VMC (ViT)	Rende & Viteritti (2024)	model code	2024
-0.4968000	8.9e-4	4.0e-4	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.4967830	9.1e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.4961255	1.6e-3	1.5e-5	variational	VMC (ViT)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4961020	1.6e-3	7.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.4960894	1.6e-3	1.8e-5	variational	VMC (ViT)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4960640	1.6e-3	n/a	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.4959590	1.7e-3	5.0e-6	variational	VMC (ResNet)	Wang et al. (2026)		2026
-0.4959410	1.8e-3	6.0e-6	variational	VMC (ResNet)	Wang et al. (2026)		2026
-0.4958920	1.8e-3	6.0e-6	variational	VMC (ResNet)	Wang et al. (2026)		2026
-0.4958600	1.8e-3	4.0e-5	variational	VMC (CNN)	Reh et al. (2023)	uses jVMC	2023
-0.4958000	1.9e-3	2.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.4957500	1.9e-3	3.0e-5	variational	VMC (RBM)	Ferrari et al. (2019)		2019
-0.4956423	2.1e-3	2.3e-5	variational	VMC (GCNN)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4956270	2.1e-3	6.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.4955975	2.1e-3	4.3e-5	variational	VMC (RNN)	Wu et al. (2024)	run script	2024
-0.4955300	2.2e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.4955020	2.2e-3	n/a	variational	VMC (PEPS + CNN)	Liang et al. (2020)		2020
-0.4954281	2.3e-3	2.7e-5	variational	VMC (GCNN)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4953925	2.3e-3	7.5e-6	variational	VMC (RNN)	Wu et al. (2024)	run script	2024
-0.4953010	2.4e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.4952100	2.5e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.4951600	2.5e-3	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.4951500	2.5e-3	2.2e-5	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.4950440	2.6e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.4947570	2.9e-3	1.2e-5	variational	VMC (CNN)	Szabó & Castelnovo (2020)	uses NetKet	2020
-0.4947359	n/a	1.0e-7	variational quote-not-in-primary	VMC (CNN)	Liang et al. (2018)		2018
-0.4923350	5.4e-3	n/a	variational	VMC (PEPS + CNN)	Liang et al. (2020)		2020
-0.4921618	5.5e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4913983	6.3e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.4912262	6.5e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4903071	7.4e-3	4.0e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4903071	7.4e-3	4.0e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4894100	8.3e-3	n/a	variational	VMC (MLP)	Ledinauskas & Anisimovas (2023)	uses NetKet	2023
-0.4891721	8.5e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4829860	1.5e-2	n/a	variational	VMC (CNN)	Liang et al. (2020)		2020
-0.4770018	2.1e-2	2.1e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.4739018	2.4e-2	2.1e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.4735910	2.4e-2	n/a	variational	VMC (CNN)	Liang et al. (2018)		2018
-0.4717716	2.6e-2	7.0e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4714424	2.6e-2	6.8e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4957best projected	0	2.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.4954tied with best projected at 2σ	3.0e-4	6.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.4988best extrapolated	0	n/a	extrapolated	DMRG	Gong et al. (2013)		2013
-0.4978	9.9e-4	2.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.4977	1.1e-3	9.0e-6	extrapolated	VMC (ResNet)	Chen & Heyl (2023)	ChenAo-Phys/MinSR	2023

best variational

-0.48693(3)

VMC (Gutzwiller)

best projected

-0.4853(4)

FN-GFMC (PEPS)

best extrapolated

-0.488

DMRG

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.48693best variational	0	3.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.48677	1.6e-4	1.1e-5	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.48670	2.3e-4	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.48622	7.1e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.48611	8.2e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022
-0.48590tied with best variational at 2σ	1.0e-3	5.0e-4	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.48576	1.2e-3	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.48543	1.5e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.48524	1.7e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.48489	2.0e-3	n/a	variational	DMRG	Gong et al. (2013)		2013
-0.48481	2.1e-3	8.0e-6	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.48410	2.8e-3	3.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.48401	2.9e-3	n/a	variational	VMC (ResNet)	Wang et al. (2026)	QTMEC-RUC/nqs-lanczos	2026
-0.48349	3.4e-3	5.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.48335	3.6e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.48317	3.8e-3	5.0e-6	variational	VMC (aCNN)	Wang et al. (2023)	rqHe1/aCNN	2023
-0.48277	4.2e-3	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.4853best projected	0	4.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.4852tied with best projected at 2σ	<1e-4	3.0e-4	projected	FN-GFMC (PEPS)	Lin et al. (2024)		2024
-0.488best extrapolated	0	n/a	extrapolated	DMRG	Gong et al. (2013)		2013
-0.488	<1e-3	6.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013

best variational

-0.47839

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.47839best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.47762	7.7e-4	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.47746	9.3e-4	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.47713	1.3e-3	n/a	variational	VMC (CNN)	Li et al. (2022)		2022
-0.47662	1.8e-3	3.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.47604	2.3e-3	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.47259	5.8e-3	1.0e-5	variational	VMC (Gutzwiller)	Ferrari & Becca (2019), quoted in Choo et al. (2019)		2019
-0.45333	2.5e-2	1.9e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.44467	3.4e-2	2.5e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-0.494672

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.494672best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026

best variational

-0.519035

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.519035best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.518890	1.4e-4	2.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.516431	2.6e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.473250	4.6e-2	4.0e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.438067	8.1e-2	8.8e-6	variational	VMC (RBM)	Wu et al. (2024)	run script	2024

best variational

-0.57413

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.57413best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.57404	9.0e-5	2.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.57383	3.0e-4	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.56926	4.9e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.56899	5.1e-3	1.0e-5	variational	VMC (Gutzwiller)	Ferrari & Becca (2019), quoted in Choo et al. (2019)		2019
-0.55035	2.4e-2	2.1e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.54283	3.1e-2	3.0e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024

best variational

-0.63417

VMC (ViT)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.63417best variational	0	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.62697	7.2e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.59742	3.7e-2	3.2e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.58976	4.4e-2	2.5e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-0.69670(2)

VMC (RBM)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.69670best variational	0	2.0e-5	variational	VMC (RBM)	Chen et al. (2022)		2022
-0.69664	5.9e-5	n/a	variational	VMC (ViT)	Golubev et al. (2026)	uses NetKet	2026
-0.69636	3.4e-4	1.0e-5	variational	VMC (CNN)	Choo et al. (2019)	uses NetKet	2019
-0.69123	5.5e-3	1.0e-5	variational	VMC (Gutzwiller)	Ferrari & Becca (2019), quoted in Choo et al. (2019)		2019
-0.68818	8.5e-3	2.1e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.68726	9.4e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.64681	5.0e-2	3.0e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-0.51225

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.51225best variational	0	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best extrapolated

-0.5088(1)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5088best extrapolated	0	1.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best variational

-0.50697

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50697best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.50679	1.8e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.50183

VMC (CNN)

best extrapolated

-0.5008(1)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.50183best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)	2023
-0.50159	2.4e-4	n/a	variational	VMC (CNN)	Li et al. (2022)	2022
-0.5008best extrapolated	0	1.0e-4	extrapolated	TPS	Wang et al. (2011)	2011

best variational

-0.496989

VMC (CNN)

best extrapolated

-0.4963(2)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.496989best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.496791	2.0e-4	4.0e-6	variational	VMC (PP + RBM)	Nomura (2023), quoted in Roth et al. (2022)	uses mVMC	2023
-0.496769	2.2e-4	9.0e-6	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.496650	3.4e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022
-0.495649	1.3e-3	1.5e-5	variational	VMC (ViT)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.494940	2.0e-3	1.9e-5	variational	VMC (GCNN)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.490391	6.6e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.489999	7.0e-3	3.1e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.487971	9.0e-3	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.484348	1.3e-2	n/a	variational	DMRG	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.466490	3.0e-2	6.8e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4963best extrapolated	0	2.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best extrapolated

-0.4920(1)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4920best extrapolated	0	1.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best variational

-0.48607(1)

VMC (GCNN)

uses NetKet

best extrapolated

-0.4862(2)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.48607best variational	0	1.0e-5	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.48603	3.8e-5	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.48574	3.3e-4	7.0e-6	variational	VMC (PP + RBM)	Nomura (2023), quoted in Roth et al. (2022)	uses mVMC	2023
-0.48545	6.2e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022
-0.4862best extrapolated	0	2.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best variational

-0.47715

VMC (CNN)

best extrapolated

-0.4784(3)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.47715best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)	2023
-0.47601	1.1e-3	n/a	variational	VMC (CNN)	Li et al. (2022)	2022
-0.4784best extrapolated	0	3.0e-4	extrapolated	TPS	Wang et al. (2011)	2011

best variational

-0.52287(1)

VMC (Gutzwiller)

best extrapolated

-0.52351(2)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.52287best variational	0	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.52124	1.6e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.52351best extrapolated	0	2.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)	2013

best variational

-0.512

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.512best variational	0	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.50899(1)

VMC (Gutzwiller)

best extrapolated

-0.50953(1)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.50899best variational	0	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.50745	1.5e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.50953best extrapolated	0	1.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)	2013

best variational

-0.50675

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50675best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.50655	2.0e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.50159

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50159best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.50135	2.4e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.49674

VMC (CNN)

best extrapolated

-0.49722(2)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.49674best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.49640	3.4e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022
-0.49638	3.6e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.49541	1.3e-3	1.3e-5	variational	VMC (ViT)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.49447	2.3e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.49443	2.3e-3	1.3e-5	variational	VMC (Gutzwiller)	Wu et al. (2024)	run script	2024
-0.48967	7.1e-3	2.8e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.48839	8.4e-3	3.3e-5	variational	VMC (GCNN)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.48238	1.4e-2	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.47230	2.4e-2	1.4e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-0.47069	2.6e-2	1.8e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-0.46615	3.1e-2	5.6e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.49722best extrapolated	0	2.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013

best variational

-0.48581

VMC (CNN)

best extrapolated

-0.48696(5)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.48581best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)	2023
-0.48519	6.2e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.48515	6.6e-4	n/a	variational	VMC (CNN)	Li et al. (2022)	2022
-0.48242	3.4e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.48696best extrapolated	0	5.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)	2013

best variational

-0.47678

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.47678best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.47558	1.2e-3	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.51188

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.51188best variational	0	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best extrapolated

-0.5087(1)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5087best extrapolated	0	1.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best variational

-0.50662

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50662best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.50642	2.0e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.50147

VMC (CNN)

best extrapolated

-0.5008(2)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.50147best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)	2023
-0.50122	2.5e-4	n/a	variational	VMC (CNN)	Li et al. (2022)	2022
-0.5008best extrapolated	0	2.0e-4	extrapolated	TPS	Wang et al. (2011)	2011

best variational

-0.4969140(5)

VMC (CNN-MPS)

Fan et al. (2026)

best extrapolated

-0.4966(3)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4969140best variational	0	5.0e-7	variational	VMC (CNN-MPS)	Fan et al. (2026)		2026
-0.4967860	1.3e-4	1.0e-6	variational	VMC (T-MPS)	Fan et al. (2026)		2026
-0.4967163	2.0e-4	8.0e-7	variational	VMC (ResNet)	Chen & Heyl (2023)	ChenAo-Phys/MinSR	2023
-0.4965900	3.2e-4	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.4965090	4.1e-4	6.0e-6	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.4962600	6.5e-4	n/a	variational	VMC (CNN)	Li et al. (2021)		2021
-0.4962130	7.0e-4	3.0e-6	variational	VMC (PP + RBM)	Nomura (2023), quoted in Roth et al. (2022)	uses mVMC	2023
-0.4948384	2.1e-3	1.1e-5	variational	VMC (ViT)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4897370	7.2e-3	2.4e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4658944	3.1e-2	4.9e-5	variational	VMC (RBM)	QMBL cost-to-reproduce run, checks/cost/	rerun (QMBL code)	2026
-0.4966best extrapolated	0	3.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best extrapolated

-0.4920(1)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4920best extrapolated	0	1.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best variational

-0.48565

VMC (CNN)

best extrapolated

-0.4859(4)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.48565best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.48558	6.7e-5	8.0e-6	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.48521	4.4e-4	4.0e-6	variational	VMC (PP + RBM)	Nomura (2023), quoted in Roth et al. (2022)	uses mVMC	2023
-0.48499	6.6e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022
-0.4859best extrapolated	0	4.0e-4	extrapolated	TPS	Wang et al. (2011)		2011

best variational

-0.47656

VMC (CNN)

best extrapolated

-0.4777(3)

TPS

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.47656best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)	2023
-0.47535	1.2e-3	n/a	variational	VMC (CNN)	Li et al. (2022)	2022
-0.4777best extrapolated	0	3.0e-4	extrapolated	TPS	Wang et al. (2011)	2011

best variational

-0.52259(1)

VMC (Gutzwiller)

best extrapolated

-0.52333(1)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.52259best variational	0	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.52107	1.5e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.52333best extrapolated	0	1.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)	2013

best variational

-0.51179

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.51179best variational	0	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.50874(1)

VMC (Gutzwiller)

best extrapolated

-0.50940(1)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.50874best variational	0	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.50728	1.5e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.50940best extrapolated	0	1.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)	2013

best variational

-0.50651

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50651best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.50635	1.6e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.50139

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50139best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.50114	2.5e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.496513

VMC (CNN)

best extrapolated

-0.49717(2)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.496513best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.496275	2.4e-4	3.0e-6	variational	VMC (RBM + PP)	Nomura & Imada (2021)	uses mVMC	2021
-0.496170	3.4e-4	n/a	variational	VMC (CNN)	Li et al. (2022)		2022
-0.496110	4.0e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.494260	2.3e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)		2013
-0.49717best extrapolated	0	2.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)		2013

best variational

-0.48557

VMC (CNN)

best extrapolated

-0.48698(5)

VMC (Gutzwiller)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.48557best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)	2023
-0.48488	6.9e-4	n/a	variational	VMC (CNN)	Li et al. (2022)	2022
-0.48475	8.2e-4	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.48215	3.4e-3	1.0e-5	variational	VMC (Gutzwiller)	Hu et al. (2013)	2013
-0.48698best extrapolated	0	5.0e-5	extrapolated	VMC (Gutzwiller)	Hu et al. (2013)	2013

best variational

-0.47652

VMC (CNN)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.47652best variational	0	n/a	variational	VMC (CNN)	Liang et al. (2023)		2023
-0.47520	1.3e-3	n/a	variational	VMC (CNN)	Li et al. (2022)		2022

best variational

-0.4967987(6)

VMC (CNN-MPS)

Fan et al. (2026)

best extrapolated

-0.49684(1)

VMC (ViT)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.4967987best variational	0	6.0e-7	variational	VMC (CNN-MPS)	Fan et al. (2026)	2026
-0.4967320	6.7e-5	1.0e-6	variational	VMC (ViT)	Viteritti et al. (2026)	2026
-0.49684best extrapolated	0	1.0e-5	extrapolated	VMC (ViT)	Viteritti et al. (2026)	2026

exact

-0.5173144

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5173144exact	0	n/a	exact	ED	Wu et al. (2024)		2024

best variational

-0.51268(9)

VMC (GCNN)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.51268best variational	0	9.0e-5	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.51175	9.3e-4	7.0e-5	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.50690	5.8e-3	8.0e-4	variational	VMC (GNN)	Kochkov et al. (2021)		2021

best variational

-0.51218(9)

VMC (GCNN)

uses NetKet

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.51218best variational	0	9.0e-5	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.51101	1.2e-3	6.0e-5	variational	VMC (GCNN)	Roth et al. (2022)	uses NetKet	2022
-0.51056	1.6e-3	5.0e-6	variational	VMC (Gutzwiller)	Iqbal et al. (2016)		2016

Kitaev (K-J-Γ)#

7 instances, energies as E/N (S.S)

lattice size

instance

value

energy

method

source

code

energies

exact

-0.1882584

Exact solution

best variational

-0.1820213

DMRG

best projected

-0.1867058

isoTNS

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.1882584exact	0	n/a	exact	Exact solution	Lin et al. (2022)	2022
-0.1820213best variational	0	n/a	variational	DMRG	Lin et al. (2022)	2022
-0.1810139	1.0e-3	n/a	variational	DMRG	Lin et al. (2022)	2022
-0.1867058best projected	0	n/a	projected	isoTNS	Lin et al. (2022)	2022
-0.1861212	5.8e-4	n/a	projected	isoTNS	Lin et al. (2022)	2022

exact

-0.1988727

best variational

-0.19887(2)

VMC (PP)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.1988727exact	0	n/a	exact	ED	Kurita et al. (2015)	2015
-0.19887best variational	0	2.1e-5	variational	VMC (PP)	Kurita et al. (2015)	2015
-0.19883tied with best variational at 2σ	4.2e-5	8.3e-5	variational	VMC (PP)	Kurita et al. (2015)	2015
-0.19881tied with best variational at 2σ	6.3e-5	8.3e-5	variational	VMC (PP)	Kurita et al. (2015)	2015
-0.18792	1.1e-2	4.2e-4	variational	VMC (PP)	Kurita et al. (2015)	2015

exact

-0.1963139

best variational

-0.19617(8)

VMC (PP)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.1963139exact	0	n/a	exact	ED	Kurita et al. (2015)	2015
-0.19617best variational	0	7.8e-5	variational	VMC (PP)	Kurita et al. (2015)	2015
-0.19609tied with best variational at 2σ	7.8e-5	1.6e-4	variational	VMC (PP)	Kurita et al. (2015)	2015
-0.19422	2.0e-3	3.1e-4	variational	VMC (PP)	Kurita et al. (2015)	2015
-0.18672	9.5e-3	4.7e-4	variational	VMC (PP)	Kurita et al. (2015)	2015

exact

-0.178506

Exact solution

best variational

-0.1785027

DMRG

best projected

-0.1767248

isoTNS

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.178506exact	0	n/a	exact	Exact solution	Lin et al. (2022)	2022
-0.1785027best variational	0	n/a	variational	DMRG	Lin et al. (2022)	2022
-0.1784073	9.5e-5	n/a	variational	DMRG	Lin et al. (2022)	2022
-0.1767248best projected	0	n/a	projected	isoTNS	Lin et al. (2022)	2022

exact

-0.1891314

Exact solution

Jin et al. (2021)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.1891314exact	0	n/a	exact	Exact solution	Jin et al. (2021)		2021

exact

-0.1835418

Exact solution

best variational

-0.1826

DMRG

best projected

-0.1824684

isoTNS

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.1835418exact	0	n/a	exact	Exact solution	Lin et al. (2022)	2022
-0.1826best variational	0	n/a	variational	DMRG	Lin et al. (2022)	2022
-0.1815	1.1e-3	n/a	variational	DMRG	Lin et al. (2022)	2022
-0.1824684best projected	0	n/a	projected	isoTNS	Lin et al. (2022)	2022
-0.1817416	7.3e-4	n/a	projected	isoTNS	Lin et al. (2022)	2022

exact

-0.1985125

best variational

-0.198510(6)

VMC (PP)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.1985125exact	0	n/a	exact	ED	Kurita et al. (2015)	2015
-0.198510best variational	0	6.2e-6	variational	VMC (PP)	Kurita et al. (2015)	2015
-0.198500tied with best variational at 2σ	1.0e-5	4.2e-5	variational	VMC (PP)	Kurita et al. (2015)	2015
-0.198479tied with best variational at 2σ	3.1e-5	6.3e-5	variational	VMC (PP)	Kurita et al. (2015)	2015
-0.197292	1.2e-3	2.1e-4	variational	VMC (PP)	Kurita et al. (2015)	2015

Munehisa & Munehisa (2004)

Shastry-Sutherland#

29 instances, energies as E/N (S.S)

lattice size

instance

value

energy

method

source

code

energies

exact

-0.3968907

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3968907exact	0	n/a	exact	ED	Munehisa & Munehisa (2004)		2004

exact

-0.375

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.375exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.375

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.375exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.375004

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.375004exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.3752862

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3752862exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.3777047

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3777047exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.3885784

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3885784exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.4517531

best variational

-0.451717(6)

VMC (ConvNeXt)

Nutakki et al. (2025)

NeuralQXLab/convnextnnqs

best extrapolated

-0.45175

VMC (Transformer)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.4517531exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006
-0.4517531	0	n/a	exact	ED	Viteritti et al. (2025)		2025
-0.451717best variational	0	6.0e-6	variational	VMC (ConvNeXt)	Nutakki et al. (2025)	NeuralQXLab/convnextnnqs	2025
-0.451707tied with best variational at 2σ	9.8e-6	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)		2025
-0.451699	1.8e-5	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)		2025
-0.451664	5.3e-5	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)		2025
-0.451633	8.4e-5	6.0e-6	variational	VMC (ConvNeXt)	Nutakki et al. (2025)	NeuralQXLab/convnextnnqs	2025
-0.45175best extrapolated	0	n/a	extrapolated	VMC (Transformer)	Viteritti et al. (2025)		2025

exact

-0.4843341

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4843341exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

best variational

-0.449829

VMC (Transformer)

best extrapolated

-0.44995

VMC (Transformer)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.449829best variational	0	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)	2025
-0.449802	2.7e-5	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)	2025
-0.449641	1.9e-4	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)	2025
-0.44995best extrapolated	0	n/a	extrapolated	VMC (Transformer)	Viteritti et al. (2025)	2025

best variational

-0.449342(4)

VMC (ConvNeXt)

Nutakki et al. (2025)

NeuralQXLab/convnextnnqs

best extrapolated

-0.44947

VMC (Transformer)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year
-0.449342best variational	0	4.0e-6	variational	VMC (ConvNeXt)	Nutakki et al. (2025)	NeuralQXLab/convnextnnqs	2025
-0.449329	1.3e-5	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)		2025
-0.449221	1.2e-4	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)		2025
-0.449062	2.8e-4	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)		2025
-0.44947best extrapolated	0	n/a	extrapolated	VMC (Transformer)	Viteritti et al. (2025)		2025

best variational

-0.37627

VMC (Gutzwiller)

Chen & Liu (2026)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.37627best variational	0	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.37622	5.0e-5	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.37621	6.0e-5	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.37539	8.8e-4	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.37537	9.0e-4	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.37527	1.0e-3	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.37512	1.1e-3	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.37398	2.3e-3	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.37392	2.4e-3	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.37308	3.2e-3	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.37038	5.9e-3	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026
-0.36134	1.5e-2	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)	2026

best variational

-0.449078

VMC (Transformer)

best extrapolated

-0.44931

VMC (Transformer)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.449078best variational	0	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)	2025
-0.449013	6.5e-5	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)	2025
-0.448861	2.2e-4	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)	2025
-0.44931best extrapolated	0	n/a	extrapolated	VMC (Transformer)	Viteritti et al. (2025)	2025

best variational

-0.448929

VMC (Transformer)

best extrapolated

-0.4492

VMC (Transformer)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.448929best variational	0	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)	2025
-0.448812	1.2e-4	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)	2025
-0.448551	3.8e-4	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)	2025
-0.4492best extrapolated	0	n/a	extrapolated	VMC (Transformer)	Viteritti et al. (2025)	2025

best variational

-0.37642

VMC (Gutzwiller)

Chen & Liu (2026)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.37642best variational	0	n/a	variational	VMC (Gutzwiller)	Chen & Liu (2026)		2026

best variational

-0.448881

VMC (Transformer)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.448881best variational	0	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)		2025

best variational

-0.448859

VMC (Transformer)

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.448859best variational	0	n/a	variational	VMC (Transformer)	Viteritti et al. (2025)		2025

best variational

-0.442928(3)

PEPS

Liu et al. (2024)

E/N (S.S)	distance to class best	σ	bound type	method	source	year
-0.442928best variational	0	3.0e-6	variational	PEPS	Liu et al. (2024)	2024
-0.442920tied with best variational at 2σ	8.0e-6	2.0e-6	variational	PEPS	Liu et al. (2024)	2024
-0.442861	6.7e-5	9.0e-6	variational	PEPS	Liu et al. (2024)	2024
-0.442104	8.2e-4	8.0e-6	variational	PEPS	Liu et al. (2024)	2024

exact

-0.375

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.375exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.375

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.375exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.375

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.375exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.375

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.375exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.375

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.375exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.375

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.375exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.3750238

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3750238exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.3751152

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3751152exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.3752526

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3752526exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.3762717

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3762717exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

exact

-0.3867209

E/N (S.S)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3867209exact	0	n/a	exact	ED	Sindermann et al. (2006)		2006

Hubbard#

231 instances, energies as E/site

lattice size

instance

value

energy

method

source

code

energies

exact

-0.9116302

best variational

-0.9116293

DMRG

best extrapolated

-0.9116302(1)

DMRG

E/site	σ	bound type	method	source	code	year
-0.9116302exact	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.9116293best variational	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.9116302best extrapolated	1.4e-7	extrapolated	DMRG	Wu et al. (2024)	run script	2024

exact

-0.8761535

best variational

-0.8761535

DMRG

best extrapolated

-0.876153552(4)

DMRG

E/site	σ	bound type	method	source	code	year
-0.8761535exact	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.8761535best variational	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.876153552best extrapolated	3.6e-9	extrapolated	DMRG	Wu et al. (2024)	run script	2024

exact

-0.8542284

best variational

-0.8542284

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8542284exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.8542284best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-0.8300032

best variational

-0.8300032

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8300032exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.8300032best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-0.804323

best variational

-0.804323

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.804323exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.804323best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-0.7783541

best variational

-0.7783541

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7783541exact	0	n/a	exact	ED	QMBL check, checks/hubbard-u-labels/	QMBL code	n/a
-0.7783541best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-0.7783541

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7783541exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024

exact

-0.7304717

best variational

-0.7304717

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7304717exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.7304717best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-0.7103639

best variational

-0.7103637

DMRG

best extrapolated

-0.71036386(2)

DMRG

E/site	σ	bound type	method	source	code	year
-0.7103639exact	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.7103637best variational	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.71036386best extrapolated	2.1e-8	extrapolated	DMRG	Wu et al. (2024)	run script	2024

best variational

-0.7434

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7434best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026

best variational

-0.7562

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7562best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026

best variational

-0.744

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.744best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026

best variational

-0.75830(4)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.75830best variational	0	4.3e-5	variational	VAFQMC	Wu et al. (2024)		2024

best variational

-0.7507

VMC (SCALE)

uses LaQX

best projected

-0.7547

FN-GFMC (SCALE)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7507best variational	0	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-0.7507tied with best variational at 2σ	<1e-4	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-0.7547best projected	0	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026
-0.7546	<1e-4	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026

best variational

-0.7371

VMC (SCALE)

uses LaQX

best projected

-0.7406

FN-GFMC (SCALE)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7371best variational	0	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-0.7359	1.2e-3	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-0.7406best projected	0	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026
-0.7397	9.0e-4	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026

best variational

-0.76608(1)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.76608best variational	0	1.0e-5	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026

best variational

-0.76623(1)

VMC (ACE)

uses LaQX

best projected

-0.76647(2)

FN-GFMC (ACE)

best extrapolated

-0.76748

VMC (NNBF)

Loehr & Clark (2025)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.76623best variational	0	1.0e-5	variational	VMC (ACE)	Gu et al. (2026)	uses LaQX	2026
-0.76560	6.3e-4	1.0e-5	variational	VMC (NNBF)	Loehr & Clark (2025)		2025
-0.76486	1.4e-3	2.0e-5	variational	VMC (NNBF)	Loehr & Clark (2025)		2025
-0.76464	1.6e-3	1.0e-5	variational	VMC (ACE)	Gu et al. (2026)	uses LaQX	2026
-0.76413	2.1e-3	3.0e-5	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026
-0.76340	2.8e-3	2.0e-5	variational	VMC (NNBF)	Loehr & Clark (2025)		2025
-0.76298	3.2e-3	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.76258	3.6e-3	1.0e-5	variational	VMC (NNBF)	Loehr & Clark (2025)		2025
-0.76256	3.7e-3	n/a	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026
-0.76180	4.4e-3	n/a	variational	VMC (tensor BF)	Zhou et al. (2023)		2023
-0.76110	5.1e-3	n/a	variational	VMC (residual HB)	Zhou et al. (2026)		2026
-0.75970	6.5e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.75970	6.5e-3	n/a	variational	VMC (tensor BF)	Zhou et al. (2023)		2023
-0.75850	7.7e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.75300	1.3e-2	4.7e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-0.75066	1.6e-2	2.0e-5	variational	VMC (NNBF)	Loehr & Clark (2025)		2025
-0.74602	2.0e-2	6.0e-5	variational	VMC (NNBF)	Luo & Clark (2018)		2018
-0.60350	1.6e-1	n/a	variational	HF	Zhou et al. (2026)		2026
-0.76647best projected	0	2.0e-5	projected	FN-GFMC (ACE)	Gu et al. (2026)		2026
-0.76748best extrapolated	0	n/a	extrapolated	VMC (NNBF)	Loehr & Clark (2025)		2025
-0.76730	1.8e-4	n/a	extrapolated	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.76420	3.3e-3	n/a	extrapolated	VMC (tensor BF)	Liang (2025)		2025

best variational

-1.2852656

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.2852656best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-0.853

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.853best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-1.2611875

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.2611875best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-0.7508328

DMRG

best extrapolated

-0.75114(6)

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7508328best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.7465937	4.2e-3	7.8e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-0.75114best extrapolated	0	6.3e-5	extrapolated	DMRG	Wu et al. (2024)	run script	2024

best variational

-1.2199062

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.2199062best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-0.637875

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.637875best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-1.1710781

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.1710781best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-0.5144219

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5144219best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-1.07872(3)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.07872best variational	0	3.0e-5	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-1.07779	9.3e-4	5.0e-5	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-0.768337(2)

VMC (NNBF)

Loehr & Clark (2025)

best extrapolated

-0.768416

VMC (NNBF)

Loehr & Clark (2025)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.768337best variational	0	2.0e-6	variational	VMC (NNBF)	Loehr & Clark (2025)		2025
-0.766900	1.4e-3	1.0e-5	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026
-0.764100	4.2e-3	n/a	variational	VMC (residual HB)	Zhou et al. (2026)		2026
-0.763312	5.0e-3	6.3e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-0.763300	5.0e-3	n/a	variational	VMC (tensor BF)	Zhou et al. (2023)		2023
-0.761700	6.6e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.759900	8.4e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.759100	9.2e-3	n/a	variational	VMC (tensor BF)	Zhou et al. (2023)		2023
-0.755000	1.3e-2	4.0e-5	variational	VMC (NNBF)	Luo & Clark (2018)		2018
-0.614600	1.5e-1	n/a	variational	HF	Zhou et al. (2026)		2026
-0.768416best extrapolated	0	n/a	extrapolated	VMC (NNBF)	Loehr & Clark (2025)		2025

best variational

-0.7363906

DMRG

best extrapolated

-0.736431(9)

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7363906best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.7363290	6.2e-5	n/a	variational	DMRG	Sharma et al. (2025)		2025
-0.7350000	1.4e-3	3.1e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-0.7334200	3.0e-3	8.0e-5	variational	VMC (HFDS-ViT)	Sharma et al. (2025)	uses NetKet	2025
-0.7332000	3.2e-3	6.0e-4	variational	VMC (JBf-ViT)	Sharma et al. (2025)	uses NetKet	2025
-0.736431best extrapolated	0	9.4e-6	extrapolated	DMRG	Wu et al. (2024)	run script	2024

best variational

-0.7486

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7486best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.7439	4.7e-3	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.7483

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7483best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.7437	4.6e-3	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6206

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6206best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6187

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6187best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.619

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.619best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6202

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6202best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.622

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.622best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.624

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.624best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.626

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.626best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.82075(3)

VMC (Jastrow + BF)

best projected

-0.82575(2)

FN-GFMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.82075best variational	0	3.1e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.81909	1.7e-3	1.4e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.82575best projected	0	2.1e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.82339	2.4e-3	1.4e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.74834(3)

VMC (Jastrow + BF)

best projected

-0.75398(2)

FN-GFMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.74834best variational	0	3.1e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.74820	1.4e-4	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.74365	4.7e-3	3.5e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.74350	4.8e-3	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.75398best projected	0	2.1e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.74997	4.0e-3	2.1e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.62556(3)

VMC (Jastrow + BF)

best projected

-0.63217(2)

FN-GFMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.62556best variational	0	3.5e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.62550tied with best variational at 2σ	5.6e-5	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.62270	2.9e-3	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.62226	3.3e-3	2.8e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.63217best projected	0	1.7e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.62965	2.5e-3	1.4e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.6147

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6147best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6113

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6113best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6118

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6118best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6135

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6135best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6162

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6162best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6202

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6202best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6261

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6261best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6375

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6375best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.6355	2.0e-3	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6464

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6464best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.6447	1.7e-3	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6562

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6562best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.6553	9.0e-4	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.6669

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6669best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.6669tied with best variational at 2σ	<1e-4	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.67269(3)

VMC (Jastrow + BF)

best projected

-0.6862(2)

CP-AFQMC (stripe)

Xu et al. (2022)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.67269best variational	0	3.1e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.66615	6.5e-3	3.5e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.6862best projected	0	2.0e-4	projected	CP-AFQMC (stripe)	Xu et al. (2022)		2022
-0.6855tied with best projected at 2σ	7.0e-4	2.0e-4	projected	CP-AFQMC (stripe)	Xu et al. (2022)		2022
-0.6820	4.2e-3	2.0e-4	projected	CP-AFQMC (stripe)	Xu et al. (2022)		2022
-0.6782	8.0e-3	3.1e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.6731	1.3e-2	3.5e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.7482

VMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7482best variational	0	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022
-0.7435	4.7e-3	n/a	variational	VMC (Jastrow + BF)	Marino et al. (2022)		2022

best variational

-0.7427

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7427best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026

best variational

-0.7456

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7456best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026

best variational

-0.7568

VMC (tensor BF)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7568best variational	0	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.7568tied with best variational at 2σ	<1e-4	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.7529	3.9e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025

best variational

-0.7419

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7419best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.7410	9.0e-4	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.7406	1.3e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.7359	6.0e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.7354	6.5e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025

best variational

-0.7421

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7421best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026

best variational

-0.7433

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7433best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026

best variational

-0.7546

VMC (tensor BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7546best variational	0	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.7500	4.6e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025

best variational

-0.7423

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7423best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026

best variational

-0.7547

VMC (tensor BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7547best variational	0	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.7505	4.2e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025

best variational

-0.742

VMC (transformer BF)

best extrapolated

-0.7491

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.742best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.7491best extrapolated	0	n/a	extrapolated	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026

best projected

-0.6854(2)

CP-AFQMC (stripe)

Xu et al. (2022)

E/site	distance to class best	σ	bound type	method	source	year
-0.6854best projected	0	2.0e-4	projected	CP-AFQMC (stripe)	Xu et al. (2022)	2022
-0.6852tied with best projected at 2σ	2.0e-4	2.0e-4	projected	CP-AFQMC (stripe)	Xu et al. (2022)	2022
-0.6821	3.3e-3	2.0e-4	projected	CP-AFQMC (stripe)	Xu et al. (2022)	2022

exact

-1.2442068

best variational

-1.2441738(2)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year
-1.2442068exact	0	n/a	exact	ED	Moreno et al. (2022)		2022
-1.2441738best variational	0	1.9e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2441604	1.3e-5	4.4e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2441250tied with best variational at 2σ	4.9e-5	4.4e-4	variational	HF	Moreno et al. (2022)		2022
-1.2440844	8.9e-5	6.3e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2440559	1.2e-4	2.5e-7	variational	VMC (RBM)	Moreno et al. (2022)		2022
-1.2440306	1.4e-4	6.3e-7	variational	VMC (SJ)	Moreno et al. (2022)		2022
-1.2440267	1.5e-4	3.1e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2440250	1.5e-4	4.4e-5	variational	VMC (SJ)	Moreno et al. (2022)		2022

exact

-1.2171727

best variational

-1.2171594(6)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year
-1.2171727exact	0	n/a	exact	ED	Moreno et al. (2022)		2022
-1.2171594best variational	0	6.3e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2170525	1.1e-4	6.3e-7	variational	VMC (RBM)	Moreno et al. (2022)		2022
-1.2168238	3.4e-4	6.3e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2167700	3.9e-4	3.8e-6	variational	VMC (SJ)	Moreno et al. (2022)		2022
-1.2167500	4.1e-4	6.3e-5	variational	VMC (SJ)	Moreno et al. (2022)		2022
-1.2166669	4.9e-4	1.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2156113	1.5e-3	2.5e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2143750tied with best variational at 2σ	2.8e-3	1.9e-3	variational	HF	Moreno et al. (2022)		2022

exact

-1.1976241

best variational

-1.197511(2)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year
-1.1976241exact	0	n/a	exact	ED	Moreno et al. (2022)		2022
-1.197511best variational	0	1.9e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.196853	6.6e-4	1.9e-6	variational	VMC (RBM)	Moreno et al. (2022)		2022
-1.196687	8.2e-4	1.3e-4	variational	VMC (SJ)	Moreno et al. (2022)		2022
-1.196482	1.0e-3	1.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.196450	1.1e-3	6.3e-6	variational	VMC (SJ)	Moreno et al. (2022)		2022
-1.196411	1.1e-3	1.9e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.193429	4.1e-3	4.4e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.191875	5.6e-3	2.5e-3	variational	HF	Moreno et al. (2022)		2022

exact

-1.1559648

best variational

-1.1559648

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.1559648exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.1559648best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-1.1503325

best variational

-1.148627(3)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year
-1.1503325exact	0	n/a	exact	ED	Moreno et al. (2022)		2022
-1.148627best variational	0	3.1e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.148387	2.4e-4	4.4e-6	variational	VMC (RBM)	Moreno et al. (2022)		2022
-1.146052	2.6e-3	4.4e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.145216	3.4e-3	5.0e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.144831	3.8e-3	1.3e-5	variational	VMC (SJ)	Moreno et al. (2022)		2022
-1.144125	4.5e-3	1.9e-4	variational	VMC (SJ)	Moreno et al. (2022)		2022
-1.128750	2.0e-2	3.7e-3	variational	HF	Moreno et al. (2022)		2022
-1.114331	3.4e-2	1.3e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact

-1.1061269

best variational

-1.105848(3)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year
-1.1061269exact	0	n/a	exact	ED	Moreno et al. (2022)		2022
-1.105848best variational	0	2.5e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.105806tied with best variational at 2σ	4.2e-5	5.0e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.105781tied with best variational at 2σ	6.7e-5	3.7e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.105606	2.4e-4	2.5e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.105581	2.7e-4	6.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.105239	6.1e-4	5.6e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.103532	2.3e-3	4.4e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.102726	3.1e-3	5.6e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.101150	4.7e-3	6.3e-6	variational	VMC (RBM)	Moreno et al. (2022)		2022
-1.098930	6.9e-3	5.0e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.098918	6.9e-3	5.6e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.097000	8.8e-3	6.3e-5	variational	VMC (SJ)	Moreno et al. (2022)		2022
-1.096794	9.1e-3	1.9e-5	variational	VMC (SJ)	Moreno et al. (2022)		2022
-1.054337	5.2e-2	1.3e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.053125	5.3e-2	5.0e-3	variational	HF	Moreno et al. (2022)		2022

exact

-1.1060147

best variational

-1.1060144

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.1060147exact	0	n/a	exact	ED	QMBL check, checks/hubbard-u-labels/	QMBL code	n/a
-1.1060144best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-1.0959311

best variational

-1.095931

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.0959311exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.095931best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-1.0562454

best variational

-1.0562454

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.0562454exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.0562454best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-1.0318222

best variational

-1.031562(6)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year
-1.0318222exact	0	n/a	exact	ED	Moreno et al. (2022)		2022
-1.031562best variational	0	6.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.031375tied with best variational at 2σ	1.9e-4	1.9e-4	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.031000	5.6e-4	1.9e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.030994	5.7e-4	2.5e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.030581	9.8e-4	1.9e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.030144	1.4e-3	3.7e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.026225	5.3e-3	2.5e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.024981	6.6e-3	1.3e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.022544	9.0e-3	1.3e-5	variational	VMC (RBM)	Moreno et al. (2022)		2022
-1.018325	1.3e-2	3.1e-5	variational	VMC (SJ)	Moreno et al. (2022)		2022
-1.014969	1.7e-2	6.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.013688	1.8e-2	6.3e-5	variational	VMC (SJ)	Moreno et al. (2022)		2022
-0.897500	1.3e-1	5.0e-3	variational	HF	Moreno et al. (2022)		2022
-0.882831	1.5e-1	2.5e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact

-1.0318221

best variational

-1.0318221

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.0318221exact	0	n/a	exact	ED	QMBL check, checks/hubbard-u-labels/	QMBL code	n/a
-1.0318221best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-1.0287892

best variational

-1.0287892

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.0287892exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.0287892best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-1.0089505

best variational

-1.0089505

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-1.0089505exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.0089505best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1.0086438	3.1e-4	6.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.0084250	5.3e-4	3.1e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.0083062	6.4e-4	2.5e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.0075250	1.4e-3	3.1e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.0068937	2.1e-3	5.0e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.0062187	2.7e-3	3.1e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.0028563	6.1e-3	6.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-0.9986750	1.0e-2	1.3e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-0.9963500	1.3e-2	1.3e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-0.9958687	1.3e-2	1.3e-5	variational	VMC (RBM)	Moreno et al. (2022)		2022
-0.9872062	2.2e-2	1.3e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-0.9840188	2.5e-2	3.7e-5	variational	VMC (SJ)	Moreno et al. (2022)		2022
-0.9803125	2.9e-2	1.3e-4	variational	VMC (SJ)	Moreno et al. (2022)		2022
-0.8587500	1.5e-1	4.4e-3	variational	HF	Moreno et al. (2022)		2022
-0.8262312	1.8e-1	3.1e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact

-1.3360594

best variational

-1.3360594

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.3360594exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.3360594best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-1.325767

best variational

-1.325767

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.325767exact	0	n/a	exact	ED	QMBL check, checks/hubbard-u-labels/	QMBL code	n/a
-1.325767best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-1.3257647

best variational

-1.3257435(1)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year
-1.3257647exact	0	n/a	exact	ED	Moreno et al. (2022)		2022
-1.3257435best variational	0	1.2e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.3257408	2.7e-6	1.9e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.3257382	5.3e-6	2.5e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.3257132	3.0e-5	2.5e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact

-1.2432273

best variational

-1.2431527(4)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year
-1.2432273exact	0	n/a	exact	ED	Moreno et al. (2022)		2022
-1.2431527best variational	0	3.8e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2431402	1.2e-5	3.8e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2430781	7.5e-5	4.4e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.2430509	1.0e-4	5.0e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact

-1.2430143

best variational

-1.2430143

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.2430143exact	0	n/a	exact	ED	QMBL check, checks/hubbard-u-labels/	QMBL code	n/a
-1.2430143best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-1.2238086

best variational

-1.2238086

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-1.2238086exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.2238086best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1.2238070tied with best variational at 2σ	1.6e-6	7.0e-6	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026

exact

-1.1473978

best variational

-1.1473978

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-1.1473978exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.1473978best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1.1473960tied with best variational at 2σ	1.8e-6	7.0e-6	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026

exact

-1.1002332

best variational

-1.1001250(6)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year
-1.1002332exact	0	n/a	exact	ED	Moreno et al. (2022)		2022
-1.1001250best variational	0	6.3e-7	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.1000875	3.7e-5	1.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.1000625	6.3e-5	1.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.1000106	1.1e-4	1.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact

-1.1002331

best variational

-1.1002331

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.1002331exact	0	n/a	exact	ED	QMBL check, checks/hubbard-u-labels/	QMBL code	n/a
-1.1002331best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-1.0943979

best variational

-1.0943979

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-1.0943979exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.0943979best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1.0943960tied with best variational at 2σ	1.9e-6	4.0e-6	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026

exact

-1.0564725

best variational

-1.0564725

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-1.0564725exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.0564725best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1.0564680tied with best variational at 2σ	4.5e-6	9.0e-6	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026
-1.0563644	1.1e-4	1.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.0563419	1.3e-4	1.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.0563244	1.5e-4	1.3e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022
-1.0562625	2.1e-4	1.9e-6	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

best variational

-0.74177(5)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.74177best variational	0	5.0e-5	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026
-0.74090	8.7e-4	1.0e-4	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-1.1265(4)

AFQMC

best variational

-1.1248

VMC (HB)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.1265exact (stochastic)	0	3.8e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-1.1248best variational	0	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026

QMBL check, checks/hubbard-4x4-half-filling-ed/

exact

-0.8513659

best variational

-0.8511(1)

VMC (TQS)

Yamazaki et al. (2026)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.8513659exact	0	n/a	exact	ED	QMBL check, checks/hubbard-4x4-half-filling-ed/	QMBL code	n/a
-0.8510000	3.7e-4	3.8e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.8511best variational	0	1.3e-4	variational	VMC (TQS)	Yamazaki et al. (2026)		2026
-0.8511tied with best variational at 2σ	<1e-4	2.2e-4	variational	VMC (PITQS)	Yamazaki et al. (2026)	Zenodo 18334851	2026
-0.8486	2.5e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026

exact (stochastic)

-0.6588(3)

AFQMC

best variational

-0.6577

VMC (HB)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6588exact (stochastic)	0	2.5e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.6577best variational	0	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026

QMBL check, checks/hubbard-4x4-half-filling-ed/

exact

-0.5293047

best variational

-0.5292(3)

VMC (PITQS)

Yamazaki et al. (2026)

Zenodo 18334851

E/site	distance to class best	σ	bound type	method	source	code	year
-0.5297500	−4.5e-4	5.6e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.5293047exact	0	n/a	exact	ED	QMBL check, checks/hubbard-4x4-half-filling-ed/	QMBL code	n/a
-0.5292best variational	0	3.5e-4	variational	VMC (PITQS)	Yamazaki et al. (2026)	Zenodo 18334851	2026
-0.5291tied with best variational at 2σ	<1e-4	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.5291tied with best variational at 2σ	1.0e-4	2.5e-4	variational	VMC (TQS)	Yamazaki et al. (2026)		2026
-0.5281	1.1e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.4898	3.9e-2	n/a	variational	HF	Zhou et al. (2026)		2026

exact (stochastic)

-1.2571(1)

AFQMC

best variational

-1.25693(1)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.2571exact (stochastic)	0	1.3e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-1.25693best variational	0	1.0e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-0.9121(2)

AFQMC

best variational

-0.9120(1)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.9121exact (stochastic)	0	1.9e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.9120best variational	0	1.0e-4	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-0.6814(4)

AFQMC

best variational

-0.68135(1)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6814exact (stochastic)	0	4.4e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.68135best variational	0	1.0e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-0.5404(5)

AFQMC

best variational

-0.5401(1)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5404exact (stochastic)	0	5.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.5401best variational	0	1.0e-4	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

best variational

-1.1834(1)

VAFQMC

best projected

-1.18525(4)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.1834best variational	0	1.0e-4	variational	VAFQMC	Levy et al. (2023)		2023
-1.18525best projected	0	4.0e-5	projected	CP-AFQMC	Shi & Zhang (2013)		2013

exact (stochastic)

-1.1516(1)

AFQMC

best variational

-1.1506

VMC (HB)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.1516exact (stochastic)	0	1.4e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-1.1506best variational	0	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026

exact (stochastic)

-0.8574(3)

AFQMC

best variational

-0.8554

VMC (HB)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8574exact (stochastic)	0	2.5e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.8554best variational	0	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026

exact (stochastic)

-0.6594(3)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6594exact (stochastic)	0	2.8e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.5278(6)

AFQMC

best variational

-0.5266

VMC (HB)

E/site	distance to class best	σ	bound type	method	source	year
-0.5278exact (stochastic)	0	5.6e-4	exact (stochastic)	AFQMC	Qin et al. (2016)	2016
-0.5266best variational	0	n/a	variational	VMC (HB)	Zhou et al. (2026)	2026
-0.5257	9.0e-4	n/a	variational	VMC (tensor BF)	Zhou et al. (2023)	2023
-0.5255	1.1e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)	2026
-0.5186	8.0e-3	n/a	variational	VMC (tensor BF)	Zhou et al. (2023)	2023
-0.4797	4.7e-2	n/a	variational	HF	Zhou et al. (2026)	2026

best projected

0.14809(4)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
0.14809best projected	0	4.0e-5	projected	CP-AFQMC	Shi & Zhang (2013)		2013

exact (stochastic)

-1.20831(6)

AFQMC

best variational

-1.2079(1)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.20831exact (stochastic)	0	5.6e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-1.2079best variational	0	1.0e-4	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-0.8731(6)

AFQMC

best variational

-0.87173(2)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8731exact (stochastic)	0	5.6e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.87173best variational	0	2.2e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-0.6622(3)

AFQMC

best variational

-0.66094(3)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6622exact (stochastic)	0	2.8e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.66094best variational	0	2.8e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-0.5281(3)

AFQMC

best variational

-0.52705(3)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5281exact (stochastic)	0	2.8e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.52705best variational	0	2.8e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

best variational

-0.82328(3)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.82328best variational	0	3.2e-5	variational	VAFQMC	Wu et al. (2024)		2024

best projected

-1.07180(2)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.07180best projected	0	2.0e-5	projected	CP-AFQMC	Shi & Zhang (2013)		2013

best variational

-1.1846

VMC (tensor BF)

best projected

-1.1858(2)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	year
-1.1846best variational	0	n/a	variational	VMC (tensor BF)	Liang (2025)	2025
-1.1842	4.1e-4	7.0e-5	variational	VAFQMC	Levy et al. (2023)	2023
-1.1833	1.3e-3	n/a	variational	VMC (tensor BF)	Liang (2025)	2025
-1.1858best projected	0	2.0e-4	projected	CP-AFQMC	Shi & Zhang (2013)	2013

exact (stochastic)

-3.6258(1)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-3.6258exact (stochastic)	0	1.1e-4	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024

exact (stochastic)

-2.39630(9)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-2.39630exact (stochastic)	0	9.4e-5	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024

best variational

-1.13048(8)

VAFQMC

best projected

-1.13253(3)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year
-1.13048best variational	0	8.0e-5	variational	VAFQMC	Levy et al. (2023)		2023
-1.13037tied with best variational at 2σ	1.1e-4	5.2e-6	variational	VMC (PP + RBM)	Wu et al. (2024)	run script	2024
-1.12683	3.6e-3	1.4e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-1.13253best projected	0	3.0e-5	projected	CP-AFQMC	Levy et al. (2023)		2023
-1.12840	4.1e-3	9.4e-6	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.91483(2)

VMC (PP + RBM)

best projected

-0.9252(1)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year
-0.91483best variational	0	1.6e-5	variational	VMC (PP + RBM)	Wu et al. (2024)	run script	2024
-0.91480tied with best variational at 2σ	2.8e-5	1.0e-4	variational	VAFQMC	Levy et al. (2023)		2023
-0.91012	4.7e-3	2.2e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.9252best projected	0	1.0e-4	projected	CP-AFQMC	Levy et al. (2023)		2023
-0.9138	1.1e-2	9.4e-6	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

exact (stochastic)

-4.01700(9)

AFQMC

best variational

-4.0169(1)

VMC (transformer BF)

best projected

-4.0168

FN-GFMC (ACE)

E/site	distance to class best	σ	bound type	method	source	code	year
-4.01700exact (stochastic)	0	9.4e-5	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024
-4.0169best variational	0	1.0e-4	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-4.0167tied with best variational at 2σ	2.0e-4	1.0e-4	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-4.0165	4.0e-4	n/a	variational	VMC (ACE)	Gu et al. (2026)	uses LaQX	2026
-4.0161	8.0e-4	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-4.0152	1.7e-3	1.0e-4	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-3.9950	2.2e-2	1.0e-4	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-4.0168best projected	0	n/a	projected	FN-GFMC (ACE)	Gu et al. (2026)		2026
-4.0167	<1e-4	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026

exact (stochastic)

-2.60123(8)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-2.60123exact (stochastic)	0	7.8e-5	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024

best variational

-2.0338

VMC (ACE)

uses LaQX

best projected

-2.0339

FN-GFMC (ACE)

E/site	distance to class best	σ	bound type	method	source	code	year
-2.0338best variational	0	n/a	variational	VMC (ACE)	Gu et al. (2026)	uses LaQX	2026
-2.0337	<1e-4	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-2.0339best projected	0	n/a	projected	FN-GFMC (ACE)	Gu et al. (2026)		2026
-2.0338	1.0e-4	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026

best variational

-1.01391(8)

VAFQMC

best projected

-1.01923(6)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year
-1.01391best variational	0	8.0e-5	variational	VAFQMC	Levy et al. (2023)		2023
-1.00580	8.1e-3	3.1e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-1.01923best projected	0	6.0e-5	projected	CP-AFQMC	Levy et al. (2023)		2023
-1.00864	1.1e-2	1.6e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.7532

VMC (transformer BF)

best projected

-0.7616(1)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7532best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.7469	6.3e-3	2.0e-4	variational	VAFQMC	Levy et al. (2023)		2023
-0.7458	7.4e-3	6.0e-4	variational	VMC (JBf-ViT)	Sharma et al. (2025)	uses NetKet	2025
-0.7454	7.8e-3	9.0e-4	variational	VMC (HFDS-ViT)	Sharma et al. (2025)	uses NetKet	2025
-0.7422	1.1e-2	3.1e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.7422	1.1e-2	3.0e-4	variational	VMC (JBf-ViT)	Sharma et al. (2025)	uses NetKet	2025
-0.7360	1.7e-2	1.0e-3	variational	VMC (HFDS-ViT)	Sharma et al. (2025)	uses NetKet	2025
-0.7290	2.4e-2	4.0e-3	variational	VMC (HFDS-ViT)	Sharma et al. (2025)	uses NetKet	2025
-0.7260	2.7e-2	9.0e-3	variational	VMC (JBf-ViT)	Sharma et al. (2025)	uses NetKet	2025
-0.7616best projected	0	1.0e-4	projected	CP-AFQMC	Levy et al. (2023)		2023
-0.7493	1.2e-2	1.6e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.75058(1)

VMC (transformer BF)

best extrapolated

-0.7540(4)

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.75058best variational	0	1.0e-5	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-0.75026	3.2e-4	1.0e-5	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-0.74993	6.5e-4	1.0e-5	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-0.74952	1.1e-3	1.0e-5	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-0.74934	1.2e-3	1.0e-5	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-0.74834	2.2e-3	1.0e-5	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-0.74705	3.5e-3	1.0e-5	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-0.74649	4.1e-3	1.0e-5	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-0.74512	5.5e-3	1.0e-5	variational	VMC (transformer BF)	Viteritti et al. (2026)		2026
-0.74470	5.9e-3	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.74410	6.5e-3	8.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.74320	7.4e-3	8.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.74310	7.5e-3	8.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.74240	8.2e-3	3.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.73950	1.1e-2	4.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.73840	1.2e-2	4.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.73830	1.2e-2	4.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.73740	1.3e-2	4.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.7540best extrapolated	0	4.0e-4	extrapolated	VMC (transformer BF)	Viteritti et al. (2026)		2026
-0.7455	8.5e-3	n/a	extrapolated	VMC (tensor BF)	Liang (2026)		2026

exact (stochastic)

-4.52589(9)

AFQMC

best variational

-4.525834

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-4.52589exact (stochastic)	0	9.4e-5	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024
-4.525834best variational	0	n/a	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026

exact (stochastic)

-2.86037(6)

AFQMC

best variational

-2.859578

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-2.86037exact (stochastic)	0	6.3e-5	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024
-2.859578best variational	0	n/a	variational	VMC (HFPS)	Chen et al. (2026)	uses Quantax	2026

exact (stochastic)

-1.16359(8)

AFQMC

best variational

-1.1626

VMC (HB)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.16359exact (stochastic)	0	7.8e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-1.1626best variational	0	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026

exact (stochastic)

-0.86036(6)

AFQMC

best variational

-0.859156(8)

VMC (PP + RBM)

best projected

-0.857653(9)

FN-GFMC (Jastrow + BF)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.86036exact (stochastic)	0	6.3e-5	exact (stochastic)	AFQMC	Wu et al. (2024)		2024
-0.86016	2.0e-4	1.6e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.859156best variational	0	7.7e-6	variational	VMC (PP + RBM)	Wu et al. (2024)	run script	2024
-0.858100	1.1e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.856506	2.7e-3	1.1e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.857653best projected	0	9.4e-6	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

exact (stochastic)

-0.6587(3)

AFQMC

best variational

-0.6554

VMC (HB)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6587exact (stochastic)	0	3.1e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.6554best variational	0	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026

exact (stochastic)

-0.52566(8)

AFQMC

best variational

-0.52459(1)

VMC (PP + RBM)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.52625	−5.9e-4	4.7e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.52566exact (stochastic)	0	7.8e-5	exact (stochastic)	AFQMC	Wu et al. (2024)		2024
-0.52582	n/a	n/a	variational likely below exact	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.52459best variational	0	9.5e-6	variational	VMC (PP + RBM)	Wu et al. (2024)	run script	2024
-0.52450	9.4e-5	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.52410	4.9e-4	n/a	variational	VMC (tensor BF)	Zhou et al. (2023)		2023
-0.52290	1.7e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.51880	5.8e-3	n/a	variational	VMC (tensor BF)	Zhou et al. (2023)		2023
-0.47430	5.0e-2	n/a	variational	HF	Zhou et al. (2026)		2026

exact (stochastic)

-1.19231(5)

AFQMC

best variational

-1.19003(9)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.19231exact (stochastic)	0	4.7e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-1.19003best variational	0	9.4e-5	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-0.8642(2)

AFQMC

best variational

-0.8622(2)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8642exact (stochastic)	0	1.6e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.8622best variational	0	1.6e-4	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-0.6589(3)

AFQMC

best variational

-0.6574(2)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6589exact (stochastic)	0	3.1e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.6574best variational	0	2.0e-4	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-0.5259(3)

AFQMC

best variational

-0.5244(2)

VMC (HFDS)

uses NetKet

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5259exact (stochastic)	0	3.1e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.5244best variational	0	1.6e-4	variational	VMC (HFDS)	Moreno et al. (2022)	uses NetKet	2022

exact (stochastic)

-0.5005(2)

AFQMC

best variational

-0.49944(4)

VAFQMC

best extrapolated

-0.5000(3)

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.5005exact (stochastic)	0	2.3e-4	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024
-0.49944best variational	0	3.6e-5	variational	VAFQMC	Wu et al. (2024)		2024
-0.49843	1.0e-3	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.5000best extrapolated	0	3.2e-4	extrapolated	DMRG	Wu et al. (2024)	run script	2024

best variational

-1.11097(6)

VAFQMC

best projected

-1.1135(2)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	year
-1.11097best variational	0	6.0e-5	variational	VAFQMC	Levy et al. (2023)	2023
-1.11090tied with best variational at 2σ	7.0e-5	n/a	variational	VMC (tensor BF)	Liang (2025)	2025
-1.10860	2.4e-3	n/a	variational	VMC (tensor BF)	Liang (2025)	2025
-1.1135best projected	0	2.0e-4	projected	CP-AFQMC	Shi & Zhang (2013)	2013

exact (stochastic)

-1.16908(4)

AFQMC

best variational

-1.1677

VMC (HB)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.16908exact (stochastic)	0	4.0e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-1.1677best variational	0	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026

exact (stochastic)

-0.8612(4)

AFQMC

best variational

-0.8585

VMC (HB)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8612exact (stochastic)	0	4.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.8585best variational	0	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026

exact (stochastic)

-0.6580(2)

AFQMC

best variational

-0.655

VMC (HB)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6580exact (stochastic)	0	2.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.655best variational	0	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026

exact (stochastic)

-0.5254(3)

AFQMC

best variational

-0.52492

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.5254exact (stochastic)	0	3.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.52492best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.52400	9.2e-4	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.52300	1.9e-3	n/a	variational	VMC (tensor BF)	Zhou et al. (2023)		2023
-0.52260	2.3e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.51810	6.8e-3	n/a	variational	VMC (tensor BF)	Zhou et al. (2023)		2023
-0.46900	5.6e-2	n/a	variational	HF	Zhou et al. (2026)		2026

exact (stochastic)

-1.18505(4)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.18505exact (stochastic)	0	4.0e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.8620(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8620exact (stochastic)	0	2.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.6576(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6576exact (stochastic)	0	2.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.5249(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5249exact (stochastic)	0	2.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

best variational

-1.1061

VMC (tensor BF)

best projected

-1.1089(2)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	year
-1.1061best variational	0	n/a	variational	VMC (tensor BF)	Liang (2025)	2025
-1.1038	2.3e-3	n/a	variational	VMC (tensor BF)	Liang (2025)	2025
-1.1089best projected	0	2.0e-4	projected	CP-AFQMC	Shi & Zhang (2013)	2013

best variational

-1.29500(3)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.29500best variational	0	3.0e-5	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-1.0751(1)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year
-1.0751best variational	0	1.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-1.0751tied with best variational at 2σ	<1e-4	4.0e-5	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-1.0743	8.0e-4	1.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-1.0737	1.4e-3	1.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-1.0717	3.4e-3	2.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-1.0700	5.1e-3	2.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-0.92516(5)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.92516best variational	0	5.0e-5	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-0.76179(5)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.76179best variational	0	5.0e-5	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-0.66690(5)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.66690best variational	0	5.0e-5	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-4.0159

VMC (ACE)

uses LaQX

best projected

-4.0161

FN-GFMC (ACE)

E/site	distance to class best	σ	bound type	method	source	code	year
-4.0159best variational	0	n/a	variational	VMC (ACE)	Gu et al. (2026)	uses LaQX	2026
-4.0141	1.8e-3	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-4.0161best projected	0	n/a	projected	FN-GFMC (ACE)	Gu et al. (2026)		2026
-4.0158	3.0e-4	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026

best variational

-2.0405

VMC (ACE)

uses LaQX

best projected

-2.0407

FN-GFMC (ACE)

E/site	distance to class best	σ	bound type	method	source	code	year
-2.0405best variational	0	n/a	variational	VMC (ACE)	Gu et al. (2026)	uses LaQX	2026
-2.0404	<1e-4	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-2.0407best projected	0	n/a	projected	FN-GFMC (ACE)	Gu et al. (2026)		2026
-2.0406	<1e-4	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026

best variational

-0.7567

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7567best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026

best variational

-0.74425(1)

VMC (SBP)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.74425best variational	0	1.0e-5	variational	VMC (SBP)	Rende et al. (2026)		2026
-0.74200	2.2e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.74140	2.8e-3	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.73950	4.7e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.73880	5.4e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.73700	7.2e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.73440	9.8e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.73350	1.1e-2	n/a	variational	VMC (tensor BF)	Liang (2025)		2025

exact (stochastic)

-1.17187(5)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.17187exact (stochastic)	0	4.9e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.8608(1)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8608exact (stochastic)	0	1.4e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.6574(1)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6574exact (stochastic)	0	1.4e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.5246(1)

AFQMC

best variational

-0.5244

VMC (transformer BF)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.5246exact (stochastic)	0	1.4e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.5244best variational	0	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.5224	2.0e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.5209	3.5e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025

exact (stochastic)

-1.18133(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.18133exact (stochastic)	0	2.1e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.8610(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8610exact (stochastic)	0	2.1e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.6574(1)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6574exact (stochastic)	0	1.4e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.5249(2)

AFQMC

best variational

-0.5224

VMC (tensor BF)

E/site	distance to class best	σ	bound type	method	source	year
-0.5249exact (stochastic)	0	2.1e-4	exact (stochastic)	AFQMC	Qin et al. (2016)	2016
-0.5224best variational	0	n/a	variational	VMC (tensor BF)	Liang (2025)	2025
-0.5205	1.9e-3	n/a	variational	VMC (tensor BF)	Liang (2025)	2025

exact (stochastic)

-1.17337(3)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.17337exact (stochastic)	0	3.1e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.8606(1)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8606exact (stochastic)	0	1.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.6569(1)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6569exact (stochastic)	0	1.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.5247(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5247exact (stochastic)	0	1.5e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-1.17926(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.17926exact (stochastic)	0	2.0e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.8607(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8607exact (stochastic)	0	1.5e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.6570(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6570exact (stochastic)	0	1.5e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.5246(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5246exact (stochastic)	0	2.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

best variational

-0.728

VMC (ACE)

uses LaQX

best projected

-0.7288

FN-GFMC (ACE)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.728best variational	0	n/a	variational	VMC (ACE)	Gu et al. (2026)	uses LaQX	2026
-0.724	4.4e-3	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-0.7288best projected	0	n/a	projected	FN-GFMC (ACE)	Gu et al. (2026)		2026
-0.7267	2.1e-3	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026

best variational

-0.7097(1)

VMC (tensor BF)

Liang (2026)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7097best variational	0	1.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.7048	4.9e-3	7.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026

best variational

-0.83788(6)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.83788best variational	0	5.8e-5	variational	VAFQMC	Wu et al. (2024)		2024

best variational

-0.81198(6)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.81198best variational	0	5.5e-5	variational	VAFQMC	Wu et al. (2024)		2024

best variational

-0.79896(5)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.79896best variational	0	5.2e-5	variational	VAFQMC	Wu et al. (2024)		2024

best variational

-0.78530(6)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.78530best variational	0	5.9e-5	variational	VAFQMC	Wu et al. (2024)		2024
-0.77524	1.0e-2	2.3e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.77196(6)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.77196best variational	0	5.7e-5	variational	VAFQMC	Wu et al. (2024)		2024

exact (stochastic)

-4.01629(5)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-4.01629exact (stochastic)	0	5.5e-5	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024

exact (stochastic)

-2.60067(6)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-2.60067exact (stochastic)	0	6.3e-5	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024

best variational

-1.02916(2)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.02916best variational	0	1.8e-5	variational	VAFQMC	Wu et al. (2024)		2024
-1.02139	7.8e-3	1.2e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.86592(2)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.86592best variational	0	2.2e-5	variational	VAFQMC	Wu et al. (2024)		2024
-0.85627	9.7e-3	2.7e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.75865(3)

VAFQMC

best projected

-0.7583

FN-GFMC (ACE)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.75865best variational	0	2.7e-5	variational	VAFQMC	Wu et al. (2024)		2024
-0.75730	1.4e-3	n/a	variational	VMC (ACE)	Gu et al. (2026)	uses LaQX	2026
-0.75630	2.4e-3	n/a	variational	VMC (transformer BF)	Gu et al. (2026)	bytedance/laqx	2026
-0.75520	3.5e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.75430	4.4e-3	2.0e-4	variational	VMC (residual HB)	Zhou et al. (2026)		2026
-0.75290	5.8e-3	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-0.75260	6.1e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.75150	7.2e-3	1.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-0.75100	7.7e-3	n/a	variational	VMC (HB)	Zhou et al. (2026)		2026
-0.75090	7.8e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.74885	9.8e-3	1.6e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.74395	1.5e-2	3.1e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.74010	1.9e-2	1.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-0.72710	3.2e-2	3.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-0.7583best projected	0	n/a	projected	FN-GFMC (ACE)	Gu et al. (2026)		2026
-0.7560	2.3e-3	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026
-0.7544	3.9e-3	3.9e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024
-0.7499	8.4e-3	2.7e-5	projected	FN-GFMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.7370(1)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7370best variational	0	1.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-0.7367tied with best variational at 2σ	3.0e-4	1.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-0.74411(1)

VMC (SBP)

best projected

-0.744

FN-GFMC (ACE)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.74411best variational	0	1.0e-5	variational	VMC (SBP)	Rende et al. (2026)		2026
-0.74300	1.1e-3	n/a	variational	VMC (ACE)	Gu et al. (2026)	uses LaQX	2026
-0.74080	3.3e-3	1.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.74010	4.0e-3	2.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.74000	4.1e-3	1.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.73960	4.5e-3	1.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.73860	5.5e-3	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.73730	6.8e-3	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-0.73600	8.1e-3	7.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.73600	8.1e-3	1.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-0.73510	9.0e-3	2.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.73490	9.2e-3	7.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.73420	9.9e-3	2.0e-4	variational	VMC (tensor BF)	Liang (2026)		2026
-0.73350	1.1e-2	n/a	variational	VMC (tensor BF)	Liang (2025)		2025
-0.72610	1.8e-2	1.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-0.744best projected	0	n/a	projected	FN-GFMC (ACE)	Gu et al. (2026)		2026
-0.741	3.5e-3	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026

best variational

-0.7375(1)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7375best variational	0	1.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025
-0.7245	1.3e-2	3.0e-4	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-0.74455(3)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.74455best variational	0	2.6e-5	variational	VAFQMC	Wu et al. (2024)		2024

best variational

-1.00849(2)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.00849best variational	0	2.2e-5	variational	VAFQMC	Wu et al. (2024)		2024
-0.99898	9.5e-3	9.8e-6	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.84058(2)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.84058best variational	0	2.2e-5	variational	VAFQMC	Wu et al. (2024)		2024
-0.83072	9.9e-3	1.6e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.73038(5)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.73038best variational	0	4.7e-5	variational	VAFQMC	Wu et al. (2024)		2024
-0.72030	1.0e-2	2.7e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.71584(5)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.71584best variational	0	4.6e-5	variational	VAFQMC	Wu et al. (2024)		2024

best variational

-0.70135(3)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.70135best variational	0	3.2e-5	variational	VAFQMC	Wu et al. (2024)		2024
-0.69132	1.0e-2	2.3e-5	variational	VMC (Jastrow + BF)	Wu et al. (2024)	run script	2024

best variational

-0.68678(5)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.68678best variational	0	5.2e-5	variational	VAFQMC	Wu et al. (2024)		2024

best variational

-0.67215(5)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.67215best variational	0	5.2e-5	variational	VAFQMC	Wu et al. (2024)		2024

best variational

-0.64053(5)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.64053best variational	0	4.9e-5	variational	VAFQMC	Wu et al. (2024)		2024

exact (stochastic)

-4.52446(6)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-4.52446exact (stochastic)	0	5.9e-5	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024

exact (stochastic)

-2.8605(1)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-2.8605exact (stochastic)	0	1.1e-4	exact (stochastic)	AFQMC	Wu et al. (2024)	run scripts	2024

exact (stochastic)

-1.17420(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.17420exact (stochastic)	0	2.3e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.8605(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8605exact (stochastic)	0	1.6e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.6570(1)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6570exact (stochastic)	0	1.2e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.5243(1)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5243exact (stochastic)	0	1.2e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

best variational

-0.82333(3)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.82333best variational	0	3.0e-5	variational	VAFQMC	Wu et al. (2024)		2024
-0.79875	2.5e-2	6.8e-5	variational	VMC (PP + RBM)	Wu et al. (2024)	run script	2024

best variational

-0.79937(4)

VMC (PP + RBM)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.79937best variational	0	3.7e-5	variational	VMC (PP + RBM)	Wu et al. (2024)	run script	2024

best variational

1.25918(3)

VMC (PP + RBM)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
1.25918best variational	0	2.7e-5	variational	VMC (PP + RBM)	Wu et al. (2024)	run script	2024

exact (stochastic)

-1.17798(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.17798exact (stochastic)	0	2.0e-5	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.8605(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8605exact (stochastic)	0	1.6e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.6571(2)

AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6571exact (stochastic)	0	2.0e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016

exact (stochastic)

-0.5244(1)

AFQMC

best variational

-0.52427(4)

VAFQMC

E/site	distance to class best	σ	bound type	method	source	code	year
-0.5244exact (stochastic)	0	1.2e-4	exact (stochastic)	AFQMC	Qin et al. (2016)		2016
-0.52427best variational	0	3.6e-5	variational	VAFQMC	Wu et al. (2024)		2024
-0.51898	5.3e-3	1.7e-5	variational	VMC (PP + RBM)	Wu et al. (2024)	run script	2024

best variational

-1.29563(3)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.29563best variational	0	3.0e-5	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-1.07256(5)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.07256best variational	0	5.0e-5	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-0.91859(6)

VMC (HFPS)

uses Quantax

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.91859best variational	0	6.0e-5	variational	VMC (HFPS)	Roth et al. (2025)	uses Quantax	2025

best variational

-0.74382(1)

VMC (SBP)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.74382best variational	0	1.0e-5	variational	VMC (SBP)	Rende et al. (2026)		2026

best variational

-0.74397(1)

VMC (SBP)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.74397best variational	0	1.0e-5	variational	VMC (SBP)	Rende et al. (2026)		2026

best variational

-0.7501

VMC (SCALE)

uses LaQX

best projected

-0.7548

FN-GFMC (SCALE)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.7501best variational	0	n/a	variational	VMC (SCALE)	Gu et al. (2026)	uses LaQX	2026
-0.7548best projected	0	n/a	projected	FN-GFMC (SCALE)	Gu et al. (2026)		2026

best extrapolated

-1.306(2)

CP-AFQMC

best approximate

-1.3062(4)

DMET

E/site	distance to class best	σ	bound type	method	source	year
-1.306best extrapolated	0	2.0e-3	extrapolated	CP-AFQMC	LeBlanc et al. (2015)	2015
-1.304tied with best extrapolated at 2σ	1.6e-3	7.0e-4	extrapolated	FN-DMC	LeBlanc et al. (2015)	2015
-1.3062best approximate	0	4.0e-4	approximate	DMET	LeBlanc et al. (2015)	2015

best extrapolated

-1.270(2)

FN-DMC

best approximate

-1.2721(6)

DMET

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.270best extrapolated	0	2.0e-3	extrapolated	FN-DMC	LeBlanc et al. (2015)		2015
-1.2721best approximate	0	6.0e-4	approximate	DMET	LeBlanc et al. (2015)		2015

best extrapolated

-1.1763(2)

AFQMC

best approximate

-1.1764(3)

DMET

E/site	distance to class best	σ	bound type	method	source	year
-1.1763best extrapolated	0	2.0e-4	extrapolated	AFQMC	LeBlanc et al. (2015)	2015
-1.1760tied with best extrapolated at 2σ	3.0e-4	1.0e-3	extrapolated	DMRG	LeBlanc et al. (2015)	2015
-1.1760tied with best extrapolated at 2σ	3.0e-4	2.0e-4	extrapolated	AFQMC	Qin et al. (2016)	2016
-1.1750tied with best extrapolated at 2σ	1.3e-3	1.0e-3	extrapolated	FN-DMC	LeBlanc et al. (2015)	2015
-1.1764best approximate	0	3.0e-4	approximate	DMET	LeBlanc et al. (2015)	2015
-1.1749	1.5e-3	n/a	approximate	UCCSDTQ*	LeBlanc et al. (2015)	2015
-1.1735	2.9e-3	4.0e-4	approximate	UCCSD	LeBlanc et al. (2015)	2015

best extrapolated

-0.8793(2)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8793best extrapolated	0	2.0e-4	extrapolated	CP-AFQMC	Qin et al. (2016)		2016

best extrapolated

-1.141(2)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.141best extrapolated	0	2.0e-3	extrapolated	CP-AFQMC	Qin et al. (2016)		2016

best extrapolated

-1.1845(5)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.1845best extrapolated	0	5.0e-4	extrapolated	CP-AFQMC	Qin et al. (2016)		2016

best extrapolated

-1.1491(2)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.1491best extrapolated	0	2.0e-4	extrapolated	CP-AFQMC	Qin et al. (2016)		2016

best extrapolated

-1.110(3)

CP-AFQMC

best approximate

-1.108(2)

DMET

E/site	distance to class best	σ	bound type	method	source	year
-1.110best extrapolated	0	3.0e-3	extrapolated	CP-AFQMC	LeBlanc et al. (2015)	2015
-1.104tied with best extrapolated at 2σ	6.0e-3	1.4e-3	extrapolated	DMRG	LeBlanc et al. (2015)	2015
-1.103tied with best extrapolated at 2σ	6.8e-3	7.0e-4	extrapolated	FN-DMC	LeBlanc et al. (2015)	2015
-1.108best approximate	0	2.0e-3	approximate	DMET	LeBlanc et al. (2015)	2015

best extrapolated

-1.032(1)

CP-AFQMC

best approximate

-1.031(3)

DMET

E/site	distance to class best	σ	bound type	method	source	year
-1.032best extrapolated	0	1.0e-3	extrapolated	CP-AFQMC	Qin et al. (2016)	2016
-1.026	6.0e-3	1.0e-3	extrapolated	CP-AFQMC	LeBlanc et al. (2015)	2015
-1.026	6.0e-3	1.0e-3	extrapolated	CP-AFQMC	Qin et al. (2016)	2016
-1.022	9.5e-3	1.5e-3	extrapolated	FN-DMC	LeBlanc et al. (2015)	2015
-1.031best approximate	0	3.0e-3	approximate	DMET	LeBlanc et al. (2015)	2015

best extrapolated

-0.8605(5)

DMRG

best approximate

-0.861

UCCSDTQ*

E/site	distance to class best	σ	bound type	method	source	year
-0.8605best extrapolated	0	5.0e-4	extrapolated	DMRG	LeBlanc et al. (2015)	2015
-0.8603tied with best extrapolated at 2σ	2.0e-4	2.0e-4	extrapolated	AFQMC	LeBlanc et al. (2015)	2015
-0.8603tied with best extrapolated at 2σ	2.0e-4	2.0e-4	extrapolated	AFQMC	Qin et al. (2016)	2016
-0.8575	3.0e-3	3.0e-4	extrapolated	FN-DMC	LeBlanc et al. (2015)	2015
-0.861best approximate	0	n/a	approximate	UCCSDTQ*	LeBlanc et al. (2015)	2015
-0.860tied with best approximate at 2σ	<1e-3	3.0e-4	approximate	DMET	LeBlanc et al. (2015)	2015

best extrapolated

-0.967(1)

FN-DMC

best approximate

-0.977(4)

DMET

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.967best extrapolated	0	1.0e-3	extrapolated	FN-DMC	LeBlanc et al. (2015)		2015
-0.977best approximate	0	4.0e-3	approximate	DMET	LeBlanc et al. (2015)		2015

best extrapolated

-0.854(2)

FN-DMC

best approximate

-0.8767(7)

DMET

Zheng et al. (2017)

E/site	distance to class best	σ	bound type	method	source	year
-0.854best extrapolated	0	2.0e-3	extrapolated	FN-DMC	LeBlanc et al. (2015)	2015
-0.8767best approximate	0	7.0e-4	approximate	DMET	Zheng et al. (2017)	2017
-0.8736	3.0e-3	2.0e-5	approximate	DMET	Zheng et al. (2017)	2017
-0.8725	4.2e-3	1.0e-5	approximate	DMET	Zheng et al. (2017)	2017
-0.8684	8.3e-3	1.0e-5	approximate	DMET	Zheng et al. (2017)	2017
-0.8679	8.8e-3	7.0e-4	approximate	DMET	Zheng et al. (2017)	2017
-0.8630tied with best approximate at 2σ	1.4e-2	1.3e-2	approximate	DMET	LeBlanc et al. (2015)	2015
-0.8589	1.8e-2	4.0e-5	approximate	DMET	Zheng et al. (2017)	2017
-0.8587	1.8e-2	4.0e-5	approximate	DMET	Zheng et al. (2017)	2017

best extrapolated

-0.6568(3)

AFQMC

best approximate

-0.6582

UCCSDTQ*

E/site	distance to class best	σ	bound type	method	source	year
-0.6568best extrapolated	0	3.0e-4	extrapolated	AFQMC	LeBlanc et al. (2015)	2015
-0.6567tied with best extrapolated at 2σ	1.0e-4	3.0e-4	extrapolated	AFQMC	Qin et al. (2016)	2016
-0.6565tied with best extrapolated at 2σ	3.0e-4	1.0e-4	extrapolated	DMRG	LeBlanc et al. (2015)	2015
-0.6551	1.7e-3	1.0e-4	extrapolated	FN-DMC	LeBlanc et al. (2015)	2015
-0.6582best approximate	0	n/a	approximate	UCCSDTQ*	LeBlanc et al. (2015)	2015
-0.6562	2.0e-3	5.0e-4	approximate	DMET	LeBlanc et al. (2015)	2015

best extrapolated

-0.8534(1)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.8534best extrapolated	0	1.0e-4	extrapolated	CP-AFQMC	Qin et al. (2016)		2016

best extrapolated

-1.066(2)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.066best extrapolated	0	2.0e-3	extrapolated	CP-AFQMC	Qin et al. (2016)		2016

best extrapolated

-1.0729(1)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-1.0729best extrapolated	0	1.0e-4	extrapolated	CP-AFQMC	Qin et al. (2016)		2016

best extrapolated

-0.9666(4)

CP-AFQMC

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.9666best extrapolated	0	4.0e-4	extrapolated	CP-AFQMC	Qin et al. (2016)		2016

best extrapolated

-0.877(1)

FN-DMC

best approximate

-0.88(3)

DMET

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.877best extrapolated	0	1.0e-3	extrapolated	FN-DMC	LeBlanc et al. (2015)		2015
-0.88best approximate	0	3.0e-2	approximate	DMET	LeBlanc et al. (2015)		2015

best extrapolated

-0.773(1)

CP-AFQMC

best approximate

-0.77063(1)

DMET

Zheng et al. (2017)

E/site	distance to class best	σ	bound type	method	source	year
-0.773best extrapolated	0	1.0e-3	extrapolated	CP-AFQMC	Qin et al. (2016)	2016
-0.767tied with best extrapolated at 2σ	5.7e-3	2.0e-3	extrapolated	iPEPS	Zheng et al. (2017)	2017
-0.766	7.0e-3	1.0e-3	extrapolated	CP-AFQMC	LeBlanc et al. (2015)	2015
-0.766	7.0e-3	1.0e-3	extrapolated	CP-AFQMC	Qin et al. (2016)	2016
-0.766	7.0e-3	1.0e-3	extrapolated	CP-AFQMC	Zheng et al. (2017)	2017
-0.763	9.8e-3	1.8e-3	extrapolated	iPEPS	Zheng et al. (2017)	2017
-0.763	1.0e-2	2.6e-3	extrapolated	iPEPS	Zheng et al. (2017)	2017
-0.759	1.4e-2	4.0e-3	extrapolated	DMRG	LeBlanc et al. (2015)	2015
-0.758	1.5e-2	1.4e-3	extrapolated	iPEPS	Zheng et al. (2017)	2017
-0.756	1.7e-2	2.5e-3	extrapolated	iPEPS	Zheng et al. (2017)	2017
-0.749	2.4e-2	2.0e-3	extrapolated	FN-DMC	LeBlanc et al. (2015)	2015
-0.77063best approximate	0	1.0e-5	approximate	DMET	Zheng et al. (2017)	2017
-0.77060tied with best approximate at 2σ	3.0e-5	7.0e-5	approximate	DMET	Zheng et al. (2017)	2017
-0.77060tied with best approximate at 2σ	3.0e-5	1.0e-5	approximate	DMET	Zheng et al. (2017)	2017
-0.77040tied with best approximate at 2σ	2.3e-4	3.0e-4	approximate	DMET	Zheng et al. (2017)	2017
-0.76910tied with best approximate at 2σ	1.5e-3	1.0e-3	approximate	DMET	Zheng et al. (2017)	2017
-0.76890	1.7e-3	8.0e-4	approximate	DMET	Zheng et al. (2017)	2017
-0.76580	4.8e-3	8.0e-4	approximate	DMET	Zheng et al. (2017)	2017
-0.76200	8.6e-3	1.0e-5	approximate	DMET	Zheng et al. (2017)	2017
-0.76140	9.2e-3	5.0e-5	approximate	DMET	Zheng et al. (2017)	2017
-0.75800	1.3e-2	5.0e-4	approximate	DMET	Zheng et al. (2017)	2017
-0.75500	1.6e-2	7.0e-3	approximate	DMET	LeBlanc et al. (2015)	2015
-0.74370	2.7e-2	9.0e-4	approximate	DMET	Zheng et al. (2017)	2017

best extrapolated

-0.5247(2)

AFQMC

best approximate

-0.5255

UCCSDTQ*

E/site	distance to class best	σ	bound type	method	source	year
-0.5247best extrapolated	0	2.0e-4	extrapolated	AFQMC	LeBlanc et al. (2015)	2015
-0.5243tied with best extrapolated at 2σ	4.0e-4	2.0e-4	extrapolated	AFQMC	Qin et al. (2016)	2016
-0.5241	6.0e-4	1.0e-4	extrapolated	DMRG	LeBlanc et al. (2015)	2015
-0.5232	1.6e-3	5.0e-5	extrapolated	FN-DMC	LeBlanc et al. (2015)	2015
-0.5255best approximate	0	n/a	approximate	UCCSDTQ*	LeBlanc et al. (2015)	2015
-0.5234	2.1e-3	1.0e-3	approximate	DMET	LeBlanc et al. (2015)	2015

best approximate

-0.6531(1)

DMET

Zheng et al. (2017)

E/site	distance to class best	σ	bound type	method	source	year
-0.6531best approximate	0	1.0e-4	approximate	DMET	Zheng et al. (2017)	2017
-0.6526tied with best approximate at 2σ	5.0e-4	2.0e-4	approximate	DMET	Zheng et al. (2017)	2017
-0.6514	1.7e-3	1.0e-4	approximate	DMET	Zheng et al. (2017)	2017
-0.6505	2.6e-3	1.0e-4	approximate	DMET	Zheng et al. (2017)	2017
-0.6394	1.4e-2	1.0e-5	approximate	DMET	Zheng et al. (2017)	2017

best extrapolated

-0.3693(2)

AFQMC

best approximate

-0.3696

UCCSDTQ*

E/site	distance to class best	σ	bound type	method	source	year
-0.3693best extrapolated	0	2.0e-4	extrapolated	AFQMC	LeBlanc et al. (2015)	2015
-0.3689tied with best extrapolated at 2σ	4.0e-4	1.0e-4	extrapolated	DMRG	LeBlanc et al. (2015)	2015
-0.3684	9.5e-4	5.0e-5	extrapolated	FN-DMC	LeBlanc et al. (2015)	2015
-0.3696best approximate	0	n/a	approximate	UCCSDTQ*	LeBlanc et al. (2015)	2015
-0.3685tied with best approximate at 2σ	1.1e-3	1.0e-3	approximate	DMET	LeBlanc et al. (2015)	2015

Spinless t-V#

14 instances, energies as E/site

lattice size

instance

value

energy

method

source

code

energies

exact

-0.498339

best variational

-0.498339

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.498339exact	0	n/a	exact	ED	run script, Wu et al. (2024)		2024
-0.498319	2.0e-5	3.2e-5	exact (stochastic)	CT-QMC	Wu et al. (2024)	run script	2024
-0.498339best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.498339	<1e-6	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-0.3852719

best variational

-0.3852719

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.3852719exact	0	n/a	exact	ED	run script, Wu et al. (2024)		2024
-0.3851545	1.2e-4	1.6e-4	exact (stochastic)	CT-QMC	Wu et al. (2024)	run script	2024
-0.3852719best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-0.2344426

best variational

-0.2344426

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.2344426exact	0	n/a	exact	ED	run script, Wu et al. (2024)		2024
-0.2340127	4.3e-4	6.4e-4	exact (stochastic)	CT-QMC	Wu et al. (2024)	run script	2024
-0.2344426best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-0.7487516

best variational

-0.7487521(6)

VMC (SJ + RBM)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7487516exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.7487521best variational	0	6.4e-7	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024
-0.7487516tied with best variational at 2σ	4.5e-7	7.3e-8	variational	VMC (SJB + RBM)	Wu et al. (2024)	run script	2024
-0.7487500	2.1e-6	n/a	variational	HF	Humeniuk et al. (2022)		2022

exact

-0.7376632

best variational

-0.7376632(3)

VMC (SJB + RBM)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7376632exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.7376632best variational	0	2.7e-7	variational	VMC (SJB + RBM)	Wu et al. (2024)	run script	2024
-0.7376632tied with best variational at 2σ	<1e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.7376629tied with best variational at 2σ	3.3e-7	2.8e-7	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024
-0.7376623tied with best variational at 2σ	8.8e-7	1.8e-6	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024
-0.7376187tied with best variational at 2σ	4.4e-5	3.7e-5	variational	VMC (arSJVMC)	Humeniuk et al. (2022)	shifushuimenu/autoregressive_Slater-Jastrow	2022
-0.7375000	1.6e-4	n/a	variational	HF	Humeniuk et al. (2022)		2022

exact

-0.6400407

best variational

-0.6400407

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.6400407exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.6400407best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.6400388tied with best variational at 2σ	1.8e-6	2.8e-6	variational	VMC (SJB + RBM)	Wu et al. (2024)	run script	2024
-0.6399976	4.3e-5	8.8e-6	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024
-0.6399644	7.6e-5	9.5e-6	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024
-0.6398750	1.7e-4	6.3e-5	variational	VMC (arSJVMC)	Humeniuk et al. (2022)	shifushuimenu/autoregressive_Slater-Jastrow	2022
-0.6250000	1.5e-2	n/a	variational	HF	Humeniuk et al. (2022)		2022

exact

-0.2532535

best variational

-0.2532535

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.2532535exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-0.2532535best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.2511097tied with best variational at 2σ	2.1e-3	1.5e-3	variational	VMC (SJB + RBM)	Wu et al. (2024)	run script	2024
-0.2456250	7.6e-3	6.3e-4	variational	VMC (arSJVMC)	Humeniuk et al. (2022)	shifushuimenu/autoregressive_Slater-Jastrow	2022
-0.2374764	1.6e-2	1.2e-3	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024
-0.2361528	1.7e-2	2.2e-4	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024
-0.2020479	5.1e-2	n/a	variational	HF	Humeniuk et al. (2022)		2022

exact

-0.7759279

uses QuSpin

best variational

-0.7759280(1)

VMC (SJ + RBM)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7759279exact	0	n/a	exact	ED	Humeniuk et al. (2022)	uses QuSpin	2022
-0.7759280best variational	0	1.3e-7	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024
-0.7759279tied with best variational at 2σ	<1e-7	2.7e-7	variational	VMC (SJB + RBM)	Wu et al. (2024)	run script	2024
-0.7759259	2.0e-6	n/a	variational	HF	Humeniuk et al. (2022)		2022
-0.7759222tied with best variational at 2σ	5.7e-6	1.1e-5	variational	VMC (arSJVMC)	Humeniuk et al. (2022)	shifushuimenu/autoregressive_Slater-Jastrow	2022

exact

-0.7594596

uses QuSpin

best variational

-0.759460(1)

VMC (SJ + RBM)

E/site	distance to class best	σ	bound type	method	source	code	year
-0.7594596exact	0	n/a	exact	ED	Humeniuk et al. (2022)	uses QuSpin	2022
-0.759460best variational	0	1.4e-6	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024
-0.75945956	n/a	8.7e-8	variational energy-equals-exact	VMC (SJB + RBM)	Wu et al. (2024)	run script	2024
-0.759459tied with best variational at 2σ	<1e-6	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.759259	2.0e-4	n/a	variational	HF	Humeniuk et al. (2022)		2022

exact

-0.6132603

uses QuSpin

best variational

-0.6132263

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.6132603exact	0	n/a	exact	ED	Humeniuk et al. (2022)	uses QuSpin	2022
-0.6132263best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.6131929	3.3e-5	6.6e-6	variational	VMC (SJB + RBM)	Wu et al. (2024)	run script	2024
-0.6116091	1.6e-3	1.0e-4	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024
-0.6069444	6.3e-3	2.8e-4	variational	VMC (arSJVMC)	Humeniuk et al. (2022)	shifushuimenu/autoregressive_Slater-Jastrow	2022
-0.5925926	2.1e-2	n/a	variational	HF	Humeniuk et al. (2022)		2022

exact

-0.220223

uses QuSpin

best variational

-0.2201239

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.220223exact	0	n/a	exact	ED	Humeniuk et al. (2022)	uses QuSpin	2022
-0.2201239best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.2101835	9.9e-3	2.0e-4	variational	VMC (SJB + RBM)	Wu et al. (2024)	run script	2024
-0.2008333	1.9e-2	8.3e-4	variational	VMC (arSJVMC)	Humeniuk et al. (2022)	shifushuimenu/autoregressive_Slater-Jastrow	2022
-0.1919060	2.8e-2	n/a	variational	HF	Humeniuk et al. (2022)		2022
-0.1713346	4.9e-2	2.4e-3	variational	VMC (SJ + RBM)	Wu et al. (2024)	run script	2024

exact (stochastic)

-0.4607(4)

CT-QMC

best variational

-0.4590635

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.4607exact (stochastic)	0	3.6e-4	exact (stochastic)	CT-QMC	Wu et al. (2024)	run script	2024
-0.4590635best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.4561552	2.9e-3	n/a	variational	HF	Humeniuk et al. (2022)		2022
-0.4496875	9.4e-3	3.1e-4	variational	VMC (arSJVMC)	Humeniuk et al. (2022)	shifushuimenu/autoregressive_Slater-Jastrow	2022

exact (stochastic)

-0.292(1)

CT-QMC

best variational

-0.2911555

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.292exact (stochastic)	0	1.5e-3	exact (stochastic)	CT-QMC	Wu et al. (2024)	run script	2024
-0.2911555best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.2891614	2.0e-3	n/a	variational	HF	Humeniuk et al. (2022)		2022
-0.2743750	1.7e-2	6.3e-4	variational	VMC (arSJVMC)	Humeniuk et al. (2022)	shifushuimenu/autoregressive_Slater-Jastrow	2022

best variational

-0.1601344

DMRG

E/site	distance to class best	σ	bound type	method	source	code	year
-0.153	n/a	2.6e-3	exact (stochastic) above a variational bound	CT-QMC	Wu et al. (2024)	run script	2024
-0.1601344best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-0.1597047	4.3e-4	n/a	variational	HF	Humeniuk et al. (2022)		2022
-0.1450000	1.5e-2	6.3e-4	variational	VMC (arSJVMC)	Humeniuk et al. (2022)	shifushuimenu/autoregressive_Slater-Jastrow	2022

t-J#

27 instances, energies as E/site

lattice size

instance

value

energy

method

source

code

energies

exact

-0.3441916

best variational

-0.3366806

VMC (phase string)

E/site	distance to class best	σ	bound type	method	source	year
-0.3441916exact	0	n/a	exact	ED	Cui et al. (2024)	2024
-0.3366806best variational	0	n/a	variational	VMC (phase string)	Cui et al. (2024)	2024
-0.3185278	1.8e-2	n/a	variational	VMC (phase string)	Cui et al. (2024)	2024
-0.2804028	5.6e-2	n/a	variational	VMC (Bloch wave)	Cui et al. (2024)	2024

exact

-0.4143583

best variational

-0.398

VMC (phase string)

E/site	distance to class best	σ	bound type	method	source	year
-0.4143583exact	0	n/a	exact	ED	Cui et al. (2024)	2024
-0.398best variational	0	n/a	variational	VMC (phase string)	Cui et al. (2024)	2024
-0.370	2.8e-2	n/a	variational	VMC (phase string)	Cui et al. (2024)	2024
-0.299	9.9e-2	n/a	variational	VMC (Bloch wave)	Cui et al. (2024)	2024

exact

-0.5908993

Chiappa et al. (2001)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5908993exact	0	n/a	exact	ED	Chiappa et al. (2001)		2001

exact

-0.5733713

Chiappa et al. (2001)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5733713exact	0	n/a	exact	ED	Chiappa et al. (2001)		2001

exact

-0.5781986

Rice et al. (1997)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5781986exact	0	n/a	exact	ED	Rice et al. (1997)		1997

exact

-0.6559335

Rice et al. (1997)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6559335exact	0	n/a	exact	ED	Rice et al. (1997)		1997

best variational

-0.5470833

DMRG

McCulloch et al. (2001)

best extrapolated

-0.5484(5)

DMRG

McCulloch et al. (2001)

E/site	distance to class best	σ	bound type	method	source	year
-0.5470833best variational	0	n/a	variational	DMRG	McCulloch et al. (2001)	2001
-0.5464896	5.9e-4	n/a	variational	DMRG	McCulloch et al. (2001)	2001
-0.5446250	2.5e-3	n/a	variational	DMRG	McCulloch et al. (2001)	2001
-0.5484best extrapolated	0	5.2e-4	extrapolated	DMRG	McCulloch et al. (2001)	2001

exact

-0.5643668

Dong et al. (2020)

best variational

-0.56428(2)

fPEPS

Dong et al. (2020)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5643668exact	0	n/a	exact	ED	Dong et al. (2020)		2020
-0.56428best variational	0	2.0e-5	variational	fPEPS	Dong et al. (2020)		2020

exact

-0.6590431

Becca et al. (2001)

best variational

-0.65904

VMC (Gutzwiller)

Becca et al. (2001)

E/site	distance to class best	σ	bound type	method	source	year
-0.6590431exact	0	n/a	exact	ED	Becca et al. (2001)	2001
-0.65904best variational	0	n/a	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.65904tied with best variational at 2σ	<1e-5	n/a	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.65902	2.0e-5	n/a	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.65898	6.0e-5	n/a	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.65882	2.2e-4	n/a	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.65830	7.4e-4	1.0e-4	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.65826	7.8e-4	n/a	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.65638	2.7e-3	n/a	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.65420	4.8e-3	n/a	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.65410	4.9e-3	1.0e-4	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.64559	1.3e-2	n/a	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001
-0.63847	2.1e-2	n/a	variational	VMC (Gutzwiller)	Becca et al. (2001)	2001

exact

-0.5009718

best variational

-0.48476(1)

VMC (Pfaffian)

best projected

-0.49445(2)

FN-GFMC (Pfaffian)

E/site	distance to class best	σ	bound type	method	source	year
-0.5009718exact	0	n/a	exact	ED	Lugas et al. (2006)	2006
-0.48476best variational	0	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-0.48334	1.4e-3	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-0.49445best projected	0	2.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.49325	1.2e-3	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.49256	1.9e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-0.5945167

best variational

-0.57978(1)

VMC (Pfaffian)

best projected

-0.58881(2)

FN-GFMC (Pfaffian)

E/site	distance to class best	σ	bound type	method	source	year
-0.5945167exact	0	n/a	exact	ED	Lugas et al. (2006)	2006
-0.57978best variational	0	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-0.57664	3.1e-3	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-0.58881best projected	0	2.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.58770	1.1e-3	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.58625	2.6e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-0.6894488

best variational

-0.67568(1)

VMC (Pfaffian)

best projected

-0.68434(3)

FN-GFMC (Pfaffian)

E/site	distance to class best	σ	bound type	method	source	year
-0.6894488exact	0	n/a	exact	ED	Lugas et al. (2006)	2006
-0.67568best variational	0	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-0.67045	5.2e-3	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-0.68434best projected	0	3.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.68327	1.1e-3	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.68091	3.4e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-0.7853745

best variational

-0.77228(1)

VMC (Pfaffian)

best projected

-0.78062(3)

FN-GFMC (Pfaffian)

E/site	distance to class best	σ	bound type	method	source	year
-0.7853745exact	0	n/a	exact	ED	Lugas et al. (2006)	2006
-0.77228best variational	0	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-0.76463	7.7e-3	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-0.78062best projected	0	3.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.77960	1.0e-3	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.77645	4.2e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-0.9793539

best variational

-0.96706(1)

VMC (Pfaffian)

best projected

-0.97505(3)

FN-GFMC (Pfaffian)

E/site	distance to class best	σ	bound type	method	source	year
-0.9793539exact	0	n/a	exact	ED	Lugas et al. (2006)	2006
-0.96706best variational	0	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-0.95410	1.3e-2	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-0.97505best projected	0	3.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.97414	9.1e-4	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.96920	5.8e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-1.1753789

best variational

-1.16352(1)

VMC (Pfaffian)

best projected

-1.17136(2)

FN-GFMC (Pfaffian)

E/site	distance to class best	σ	bound type	method	source	year
-1.1753789exact	0	n/a	exact	ED	Lugas et al. (2006)	2006
-1.16352best variational	0	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-1.14483	1.9e-2	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-1.17136best projected	0	2.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-1.17052	8.4e-4	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-1.16385	7.5e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-0.6426164

D. Poilblanc (unpublished), quoted in Sorella (2001)

best variational

-0.6387(1)

VMC (Gutzwiller)

best projected

-0.6371(1)

FN-GFMC (Gutzwiller)

E/site	distance to class best	σ	bound type	method	source	year
-0.6426164exact	0	n/a	exact	ED	D. Poilblanc (unpublished), quoted in Sorella (2001)	2001
-0.6387best variational	0	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-0.6381	6.0e-4	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-0.6332	5.5e-3	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-0.6148	2.4e-2	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-0.6138	2.5e-2	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-0.6137	2.5e-2	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-0.6371best projected	0	1.0e-4	projected	FN-GFMC (Gutzwiller)	Sorella (2001)	2001
-0.6296	7.5e-3	3.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.6277	9.4e-3	1.0e-4	projected	FN-GFMC (Gutzwiller)	Sorella (2001)	2001
-0.6275	9.6e-3	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.6275	9.6e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-0.7143669

best variational

-0.68946(1)

VMC (Pfaffian)

best projected

-0.70292(2)

FN-GFMC (Pfaffian)

E/site	distance to class best	σ	bound type	method	source	year
-0.7143669exact	0	n/a	exact	ED	Lugas et al. (2006)	2006
-0.68946best variational	0	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-0.68894	5.2e-4	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-0.70292best projected	0	2.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.70106	1.9e-3	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.70101	1.9e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-0.7881242

D. Poilblanc (unpublished), quoted in Sorella (2001)

best variational

-0.7855(1)

VMC (Gutzwiller)

best projected

-0.7841(1)

FN-GFMC (Gutzwiller)

E/site	distance to class best	σ	bound type	method	source	year
-0.7881242exact	0	n/a	exact	ED	D. Poilblanc (unpublished), quoted in Sorella (2001)	2001
-0.7855best variational	0	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-0.7852tied with best variational at 2σ	3.0e-4	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-0.7812	4.3e-3	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-0.7651	2.0e-2	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-0.7647	2.1e-2	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-0.7646	2.1e-2	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-0.7841best projected	0	1.0e-4	projected	FN-GFMC (Gutzwiller)	Sorella (2001)	2001
-0.7777	6.4e-3	4.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.7760	8.1e-3	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.7759	8.2e-3	1.0e-4	projected	FN-GFMC (Gutzwiller)	Sorella (2001)	2001
-0.7757	8.4e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-0.8633713

best variational

-0.84170(1)

VMC (Pfaffian)

best projected

-0.85348(3)

FN-GFMC (Pfaffian)

E/site	distance to class best	σ	bound type	method	source	year
-0.8633713exact	0	n/a	exact	ED	Lugas et al. (2006)	2006
-0.84170best variational	0	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-0.84065	1.1e-3	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-0.85348best projected	0	3.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.85189	1.6e-3	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-0.85132	2.2e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-1.0173302

best variational

-0.99709(1)

VMC (Pfaffian)

best projected

-1.00806(2)

FN-GFMC (Pfaffian)

E/site	distance to class best	σ	bound type	method	source	year
-1.0173302exact	0	n/a	exact	ED	Lugas et al. (2006)	2006
-0.99709best variational	0	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-0.99361	3.5e-3	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-1.00806best projected	0	2.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-1.00659	1.5e-3	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-1.00476	3.3e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-1.1749259

D. Poilblanc (unpublished), quoted in Sorella (2001)

best variational

-1.1724(1)

VMC (Gutzwiller)

best projected

-1.1706(1)

FN-GFMC (Gutzwiller)

E/site	distance to class best	σ	bound type	method	source	year
-1.1749259exact	0	n/a	exact	ED	D. Poilblanc (unpublished), quoted in Sorella (2001)	2001
-1.1724best variational	0	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-1.1719	5.0e-4	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-1.1672	5.2e-3	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-1.1548	1.8e-2	1.0e-5	variational	VMC (Pfaffian)	Lugas et al. (2006)	2006
-1.1476	2.5e-2	1.0e-5	variational	VMC (RVB)	Lugas et al. (2006)	2006
-1.1476	2.5e-2	1.0e-4	variational	VMC (Gutzwiller)	Sorella (2001)	2001
-1.1706best projected	0	1.0e-4	projected	FN-GFMC (Gutzwiller)	Sorella (2001)	2001
-1.1657	4.9e-3	3.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-1.1642	6.4e-3	1.0e-5	projected	FN-GFMC (Pfaffian)	Lugas et al. (2006)	2006
-1.1608	9.8e-3	1.0e-4	projected	FN-GFMC (Gutzwiller)	Sorella (2001)	2001
-1.1607	9.9e-3	1.0e-5	projected	FN-GFMC (RVB)	Lugas et al. (2006)	2006

exact

-0.4348005

Leung (2006)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.4348005exact	0	n/a	exact	ED	Leung (2006)		2006

exact

-0.5188028

Leung (2006)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.5188028exact	0	n/a	exact	ED	Leung (2006)		2006

exact

-0.6394265

Leung (2006)

E/site	distance to class best	σ	bound type	method	source	code	year	comment
-0.6394265exact	0	n/a	exact	ED	Leung (2006)		2006

best variational

-0.380099

DMRG

Cui et al. (2026)

E/site	distance to class best	σ	bound type	method	source	year
-0.380099best variational	0	n/a	variational	DMRG	Cui et al. (2026)	2026
-0.372224	7.9e-3	n/a	variational	VMC (phase string)	Cui et al. (2026)	2026
-0.371979	8.1e-3	n/a	variational	VMC (Bloch wave)	Cui et al. (2026)	2026
-0.354063	2.6e-2	n/a	variational	VMC (Bloch wave)	Cui et al. (2026)	2026

best variational

-0.685(1)

Power-Lanczos

Shih et al. (2001)

best extrapolated

-0.690(5)

Power-Lanczos

Shih et al. (2001)

E/site	distance to class best	σ	bound type	method	source	year
-0.685best variational	0	1.3e-3	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.685tied with best variational at 2σ	<1e-3	2.9e-3	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.683tied with best variational at 2σ	2.2e-3	1.1e-3	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.682tied with best variational at 2σ	3.5e-3	8.0e-4	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.682tied with best variational at 2σ	3.6e-3	1.1e-3	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.680	5.2e-3	6.0e-4	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.677	8.6e-3	1.2e-3	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.677	8.7e-3	2.0e-4	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.673	1.2e-2	9.0e-4	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.671	1.5e-2	1.0e-4	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.666	2.0e-2	6.0e-4	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.657	2.8e-2	4.0e-4	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.644	4.1e-2	1.0e-4	variational	Power-Lanczos	Shih et al. (2001)	2001
-0.690best extrapolated	0	4.8e-3	extrapolated	Power-Lanczos	Shih et al. (2001)	2001
-0.688tied with best extrapolated at 2σ	2.3e-3	3.5e-3	extrapolated	Power-Lanczos	Shih et al. (2001)	2001

best variational

-0.64266(8)

VMC (Gutzwiller)

Sorella et al. (2002)

best projected

-0.66672(6)

FN-GFMC (Gutzwiller)

Sorella et al. (2002)

best extrapolated

-0.671(1)

VMC (Gutzwiller)

Sorella et al. (2002)

E/site	σ	bound type	method	source	year
-0.64266best variational	8.0e-5	variational	VMC (Gutzwiller)	Sorella et al. (2002)	2002
-0.66672best projected	6.0e-5	projected	FN-GFMC (Gutzwiller)	Sorella et al. (2002)	2002
-0.671best extrapolated	1.0e-3	extrapolated	VMC (Gutzwiller)	Sorella et al. (2002)	2002

Transverse-field Ising#

12 instances, energies as E/N (Pauli)

lattice size

instance

value

energy

method

source

code

energies

exact

-1.238149

best variational

-1.238149

DMRG

E/N (Pauli)	distance to class best	σ	bound type	method	source	code	year
-1.238149exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-1.238172	n/a	2.2e-6	variational below exact energy	VMC (RBM)	Wu et al. (2024)	run script	2024
-1.2381549	n/a	7.0e-7	variational below exact energy	VMC (LRU)	Merali et al. (2026)	ParallelScan-RNNs/PSR-NQS	2026
-1.238149best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1.238134	1.5e-5	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-1.238004	1.5e-4	n/a	variational	VQE	Wu et al. (2024)	run script	2024
-1.237844	3.0e-4	1.9e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-1.2784906

Exact solution

best variational

-1.2784906

DMRG

E/N (Pauli)	distance to class best	σ	bound type	method	source	code	year
-1.2784906exact	0	n/a	exact	Exact solution	Wu et al. (2024)	run script	2024
-1.278523	n/a	4.8e-6	variational below exact energy	VMC (RBM)	Wu et al. (2024)	run script	2024
-1.2784906best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1.2772460	1.2e-3	3.0e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-1.0635444

Exact solution

best variational

-1.0635444

DMRG

E/N (Pauli)	distance to class best	σ	bound type	method	source	code	year
-1.0635444exact	0	n/a	exact	Exact solution	Wu et al. (2024)	run script	2024
-1.063551	n/a	1.7e-6	variational below exact energy	VMC (RBM)	Wu et al. (2024)	run script	2024
-1.0635444best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1.0635431	1.3e-6	5.9e-7	variational	VMC (FFN)	Wu et al. (2024)	run script	2024
-1.0630475	5.0e-4	1.0e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-1.273751

Exact solution

best variational

-1.273751

DMRG

E/N (Pauli)	distance to class best	σ	bound type	method	source	code	year
-1.273751exact	0	n/a	exact	Exact solution	Wu et al. (2024)	run script	2024
-1.273751best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1.273750	<1e-6	1.8e-7	variational	VMC (FFN)	Wu et al. (2024)	run script	2024
-1.273676	7.5e-5	4.4e-6	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-1.271914	1.8e-3	1.7e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

exact

-3.2009085

best variational

-3.2009084

DMRG

E/N (Pauli)	distance to class best	σ	bound type	method	source	code	year
-3.2009085exact	0	n/a	exact	ED	Wu et al. (2024)	run script	2024
-3.2009084best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-3.2008792	2.9e-5	7.8e-6	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-3.1998567	1.1e-3	1.7e-5	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024

best variational

-3.1641828

DMRG

Dao (2026)

E/N (Pauli)	distance to class best	σ	bound type	method	source	year
-3.1641828best variational	0	n/a	variational	DMRG	Dao (2026)	2026
-3.1634328	7.5e-4	1.2e-4	variational	VMC (2D RNN)	Dao (2026)	2026
-3.1628594	1.3e-3	1.5e-4	variational	VMC (2D RNN)	Dao (2026)	2026
-3.1525422	1.2e-2	4.2e-4	variational	VMC (RNN)	Dao (2026)	2026
-3.1525375	1.2e-2	4.6e-4	variational	VMC (RNN)	Dao (2026)	2026
-3.1488375	1.5e-2	4.9e-4	variational	VMC (RNN)	Dao (2026)	2026
-3.1469656	1.7e-2	4.9e-4	variational	VMC (RNN)	Dao (2026)	2026
-3.1405297	2.4e-2	6.9e-4	variational	VMC (RNN)	Dao (2026)	2026
-3.1379625	2.6e-2	7.0e-4	variational	VMC (RNN)	Dao (2026)	2026

best variational

-3.16977

DMRG

Dao (2026)

E/N (Pauli)	distance to class best	σ	bound type	method	source	year
-3.16977best variational	0	n/a	variational	DMRG	Dao (2026)	2026
-3.16935	4.2e-4	7.7e-5	variational	VMC (2D RNN)	Dao (2026)	2026
-3.16899	7.8e-4	8.9e-5	variational	VMC (2D RNN)	Dao (2026)	2026
-3.15349	1.6e-2	4.5e-4	variational	VMC (RNN)	Dao (2026)	2026
-3.15162	1.8e-2	4.1e-4	variational	VMC (RNN)	Dao (2026)	2026
-3.14857	2.1e-2	5.2e-4	variational	VMC (RNN)	Dao (2026)	2026
-3.14697	2.3e-2	5.4e-4	variational	VMC (RNN)	Dao (2026)	2026
-3.14118	2.9e-2	6.1e-4	variational	VMC (RNN)	Dao (2026)	2026
-3.09132	7.8e-2	7.8e-4	variational	VMC (RNN)	Dao (2026)	2026

Hibat-Allah et al. (2020)

best variational

-2.4096026

DMRG

E/N (Pauli)	distance to class best	σ	bound type	method	source	year
-2.4096026best variational	0	n/a	variational	DMRG	Hibat-Allah et al. (2020)	2020
-2.4086806	9.2e-4	6.0e-5	variational	VMC (2D RNN)	Dao (2026)	2026
-2.4055799	4.0e-3	1.2e-4	variational	VMC (2D RNN)	Dao (2026)	2026
-2.4051618	4.4e-3	1.3e-4	variational	VMC (2D RNN)	Dao (2026)	2026

Hibat-Allah et al. (2020)

best variational

-3.1739018(2)

VMC (2D RNN)

E/N (Pauli)	distance to class best	σ	bound type	method	source	code	year
-3.1739018best variational	0	1.9e-7	variational	VMC (2D RNN)	Hibat-Allah et al. (2020)	run script	2020
-3.1739009	9.4e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-3.1738997	2.2e-6	n/a	variational	DMRG	Hibat-Allah et al. (2020)		2020
-3.1738969	4.9e-6	5.0e-7	variational	VMC (RNN)	Hibat-Allah et al. (2020)	mhibatallah/RNNWavefunctions	2020
-3.1737990	1.0e-4	4.2e-6	variational	VMC (RBM)	Wu et al. (2024)	run script	2024
-3.1737114	1.9e-4	5.1e-6	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-3.1733819	5.2e-4	6.1e-5	variational	VMC (2D RNN)	Dao (2026)		2026
-3.1733299	5.7e-4	5.8e-5	variational	VMC (2D RNN)	Dao (2026)		2026
-3.1728382	1.1e-3	8.5e-5	variational	VMC (2D RNN)	Dao (2026)		2026
-3.1542500	2.0e-2	4.4e-4	variational	VMC (RNN)	Dao (2026)		2026
-3.1493694	2.5e-2	4.8e-4	variational	VMC (RNN)	Dao (2026)		2026
-3.1410681	3.3e-2	5.3e-4	variational	VMC (RNN)	Dao (2026)		2026
-3.1065743	6.7e-2	5.9e-4	variational	VMC (RNN)	Dao (2026)		2026
-3.0951208	7.9e-2	6.6e-4	variational	VMC (RNN)	Dao (2026)		2026
-3.0936056	8.0e-2	6.5e-4	variational	VMC (RNN)	Dao (2026)		2026

Hibat-Allah et al. (2020)

best variational

-4.1217979

DMRG

E/N (Pauli)	distance to class best	σ	bound type	method	source	year
-4.1217979best variational	0	n/a	variational	DMRG	Hibat-Allah et al. (2020)	2020
-4.1215319	2.7e-4	5.0e-5	variational	VMC (2D RNN)	Dao (2026)	2026
-4.1214951	3.0e-4	5.3e-5	variational	VMC (2D RNN)	Dao (2026)	2026
-4.1213326	4.7e-4	4.7e-5	variational	VMC (2D RNN)	Dao (2026)	2026

best variational

-3.18197

DMRG

Ganahl et al. (2023)

E/N (Pauli)	distance to class best	σ	bound type	method	source	code	year
-3.18197best variational	0	n/a	variational	DMRG	Ganahl et al. (2023)		2023
-3.18190	6.6e-5	1.2e-6	variational	VMC (Tensor-RNN)	Wu et al. (2024)	cqsl/mps-rnn	2024
-3.18187	9.8e-5	1.5e-6	variational	VMC (2D MPS-RNN)	Wu et al. (2024)	cqsl/mps-rnn	2024
-3.18158	3.9e-4	3.5e-6	variational	VMC (Jastrow)	Wu et al. (2024)	run script	2024
-3.18143	5.4e-4	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-3.17401	8.0e-3	2.1e-5	variational	VMC (1D MPS-RNN)	Wu et al. (2024)	cqsl/mps-rnn	2024
-3.16681	1.5e-2	2.4e-5	variational	VMC (RBM)	Wu et al. (2024)	run script	2024

best variational

-3.2342607

iPEPS

Rader & Läuchli (2018)

best extrapolated

-3.2342623

iPEPS

Rader & Läuchli (2018)

E/N (Pauli)	distance to class best	σ	bound type	method	source	year
-3.2342607best variational	0	n/a	variational	iPEPS	Rader & Läuchli (2018)	2018
-3.2335734	6.9e-4	n/a	variational	iPEPS	Rader & Läuchli (2018)	2018
-3.2342623best extrapolated	0	n/a	extrapolated	iPEPS	Rader & Läuchli (2018)	2018

Impurity#

12 instances, energies as E (total)

lattice size

instance

value

energy

method

source

code

energies

exact

-34.5805205

best variational

-34.5805205

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year	comment
-34.5805205exact	0	n/a	exact	ED	run script, Wu et al. (2024)		2024
-34.5805205best variational	0	n/a	variational	DMRG	run script, Wu et al. (2024)		2024

exact

-13.8893249

best variational

-13.8893249

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year	comment
-13.8893249exact	0	n/a	exact	ED	run script, Wu et al. (2024)		2024
-13.8893249best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-23.3009472

best variational

-23.3009472

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year	comment
-23.3009472exact	0	n/a	exact	ED	run script, Wu et al. (2024)		2024
-23.3009472best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

exact

-10.4871285

best variational

-10.4871285

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year	comment
-10.4871285exact	0	n/a	exact	ED	run script, Wu et al. (2024)		2024
-10.4871285best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-112.9042852

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year
-112.9042852best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-112.9042852	<1e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-112.9042852	<1e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-224.3360713

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year
-224.3360713best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-224.3360713	<1e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-224.3360713	<1e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-1307.5645417

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year
-1307.5645417best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1307.5645415	1.6e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1307.5645412	4.5e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-3378.6762368

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year
-3378.6762368best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-3378.6762363	5.4e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-3378.6762356	1.2e-6	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-112.8717703

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year
-112.8717703best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-112.8717703	<1e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-112.8717703	<1e-7	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-219.766911

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year
-219.766911best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-219.766911	<1e-6	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-219.766911	<1e-6	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-1305.3902308

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year
-1305.3902308best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1305.3902296	1.3e-6	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-1305.3902264	4.5e-6	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

best variational

-3351.7573592

DMRG

E (total)	distance to class best	σ	bound type	method	source	code	year
-3351.7573592best variational	0	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-3351.7573530	6.2e-6	n/a	variational	DMRG	Wu et al. (2024)	run script	2024
-3351.7573502	9.0e-6	n/a	variational	DMRG	Wu et al. (2024)	run script	2024

Electron gas, 3D#

138 instances, energies as E/N (Ha)

lattice size

instance

value

energy

method

source

code

energies

best variational

44.18067(2)

VMC (FermiNet)

uses FermiNet

best projected

44.18224(1)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
44.18067best variational	0	2.0e-5	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
44.18235	1.7e-3	4.0e-5	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
44.18482	4.1e-3	4.0e-6	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
44.18224best projected	0	1.0e-5	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
44.18468	2.4e-3	3.0e-5	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

6.318704(2)

VMC (FermiNet)

uses FermiNet

best projected

6.319754(7)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
6.318704best variational	0	2.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
6.319830	1.1e-3	2.0e-5	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
6.322090	3.4e-3	8.0e-6	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
6.319754best projected	0	7.0e-6	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
6.321300	1.5e-3	6.0e-5	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

1.261547(1)

VMC (FermiNet)

uses FermiNet

best projected

1.261975(2)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
1.261547best variational	0	1.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
1.262022	4.7e-4	8.0e-6	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
1.262860	1.3e-3	1.0e-5	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
1.261975best projected	0	2.0e-6	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
1.262540	5.7e-4	2.0e-5	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

-0.050320(5)

VMC (FermiNet)

uses FermiNet

best projected

-0.0503349(8)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.050320best variational	0	5.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.050278	4.2e-5	7.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.050150	1.7e-4	6.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.0503349best projected	0	8.0e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.0502038	1.3e-4	1.0e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

0.152086(1)

VMC (FermiNet)

uses FermiNet

best projected

0.152077(4)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
0.152086best variational	0	1.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
0.152120	3.5e-5	4.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
0.152393	3.1e-4	3.0e-6	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
0.152077best projected	0	4.0e-6	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
0.152344	2.7e-4	3.0e-6	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

-0.006961(2)

VMC (FermiNet)

uses FermiNet

best projected

-0.006966(2)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.006961best variational	0	2.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.006915	4.6e-5	2.0e-6	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.006693	2.7e-4	2.0e-6	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.006966best projected	0	2.0e-6	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.006742	2.2e-4	7.0e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

-0.022541(5)

VMC (FermiNet)

uses FermiNet

best projected

-0.0225620(2)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.022541best variational	0	5.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.022512	2.9e-5	3.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.022451	9.0e-5	2.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.0225620best projected	0	2.0e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.0224987	6.3e-5	5.0e-8	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

-0.057691(4)

VMC (FermiNet)

uses FermiNet

best projected

-0.057702(1)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.057691best variational	0	4.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.057650	4.1e-5	9.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.057453	2.4e-4	1.0e-6	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.057702best projected	0	1.0e-6	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.057502	2.0e-4	4.0e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

-0.014478(4)

VMC (FermiNet)

uses FermiNet

best projected

-0.0144918(1)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.014478best variational	0	4.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.014453	2.5e-5	1.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.014403	7.5e-5	1.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.0144918best projected	0	1.0e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.0144441	4.8e-5	5.0e-8	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

-0.010693(3)

VMC (FermiNet)

uses FermiNet

best projected

-0.0107118(1)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.010693best variational	0	3.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.010682	1.1e-5	1.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.010635	5.8e-5	1.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.0107118best projected	0	1.0e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.0106735	3.8e-5	1.0e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

-0.008496(1)

VMC (FermiNet)

uses FermiNet

best projected

-0.0085137(2)

FN-DMC (SJB)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.008496best variational	0	1.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.008494	2.4e-6	7.0e-8	variational	VMC (SJB)	Azadi & Drummond (2022)	uses CASINO	2022
-0.008493	3.3e-6	7.0e-8	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.008493	3.3e-6	7.0e-8	variational	VMC (SJB)	Azadi & Drummond (2022)	uses CASINO	2022
-0.008493	3.4e-6	7.0e-8	variational	VMC (SJB)	Azadi & Drummond (2022)	uses CASINO	2022
-0.008493	3.5e-6	7.0e-8	variational	VMC (SJB)	Azadi & Drummond (2022)	uses CASINO	2022
-0.008493	3.5e-6	7.0e-8	variational	VMC (SJB)	Azadi & Drummond (2022)	uses CASINO	2022
-0.008428	6.8e-5	1.0e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.008422	7.4e-5	3.0e-7	variational	VMC (SJB)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0085137best projected	0	2.0e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.0084862	2.7e-5	1.0e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023

best variational

-0.00767129(8)

VMC (SJ)

uses CASINO

best projected

-0.0076974(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00767129best variational	0	8.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0076974best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.0062378(1)

VMC (SJ)

uses CASINO

best projected

-0.0062597(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0062378best variational	0	1.0e-7	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0062597best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.0093993(3)

VMC (SJ)

uses CASINO

best projected

-0.0094484(2)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0093993best variational	0	3.0e-7	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0094484best projected	0	2.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00844873(6)

VMC (SJ)

uses CASINO

best projected

-0.0084813(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00844873best variational	0	6.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0084813best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.0076803(2)

VMC (SJB)

uses CASINO

best projected

-0.00769619(9)

FN-DMC

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0076803best variational	0	2.0e-7	variational	VMC (SJB)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0076786	1.7e-6	2.0e-7	variational	VMC (SJB)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0076737	6.6e-6	2.0e-7	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0076719	8.4e-6	3.0e-7	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0076715	8.8e-6	2.0e-7	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.00769619best projected	0	9.0e-8	projected	FN-DMC	Azadi & Drummond (2022)	uses CASINO	2022
-0.00769616tied with best projected at 2σ	3.0e-8	8.0e-8	projected	FN-DMC	Azadi & Drummond (2022)	uses CASINO	2022
-0.00769600tied with best projected at 2σ	1.9e-7	1.0e-7	projected	FN-DMC	Azadi & Drummond (2022)	uses CASINO	2022
-0.00769570tied with best projected at 2σ	4.9e-7	2.0e-7	projected	FN-DMC	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00624309(3)

VMC (SJ)

uses CASINO

best projected

-0.0062592(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00624309best variational	0	3.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0062592best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.0094086(1)

VMC (SJ)

uses CASINO

best projected

-0.00944340(6)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0094086best variational	0	1.0e-7	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.00944340best projected	0	6.0e-8	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00845026(5)

VMC (SJ)

uses CASINO

best projected

-0.00847899(9)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00845026best variational	0	5.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.00847899best projected	0	9.0e-8	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00765917(9)

VMC (SJ)

uses CASINO

best projected

-0.0076828(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00765917best variational	0	9.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0076828best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00623503(4)

VMC (SJ)

uses CASINO

best projected

-0.00624956(9)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00623503best variational	0	4.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.00624956best projected	0	9.0e-8	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.0093763(1)

VMC (SJ)

uses CASINO

best projected

-0.0094299(3)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0093763best variational	0	1.0e-7	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0094299best projected	0	3.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00843572(7)

VMC (SJ)

uses CASINO

best projected

-0.0084658(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00843572best variational	0	7.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0084658best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.0076584(2)

VMC (SJ)

uses CASINO

best projected

-0.0076816(4)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0076584best variational	0	2.0e-7	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0076816best projected	0	4.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00623504(4)

VMC (SJ)

uses CASINO

best projected

-0.00624968(7)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00623504best variational	0	4.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.00624968best projected	0	7.0e-8	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00939055(8)

VMC (SJ)

uses CASINO

best projected

-0.0094277(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00939055best variational	0	8.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0094277best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00843484(6)

VMC (SJ)

uses CASINO

best projected

-0.0084646(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00843484best variational	0	6.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0084646best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00765566(9)

VMC (SJ)

uses CASINO

best projected

-0.0076790(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00765566best variational	0	9.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0076790best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00623185(4)

VMC (SJ)

uses CASINO

best projected

-0.00624652(5)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00623185best variational	0	4.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.00624652best projected	0	5.0e-8	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.0093843(1)

VMC (SJ)

uses CASINO

best projected

-0.0094232(2)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0093843best variational	0	1.0e-7	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0094232best projected	0	2.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00843112(8)

VMC (SJ)

uses CASINO

best projected

-0.0084611(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00843112best variational	0	8.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0084611best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.0076578(4)

VMC (SJ)

uses CASINO

best projected

-0.0076795(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0076578best variational	0	4.0e-7	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0076795best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00623263(4)

VMC (SJ)

uses CASINO

best projected

-0.00624666(6)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00623263best variational	0	4.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.00624666best projected	0	6.0e-8	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00938865(8)

VMC (SJ)

uses CASINO

best projected

-0.00942260(9)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00938865best variational	0	8.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.00942260best projected	0	9.0e-8	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best variational

-0.00843318(7)

VMC (SJ)

uses CASINO

best projected

-0.0084605(1)

FN-DMC (SJ)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00843318best variational	0	7.0e-8	variational	VMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022
-0.0084605best projected	0	1.0e-7	projected	FN-DMC (SJ)	Azadi & Drummond (2022)	uses CASINO	2022

best projected

0.00426(2)

FN-DMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
0.00426best projected	0	2.0e-5	projected	FN-DMC	Gurtubay et al. (2010)	uses CASINO 2.1.400	2010

best projected

0.00081(2)

FN-DMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
0.00081best projected	0	2.0e-5	projected	FN-DMC	Gurtubay et al. (2010)	uses CASINO 2.1.400	2010

best projected

0.00892(2)

FN-DMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
0.00892best projected	0	2.0e-5	projected	FN-DMC	Gurtubay et al. (2010)	uses CASINO 2.1.400	2010

best projected

0.00202(2)

FN-DMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
0.00202best projected	0	2.0e-5	projected	FN-DMC	Gurtubay et al. (2010)	uses CASINO 2.1.400	2010

best variational

-0.0537396(1)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0537396best variational	0	1.1e-7	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.0537389	7.2e-7	5.6e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.0537150	2.5e-5	2.5e-7	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.0537124	2.7e-5	2.2e-7	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.00769287(1)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.00769287best variational	0	1.1e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00769280	6.9e-8	5.6e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00768779	5.1e-6	1.7e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00768767	5.2e-6	8.3e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.02272554(2)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.02272554best variational	0	1.9e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.02272548	6.9e-8	1.1e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.02271169	1.4e-5	8.3e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.02271122	1.4e-5	5.6e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.0756267(6)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0756267best variational	0	5.6e-7	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.0756261tied with best variational at 2σ	5.6e-7	2.8e-7	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.0755986	2.8e-5	1.1e-6	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.0755942	3.3e-5	8.3e-7	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.01449795(2)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.01449795best variational	0	2.2e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.01449787	7.8e-8	5.6e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.01449008	7.9e-6	2.8e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.01448968	8.3e-6	2.2e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.00945620(2)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.00945620best variational	0	1.7e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00945607	1.3e-7	1.7e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00944919	7.0e-6	2.5e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00944896	7.2e-6	8.3e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.00879026(2)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.00879026best variational	0	1.9e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00879018	7.5e-8	1.4e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00879010	1.6e-7	8.3e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00879008	1.8e-7	5.6e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.00878092(1)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.00878092best variational	0	1.4e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00878087tied with best variational at 2σ	5.0e-8	1.1e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00878080	1.2e-7	8.3e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00878079	1.3e-7	5.6e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.00877159(1)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.00877159best variational	0	1.4e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00877152	6.9e-8	1.1e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00877151	7.8e-8	8.3e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00877151	8.3e-8	5.6e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.00876228(1)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.00876228best variational	0	1.4e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00876227tied with best variational at 2σ	<1e-8	8.3e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00876226tied with best variational at 2σ	2.5e-8	5.6e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.00876222	6.1e-8	8.3e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.008753017(8)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.008753017best variational	0	8.3e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.008753006tied with best variational at 2σ	1.1e-8	5.6e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.008752911	1.1e-7	1.1e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.008752808	2.1e-7	1.1e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

-0.008743822(8)

VMC (MP-NQS)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.008743822best variational	0	8.3e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.008743811tied with best variational at 2σ	1.1e-8	5.6e-9	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.008743647	1.8e-7	1.9e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026
-0.008743558	2.6e-7	1.4e-8	variational	VMC (MP-NQS)	Liu et al. (2026)	2026

best variational

1.120358(3)

VMC (WAP-net)

best projected

1.120400(5)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
1.120358best variational	0	3.5e-6	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
1.120392	3.5e-5	3.5e-6	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
1.120420	6.2e-5	1.0e-5	variational	VMC (iterative BF)	Wilson et al. (2023)	2023
1.120400best projected	0	5.0e-6	projected	FN-DMC (iterative BF)	Wilson et al. (2023)	2023

best variational

-0.0531436(2)

VMC (WAP-net)

best projected

-0.0531380(5)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0531436best variational	0	2.5e-7	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
-0.0531398	3.8e-6	2.5e-7	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
-0.0531188	2.5e-5	3.0e-7	variational	VMC (iterative BF)	Wilson et al. (2023)	2023
-0.0531380best projected	0	5.0e-7	projected	FN-DMC (iterative BF)	Wilson et al. (2023)	2023

best variational

-0.00774654(1)

VMC (WAP-net)

best projected

-0.00774625(5)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.00774654best variational	0	1.0e-8	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
-0.00774652tied with best variational at 2σ	2.5e-8	5.0e-9	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
-0.00773814	8.4e-6	3.5e-8	variational	VMC (iterative BF)	Wilson et al. (2023)	2023
-0.00774625best projected	0	5.0e-8	projected	FN-DMC (iterative BF)	Wilson et al. (2023)	2023

best variational

0.110850(1)

VMC (WAP-net)

best projected

0.110879(2)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
0.110850best variational	0	1.0e-6	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
0.110883	3.3e-5	2.5e-6	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
0.110902	5.1e-5	1.5e-6	variational	VMC (iterative BF)	Wilson et al. (2023)	2023
0.110879best projected	0	2.0e-6	projected	FN-DMC (iterative BF)	Wilson et al. (2023)	2023

best variational

-0.0322689(1)

VMC (WAP-net)

best projected

-0.032266(2)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0322689best variational	0	1.5e-7	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
-0.0322689tied with best variational at 2σ	<1e-7	1.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
-0.0322412	2.8e-5	1.5e-7	variational	VMC (iterative BF)	Wilson et al. (2023)	2023
-0.032266best projected	0	2.0e-6	projected	FN-DMC (iterative BF)	Wilson et al. (2023)	2023

best variational

-0.0664225(5)

VMC (WAP-net)

best projected

-0.0664055(5)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0664225best variational	0	5.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
-0.0664125	1.0e-5	1.0e-6	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
-0.0663865	3.6e-5	5.0e-7	variational	VMC (iterative BF)	Wilson et al. (2023)	2023
-0.0664055best projected	0	5.0e-7	projected	FN-DMC (iterative BF)	Wilson et al. (2023)	2023

best variational

-0.01466089(1)

VMC (WAP-net)

best projected

-0.0146604(1)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.01466089best variational	0	1.5e-8	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
-0.01466081	8.5e-8	2.0e-8	variational	VMC (WAP-net)	Wilson et al. (2023)	2023
-0.01464785	1.3e-5	5.0e-8	variational	VMC (iterative BF)	Wilson et al. (2023)	2023
-0.0146604best projected	0	1.0e-7	projected	FN-DMC (iterative BF)	Wilson et al. (2023)	2023

best projected

106.90015

CCD

Butler et al. (2024)

butler-julie/HEG-SRE

best extrapolated

106.89994(1)

CCSDT

Spencer & Thom (2016)

best approximate

106.87643

dRPA

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
106.90015best projected	0	n/a	projected	CCD	Butler et al. (2024)	butler-julie/HEG-SRE	2024
106.89994best extrapolated	0	1.4e-5	extrapolated	CCSDT	Spencer & Thom (2016)		2016
106.90008	1.4e-4	7.1e-6	extrapolated	CCSD	Spencer & Thom (2016)		2016
106.90014	2.1e-4	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
106.87643best approximate	0	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
106.87886	2.4e-3	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
106.89757	2.1e-2	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
106.89907	2.3e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
106.90043	2.4e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
106.90050	2.4e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
106.90214	2.6e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
106.90272	2.6e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best extrapolated

25.4050004

CCD

best approximate

25.3821433

dRPA

E/N (Ha)	distance to class best	σ	bound type	method	source	year
25.4050004best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
25.3821433best approximate	0	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
25.3865004	4.4e-3	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
25.4000004	1.8e-2	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
25.4029290	2.1e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
25.4055719	2.3e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
25.4056433	2.4e-2	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
25.4085004	2.6e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
25.4095719	2.7e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

10.6954209

CCD

best approximate

10.6732066

dRPA

E/N (Ha)	distance to class best	σ	bound type	method	source	year
10.6954209best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
10.6732066best approximate	0	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
10.6791351	5.9e-3	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
10.6879923	1.5e-2	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
10.6924923	1.9e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
10.6961351	2.3e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
10.6963494	2.3e-2	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
10.7000637	2.7e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
10.7015637	2.8e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

5.6765448

CCD

best approximate

5.6547591

dRPA

E/N (Ha)	distance to class best	σ	bound type	method	source	year
5.6765448best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
5.6547591best approximate	0	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
5.6620448	7.3e-3	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
5.6666876	1.2e-2	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
5.6727591	1.8e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
5.6772591	2.2e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
5.6776876	2.3e-2	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
5.6820448	2.7e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
5.6838305	2.9e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best variational

3.412684(4)

VMC (FermiNet)

uses FermiNet

best projected

3.41253(4)

ph-AFQMC (RHF)

uses PAUXY

best extrapolated

3.41226(2)

FCIQMC

best approximate

3.3916087

dRPA

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
3.412684best variational	0	4.3e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
3.412779	9.4e-5	4.3e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
3.412827	1.4e-4	4.3e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
3.412872	1.9e-4	5.0e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
3.413020	3.4e-4	7.1e-7	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
3.41253best projected	0	4.3e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses PAUXY	2019
3.41291	3.8e-4	n/a	projected	CCD	Butler et al. (2024)	butler-julie/HEG-SRE	2024
3.41291	3.8e-4	7.1e-7	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
3.41226best extrapolated	0	2.1e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
3.41229tied with best extrapolated at 2σ	2.9e-5	1.4e-5	extrapolated	CCSDT	Spencer & Thom (2016)		2016
3.41233tied with best extrapolated at 2σ	7.1e-5	5.0e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
3.41242	1.6e-4	6.4e-6	extrapolated	FCIQMC	Neufeld & Thom (2017)	uses HANDE-QMC	2017
3.41242	1.6e-4	5.7e-6	extrapolated	CCSDTQ	Neufeld & Thom (2017)	uses HANDE-QMC	2017
3.41243	1.7e-4	5.0e-6	extrapolated	CCSDT	Neufeld & Thom (2017)	uses HANDE-QMC	2017
3.41252	2.6e-4	n/a	extrapolated	DCD	Liao et al. (2021)		2021
3.41277	5.1e-4	7.1e-6	extrapolated	CCSD	Spencer & Thom (2016)		2016
3.41278	5.2e-4	n/a	extrapolated	CCD	Liao et al. (2021)		2021
3.41286	6.0e-4	4.3e-6	extrapolated	CCSD	Neufeld & Thom (2017)	uses HANDE-QMC	2017
3.41286	6.0e-4	5.0e-6	extrapolated	CCSD	Neufeld & Thom (2017)	uses HANDE-QMC	2017
3.41289	6.4e-4	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
3.3916087best approximate	0	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
3.3999658	8.4e-3	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
3.4007515	9.1e-3	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
3.4083944	1.7e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
3.4124087	2.1e-2	1.4e-5	approximate	Transcorrelated FCIQMC	Luo & Alavi (2018)	uses NECI	2018
3.4124400	2.1e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
3.4125800	2.1e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
3.4136801	2.2e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
3.4137914	2.2e-2	7.1e-8	approximate	MP2	Shepherd et al. (2012)		2012
3.4142515	2.3e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
3.4190373	2.7e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
3.4211801	3.0e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best extrapolated

2.2154921

CCD

best approximate

2.1945636

dRPA

E/N (Ha)	distance to class best	σ	bound type	method	source	year
2.2154921best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
2.1945636best approximate	0	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
2.2010636	6.5e-3	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
2.2038493	9.3e-3	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
2.2104207	1.6e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
2.2162779	2.2e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
2.2171350	2.3e-2	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
2.2222064	2.8e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
2.2245636	3.0e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

1.5130365

CCD

best approximate

1.4923937

dRPA

E/N (Ha)	distance to class best	σ	bound type	method	source	year
1.5130365best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
1.4923937best approximate	0	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
1.4963222	3.9e-3	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
1.5023937	1.0e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
1.5073222	1.5e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
1.5136794	2.1e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
1.5148222	2.2e-2	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
1.5201079	2.8e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
1.5226794	3.0e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

1.0698103

CCD

best approximate

1.0493818

dRPA

E/N (Ha)	distance to class best	σ	bound type	method	source	year
1.0698103best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
1.0493818best approximate	0	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
1.0508103	1.4e-3	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
1.0600960	1.1e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
1.0635960	1.4e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
1.0703818	2.1e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
1.0716675	2.2e-2	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
1.0771675	2.8e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
1.0798818	3.0e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

0.7746685

CCD

best approximate

0.7534542

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
0.7746685best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
0.7534542best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
0.7545256	1.1e-3	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
0.7657399	1.2e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
0.7679542	1.4e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
0.7750971	2.2e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
0.7766685	2.3e-2	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
0.7822399	2.9e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
0.7851685	3.2e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best variational

0.568851(1)

VMC (FermiNet)

best projected

0.56869(6)

ph-AFQMC (RHF)

uses QMCPACK

best extrapolated

0.56850(3)

FCIQMC

best approximate

0.5464629

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
0.568851best variational	0	1.4e-6	variational	VMC (FermiNet)	Liu et al. (2026)		2026
0.568904	5.4e-5	2.1e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
0.568956	1.1e-4	4.5e-6	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
0.568965	1.1e-4	5.0e-6	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
0.568967	1.2e-4	6.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
0.568979	1.3e-4	5.0e-6	variational	VMC (FermiNet)	Liu et al. (2026)		2026
0.568979	1.3e-4	3.6e-6	variational	VMC (FermiNet)	Liu et al. (2026)		2026
0.568986	1.4e-4	2.1e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
0.568993	1.4e-4	2.1e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
0.569006	1.6e-4	7.1e-6	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
0.569015	1.6e-4	1.4e-6	variational	VMC (FermiNet)	Liu et al. (2026)		2026
0.569016	1.6e-4	4.3e-6	variational	VMC (FermiNet)	Liu et al. (2026)		2026
0.569027	1.8e-4	2.1e-6	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
0.569160	3.1e-4	5.0e-6	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
0.56869best projected	0	5.7e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019
0.56898	2.8e-4	5.0e-6	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023
0.56901	3.1e-4	7.1e-6	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
0.56850best extrapolated	0	2.9e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
0.56856tied with best extrapolated at 2σ	5.7e-5	2.1e-5	extrapolated	CCSDT	Spencer & Thom (2016)		2016
0.56856tied with best extrapolated at 2σ	6.4e-5	2.9e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
0.56858	8.6e-5	1.4e-5	extrapolated	FCIQMC	Neufeld & Thom (2017)	uses HANDE-QMC	2017
0.56860	1.0e-4	1.4e-5	extrapolated	CCSDTQ	Neufeld & Thom (2017)	uses HANDE-QMC	2017
0.56863	1.3e-4	1.4e-5	extrapolated	CCSDT	Neufeld & Thom (2017)	uses HANDE-QMC	2017
0.56909	5.9e-4	n/a	extrapolated	DCD	Liao et al. (2021)		2021
0.56971	1.2e-3	2.1e-5	extrapolated	CCSD	Spencer & Thom (2016)		2016
0.56975	1.3e-3	n/a	extrapolated	CCD	Liao et al. (2021)		2021
0.56978	1.3e-3	6.4e-6	extrapolated	CCSD	Neufeld & Thom (2017)	uses HANDE-QMC	2017
0.56982	1.3e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
0.5464629best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
0.5498200	3.4e-3	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
0.5616058	1.5e-2	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
0.5627486	1.6e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
0.5685900	2.2e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
0.5686129	2.2e-2	1.4e-5	approximate	Transcorrelated FCIQMC	Luo & Alavi (2018)	uses NECI	2018
0.5689100	2.2e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
0.5701772	2.4e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
0.5708673	2.4e-2	1.4e-7	approximate	MP2	Shepherd et al. (2012)		2012
0.5719629	2.5e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
0.5775343	3.1e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
0.5806058	3.4e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best variational

-0.0552126(6)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.0552180(5)

FN-DMC (iterative BF)

best extrapolated

-0.05289

DCD

best approximate

-0.0791573

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0552126best variational	0	6.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0552038	8.8e-6	3.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0552025	1.0e-5	3.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0551799	3.3e-5	2.1e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0551786	3.4e-5	2.9e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0551699	4.3e-5	2.1e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0551615	5.1e-5	3.5e-7	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.0551086	1.0e-4	2.9e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0551037	1.1e-4	2.9e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0550894	1.2e-4	2.1e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0550893	1.2e-4	2.9e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0550869	1.3e-4	2.9e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0550698	1.4e-4	2.1e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0552180best projected	0	5.0e-7	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023
-0.05289best extrapolated	0	n/a	extrapolated	DCD	Liao et al. (2021)		2021
-0.05137	1.5e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.05137	1.5e-3	n/a	extrapolated	CCD	Liao et al. (2021)		2021
-0.0791573best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.0668716	1.2e-2	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0575144	2.2e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.0558002	2.3e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
-0.0550900	2.4e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
-0.0542000	2.5e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
-0.0531573	2.6e-2	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0519395	2.7e-2	4.3e-7	approximate	MP2	Shepherd et al. (2012)		2012
-0.0499430	2.9e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
-0.0482287	3.1e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
-0.0454430	3.4e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best variational

-0.00773024(1)

VMC (WAP-net)

best projected

-0.00773430(2)

FN-DMC (iterative BF)

best extrapolated

-0.0064603

CCD

best approximate

-0.0104603

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.00773024best variational	0	1.5e-8	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.00773018tied with best variational at 2σ	6.0e-8	3.0e-8	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.00772998	2.6e-7	1.5e-8	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.00772763	2.6e-6	3.0e-8	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.00773430best projected	0	2.5e-8	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023
-0.0064603best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.0104603best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.0075317	2.9e-3	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.0069603	3.5e-3	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0063174	4.1e-3	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
-0.0061746	4.3e-3	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
-0.0056031	4.9e-3	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best variational

-0.0408619(1)

VMC (FermiNet)

best approximate

-0.0580244

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0408619best variational	0	1.4e-7	variational	VMC (FermiNet)	Liu et al. (2026)	2026
-0.0408578	4.1e-6	1.4e-7	variational	VMC (FermiNet)	Liu et al. (2026)	2026
-0.0408060	5.6e-5	6.4e-7	variational	VMC (FermiNet)	Liu et al. (2026)	2026
-0.0408036	5.8e-5	1.4e-6	variational	VMC (FermiNet)	Liu et al. (2026)	2026
-0.0407969	6.5e-5	5.7e-7	variational	VMC (FermiNet)	Liu et al. (2026)	2026
-0.0407736	8.8e-5	3.6e-6	variational	VMC (FermiNet)	Liu et al. (2026)	2026
-0.0580244best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0421672	1.6e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0389529	1.9e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0351672	2.3e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0329529	2.5e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best variational

-0.0084275(7)

VMC (FermiNet)

uses FermiNet

best projected

-0.00853(6)

ph-AFQMC (RHF)

uses QMCPACK

best extrapolated

-0.00873(3)

FCIQMC

best approximate

-0.0478896

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0084275best variational	0	7.1e-7	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.0084162	1.1e-5	3.6e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0083910	3.6e-5	1.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0083330	9.4e-5	2.5e-6	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0083310	9.6e-5	2.5e-6	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0083277	1.0e-4	4.3e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0083046	1.2e-4	7.1e-7	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.0083011	1.3e-4	7.1e-7	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.0082957	1.3e-4	7.1e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0082951	1.3e-4	4.3e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0082768	1.5e-4	7.1e-7	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.0082040	2.2e-4	2.5e-6	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.0081753tied with best variational at 2σ	2.5e-4	2.1e-4	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.00853best projected	0	6.4e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019
-0.00833	2.1e-4	5.0e-6	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023
-0.00828	2.5e-4	2.1e-5	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.00873best extrapolated	0	2.9e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
-0.00868tied with best extrapolated at 2σ	5.0e-5	7.1e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
-0.00863tied with best extrapolated at 2σ	9.3e-5	7.1e-5	extrapolated	CCSDTQ5	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.00862tied with best extrapolated at 2σ	1.1e-4	7.1e-5	extrapolated	CCSDTQ	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.00844	2.9e-4	7.1e-5	extrapolated	CCSDT	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.00806	6.6e-4	2.9e-5	extrapolated	CCSDT	Spencer & Thom (2016)		2016
-0.00748	1.2e-3	n/a	extrapolated	DCD	Liao et al. (2021)		2021
-0.00623	2.5e-3	n/a	extrapolated	CCD	Liao et al. (2021)		2021
-0.00622	2.5e-3	7.1e-5	extrapolated	CCSD	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.00620	2.5e-3	7.1e-6	extrapolated	CCSD	Spencer & Thom (2016)		2016
-0.00618	2.5e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.0478896best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.0250325	2.3e-2	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0153182	3.3e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.0108182	3.7e-2	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0086753	3.9e-2	2.1e-5	approximate	Transcorrelated FCIQMC	Luo & Alavi (2018)	uses NECI	2018
-0.0080000	4.0e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
-0.0071753	4.1e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
-0.0070700	4.1e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
-0.0054573	4.2e-2	1.4e-7	approximate	MP2	Shepherd et al. (2012)		2012
0.0015389	4.9e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
0.0051818	5.3e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best variational

-0.0324553(2)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.0324578(2)

FN-DMC (iterative BF)

best extrapolated

-0.03035

DCD

best approximate

-0.0457024

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0324553best variational	0	2.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0324441	1.1e-5	1.5e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0324434	1.2e-5	1.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0324222	3.3e-5	1.0e-7	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.0323600	9.5e-5	2.9e-6	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0323550	1.0e-4	7.1e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0323119	1.4e-4	2.1e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0323029	1.5e-4	7.1e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0323026	1.5e-4	5.7e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0322900	1.7e-4	1.4e-6	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0324578best projected	0	2.5e-7	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023
-0.03035best extrapolated	0	n/a	extrapolated	DCD	Liao et al. (2021)		2021
-0.02927	1.1e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.02924	1.1e-3	n/a	extrapolated	CCD	Liao et al. (2021)		2021
-0.0457024best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.0332024	1.2e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.0320100	1.4e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
-0.0313600	1.4e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
-0.0306309	1.5e-2	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0298802	1.6e-2	7.1e-7	approximate	MP2	Shepherd et al. (2012)		2012
-0.0284166	1.7e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
-0.0276309	1.8e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
-0.0257024	2.0e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best projected

-0.07352(4)

ph-AFQMC (RHF)

uses QMCPACK

best extrapolated

-0.07432(2)

CCSDTQ5

Neufeld & Thom (2017)

uses HANDE-QMC

best approximate

-0.1179136

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.07352best projected	0	3.6e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019
-0.07432best extrapolated	0	2.1e-5	extrapolated	CCSDTQ5	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.07429tied with best extrapolated at 2σ	2.9e-5	2.1e-5	extrapolated	CCSDTQ	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.07391	4.1e-4	2.1e-5	extrapolated	CCSDT	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.07116	3.2e-3	7.1e-6	extrapolated	CCSD	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.07113	3.2e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.1179136best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.0894851	2.8e-2	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0804136	3.8e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.0745565	4.3e-2	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0731994	4.5e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
-0.0643422	5.4e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
-0.0605565	5.7e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best extrapolated

-0.0203291

CCD

best approximate

-0.0321148

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0203291best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.0321148best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0232576	8.9e-3	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0214719	1.1e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0198291	1.2e-2	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
-0.0192576	1.3e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0178291	1.4e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

-0.0792519

CCD

best approximate

-0.1240376

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0792519best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.1240376best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0971804	2.7e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0881804	3.6e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0821090	4.2e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0820376	4.2e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0732519	5.1e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0696090	5.4e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

-0.0155875

CCD

best approximate

-0.0247303

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0155875best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.0247303best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0178732	6.9e-3	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0165160	8.2e-3	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0151589	9.6e-3	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
-0.0148018	9.9e-3	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0135875	1.1e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best variational

-0.0798630(2)

VMC (FermiNet)

best projected

-0.079842(1)

FN-DMC (iterative BF)

best extrapolated

-0.07997(7)

FCIQMC

best approximate

-0.1175392

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0798630best variational	0	2.1e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0798602	2.8e-6	1.4e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0798544	8.6e-6	4.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0798360	2.7e-5	5.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0798345	2.9e-5	5.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0798241	3.9e-5	3.6e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0798213	4.2e-5	7.1e-7	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.0798192	4.4e-5	4.3e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0798190	4.4e-5	2.9e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0798138	4.9e-5	6.4e-7	variational	VMC (FermiNet)	Liu et al. (2026)		2026
-0.0798021	6.1e-5	7.1e-7	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.0798006	6.2e-5	7.1e-7	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.0797771	8.6e-5	7.1e-7	variational	VMC (FermiNet)	Cassella et al. (2023)	uses FermiNet	2023
-0.0797620	1.0e-4	5.0e-7	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.0797099	1.5e-4	1.4e-6	variational	VMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.079842best projected	0	1.5e-6	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023
-0.079806	3.6e-5	5.7e-6	projected	FN-DMC (SJB)	Cassella et al. (2023)	uses CASINO	2023
-0.077996	1.8e-3	2.9e-5	projected	ph-AFQMC (NOMSD)	Lee et al. (2019)	uses QMCPACK	2019
-0.077139	2.7e-3	4.3e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019
-0.076996	2.8e-3	1.4e-5	projected	ph-AFQMC (UHF)	Lee et al. (2019)	uses QMCPACK	2019
-0.07997best extrapolated	0	7.1e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
-0.07990tied with best extrapolated at 2σ	7.1e-5	7.1e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
-0.07965	3.2e-4	2.9e-5	extrapolated	CCSDTQ5	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.07957	3.9e-4	2.9e-5	extrapolated	CCSDTQ	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.07925	7.1e-4	2.9e-5	extrapolated	CCSDT	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.07788	2.1e-3	n/a	extrapolated	DCD	Liao et al. (2021)		2021
-0.07618	3.8e-3	n/a	extrapolated	CCD	Liao et al. (2021)		2021
-0.07612	3.9e-3	2.1e-5	extrapolated	CCSD	Neufeld & Thom (2017)	uses HANDE-QMC	2017
-0.07611	3.9e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.1175392best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.0936821	2.4e-2	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0845392	3.3e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.0800249	3.8e-2	2.1e-5	approximate	Transcorrelated FCIQMC	Luo & Alavi (2018)	uses NECI	2018
-0.0795392	3.8e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
-0.0792900	3.8e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
-0.0786106	3.9e-2	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0781600	3.9e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
-0.0763009	4.1e-2	2.9e-7	approximate	MP2	Shepherd et al. (2012)		2012
-0.0739678	4.4e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
-0.0708963	4.7e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
-0.0673963	5.0e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best variational

-0.01462631(6)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.0146287(1)

FN-DMC (iterative BF)

best extrapolated

-0.01323

DCD

best approximate

-0.0201249

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.01462631best variational	0	6.0e-8	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.01462223	4.1e-6	3.0e-8	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.01462211	4.2e-6	3.5e-8	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.01461460	1.2e-5	1.0e-8	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.0146287best projected	0	1.0e-7	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023
-0.01323best extrapolated	0	n/a	extrapolated	DCD	Liao et al. (2021)		2021
-0.01262	6.1e-4	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.01261	6.2e-4	n/a	extrapolated	CCD	Liao et al. (2021)		2021
-0.0201249best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.0145535	5.6e-3	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.0138400	6.3e-3	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
-0.0135000	6.6e-3	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
-0.0134821	6.6e-3	n/a	approximate	dRPA	Shepherd et al. (2014)		2014
-0.0122678	7.9e-3	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
-0.0119821	8.1e-3	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)		2014
-0.0109821	9.1e-3	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best extrapolated

-0.0706647

CCD

best approximate

-0.1085933

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0706647best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.1085933best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0877361	2.1e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0785219	3.0e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0744504	3.4e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0728790	3.6e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0659504	4.3e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0626647	4.6e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

-0.0106188

CCD

best approximate

-0.0169759

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0106188best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.0169759best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0122616	4.7e-3	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0113330	5.6e-3	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0103330	6.6e-3	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
-0.0101188	6.9e-3	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0092616	7.7e-3	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

-0.0651069

CCD

best approximate

-0.099964

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0651069best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.099964best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.081750	1.8e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.072393	2.8e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.069107	3.1e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.067178	3.3e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.060893	3.9e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.057678	4.2e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

-0.0091195

CCD

best approximate

-0.0146909

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0091195best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.0146909best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0106195	4.1e-3	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0098338	4.9e-3	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0089052	5.8e-3	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
-0.0087624	5.9e-3	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0079766	6.7e-3	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

-0.0599259

CCD

best approximate

-0.0920688

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0599259best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.0920688best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0762116	1.6e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0668545	2.5e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0641402	2.8e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0619259	3.0e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0561402	3.6e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0531402	3.9e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

-0.0080403

CCD

best approximate

-0.0129689

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0080403best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.0129689best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0093260	3.6e-3	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0086832	4.3e-3	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0078260	5.1e-3	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
-0.0076832	5.3e-3	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0069689	6.0e-3	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

-0.0553862

CCD

best approximate

-0.0851719

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0553862best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.0851719best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0712433	1.4e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0618862	2.3e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0597433	2.5e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0572433	2.8e-2	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0519576	3.3e-2	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0490290	3.6e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best extrapolated

-0.0071484

CCD

best approximate

-0.0115769

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.0071484best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)	2014
-0.0115769best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)	2014
-0.0083626	3.2e-3	n/a	approximate	rmCCD	Shepherd et al. (2014)	2014
-0.0077198	3.9e-3	n/a	approximate	dRPA	Shepherd et al. (2014)	2014
-0.0070055	4.6e-3	n/a	approximate	mCCD	Shepherd et al. (2014)	2014
-0.0068626	4.7e-3	n/a	approximate	dRPA + SOSEX	Shepherd et al. (2014)	2014
-0.0062198	5.4e-3	n/a	approximate	lmCCD	Shepherd et al. (2014)	2014

best variational

1.046242(3)

VMC (WAP-net)

best projected

1.0462250(5)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
1.046242best variational	0	2.5e-6	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
1.046247tied with best variational at 2σ	6.0e-6	2.5e-6	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
1.046262	2.1e-5	2.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
1.046272	3.1e-5	3.5e-6	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
1.0462250best projected	0	5.0e-7	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023

best variational

-0.0528624(2)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.0528652(3)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0528624best variational	0	2.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0528604	2.0e-6	1.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0528598	2.5e-6	1.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0528545	7.9e-6	3.0e-7	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.0528652best projected	0	3.0e-7	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023

best variational

-0.00771899(1)

VMC (iterative BF)

best projected

-0.00772142(1)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.00771899best variational	0	1.0e-8	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.00771832	6.7e-7	2.0e-8	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.00771760	1.4e-6	1.0e-8	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.00771362	5.4e-6	1.5e-8	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.00772142best projected	0	1.0e-8	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023

best variational

0.096303(1)

VMC (WAP-net)

best projected

0.096302(2)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
0.096303best variational	0	1.0e-6	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
0.096304tied with best variational at 2σ	<1e-6	5.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
0.096307tied with best variational at 2σ	4.0e-6	1.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
0.096319	1.5e-5	1.5e-6	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
0.096302best projected	0	1.5e-6	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023

best variational

-0.03201095(5)

VMC (WAP-net)

best projected

-0.0320167(1)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.03201095best variational	0	5.0e-8	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.03201010	8.5e-7	1.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.03201000	9.5e-7	1.0e-7	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.03200820	2.7e-6	1.0e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0320167best projected	0	1.0e-7	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023

best variational

-0.0672510(2)

VMC (WAP-net)

best projected

-0.0672540(5)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0672510best variational	0	2.5e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0672500tied with best variational at 2σ	1.0e-6	3.5e-7	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.0672489	2.1e-6	3.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0672400	1.1e-5	5.0e-7	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.0672540best projected	0	5.0e-7	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023

best variational

-0.01456685(3)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.01456920(4)

FN-DMC (iterative BF)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.01456685best variational	0	3.0e-8	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.01456574	1.1e-6	2.5e-8	variational	VMC (iterative BF)	Wilson et al. (2023)		2023
-0.01456571	1.1e-6	2.0e-8	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.01456498	1.9e-6	2.5e-8	variational	VMC (WAP-net)	Wilson et al. (2023)		2023
-0.01456920best projected	0	4.0e-8	projected	FN-DMC (iterative BF)	Wilson et al. (2023)		2023

best variational

1.051771(4)

VMC (MP-NQS)

uses NetKet 3

best projected

1.05200(3)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
1.051771best variational	0	4.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
1.05200best projected	0	3.0e-5	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best variational

-0.0526015(2)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.052540(6)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0526015best variational	0	2.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.052540best projected	0	6.0e-6	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best variational

0.098460(2)

VMC (MP-NQS)

uses NetKet 3

best projected

0.09866(2)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
0.098460best variational	0	2.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
0.09866best projected	0	2.0e-5	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best variational

-0.0228184(1)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.0228080(8)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0228184best variational	0	1.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0228080best projected	0	8.0e-7	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best variational

-0.0665523(6)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.066429(4)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0665523best variational	0	6.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.066429best projected	0	4.0e-6	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best variational

-0.01457976(5)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.0145752(6)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.01457976best variational	0	5.0e-8	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0145752best projected	0	6.0e-7	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best variational

-0.01074986(3)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.010749(2)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.01074986best variational	0	3.0e-8	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.010749best projected	0	2.0e-6	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best variational

-0.00853156(2)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.0085314(5)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00853156best variational	0	2.0e-8	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0085314best projected	0	5.0e-7	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best projected

3.2080745

CCD

Butler et al. (2024)

butler-julie/HEG-SRE

best extrapolated

3.20691(3)

FCIQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
3.2080745best projected	0	n/a	projected	CCD	Butler et al. (2024)	butler-julie/HEG-SRE	2024
3.20691best extrapolated	0	2.6e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012

best extrapolated

0.52478(3)

FCIQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
0.52478best extrapolated	0	2.6e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012

best extrapolated

-0.01422(5)

FCIQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.01422best extrapolated	0	5.3e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012

best variational

3.221226(2)

VMC (DeepSolid)

bytedance/DeepSolid

best projected

3.22087(2)

ph-AFQMC (RHF)

uses QMCPACK

best extrapolated

3.2202(2)

FCIQMC

best approximate

3.2119035

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
3.221226best variational	0	2.0e-6	variational	VMC (DeepSolid)	Li et al. (2022)	bytedance/DeepSolid	2022
3.221320tied with best variational at 2σ	9.4e-5	7.0e-5	variational	VMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
3.223300	2.1e-3	2.0e-4	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
3.223600	2.4e-3	2.0e-4	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
3.265900	4.5e-2	7.0e-4	variational	HF	López Ríos et al. (2006)	uses CASINO	2006
3.22087best projected	0	2.0e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019
3.22112	2.5e-4	4.0e-5	projected	FN-DMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
3.22117	3.0e-4	n/a	projected	CCD	Butler et al. (2024)	butler-julie/HEG-SRE	2024
3.22245	1.6e-3	9.0e-5	projected	FN-DMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
3.2202best extrapolated	0	2.0e-4	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
3.2202tied with best extrapolated at 2σ	<1e-4	1.3e-4	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
3.2205tied with best extrapolated at 2σ	3.2e-4	n/a	extrapolated	DCD	Liao et al. (2021)		2021
3.2208	5.9e-4	n/a	extrapolated	CCD	Liao et al. (2021)		2021
3.2214	1.2e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
3.2119035best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
3.2168109	4.9e-3	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
3.2204221	8.5e-3	1.9e-5	approximate	Transcorrelated FCIQMC	Luo & Alavi (2018)	uses NECI	2018
3.2207100	8.8e-3	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
3.2207700	8.9e-3	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
3.2209961	9.1e-3	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
3.2248850	1.3e-2	n/a	approximate	lmrCCD	Shepherd et al. (2014)		2014
3.2275887	1.6e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best variational

0.52973(1)

VMC (MP-NQS)

uses NetKet 3

best projected

0.52967(2)

ph-AFQMC (RHF)

uses QMCPACK

best extrapolated

0.52991(6)

FCIQMC

best approximate

0.5147818

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
0.52973best variational	0	1.0e-5	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
0.53002	2.9e-4	1.0e-6	variational	VMC (DeepSolid)	Li et al. (2022)	bytedance/DeepSolid	2022
0.53009	3.6e-4	3.0e-5	variational	VMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
0.53065	9.2e-4	2.0e-4	variational	VMC (SJB)	Kwon et al. (1998)		1998
0.53085	1.1e-3	2.0e-4	variational	VMC (SJB)	Kwon et al. (1998)		1998
0.53175	2.0e-3	7.0e-5	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
0.53211	2.4e-3	7.0e-5	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
0.53315	3.4e-3	2.5e-4	variational	VMC (SJ)	Kwon et al. (1998)		1998
0.53345	3.7e-3	3.0e-4	variational	VMC (SJ)	Kwon et al. (1998)		1998
0.56890	3.9e-2	4.0e-4	variational	HF	López Ríos et al. (2006)	uses CASINO	2006
0.52967best projected	0	2.0e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019
0.52989	2.2e-4	4.0e-5	projected	FN-DMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
0.53005	3.8e-4	1.0e-4	projected	FN-DMC (SJB)	Kwon et al. (1998)		1998
0.53089	1.2e-3	9.0e-5	projected	FN-DMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
0.53094	1.3e-3	2.0e-5	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024
0.53095	1.3e-3	2.0e-4	projected	FN-DMC (SJ)	Kwon et al. (1998)		1998
0.52991best extrapolated	0	5.6e-5	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
0.53000tied with best extrapolated at 2σ	8.9e-5	3.0e-4	extrapolated	FCIQMC	Shepherd et al. (2012)		2012
0.53001tied with best extrapolated at 2σ	9.9e-5	n/a	extrapolated	DCD	Liao et al. (2021)		2021
0.53069	7.8e-4	n/a	extrapolated	CCD	Liao et al. (2021)		2021
0.53124	1.3e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
0.5147818best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
0.5243744	9.6e-3	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
0.5296800	1.5e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
0.5297262	1.5e-2	3.7e-5	approximate	Transcorrelated FCIQMC	Luo & Alavi (2018)	uses NECI	2018
0.5298200	1.5e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
0.5311892	1.6e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
0.5359299	2.1e-2	n/a	approximate	lmrCCD	Shepherd et al. (2014)		2014
0.5396151	2.5e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best variational

-0.054448(1)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.054443(2)

FN-DMC (SJB)

López Ríos et al. (2006)

uses CASINO

best extrapolated

-0.05157

DCD

best approximate

-0.0728389

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.054448best variational	0	1.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.054445tied with best variational at 2σ	3.0e-6	1.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.054389	5.9e-5	2.0e-6	variational	VMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
-0.054279	1.7e-4	1.0e-7	variational	VMC (DeepSolid)	Li et al. (2022)	bytedance/DeepSolid	2022
-0.054175	2.7e-4	1.0e-5	variational	VMC (SJB)	Kwon et al. (1998)		1998
-0.054145	3.0e-4	1.0e-5	variational	VMC (SJB)	Kwon et al. (1998)		1998
-0.054042	4.1e-4	4.0e-6	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.053927	5.2e-4	4.0e-6	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.053865	5.8e-4	1.0e-5	variational	VMC (SJ)	Kwon et al. (1998)		1998
-0.053725	7.2e-4	1.0e-5	variational	VMC (SJ)	Kwon et al. (1998)		1998
-0.038840	1.6e-2	4.0e-5	variational	HF	López Ríos et al. (2006)	uses CASINO	2006
-0.054443best projected	0	2.0e-6	projected	FN-DMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
-0.054410	3.3e-5	1.0e-5	projected	FN-DMC (SJB)	Kwon et al. (1998)		1998
-0.054269	1.7e-4	8.0e-6	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024
-0.054255	1.9e-4	3.0e-6	projected	FN-DMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.054245	2.0e-4	1.0e-5	projected	FN-DMC (SJ)	Kwon et al. (1998)		1998
-0.05157best extrapolated	0	n/a	extrapolated	DCD	Liao et al. (2021)		2021
-0.05016	1.4e-3	n/a	extrapolated	CCD	Liao et al. (2021)		2021
-0.05006	1.5e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.0728389best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.0558018	1.7e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.0532200	2.0e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
-0.0523000	2.1e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
-0.0494685	2.3e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
-0.0469315	2.6e-2	n/a	approximate	lmrCCD	Shepherd et al. (2014)		2014
-0.0449130	2.8e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best variational

-0.00769203(5)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.007674(3)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.00769203best variational	0	5.0e-8	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.00767930	1.3e-5	1.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.007674best projected	0	3.0e-6	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best extrapolated

-0.0363669

CCD

best approximate

-0.0359224

mCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0363669best extrapolated	0	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.0359224best approximate	0	n/a	approximate	mCCD	Shepherd et al. (2014)		2014

best variational

-0.014046(8)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.01429(3)

ph-AFQMC (RHF)

uses QMCPACK

best extrapolated

-0.01286

DCD

best approximate

-0.0363623

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.014046best variational	0	8.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.013900	1.5e-4	1.0e-5	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.013840	2.1e-4	1.0e-6	variational	VMC (DeepSolid)	Li et al. (2022)	bytedance/DeepSolid	2022
-0.013820	2.3e-4	2.0e-5	variational	VMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
-0.012520	1.5e-3	3.0e-5	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.012460	1.6e-3	3.0e-5	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
0.018600	3.3e-2	2.0e-4	variational	HF	López Ríos et al. (2006)	uses CASINO	2006
-0.01429best projected	0	3.0e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019
-0.01397	3.2e-4	9.0e-6	projected	FN-DMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
-0.01326	1.0e-3	2.0e-5	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024
-0.01311	1.2e-3	2.0e-5	projected	FN-DMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.01286best extrapolated	0	n/a	extrapolated	DCD	Liao et al. (2021)		2021
-0.01162	1.2e-3	n/a	extrapolated	CCD	Liao et al. (2021)		2021
-0.01123	1.6e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.0363623best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.0196956	1.7e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.0137900	2.3e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
-0.0132400	2.3e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
-0.0107141	2.6e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
-0.0058808	3.0e-2	n/a	approximate	lmrCCD	Shepherd et al. (2014)		2014
-0.0019549	3.4e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best variational

-0.0320524(5)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.032047(2)

FN-DMC (SJB)

López Ríos et al. (2006)

uses CASINO

best extrapolated

-0.02925

DCD

best approximate

-0.0429947

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0320524best variational	0	5.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0320480	4.4e-6	6.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0319984	5.4e-5	8.0e-7	variational	VMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
-0.0318900	1.6e-4	1.0e-5	variational	VMC (SJB)	Kwon et al. (1998)		1998
-0.0318580	1.9e-4	1.0e-6	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.0318250	2.3e-4	5.0e-6	variational	VMC (SJB)	Kwon et al. (1998)		1998
-0.0317670	2.9e-4	2.0e-6	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.0317400	3.1e-4	5.0e-6	variational	VMC (SJ)	Kwon et al. (1998)		1998
-0.0316886	3.6e-4	1.0e-7	variational	VMC (DeepSolid)	Li et al. (2022)	bytedance/DeepSolid	2022
-0.0316650	3.9e-4	5.0e-6	variational	VMC (SJ)	Kwon et al. (1998)		1998
-0.0220500	1.0e-2	2.0e-5	variational	HF	López Ríos et al. (2006)	uses CASINO	2006
-0.032047best projected	0	2.0e-6	projected	FN-DMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
-0.032015	3.2e-5	5.0e-6	projected	FN-DMC (SJB)	Kwon et al. (1998)		1998
-0.031976	7.1e-5	8.0e-6	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024
-0.031973	7.4e-5	3.0e-6	projected	FN-DMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.031940	1.1e-4	5.0e-6	projected	FN-DMC (SJ)	Kwon et al. (1998)		1998
-0.02925best extrapolated	0	n/a	extrapolated	DCD	Liao et al. (2021)		2021
-0.02846	7.9e-4	n/a	extrapolated	CCD	Liao et al. (2021)		2021
-0.0429947best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.0321428	1.1e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.0311300	1.2e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
-0.0305500	1.2e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
-0.0281058	1.5e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
-0.0265317	1.6e-2	n/a	approximate	lmrCCD	Shepherd et al. (2014)		2014
-0.0253095	1.8e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best approximate

-0.0706229

mCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0706229best approximate	0	n/a	approximate	mCCD	Shepherd et al. (2014)		2014

best approximate

-0.0774134

mCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0774134best approximate	0	n/a	approximate	mCCD	Shepherd et al. (2014)		2014

best variational

-0.079090(2)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.079036(3)

FN-DMC (SJB)

López Ríos et al. (2006)

uses CASINO

best extrapolated

-0.07655

DCD

best approximate

-0.104002

rxmCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.079090best variational	0	2.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.079064	2.6e-5	4.0e-6	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.078961	1.3e-4	5.0e-6	variational	VMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
-0.078835	2.5e-4	2.0e-7	variational	VMC (DeepSolid)	Li et al. (2022)	bytedance/DeepSolid	2022
-0.078675	4.1e-4	2.5e-5	variational	VMC (SJB)	Kwon et al. (1998)		1998
-0.078645	4.4e-4	2.5e-5	variational	VMC (SJB)	Kwon et al. (1998)		1998
-0.078284	8.1e-4	9.0e-6	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.078150	9.4e-4	1.0e-5	variational	VMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.077845	1.2e-3	2.5e-5	variational	VMC (SJ)	Kwon et al. (1998)		1998
-0.077790	1.3e-3	3.5e-5	variational	VMC (SJ)	Kwon et al. (1998)		1998
-0.056250	2.3e-2	7.0e-5	variational	HF	López Ríos et al. (2006)	uses CASINO	2006
-0.079036best projected	0	3.0e-6	projected	FN-DMC (SJB)	López Ríos et al. (2006)	uses CASINO	2006
-0.078990tied with best projected at 2σ	4.6e-5	2.0e-5	projected	FN-DMC (SJB)	Kwon et al. (1998)		1998
-0.078670	3.7e-4	1.0e-5	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024
-0.078670	3.7e-4	1.5e-5	projected	FN-DMC (SJ)	Kwon et al. (1998)		1998
-0.078649	3.9e-4	7.0e-6	projected	FN-DMC (SJ)	López Ríos et al. (2006)	uses CASINO	2006
-0.075890	3.1e-3	5.0e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019
-0.07655best extrapolated	0	n/a	extrapolated	DCD	Liao et al. (2021)		2021
-0.07492	1.6e-3	n/a	extrapolated	CCD	Liao et al. (2021)		2021
-0.07472	1.8e-3	n/a	extrapolated	CCD	Shepherd et al. (2014)		2014
-0.104002best approximate	0	n/a	approximate	rxmCCD	Shepherd et al. (2014)		2014
-0.082465	2.2e-2	n/a	approximate	rmCCD	Shepherd et al. (2014)		2014
-0.078370	2.6e-2	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
-0.077500	2.7e-2	n/a	approximate	TC-CCD	Liao et al. (2021)		2021
-0.073928	3.0e-2	n/a	approximate	mCCD	Shepherd et al. (2014)		2014
-0.070298	3.4e-2	n/a	approximate	lmrCCD	Shepherd et al. (2014)		2014
-0.067243	3.7e-2	n/a	approximate	lmCCD	Shepherd et al. (2014)		2014

best variational

-0.0145015(1)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.01387(2)

FN-DMC (SJ)

best extrapolated

-0.01267

DCD

best approximate

-0.01281

TC-DCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0145015best variational	0	1.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0144999	1.6e-6	1.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.01387best projected	0	2.0e-5	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024
-0.01267best extrapolated	0	n/a	extrapolated	DCD	Liao et al. (2021)		2021
-0.01223	4.4e-4	n/a	extrapolated	CCD	Liao et al. (2021)		2021
-0.01281best approximate	0	n/a	approximate	TC-DCD	Liao et al. (2021)		2021
-0.01263	1.8e-4	n/a	approximate	TC-CCD	Liao et al. (2021)		2021

best approximate

-0.0602626

mCCD

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0602626best approximate	0	n/a	approximate	mCCD	Shepherd et al. (2014)		2014

best variational

0.5748(3)

VMC (SJ)

best projected

0.57290(3)

FN-DMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
0.5748best variational	0	2.5e-4	variational	VMC (SJ)	Kwon et al. (1998)	1998
0.57290best projected	0	3.5e-5	projected	FN-DMC	Fantoni (2013)	2013
0.57305	1.5e-4	3.0e-5	projected	FN-DMC	Fantoni (2013)	2013

best variational

-0.05318(1)

VMC (SJ)

best projected

-0.053728(3)

FN-DMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.05318best variational	0	1.0e-5	variational	VMC (SJ)	Kwon et al. (1998)	1998
-0.053728best projected	0	3.5e-6	projected	FN-DMC	Fantoni (2013)	2013
-0.053721tied with best projected at 2σ	6.5e-6	1.5e-6	projected	FN-DMC	Fantoni (2013)	2013

best projected

-0.00208(4)

FN-DMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.00208best projected	0	4.0e-5	projected	FN-DMC	Fantoni (2013)		2013
-0.00202tied with best projected at 2σ	6.2e-5	3.0e-6	projected	FN-DMC	Fantoni (2013)		2013

best variational

-0.031515(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031515best variational	0	5.0e-6	variational	VMC (SJ)	Kwon et al. (1998)		1998

best variational

-0.07583(2)

VMC (SJ)

best projected

-0.076676(2)

FN-DMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.07583best variational	0	2.0e-5	variational	VMC (SJ)	Kwon et al. (1998)	1998
-0.076676best projected	0	2.0e-6	projected	FN-DMC	Fantoni (2013)	2013
-0.076664	1.1e-5	3.0e-6	projected	FN-DMC	Fantoni (2013)	2013

best projected

3.48453(8)

ph-AFQMC (RHF)

uses QMCPACK

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
3.48453best projected	0	8.0e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019
3.48594	1.4e-3	n/a	projected	CCD	Butler et al. (2024)	butler-julie/HEG-SRE	2024

best variational

0.6039(3)

VMC (SJ)

best projected

0.59877(6)

ph-AFQMC (RHF)

uses QMCPACK

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
0.6039best variational	0	2.5e-4	variational	VMC (SJ)	Kwon et al. (1998)		1998
0.59877best projected	0	6.0e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019

best variational

-0.05276(1)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.05276best variational	0	1.0e-5	variational	VMC (SJ)	Kwon et al. (1998)		1998

best projected

0.00487(6)

ph-AFQMC (RHF)

uses QMCPACK

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
0.00487best projected	0	6.0e-5	projected	ph-AFQMC (RHF)	Lee et al. (2019)	uses QMCPACK	2019

best variational

-0.031390(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031390best variational	0	5.0e-6	variational	VMC (SJ)	Kwon et al. (1998)		1998

best variational

-0.07433(1)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.07433best variational	0	1.5e-5	variational	VMC (SJ)	Kwon et al. (1998)		1998

best variational

-0.0071121(2)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.007009518(1)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0071121best variational	0	2.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.007009518best projected	0	1.0e-9	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best variational

-0.0040615(1)

VMC (MP-NQS)

uses NetKet 3

best projected

-0.0039923(7)

FN-DMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0040615best variational	0	1.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0040023	5.9e-5	2.0e-7	variational	VMC (MP-NQS)	Pescia et al. (2024)	uses NetKet 3	2024
-0.0039923best projected	0	7.0e-7	projected	FN-DMC (SJ)	Pescia et al. (2024)		2024

best variational

0.5581(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
0.5581best variational	0	2.0e-4	variational	VMC (SJ)	Kwon et al. (1998)		1998

best variational

-0.053210(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.053210best variational	0	5.0e-6	variational	VMC (SJ)	Kwon et al. (1998)		1998

best variational

-0.031350(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031350best variational	0	5.0e-6	variational	VMC (SJ)	Kwon et al. (1998)		1998

best variational

-0.07619(1)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.07619best variational	0	1.5e-5	variational	VMC (SJ)	Kwon et al. (1998)		1998

best variational

0.5969(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
0.5969best variational	0	1.5e-4	variational	VMC (SJ)	Kwon et al. (1998)		1998

best variational

-0.052740(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.052740best variational	0	5.0e-6	variational	VMC (SJ)	Kwon et al. (1998)		1998

best variational

-0.031375(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031375best variational	0	5.0e-6	variational	VMC (SJ)	Kwon et al. (1998)		1998

best variational

-0.07443(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.07443best variational	0	1.5e-5	variational	VMC (SJ)	Kwon et al. (1998)		1998

Electron gas, 2D#

65 instances, energies as E/N (Ha)

lattice size

instance

value

energy

method

source

code

energies

best variational

-0.08492(4)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.08492best variational	0	4.5e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.04634(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.04634best variational	0	1.5e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.031965(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031965best variational	0	5.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.024434(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.024434best variational	0	4.5e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.1451(1)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.1451best variational	0	1.0e-4	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.013457(1)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.013457best variational	0	1.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.1850(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.1850best variational	0	5.0e-4	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.08433(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.08433best variational	0	2.5e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.04587(1)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.04587best variational	0	1.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.03166(1)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.03166best variational	0	1.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.14685(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.14685best variational	0	5.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.019659(4)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.019659best variational	0	4.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.08440(4)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.08440best variational	0	4.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.04614(1)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.04614best variational	0	1.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.0318870(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0318870best variational	0	5.0e-7	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.024379(4)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.024379best variational	0	4.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.14373(4)

VMC (NCT)

Xie et al. (2023)

fermiflow/CoulombGas

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.14373best variational	0	4.0e-5	variational	VMC (NCT)	Xie et al. (2023)	fermiflow/CoulombGas	2023
-0.14315	5.8e-4	5.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.0134380(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0134380best variational	0	5.0e-7	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.2225(3)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.2225best variational	0	3.5e-4	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.08450(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.08450best variational	0	2.5e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.04588(1)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.04588best variational	0	1.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.031675(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031675best variational	0	5.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.14800(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.14800best variational	0	5.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.019654(3)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.019654best variational	0	3.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.08390(5)

VMC (SJ)

best projected

-0.08427(3)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.08390best variational	0	5.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.08427best projected	0	2.5e-5	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.04607(3)

VMC (SJ)

best projected

-0.04618(1)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.04607best variational	0	2.5e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.04618best projected	0	1.0e-5	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.031825(5)

VMC (SJ)

best projected

-0.031913(4)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031825best variational	0	5.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.031913best projected	0	4.0e-6	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.024360(5)

VMC (SJ)

best projected

-0.024420(1)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.024360best variational	0	5.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.024420best projected	0	1.0e-6	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.14225(5)

VMC (SJ)

best projected

-0.14291(5)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.14225best variational	0	5.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.14291best projected	0	4.5e-5	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.0134275(5)

VMC (SJ)

best projected

-0.013473(2)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0134275best variational	0	5.0e-7	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.013473best projected	0	1.5e-6	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.1953(1)

VMC (SJ)

best projected

-0.2046(3)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.1953best variational	0	1.5e-4	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.2046best projected	0	3.0e-4	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.08426(2)

VMC (SJ)

best projected

-0.08552(4)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.08426best variational	0	2.5e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.08552best projected	0	4.0e-5	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.04582(2)

VMC (SJ)

best projected

-0.04636(1)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.04582best variational	0	2.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.04636best projected	0	1.0e-5	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.031655(3)

VMC (SJ)

best projected

-0.031967(3)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031655best variational	0	3.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.031967best projected	0	3.5e-6	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.1470(1)

VMC (SJ)

best projected

-0.14990(5)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.1470best variational	0	1.5e-4	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.14990best projected	0	5.0e-5	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.019651(3)

VMC (SJ)

best projected

-0.019763(3)

FN-GFMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.019651best variational	0	2.5e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989
-0.019763best projected	0	3.0e-6	projected	FN-GFMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.08412(3)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.08412best variational	0	3.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.046085(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.046085best variational	0	5.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.031852(4)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031852best variational	0	4.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.024375(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.024375best variational	0	2.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.14310(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.14310best variational	0	5.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.0134305(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0134305best variational	0	5.0e-7	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.2078(4)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.2078best variational	0	4.0e-4	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.08429(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.08429best variational	0	2.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.045845(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.045845best variational	0	5.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.031662(4)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031662best variational	0	4.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.14735(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.14735best variational	0	5.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.019651(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.019651best variational	0	2.5e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.0317373(2)

VMC (SJ)

Azadi et al. (2024)

uses CASINO

best projected

-0.031919(1)

FN-DMC

Azadi et al. (2024)

uses CASINO

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.0317373best variational	0	2.0e-7	variational	VMC (SJ)	Azadi et al. (2024)	uses CASINO	2024
-0.0271506	4.6e-3	7.0e-7	variational	VMC (SJ)	Azadi et al. (2024)	uses CASINO	2024
-0.0251398	6.6e-3	8.0e-7	variational	VMC (SJ)	Azadi et al. (2024)	uses CASINO	2024
-0.031919best projected	0	1.0e-6	projected	FN-DMC	Azadi et al. (2024)	uses CASINO	2024
-0.031510	4.1e-4	2.0e-5	projected	FN-DMC	Azadi et al. (2024)	uses CASINO	2024
-0.02848	n/a	2.0e-5	projected source-says-biased	FN-DMC	Azadi et al. (2024)	uses CASINO	2024
-0.02676	n/a	7.0e-5	projected source-says-biased	FN-DMC	Azadi et al. (2024)	uses CASINO	2024

best variational

-0.08396(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.08396best variational	0	2.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.046030(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.046030best variational	0	5.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.031821(3)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031821best variational	0	3.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.024356(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.024356best variational	0	2.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.14215(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.14215best variational	0	5.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.0134245(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.0134245best variational	0	5.0e-7	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.1983(4)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.1983best variational	0	4.0e-4	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.08423(1)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.08423best variational	0	1.5e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.045825(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.045825best variational	0	5.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.031647(4)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.031647best variational	0	4.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.14685(5)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.14685best variational	0	5.0e-5	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.019648(2)

VMC (SJ)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.019648best variational	0	2.0e-6	variational	VMC (SJ)	Tanatar & Ceperley (1989)		1989

best variational

-0.031990687(3)

VMC (Fermi Sets)

Li et al. (2026)

best projected

-0.03199636(7)

FP-DMC (Fermi Sets)

Li et al. (2026)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.031990687best variational	0	3.0e-9	variational	VMC (Fermi Sets)	Li et al. (2026)	2026
-0.031965678	2.5e-5	6.0e-9	variational	VMC (Fermi Sets)	Li et al. (2026)	2026
-0.031895091	9.6e-5	1.2e-8	variational	VMC (Fermi Sets)	Li et al. (2026)	2026
-0.03199636best projected	0	7.0e-8	projected	FP-DMC (Fermi Sets)	Li et al. (2026)	2026
-0.03197786	1.9e-5	8.0e-8	projected	FP-DMC (Fermi Sets)	Li et al. (2026)	2026
-0.03191139	8.5e-5	1.2e-7	projected	FP-DMC (Fermi Sets)	Li et al. (2026)	2026

best variational

-0.03193763(3)

VMC (self-attention)

best projected

-0.0319370(1)

FN-DMC (SJB)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.03193763best variational	0	3.0e-8	variational	VMC (self-attention)	Gaggioli et al. (2026)	2026
-0.03187920	5.8e-5	2.0e-7	variational	VMC (SJB)	Gaggioli et al. (2026)	2026
-0.0319370best projected	0	1.0e-7	projected	FN-DMC (SJB)	Gaggioli et al. (2026)	2026

best variational

-0.02443814(2)

VMC (self-attention)

best projected

-0.0244377(2)

FN-DMC (SJB)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.02443814best variational	0	2.0e-8	variational	VMC (self-attention)	Gaggioli et al. (2026)	2026
-0.02438320	5.5e-5	1.0e-7	variational	VMC (SJB)	Gaggioli et al. (2026)	2026
-0.0244377best projected	0	2.0e-7	projected	FN-DMC (SJB)	Gaggioli et al. (2026)	2026

best variational

-0.03192077(3)

VMC (self-attention)

best projected

-0.0319197(1)

FN-DMC (SJB)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.03192077best variational	0	3.0e-8	variational	VMC (self-attention)	Gaggioli et al. (2026)	2026
-0.03185480	6.6e-5	2.0e-7	variational	VMC (SJB)	Gaggioli et al. (2026)	2026
-0.0319197best projected	0	1.0e-7	projected	FN-DMC (SJB)	Gaggioli et al. (2026)	2026

Hydrogen chain#

228 instances, energies as E/N (Ha)

lattice size

instance

value

energy

method

source

code

energies

best variational

-0.5418875

VQE

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5418875best variational	0	n/a	variational	VQE	Li et al. (2023)	tencent-quantum-lab/TenCirChem	2023

exact

-0.547595

FCI

best variational

-0.547595

VMC (RBM)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.547595exact	0	n/a	exact	FCI	Li et al. (2023)	2023
-0.547595best variational	0	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.547595tied with best variational at 2σ	<1e-6	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.5476025	n/a	n/a	approximate below exact by > 2σ	CCSD(T)	Li et al. (2023)	2023

exact

-0.481645

FCI

best variational

-0.481645

VMC (RBM)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.481645exact	0	n/a	exact	FCI	Li et al. (2023)	2023
-0.481645best variational	0	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.481642	2.5e-6	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.4854725	n/a	n/a	approximate below exact by > 2σ	CCSD(T)	Li et al. (2023)	2023

best variational

-0.5340233

VQE

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5340233best variational	0	n/a	variational	VQE	Li et al. (2023)	tencent-quantum-lab/TenCirChem	2023

exact

-0.5444567

FCI

best variational

-0.5444567

VMC (RBM)

best approximate

-0.5444567

CCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5444567exact	0	n/a	exact	FCI	Li et al. (2023)	2023
-0.5444567best variational	0	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.5444567tied with best variational at 2σ	<1e-7	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.5444567best approximate	0	n/a	approximate	CCSD(T)	Li et al. (2023)	2023

exact

-0.5362833

best variational

-0.5362167

QFlow

best projected

-0.5363333

CCSDT

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5362833exact	0	n/a	exact	ED	Kowalski & Bauman (2023)	2023
-0.5362167best variational	0	n/a	variational	QFlow	Kowalski & Bauman (2023)	2023
-0.5278167	8.4e-3	n/a	variational	CASCI	Kowalski & Bauman (2023)	2023
-0.5176500	1.9e-2	n/a	variational	HF	Kowalski & Bauman (2023)	2023
-0.5363333best projected	0	n/a	projected	CCSDT	Kowalski & Bauman (2023)	2023
-0.5362833	5.0e-5	n/a	projected	CCSDTQ	Kowalski & Bauman (2023)	2023
-0.5362167	1.2e-4	n/a	projected	CCSD	Kowalski & Bauman (2023)	2023

exact

-0.5033663

FCI

Stair et al. (2020)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5033663exact	0	n/a	exact	FCI	Stair et al. (2020)		2020

exact

-0.5265167

best projected

-0.5265167

CCSDTQ

best approximate

-0.5264833

DUCC-QFlow

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5265167exact	0	n/a	exact	ED	Kowalski & Bauman (2023)	2023
-0.5269833	−4.7e-4	n/a	projected below exact by > 2σ	CCSDT	Kowalski & Bauman (2023)	2023
-0.5265167best projected	0	n/a	projected	CCSDTQ	Kowalski & Bauman (2023)	2023
-0.5261833	3.3e-4	n/a	projected	CCSD	Kowalski & Bauman (2023)	2023
-0.5264833best approximate	0	n/a	approximate	DUCC-QFlow	Kowalski & Bauman (2023)	2023
-0.5261667	3.2e-4	n/a	approximate	DUCC-QFlow	Kowalski & Bauman (2023)	2023

exact

-0.4929333

best variational

-0.4920167

QFlow

best projected

-0.4929

CCSDTQ

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4929333exact	0	n/a	exact	ED	Kowalski & Bauman (2023)	2023
-0.4920167best variational	0	n/a	variational	QFlow	Kowalski & Bauman (2023)	2023
-0.4670167	2.5e-2	n/a	variational	CASCI	Kowalski & Bauman (2023)	2023
-0.4459000	4.6e-2	n/a	variational	HF	Kowalski & Bauman (2023)	2023
-0.4949	−2.0e-3	n/a	projected below exact by > 2σ	CCSDT	Kowalski & Bauman (2023)	2023
-0.4945	−1.7e-3	n/a	projected below exact by > 2σ	CCSD	Kowalski & Bauman (2023)	2023
-0.4929best projected	0	n/a	projected	CCSDTQ	Kowalski & Bauman (2023)	2023

exact

-0.4817533

FCI

best variational

-0.4817517

VMC (RBM)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4817533exact	0	n/a	exact	FCI	Li et al. (2023)	2023
-0.4817517best variational	0	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.4817350	1.7e-5	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.4972	n/a	n/a	approximate below exact by > 2σ	CCSD(T)	Li et al. (2023)	2023

best variational

-0.530315

VQE

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.530315best variational	0	n/a	variational	VQE	Li et al. (2023)	tencent-quantum-lab/TenCirChem	2023

exact

-0.543135

FCI

best variational

-0.5431337

VMC (RBM)

best approximate

-0.543125

CCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.543135exact	0	n/a	exact	FCI	Li et al. (2023)	2023
-0.5431337best variational	0	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.5430075	1.3e-4	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.543125best approximate	0	n/a	approximate	CCSD(T)	Li et al. (2023)	2023

exact

-0.53575

best variational

-0.5355875

QFlow

best projected

-0.53575

CCSDTQ

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.53575exact	0	n/a	exact	ED	Kowalski & Bauman (2023)	2023
-0.5355875best variational	0	n/a	variational	QFlow	Kowalski & Bauman (2023)	2023
-0.5238250	1.2e-2	n/a	variational	CASCI	Kowalski & Bauman (2023)	2023
-0.5172750	1.8e-2	n/a	variational	HF	Kowalski & Bauman (2023)	2023
-0.53584	−8.8e-5	n/a	projected below exact by > 2σ	CCSDT	Kowalski & Bauman (2023)	2023
-0.53575best projected	0	n/a	projected	CCSDTQ	Kowalski & Bauman (2023)	2023
-0.53560	1.5e-4	n/a	projected	CCSD	Kowalski & Bauman (2023)	2023

exact

-0.503519

FCI

Stair et al. (2020)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.503519exact	0	n/a	exact	FCI	Stair et al. (2020)		2020

exact

-0.4930875

best variational

-0.491525

QFlow

best projected

-0.4929875

CCSDTQ

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4930875exact	0	n/a	exact	ED	Kowalski & Bauman (2023)	2023
-0.491525best variational	0	n/a	variational	QFlow	Kowalski & Bauman (2023)	2023
-0.458200	3.3e-2	n/a	variational	CASCI	Kowalski & Bauman (2023)	2023
-0.446537	4.5e-2	n/a	variational	HF	Kowalski & Bauman (2023)	2023
-0.4973000	−4.3e-3	n/a	projected below exact by > 2σ	CCSDT	Kowalski & Bauman (2023)	2023
-0.4965875	−3.6e-3	n/a	projected below exact by > 2σ	CCSD	Kowalski & Bauman (2023)	2023
-0.4929875best projected	0	n/a	projected	CCSDTQ	Kowalski & Bauman (2023)	2023

exact

-0.4818225

FCI

best variational

-0.4818188

VMC (RBM)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4818225exact	0	n/a	exact	FCI	Li et al. (2023)	2023
-0.4818188best variational	0	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.4796787	2.1e-3	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.4860425	n/a	n/a	approximate below exact by > 2σ	CCSD(T)	Li et al. (2023)	2023

best variational

-0.41566

best approximate

-0.43918

MP2

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.41566best variational	0	n/a	variational	HF	Motta et al. (2020)		2020
-0.43918best approximate	0	n/a	approximate	MP2	Motta et al. (2020)		2020

best variational

-0.41495

best projected

-0.44012

CCSD

best approximate

-0.43752

MP2

E/N (Ha)	σ	bound type	method	source	year
-0.41495best variational	n/a	variational	HF	Motta et al. (2020)	2020
-0.44012best projected	n/a	projected	CCSD	Motta et al. (2020)	2020
-0.43752best approximate	n/a	approximate	MP2	Motta et al. (2020)	2020

best variational

-0.4155

best projected

-0.44236(8)

ph-AFQMC

best approximate

-0.43927

MP2

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4155best variational	0	n/a	variational	HF	Motta et al. (2020)	2020
-0.4155	<1e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.4155	<1e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.44236best projected	0	8.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.43927best approximate	0	n/a	approximate	MP2	Motta et al. (2020)	2020

best variational

-0.42186

DMRG

best projected

-0.4220847

DMET

best approximate

-0.4217751

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.42186best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.42152	3.4e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.40101	2.1e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.40101	2.1e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4220847best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4219900tied with best projected at 2σ	9.5e-5	6.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.4219540	1.3e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.4214700	6.1e-4	n/a	projected	CCSD	Motta et al. (2020)	2020
-0.4214438	6.4e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.4214438	6.4e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4200776	2.0e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4217751best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.4217751tied with best approximate at 2σ	<1e-7	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4187550	3.0e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.4185204	3.3e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.4184100	3.4e-3	n/a	approximate	MP2	Motta et al. (2020)	2020

best variational

-0.41505

best projected

-0.44160(8)

ph-AFQMC

best approximate

-0.4413939

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.41505best variational	0	n/a	variational	HF	Motta et al. (2020)	2020
-0.41504	1.4e-5	n/a	variational	HF	Motta et al. (2017)	2017
-0.41504	1.4e-5	n/a	variational	HF	Motta et al. (2017)	2017
-0.44160best projected	0	8.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.44082	7.8e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.44082	7.8e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4413939best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.4413939tied with best approximate at 2σ	<1e-7	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4384200	3.0e-3	n/a	approximate	MP2	Motta et al. (2020)	2020

best variational

-0.4395

DMRG

best projected

-0.43969(6)

ph-AFQMC

best approximate

-0.4394551

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4395best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.4139	2.6e-2	n/a	variational	HF	Motta et al. (2020)	2020
-0.4139	2.6e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4139	2.6e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.43969best projected	0	6.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.43893	7.6e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.43893	7.6e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4394551best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.4394551tied with best approximate at 2σ	<1e-7	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4362000	3.3e-3	n/a	approximate	MP2	Motta et al. (2020)	2020

best variational

-0.441499(9)

VMC (JAGP)

best projected

-0.442430(7)

LR-DMC (AGP)

best extrapolated

-0.4432(3)

MRCI+Q

best approximate

-0.4427(2)

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.441499best variational	0	9.0e-6	variational	VMC (JAGP)	Motta et al. (2017)	2017
-0.440610	8.9e-4	1.0e-5	variational	VMC (SJ)	Motta et al. (2017)	2017
-0.442430best projected	0	7.0e-6	projected	LR-DMC (AGP)	Motta et al. (2017)	2017
-0.442093	3.4e-4	9.0e-6	projected	LR-DMC (LDA determinant)	Motta et al. (2017)	2017
-0.4432best extrapolated	0	3.2e-4	extrapolated	MRCI+Q	Motta et al. (2017)	2017
-0.4430tied with best extrapolated at 2σ	2.3e-4	3.1e-4	extrapolated	MRCI-F12+Q	Motta et al. (2017)	2017
-0.4428tied with best extrapolated at 2σ	4.0e-4	2.4e-4	extrapolated	ph-AFQMC	Motta et al. (2017)	2017
-0.4421	1.1e-3	2.1e-4	extrapolated	SBDMRG	Motta et al. (2017)	2017
-0.4421	1.2e-3	2.6e-4	extrapolated	RCCSD	Motta et al. (2017)	2017
-0.4421	1.2e-3	2.6e-4	extrapolated	UCCSD	Motta et al. (2017)	2017
-0.4154	2.8e-2	1.8e-4	extrapolated	HF	Motta et al. (2017)	2017
-0.4154	2.8e-2	1.6e-4	extrapolated	HF	Motta et al. (2017)	2017
-0.4427best approximate	0	2.1e-4	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.4427tied with best approximate at 2σ	<1e-4	2.1e-4	approximate	UCCSD(T)	Motta et al. (2017)	2017

exact

-0.3824389

FCI

best variational

-0.3824389

MRCI

best projected

-0.38248(3)

ph-AFQMC

best approximate

-0.382432

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.3824389exact	0	n/a	exact	FCI	Motta et al. (2017)	2017
-0.3824389best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.3824388	<1e-7	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.3751740	7.3e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.3751740	7.3e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.38248best projected	0	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.38244tied with best projected at 2σ	4.1e-5	n/a	projected	CCSDT	Low et al. (2019)	2019
-0.38244tied with best projected at 2σ	4.1e-5	n/a	projected	CCSDTQ	Low et al. (2019)	2019
-0.38244tied with best projected at 2σ	4.1e-5	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.38243tied with best projected at 2σ	5.1e-5	n/a	projected	MkMRCCSD	Low et al. (2019)	2019
-0.38239	9.3e-5	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.38239	9.3e-5	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.38220	2.8e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.38195	5.3e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.38176	7.2e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.38135	1.1e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.382996	−5.6e-4	n/a	approximate below exact by > 2σ	GW	Motta et al. (2017)	2017
-0.382449	−1.7e-5	n/a	approximate below exact by > 2σ	MkMRCCSD(T)	Low et al. (2019)	2019
-0.382432best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.382432tied with best approximate at 2σ	<1e-6	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.381016	1.4e-3	n/a	approximate	GF2	Motta et al. (2017)	2017
-0.381013	1.4e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.4884091

best projected

-0.51451(6)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4884091best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4884091	<1e-7	n/a	variational	HF	Motta et al. (2017)	2017
-0.51451best projected	0	6.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017

best variational

-0.50271

DMRG

best projected

-0.5029843

DMET

best approximate

-0.506634

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.50271best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.50232	3.9e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.48136	2.1e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.48136	2.1e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5029843best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5028700	1.1e-4	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5028120	1.7e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5022517	7.3e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5022517	7.3e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5008664	2.1e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.506634best approximate	0	n/a	approximate	GW	Motta et al. (2017)	2017
-0.502613	4.0e-3	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.502613	4.0e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.499406	7.2e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.499173	7.5e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.4882713

best projected

-0.51419(8)

ph-AFQMC

best approximate

-0.5140214

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4882713best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4882710	2.9e-7	n/a	variational	HF	Motta et al. (2017)	2017
-0.51419best projected	0	8.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.51347	7.2e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.51347	7.2e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5140214best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5140214tied with best approximate at 2σ	<1e-7	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.51302

DMRG

best projected

-0.51315(9)

ph-AFQMC

best approximate

-0.5129509

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.51302best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.51241	6.1e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.48782	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.48782	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.51315best projected	0	9.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.51312tied with best projected at 2σ	3.1e-5	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.51278	3.7e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.51243	7.2e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.51243	7.2e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5129509best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5129509tied with best approximate at 2σ	<1e-7	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5095791	3.4e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5093000	3.7e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.513646(9)

VMC (JAGP)

best projected

-0.514432(6)

LR-DMC (AGP)

best extrapolated

-0.5153(2)

MRCI+Q

best approximate

-0.5149(2)

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.513646best variational	0	9.0e-6	variational	VMC (JAGP)	Motta et al. (2017)	2017
-0.513225	4.2e-4	8.0e-6	variational	VMC (SJ)	Motta et al. (2017)	2017
-0.514432best projected	0	6.0e-6	projected	LR-DMC (AGP)	Motta et al. (2017)	2017
-0.514418tied with best projected at 2σ	1.4e-5	7.0e-6	projected	LR-DMC (LDA determinant)	Motta et al. (2017)	2017
-0.5153best extrapolated	0	1.5e-4	extrapolated	MRCI+Q	Motta et al. (2017)	2017
-0.5151tied with best extrapolated at 2σ	2.3e-4	1.2e-4	extrapolated	MRCI-F12+Q	Motta et al. (2017)	2017
-0.5149tied with best extrapolated at 2σ	4.0e-4	1.4e-4	extrapolated	ph-AFQMC	Motta et al. (2017)	2017
-0.5143	9.7e-4	1.9e-4	extrapolated	RCCSD	Motta et al. (2017)	2017
-0.5143	9.7e-4	1.9e-4	extrapolated	UCCSD	Motta et al. (2017)	2017
-0.5140	1.3e-3	1.5e-4	extrapolated	SBDMRG	Motta et al. (2017)	2017
-0.4884	2.7e-2	5.0e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.4884	2.7e-2	5.4e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.5149best approximate	0	1.9e-4	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5149tied with best approximate at 2σ	<1e-4	1.9e-4	approximate	UCCSD(T)	Motta et al. (2017)	2017

exact

-0.4766378

FCI

best variational

-0.4766378

DMRG

best projected

-0.476638

CCSDT

best approximate

-0.4766261

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.4766378exact	0	n/a	exact	FCI	Motta et al. (2017)		2017
-0.4766378best variational	0	n/a	variational	DMRG	Motta et al. (2017)		2017
-0.4766378	<1e-7	n/a	variational	MRCI	Motta et al. (2017)		2017
-0.4678060	8.8e-3	n/a	variational	HF	Motta et al. (2017)		2017
-0.4678050	8.8e-3	n/a	variational	HF	Motta et al. (2017)		2017
-0.476638best projected	0	n/a	projected	CCSDT	Low et al. (2019)		2019
-0.476638tied with best projected at 2σ	<1e-6	n/a	projected	CCSDTQ	Low et al. (2019)		2019
-0.476638tied with best projected at 2σ	<1e-6	n/a	projected	MkMRCCSD	Low et al. (2019)		2019
-0.476638	<1e-6	n/a	projected	MRCI+Q	Motta et al. (2017)		2017
-0.476610	2.8e-5	1.0e-5	projected	ph-AFQMC (UHF)	Rofougaran et al. (2026)	rr637/QC-AFQMC	2026
-0.476561	7.7e-5	n/a	projected	RCCSD	Motta et al. (2017)		2017
-0.476561	7.7e-5	n/a	projected	UCCSD	Motta et al. (2017)		2017
-0.476192	4.5e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.476092	5.5e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.475868	7.7e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.475497	1.1e-3	n/a	projected	DMET	Motta et al. (2017)		2017
-0.4768700	−2.4e-4	n/a	approximate below exact by > 2σ	GW	Motta et al. (2017)		2017
-0.4766580	−3.2e-5	n/a	approximate below exact by > 2σ	MkMRCCSD(T)	Low et al. (2019)		2019
-0.4766261best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)		2017
-0.4766261tied with best approximate at 2σ	<1e-7	n/a	approximate	UCCSD(T)	Motta et al. (2017)		2017
-0.4746056	2.0e-3	n/a	approximate	GF2	Motta et al. (2017)		2017
-0.4745706	2.1e-3	n/a	approximate	GF2	Motta et al. (2017)		2017

best variational

-0.5228716

best projected

-0.54871(9)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5228716best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5228716	<1e-7	n/a	variational	HF	Motta et al. (2017)	2017
-0.54871best projected	0	9.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017

best variational

-0.54087

DMRG

best projected

-0.5411661

DMET

best approximate

-0.54465

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.54087best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.54048	3.9e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.51891	2.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.51891	2.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5411661best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5409660	2.0e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5409000	2.7e-4	6.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5403613	8.0e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5403613	8.0e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5393183	1.8e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5392512	1.9e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.54465best approximate	0	n/a	approximate	GW	Motta et al. (2017)	2017
-0.54078	3.9e-3	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.54078	3.9e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.53778	6.9e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.53757	7.1e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.53680	7.9e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.547832

MRCI

best projected

-0.54855(5)

ph-AFQMC

best approximate

-0.5483736

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.547832best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.522781	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.522781	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.54855best projected	0	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.54855tied with best projected at 2σ	<1e-5	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.54843	1.2e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.54778	7.7e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.54778	7.7e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5483736best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5483735	1.0e-7	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5453255	3.0e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5450848	3.3e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.54769

DMRG

best projected

-0.5477564

MRCI+Q

best approximate

-0.547569

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.54769best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.54707	6.2e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.52250	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.52250	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5477564best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5477400tied with best projected at 2σ	1.6e-5	9.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5470072	7.5e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5470072	7.5e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5467297	1.0e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.547569best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.547569tied with best approximate at 2σ	<1e-6	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.544374	3.2e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.544140	3.4e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.548046(7)

VMC (JAGP)

best projected

-0.548748(7)

LR-DMC (LDA determinant)

best extrapolated

-0.5493(2)

MRCI+Q

best approximate

-0.5491(1)

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.548046best variational	0	7.0e-6	variational	VMC (JAGP)	Motta et al. (2017)	2017
-0.547650	4.0e-4	8.0e-6	variational	VMC (SJ)	Motta et al. (2017)	2017
-0.548748best projected	0	7.0e-6	projected	LR-DMC (LDA determinant)	Motta et al. (2017)	2017
-0.548742tied with best projected at 2σ	6.0e-6	6.0e-6	projected	LR-DMC (AGP)	Motta et al. (2017)	2017
-0.5493best extrapolated	0	1.5e-4	extrapolated	MRCI+Q	Motta et al. (2017)	2017
-0.5492tied with best extrapolated at 2σ	<1e-4	1.2e-4	extrapolated	MRCI-F12+Q	Motta et al. (2017)	2017
-0.5491tied with best extrapolated at 2σ	1.2e-4	1.1e-4	extrapolated	ph-AFQMC	Motta et al. (2017)	2017
-0.5491tied with best extrapolated at 2σ	2.1e-4	2.8e-4	extrapolated	DMET	Motta et al. (2017)	2017
-0.5486	6.6e-4	1.5e-4	extrapolated	SBDMRG	Motta et al. (2017)	2017
-0.5485	8.0e-4	1.4e-4	extrapolated	RCCSD	Motta et al. (2017)	2017
-0.5485	8.0e-4	1.4e-4	extrapolated	UCCSD	Motta et al. (2017)	2017
-0.5228	2.6e-2	3.5e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.5228	2.6e-2	4.0e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.5491best approximate	0	1.4e-4	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5491tied with best approximate at 2σ	<1e-4	1.4e-4	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5459	3.1e-3	3.0e-5	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5457	3.4e-3	3.0e-5	approximate	SC-NEVPT2	Motta et al. (2017)	2017

exact

-0.5205094

FCI

best variational

-0.5205094

MRCI

best projected

-0.52051(5)

ph-AFQMC

best approximate

-0.520492

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5205094exact	0	n/a	exact	FCI	Motta et al. (2017)	2017
-0.5205094best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.5205094	<1e-7	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5098620	1.1e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5098620	1.1e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.52052	−<1e-5	n/a	projected below exact by > 2σ	CCSDT	Low et al. (2019)	2019
-0.52051best projected	0	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.52051tied with best projected at 2σ	<1e-5	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.52051tied with best projected at 2σ	<1e-5	n/a	projected	CCSDTQ	Low et al. (2019)	2019
-0.52051tied with best projected at 2σ	<1e-5	n/a	projected	MkMRCCSD	Low et al. (2019)	2019
-0.52040	1.1e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.52040	1.1e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.52001	5.0e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.51995	5.6e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.51961	9.0e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.51931	1.2e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.520559	−6.7e-5	n/a	approximate below exact by > 2σ	MkMRCCSD(T)	Low et al. (2019)	2019
-0.520492best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.520492tied with best approximate at 2σ	<1e-6	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.520234	2.6e-4	n/a	approximate	GW	Motta et al. (2017)	2017
-0.517668	2.8e-3	n/a	approximate	GF2	Motta et al. (2017)	2017
-0.517623	2.9e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

exact

-0.522856

FCI

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.522856exact	0	n/a	exact	FCI	Stair & Evangelista (2020)		2020

best variational

-0.528221

VQE

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.528221best variational	0	n/a	variational	VQE	Li et al. (2023)	tencent-quantum-lab/TenCirChem	2023

best variational

-0.5368359

best projected

-0.5629322

MRCI+Q

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5368359best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5368359	<1e-7	n/a	variational	HF	Motta et al. (2017)	2017
-0.5629322best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5628100tied with best projected at 2σ	1.2e-4	8.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017

best variational

-0.55702

DMRG

best projected

-0.5573602

DMET

best approximate

-0.56045

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.55702best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.55666	3.6e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.53447	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53447	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5573602best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5571400	2.2e-4	8.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5571100	2.5e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5564384	9.2e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5564384	9.2e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5557397	1.6e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5554566	1.9e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.56045best approximate	0	n/a	approximate	GW	Motta et al. (2017)	2017
-0.55691	3.5e-3	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.55691	3.5e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.55417	6.3e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.55400	6.5e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.55255	7.9e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.5620252

MRCI

best projected

-0.5627104

MRCI+Q

best approximate

-0.562514

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5620252best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.5367633	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5367633	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5627104best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5627000tied with best projected at 2σ	1.0e-5	9.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5621559	5.5e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5618674	8.4e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5618674	8.4e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.562514best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.562514tied with best approximate at 2σ	<1e-6	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.559613	2.9e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.559414	3.1e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.56191

DMRG

best projected

-0.5620(1)

ph-AFQMC

best approximate

-0.5617783

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.56191best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.56133	5.8e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.53655	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53655	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5620best projected	0	1.1e-4	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5620tied with best projected at 2σ	<1e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5612	8.4e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5612	8.4e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5607	1.3e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5617783best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5617783tied with best approximate at 2σ	<1e-7	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5587636	3.0e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5585702	3.2e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.562237(5)

VMC (JAGP)

best projected

-0.562900(7)

LR-DMC (LDA determinant)

best extrapolated

-0.56325(8)

MRCI+Q

best approximate

-0.56311(9)

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.562237best variational	0	5.0e-6	variational	VMC (JAGP)	Motta et al. (2017)	2017
-0.561823	4.1e-4	7.0e-6	variational	VMC (SJ)	Motta et al. (2017)	2017
-0.562900best projected	0	7.0e-6	projected	LR-DMC (LDA determinant)	Motta et al. (2017)	2017
-0.562878tied with best projected at 2σ	2.2e-5	6.0e-6	projected	LR-DMC (AGP)	Motta et al. (2017)	2017
-0.56325best extrapolated	0	8.0e-5	extrapolated	MRCI+Q	Motta et al. (2017)	2017
-0.56321tied with best extrapolated at 2σ	3.6e-5	7.0e-5	extrapolated	MRCI-F12+Q	Motta et al. (2017)	2017
-0.56315tied with best extrapolated at 2σ	9.6e-5	1.2e-4	extrapolated	ph-AFQMC	Motta et al. (2017)	2017
-0.56311tied with best extrapolated at 2σ	1.3e-4	1.4e-4	extrapolated	SBDMRG	Motta et al. (2017)	2017
-0.56258tied with best extrapolated at 2σ	6.7e-4	3.0e-4	extrapolated	DMET	Motta et al. (2017)	2017
-0.53682	2.6e-2	2.6e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.53682	2.6e-2	3.0e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.56311best approximate	0	9.0e-5	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.56311tied with best approximate at 2σ	<1e-5	9.0e-5	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.56011	3.0e-3	1.0e-5	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.55991	3.2e-3	1.0e-5	approximate	SC-NEVPT2	Motta et al. (2017)	2017

exact

-0.5384361

FCI

best variational

-0.5384361

MRCI

best projected

-0.5384361

MRCI+Q

best approximate

-0.5384141

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.5384361exact	0	n/a	exact	FCI	Motta et al. (2017)		2017
-0.5384361best variational	0	n/a	variational	MRCI	Motta et al. (2017)		2017
-0.5384361	<1e-7	n/a	variational	DMRG	Motta et al. (2017)		2017
-0.5256280	1.3e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.5256280	1.3e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.5384560	−2.0e-5	n/a	projected below exact by > 2σ	CCSDT	Low et al. (2019)		2019
-0.5384460	−9.9e-6	n/a	projected below exact by > 2σ	MkMRCCSD	Low et al. (2019)		2019
-0.5384361best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)		2017
-0.5384360	1.1e-7	n/a	projected	CCSDTQ	Low et al. (2019)		2019
-0.5383603tied with best projected at 2σ	7.6e-5	5.6e-5	projected	ph-AFQMC (UHF)	Luo et al. (2026)		2026
-0.5382921	1.4e-4	n/a	projected	RCCSD	Motta et al. (2017)		2017
-0.5382921	1.4e-4	n/a	projected	UCCSD	Motta et al. (2017)		2017
-0.5382145tied with best projected at 2σ	2.2e-4	1.4e-4	projected	ph-AFQMC (UHF)	Luo et al. (2026)		2026
-0.5381900	2.5e-4	6.0e-5	projected	ph-AFQMC	Motta et al. (2017)		2017
-0.5381800	2.6e-4	3.0e-5	projected	ph-AFQMC (UHF)	Rofougaran et al. (2026)	rr637/QC-AFQMC	2026
-0.5381591tied with best projected at 2σ	2.8e-4	1.6e-4	projected	ph-AFQMC (UHF)	Luo et al. (2026)		2026
-0.5379327	5.0e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.5378685	5.7e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.5374261	1.0e-3	n/a	projected	SEET	Motta et al. (2017)		2017
-0.5371701	1.3e-3	n/a	projected	DMET	Motta et al. (2017)		2017
-0.5385160	−1.0e-4	n/a	approximate below exact by > 2σ	MkMRCCSD(T)	Low et al. (2019)		2019
-0.5384141best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)		2017
-0.5384141tied with best approximate at 2σ	<1e-7	n/a	approximate	UCCSD(T)	Motta et al. (2017)		2017
-0.5374030	1.0e-3	n/a	approximate	GW	Motta et al. (2017)		2017
-0.5344885	3.9e-3	n/a	approximate	GF2	Motta et al. (2017)		2017
-0.5344875	3.9e-3	n/a	approximate	GF2	Motta et al. (2017)		2017

best variational

-0.5401556

best projected

-0.566277

MRCI+Q

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5401556best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5397456	4.1e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.566277best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.566180tied with best projected at 2σ	9.7e-5	9.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017

best variational

-0.56141

DMRG

best projected

-0.5618118

DMET

best approximate

-0.564291

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.56141best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.56108	3.3e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.53862	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53823	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5618118best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5614860	3.3e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5614500	3.6e-4	6.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5607528	1.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5604443	1.4e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5604216	1.4e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5601336	1.7e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5596605	2.2e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.564291best approximate	0	n/a	approximate	GW	Motta et al. (2017)	2017
-0.561287	3.0e-3	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.561152	3.1e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.558792	5.5e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.558654	5.6e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.556461	7.8e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.5654171

MRCI

best projected

-0.5660681

MRCI+Q

best approximate

-0.5658519

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5654171best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.5400909	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5396808	2.6e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5660681best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5660100tied with best projected at 2σ	5.8e-5	8.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5652851	7.8e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5651432	9.2e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5648225	1.2e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5658519best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5657061	1.5e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5630795	2.8e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5629156	2.9e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.56523

DMRG

best projected

-0.5653303

MRCI+Q

best approximate

-0.5651061

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.56523best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.56472	5.1e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.53990	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53949	2.6e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5653303best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5651500	1.8e-4	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5644356	8.9e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5641258	1.2e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5641162	1.2e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5634269	1.9e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5651061best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5649612	1.4e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5622596	2.8e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5620999	3.0e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.5606055	4.5e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.565634(5)

VMC (JAGP)

best projected

-0.566255(7)

LR-DMC (LDA determinant)

best extrapolated

-0.5667(1)

SBDMRG

best approximate

-0.56638(4)

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.565634best variational	0	5.0e-6	variational	VMC (JAGP)	Motta et al. (2017)	2017
-0.565201	4.3e-4	6.0e-6	variational	VMC (SJ)	Motta et al. (2017)	2017
-0.556850	8.8e-3	n/a	variational	VMC (DeepWF)	Han et al. (2019)	2019
-0.566255best projected	0	7.0e-6	projected	LR-DMC (LDA determinant)	Motta et al. (2017)	2017
-0.566234tied with best projected at 2σ	2.1e-5	6.0e-6	projected	LR-DMC (AGP)	Motta et al. (2017)	2017
-0.5667best extrapolated	0	1.4e-4	extrapolated	SBDMRG	Motta et al. (2017)	2017
-0.5666tied with best extrapolated at 2σ	1.0e-4	5.0e-5	extrapolated	MRCI+Q	Motta et al. (2017)	2017
-0.5665tied with best extrapolated at 2σ	1.2e-4	5.0e-5	extrapolated	MRCI-F12+Q	Motta et al. (2017)	2017
-0.5664tied with best extrapolated at 2σ	2.2e-4	4.0e-5	extrapolated	ph-AFQMC	Motta et al. (2017)	2017
-0.5657	9.9e-4	2.2e-4	extrapolated	DMET	Motta et al. (2017)	2017
-0.5656	1.0e-3	4.0e-5	extrapolated	RCCSD	Motta et al. (2017)	2017
-0.5653	1.3e-3	4.0e-5	extrapolated	UCCSD	Motta et al. (2017)	2017
-0.5402	2.7e-2	2.0e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.5397	2.7e-2	1.9e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.56638best approximate	0	4.0e-5	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.56623tied with best approximate at 2σ	1.5e-4	4.0e-5	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.56350	2.9e-3	5.0e-5	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.56333	3.0e-3	6.0e-5	approximate	SC-NEVPT2	Motta et al. (2017)	2017

exact

-0.5424385

FCI

best variational

-0.5424385

MRCI

best projected

-0.542439

CCSDTQ

best approximate

-0.542419

CCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.5424385exact	0	n/a	exact	FCI	Motta et al. (2017)		2017
-0.5424385	0	n/a	exact	FCI	Li et al. (2023)		2023
-0.5424385best variational	0	n/a	variational	MRCI	Motta et al. (2017)		2017
-0.5424385	<1e-7	n/a	variational	DMRG	Motta et al. (2017)		2017
-0.5424350	3.5e-6	n/a	variational	VMC (RBM)	Li et al. (2023)		2023
-0.5418790	5.6e-4	n/a	variational	VMC (RBM)	Li et al. (2023)		2023
-0.5277450	1.5e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.5270140	1.5e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.542489	−5.0e-5	n/a	projected below exact by > 2σ	CCSDT	Low et al. (2019)		2019
-0.542469	−3.0e-5	n/a	projected below exact by > 2σ	MkMRCCSD	Low et al. (2019)		2019
-0.542439best projected	0	n/a	projected	CCSDTQ	Low et al. (2019)		2019
-0.542439	<1e-6	n/a	projected	MRCI+Q	Motta et al. (2017)		2017
-0.542255	1.8e-4	n/a	projected	RCCSD	Motta et al. (2017)		2017
-0.542190	2.5e-4	3.0e-5	projected	ph-AFQMC (UHF)	Rofougaran et al. (2026)	rr637/QC-AFQMC	2026
-0.542180	2.6e-4	6.0e-5	projected	ph-AFQMC	Motta et al. (2017)		2017
-0.541865	5.7e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.541845	5.9e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.541742	7.0e-4	n/a	projected	UCCSD	Motta et al. (2017)		2017
-0.541303	1.1e-3	n/a	projected	SEET	Motta et al. (2017)		2017
-0.541098	1.3e-3	n/a	projected	DMET	Motta et al. (2017)		2017
-0.542579	−1.6e-4	n/a	approximate below exact by > 2σ	MkMRCCSD(T)	Low et al. (2019)		2019
-0.542419best approximate	0	n/a	approximate	CCSD(T)	Li et al. (2023)		2023
-0.542419	<1e-6	n/a	approximate	RCCSD(T)	Motta et al. (2017)		2017
-0.542175	2.4e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)		2017
-0.540312	2.1e-3	n/a	approximate	GW	Motta et al. (2017)		2017
-0.537112	5.3e-3	n/a	approximate	GF2	Motta et al. (2017)		2017
-0.537103	5.3e-3	n/a	approximate	GF2	Motta et al. (2017)		2017

exact

-0.5415393

FCI

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5415393exact	0	n/a	exact	FCI	Stair & Evangelista (2020)		2020

best variational

-0.538217

best projected

-0.5638526

MRCI+Q

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.538217best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.536626	1.6e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.5638526best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5638000tied with best projected at 2σ	5.3e-5	1.0e-4	projected	ph-AFQMC	Motta et al. (2017)	2017

best variational

-0.55949

DMRG

best projected

-0.5599357

DMET

best approximate

-0.561647

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.55949best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.55919	3.0e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.53710	2.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53554	2.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5599357best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5595520	3.8e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5594200	5.2e-4	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5588340	1.1e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5587647	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5586928	1.2e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5585398	1.4e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5580494	1.9e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.561647best approximate	0	n/a	approximate	GW	Motta et al. (2017)	2017
-0.559357	2.3e-3	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.558875	2.8e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.557106	4.5e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.556997	4.6e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.553958	7.7e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.563033

MRCI

best projected

-0.5636456

MRCI+Q

best approximate

-0.5634155

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.563033best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.538159	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.536568	2.6e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5636456best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5633700	2.8e-4	8.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5628062	8.4e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5626386	1.0e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5619247	1.7e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5634155best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5629196	5.0e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5607629	2.7e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5606262	2.8e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.56282

DMRG

best projected

-0.5628926

MRCI+Q

best approximate

-0.562658

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.56282best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.56233	4.9e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.53799	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53640	2.6e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5628926best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5627500	1.4e-4	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5619244	9.7e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5618635	1.0e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5613170	1.6e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5612099	1.7e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.562658best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.562164	4.9e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.559971	2.7e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.559839	2.8e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.557571	5.1e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.563249(4)

VMC (JAGP)

best projected

-0.563852(7)

LR-DMC (LDA determinant)

best extrapolated

-0.5643(1)

SBDMRG

best approximate

-0.56391(1)

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.563249best variational	0	4.0e-6	variational	VMC (JAGP)	Motta et al. (2017)	2017
-0.562776	4.7e-4	6.0e-6	variational	VMC (SJ)	Motta et al. (2017)	2017
-0.563852best projected	0	7.0e-6	projected	LR-DMC (LDA determinant)	Motta et al. (2017)	2017
-0.563831tied with best projected at 2σ	2.1e-5	5.0e-6	projected	LR-DMC (AGP)	Motta et al. (2017)	2017
-0.5643best extrapolated	0	1.4e-4	extrapolated	SBDMRG	Motta et al. (2017)	2017
-0.5641tied with best extrapolated at 2σ	1.7e-4	3.0e-5	extrapolated	MRCI+Q	Motta et al. (2017)	2017
-0.5641tied with best extrapolated at 2σ	1.9e-4	3.0e-5	extrapolated	MRCI-F12+Q	Motta et al. (2017)	2017
-0.5640tied with best extrapolated at 2σ	3.3e-4	6.0e-5	extrapolated	ph-AFQMC	Motta et al. (2017)	2017
-0.5632	1.1e-3	1.2e-4	extrapolated	DMET	Motta et al. (2017)	2017
-0.5631	1.2e-3	1.0e-5	extrapolated	RCCSD	Motta et al. (2017)	2017
-0.5624	1.9e-3	1.0e-5	extrapolated	UCCSD	Motta et al. (2017)	2017
-0.5382	2.6e-2	2.0e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.5366	2.8e-2	1.3e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.56391best approximate	0	1.0e-5	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.56341	5.0e-4	1.0e-5	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.56114	2.8e-3	7.0e-5	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.56100	2.9e-3	8.0e-5	approximate	SC-NEVPT2	Motta et al. (2017)	2017

exact

-0.5389626

FCI

best variational

-0.5389626

DMRG

best projected

-0.538963

CCSDTQ

best approximate

-0.5380497

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.5389626exact	0	n/a	exact	FCI	Motta et al. (2017)		2017
-0.5389626best variational	0	n/a	variational	DMRG	Motta et al. (2017)		2017
-0.5389626	<1e-7	n/a	variational	MRCI	Motta et al. (2017)		2017
-0.5231370	1.6e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.5203470	1.9e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.539073	−1.1e-4	n/a	projected below exact by > 2σ	CCSDT	Low et al. (2019)		2019
-0.539003	−4.0e-5	n/a	projected below exact by > 2σ	MkMRCCSD	Low et al. (2019)		2019
-0.538963best projected	0	n/a	projected	CCSDTQ	Low et al. (2019)		2019
-0.538963	<1e-6	n/a	projected	MRCI+Q	Motta et al. (2017)		2017
-0.538780	1.8e-4	2.0e-5	projected	ph-AFQMC (UHF)	Rofougaran et al. (2026)	rr637/QC-AFQMC	2026
-0.538746	2.2e-4	n/a	projected	RCCSD	Motta et al. (2017)		2017
-0.538740	2.2e-4	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)		2017
-0.538340	6.2e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.538338	6.3e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.537695	1.3e-3	n/a	projected	SEET	Motta et al. (2017)		2017
-0.537528	1.4e-3	n/a	projected	DMET	Motta et al. (2017)		2017
-0.537504	1.5e-3	n/a	projected	UCCSD	Motta et al. (2017)		2017
-0.5391830	−1.1e-3	n/a	approximate below exact by > 2σ	MkMRCCSD(T)	Low et al. (2019)		2019
-0.5389665	−9.2e-4	n/a	approximate below exact by > 2σ	RCCSD(T)	Motta et al. (2017)		2017
-0.5380497best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)		2017
-0.5353040	2.7e-3	n/a	approximate	GW	Motta et al. (2017)		2017
-0.5318520	6.2e-3	n/a	approximate	GF2	Motta et al. (2017)		2017
-0.5318520	6.2e-3	n/a	approximate	GF2	Motta et al. (2017)		2017

best variational

-0.5281156

best projected

-0.5516514

MRCI+Q

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5281156best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5222041	5.9e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.5516514best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5513700	2.8e-4	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017

best variational

-0.54761

DMRG

best projected

-0.5480704

DMET

best approximate

-0.547728

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.54761best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.54740	2.1e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.52729	2.0e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.52139	2.6e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5480704best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5477509	3.2e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5476610	4.1e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5475900	4.8e-4	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5469889	1.1e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5468315	1.2e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5468112	1.3e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5455444	2.5e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.547728best approximate	0	n/a	approximate	GW	Motta et al. (2017)	2017
-0.547527	2.0e-4	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.546224	1.5e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.545729	2.0e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.545665	2.1e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.540400	7.3e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.5509118

MRCI

best projected

-0.5514268

MRCI+Q

best approximate

-0.5512171

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5509118best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.5280685	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5221563	2.9e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5514268best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5512400	1.9e-4	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5507672	6.6e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5502820	1.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5490856	2.3e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5512171best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5499180	1.3e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5487978	2.4e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5487054	2.5e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.55059

DMRG

best projected

-0.5506631

MRCI+Q

best approximate

-0.550459

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.55059best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.55020	3.9e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.52792	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.52200	2.9e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5506631best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5504800	1.8e-4	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5500024	6.6e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5495783	1.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5495443	1.1e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5483683	2.3e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.550459best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.549162	1.3e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.548075	2.4e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.547987	2.5e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.543697	6.8e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.551106(4)

VMC (JAGP)

best projected

-0.551699(8)

LR-DMC (LDA determinant)

best extrapolated

-0.5520(1)

SBDMRG

best approximate

-0.55167(3)

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.551106best variational	0	4.0e-6	variational	VMC (JAGP)	Motta et al. (2017)	2017
-0.550575	5.3e-4	5.0e-6	variational	VMC (SJ)	Motta et al. (2017)	2017
-0.551699best projected	0	8.0e-6	projected	LR-DMC (LDA determinant)	Motta et al. (2017)	2017
-0.551679tied with best projected at 2σ	2.0e-5	6.0e-6	projected	LR-DMC (AGP)	Motta et al. (2017)	2017
-0.5520best extrapolated	0	1.4e-4	extrapolated	SBDMRG	Motta et al. (2017)	2017
-0.5519tied with best extrapolated at 2σ	<1e-4	1.0e-5	extrapolated	MRCI+Q	Motta et al. (2017)	2017
-0.5519tied with best extrapolated at 2σ	<1e-4	1.0e-5	extrapolated	MRCI-F12+Q	Motta et al. (2017)	2017
-0.5516tied with best extrapolated at 2σ	3.3e-4	4.0e-5	extrapolated	ph-AFQMC	Motta et al. (2017)	2017
-0.5512	7.3e-4	2.0e-5	extrapolated	DMET	Motta et al. (2017)	2017
-0.5507	1.3e-3	2.0e-5	extrapolated	RCCSD	Motta et al. (2017)	2017
-0.5495	2.4e-3	2.0e-5	extrapolated	UCCSD	Motta et al. (2017)	2017
-0.5281	2.4e-2	6.0e-6	extrapolated	HF	Motta et al. (2017)	2017
-0.5222	3.0e-2	4.6e-6	extrapolated	HF	Motta et al. (2017)	2017
-0.55167best approximate	0	3.0e-5	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.55038	1.3e-3	2.0e-5	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.54912	2.6e-3	8.0e-5	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.54902	2.6e-3	9.0e-5	approximate	SC-NEVPT2	Motta et al. (2017)	2017

exact

-0.5227936

FCI

best variational

-0.5227936

MRCI

best projected

-0.522794

CCSDTQ

best approximate

-0.5207534

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.5227936exact	0	n/a	exact	FCI	Motta et al. (2017)		2017
-0.5227936best variational	0	n/a	variational	MRCI	Motta et al. (2017)		2017
-0.5227936	<1e-7	n/a	variational	DMRG	Motta et al. (2017)		2017
-0.5065710	1.6e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.4956060	2.7e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.523354	−5.6e-4	n/a	projected below exact by > 2σ	CCSDT	Low et al. (2019)		2019
-0.522794best projected	0	n/a	projected	CCSDTQ	Low et al. (2019)		2019
-0.522794	<1e-6	n/a	projected	MRCI+Q	Motta et al. (2017)		2017
-0.522764	3.0e-5	n/a	projected	MkMRCCSD	Low et al. (2019)		2019
-0.522710tied with best projected at 2σ	8.4e-5	8.0e-5	projected	ph-AFQMC	Motta et al. (2017)		2017
-0.522682	1.1e-4	n/a	projected	RCCSD	Motta et al. (2017)		2017
-0.522680	1.1e-4	2.0e-5	projected	ph-AFQMC (UHF)	Rofougaran et al. (2026)	rr637/QC-AFQMC	2026
-0.522155	6.4e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.522152	6.4e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.521279	1.5e-3	n/a	projected	SEET	Motta et al. (2017)		2017
-0.521126	1.7e-3	n/a	projected	DMET	Motta et al. (2017)		2017
-0.520417	2.4e-3	n/a	projected	UCCSD	Motta et al. (2017)		2017
-0.5231940	−2.4e-3	n/a	approximate below exact by > 2σ	MkMRCCSD(T)	Low et al. (2019)		2019
-0.5230888	−2.3e-3	n/a	approximate below exact by > 2σ	RCCSD(T)	Motta et al. (2017)		2017
-0.5207534best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)		2017
-0.5143360	6.4e-3	n/a	approximate	GW	Motta et al. (2017)		2017
-0.5120572	8.7e-3	n/a	approximate	GF2	Motta et al. (2017)		2017
-0.5105671	1.0e-2	n/a	approximate	GF2	Motta et al. (2017)		2017

best variational

-0.5174129

best projected

-0.53749(7)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5174129best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5044002	1.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53749best projected	0	7.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.53735	1.4e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017

best variational

-0.53344

DMRG

best projected

-0.5347972

SEET

best approximate

-0.5336142

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.53344best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.53332	1.2e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.51662	1.7e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.50349	3.0e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5347972best projected	0	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5338255	9.7e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5336000	1.2e-3	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5334700	1.3e-3	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5330231	1.8e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5329202	1.9e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5327302	2.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5313860	3.4e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5336142best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5320835	1.5e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5320488	1.6e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.5318261	1.8e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5304310	3.2e-3	n/a	approximate	GW	Motta et al. (2017)	2017
-0.5235295	1.0e-2	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.5367131

MRCI

best projected

-0.5370991

MRCI+Q

best approximate

-0.5370925

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5367131best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.5173682	1.9e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5043512	3.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5370991best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5370700tied with best projected at 2σ	2.9e-5	6.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5367746	3.2e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5359424	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5347884	2.3e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5370925best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5353607	1.7e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5348351	2.3e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5347768	2.3e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.53626

DMRG

best projected

-0.53633(5)

ph-AFQMC

best approximate

-0.5363253

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.53626best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.53598	2.8e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.51722	1.9e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.50418	3.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53633best projected	0	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.53631tied with best projected at 2σ	2.2e-5	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.53599	3.4e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.53568	6.5e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.53524	1.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.53405	2.3e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5363253best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5345883	1.7e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5341603	2.2e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5341060	2.2e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.5268910	9.4e-3	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.536832(3)

VMC (JAGP)

best projected

-0.537424(9)

LR-DMC (LDA determinant)

best extrapolated

-0.5377(1)

SBDMRG

best approximate

-0.53749(6)

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.536832best variational	0	3.0e-6	variational	VMC (JAGP)	Motta et al. (2017)	2017
-0.536201	6.3e-4	5.0e-6	variational	VMC (SJ)	Motta et al. (2017)	2017
-0.537424best projected	0	9.0e-6	projected	LR-DMC (LDA determinant)	Motta et al. (2017)	2017
-0.537423tied with best projected at 2σ	1.0e-6	6.0e-6	projected	LR-DMC (AGP)	Motta et al. (2017)	2017
-0.5377best extrapolated	0	1.4e-4	extrapolated	SBDMRG	Motta et al. (2017)	2017
-0.5375tied with best extrapolated at 2σ	1.0e-4	8.0e-5	extrapolated	ph-AFQMC	Motta et al. (2017)	2017
-0.5375tied with best extrapolated at 2σ	1.0e-4	3.0e-5	extrapolated	MRCI+Q	Motta et al. (2017)	2017
-0.5375tied with best extrapolated at 2σ	1.2e-4	3.0e-5	extrapolated	MRCI-F12+Q	Motta et al. (2017)	2017
-0.5373	3.9e-4	2.0e-5	extrapolated	DMET	Motta et al. (2017)	2017
-0.5363	1.3e-3	5.0e-5	extrapolated	RCCSD	Motta et al. (2017)	2017
-0.5352	2.5e-3	5.0e-5	extrapolated	UCCSD	Motta et al. (2017)	2017
-0.5174	2.0e-2	5.0e-6	extrapolated	HF	Motta et al. (2017)	2017
-0.5044	3.3e-2	3.2e-6	extrapolated	HF	Motta et al. (2017)	2017
-0.53749best approximate	0	6.0e-5	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.53577	1.7e-3	6.0e-5	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.53511	2.4e-3	9.0e-5	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.53504	2.4e-3	9.0e-5	approximate	SC-NEVPT2	Motta et al. (2017)	2017

exact

-0.5050245

FCI

best variational

-0.5050245

MRCI

best projected

-0.50507(5)

ph-AFQMC

best approximate

-0.5029597

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.5050245exact	0	n/a	exact	FCI	Motta et al. (2017)		2017
-0.5050245best variational	0	n/a	variational	MRCI	Motta et al. (2017)		2017
-0.5050244	<1e-7	n/a	variational	DMRG	Motta et al. (2017)		2017
-0.4911830	1.4e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.4658430	3.9e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.50829	−3.2e-3	n/a	projected below exact by > 2σ	CCSDT	Low et al. (2019)		2019
-0.50673	−1.7e-3	n/a	projected below exact by > 2σ	RCCSD	Motta et al. (2017)		2017
-0.50507best projected	0	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)		2017
-0.50503tied with best projected at 2σ	4.0e-5	1.0e-5	projected	ph-AFQMC (UHF)	Rofougaran et al. (2026)	rr637/QC-AFQMC	2026
-0.50502tied with best projected at 2σ	4.6e-5	n/a	projected	MRCI+Q	Motta et al. (2017)		2017
-0.50496	1.1e-4	n/a	projected	CCSDTQ	Low et al. (2019)		2019
-0.50496	1.1e-4	n/a	projected	MkMRCCSD	Low et al. (2019)		2019
-0.50456	5.1e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.50447	6.0e-4	n/a	projected	SEET	Motta et al. (2017)		2017
-0.50347	1.6e-3	n/a	projected	SEET	Motta et al. (2017)		2017
-0.50322	1.8e-3	n/a	projected	DMET	Motta et al. (2017)		2017
-0.50282	2.2e-3	n/a	projected	UCCSD	Motta et al. (2017)		2017
-0.5074866	−4.5e-3	n/a	approximate below exact by > 2σ	RCCSD(T)	Motta et al. (2017)		2017
-0.5059140	−3.0e-3	n/a	approximate below exact by > 2σ	MkMRCCSD(T)	Low et al. (2019)		2019
-0.5029597best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)		2017
-0.4937480	9.2e-3	n/a	approximate	GF2	Motta et al. (2017)		2017
-0.4889550	1.4e-2	n/a	approximate	GW	Motta et al. (2017)		2017
-0.4853231	1.8e-2	n/a	approximate	GF2	Motta et al. (2017)		2017

exact

-0.5036293

FCI

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5036293exact	0	n/a	exact	FCI	Stair & Evangelista (2020)		2020

best variational

-0.5096605

best projected

-0.52525(5)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5096605best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4869346	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.52525best projected	0	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.52494tied with best projected at 2σ	3.1e-4	1.1e-4	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.52486	3.9e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017

best variational

-0.52125

DMRG

best projected

-0.5234726

SEET

best approximate

-0.5228438

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.52125best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.52120	5.2e-5	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.50887	1.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.48577	3.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5234726best projected	0	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5216200	1.9e-3	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5215843	1.9e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5215492	1.9e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5212700	2.2e-3	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.5212600	2.2e-3	4.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5209619	2.5e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5209611	2.5e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5196058	3.9e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5228438best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5203995	2.4e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5203828	2.5e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.5198517	3.0e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5137840	9.1e-3	n/a	approximate	GW	Motta et al. (2017)	2017
-0.5074118	1.5e-2	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.5243413

MRCI

best projected

-0.52488(5)

ph-AFQMC

best approximate

-0.5254869

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5243413best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.5096151	1.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4868722	3.7e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.52488best projected	0	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.52469	1.9e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.52459	2.9e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.52457	3.1e-4	7.1e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.52396	9.2e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.52270	2.2e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5254869best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5230540	2.4e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5228005	2.7e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5227671	2.7e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.52382

DMRG

best projected

-0.52417(5)

ph-AFQMC

best approximate

-0.5248344

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.52382best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.52362	2.0e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.50947	1.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.48666	3.7e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.52417best projected	0	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.52387	3.0e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.52384	3.3e-4	7.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.52382	3.5e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.52339	7.8e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.52335	8.2e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.52199	2.2e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5248344best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5223118	2.5e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5222037	2.6e-3	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5221737	2.7e-3	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.5109416	1.4e-2	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.524373(4)

VMC (JAGP)

best projected

-0.524987(7)

LR-DMC (AGP)

best extrapolated

-0.52512(6)

DMET

best approximate

-0.5257(1)

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.524373best variational	0	4.0e-6	variational	VMC (JAGP)	Motta et al. (2017)	2017
-0.523557	8.2e-4	5.0e-6	variational	VMC (SJ)	Motta et al. (2017)	2017
-0.524987best projected	0	7.0e-6	projected	LR-DMC (AGP)	Motta et al. (2017)	2017
-0.524974tied with best projected at 2σ	1.3e-5	9.0e-6	projected	LR-DMC (LDA determinant)	Motta et al. (2017)	2017
-0.52512best extrapolated	0	6.0e-5	extrapolated	DMET	Motta et al. (2017)	2017
-0.52511tied with best extrapolated at 2σ	<1e-5	1.4e-4	extrapolated	SBDMRG	Motta et al. (2017)	2017
-0.52500tied with best extrapolated at 2σ	1.2e-4	5.0e-5	extrapolated	MRCI-F12+Q	Motta et al. (2017)	2017
-0.52500tied with best extrapolated at 2σ	1.2e-4	7.0e-5	extrapolated	ph-AFQMC	Motta et al. (2017)	2017
-0.52499tied with best extrapolated at 2σ	1.2e-4	6.0e-5	extrapolated	MRCI+Q	Motta et al. (2017)	2017
-0.52419	9.3e-4	8.0e-5	extrapolated	RCCSD	Motta et al. (2017)	2017
-0.52303	2.1e-3	8.0e-5	extrapolated	UCCSD	Motta et al. (2017)	2017
-0.50967	1.5e-2	6.0e-6	extrapolated	HF	Motta et al. (2017)	2017
-0.48695	3.8e-2	5.3e-6	extrapolated	HF	Motta et al. (2017)	2017
-0.5257best approximate	0	1.0e-4	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5234	2.3e-3	8.0e-5	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5230	2.7e-3	9.0e-5	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5230	2.7e-3	9.0e-5	approximate	SC-NEVPT2	Motta et al. (2017)	2017

exact

-0.4910383

FCI

best variational

-0.4910383

MRCI

best projected

-0.4910383

MRCI+Q

best approximate

-0.4895218

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4910383exact	0	n/a	exact	FCI	Motta et al. (2017)	2017
-0.4910383best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.4910381	1.9e-7	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.4813230	9.7e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.4366790	5.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5900768	−9.9e-2	n/a	projected below exact by > 2σ	RCCSD	Motta et al. (2017)	2017
-0.5798380	−8.9e-2	n/a	projected below exact by > 2σ	CCSDT	Low et al. (2019)	2019
-0.4911680	−1.3e-4	n/a	projected below exact by > 2σ	MkMRCCSD	Low et al. (2019)	2019
-0.4911400	−1.0e-4	2.0e-5	projected below exact by > 2σ	ph-AFQMC	Motta et al. (2017)	2017
-0.4910383best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.4908866	1.5e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.4906880	3.5e-4	n/a	projected	CCSDTQ	Low et al. (2019)	2019
-0.4906784	3.6e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.4897206	1.3e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.4894827	1.6e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4894502	1.6e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5926833	−1.0e-1	n/a	approximate below exact by > 2σ	RCCSD(T)	Motta et al. (2017)	2017
-0.4929780	−3.5e-3	n/a	approximate below exact by > 2σ	MkMRCCSD(T)	Low et al. (2019)	2019
-0.4895218best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4821763	7.3e-3	n/a	approximate	GF2	Motta et al. (2017)	2017
-0.4646870	2.5e-2	n/a	approximate	GW	Motta et al. (2017)	2017
-0.4618865	2.8e-2	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.5050291

best projected

-0.51584(8)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5050291best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4710727	3.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.51584best projected	0	8.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.51568tied with best projected at 2σ	1.6e-4	1.4e-4	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.51543	4.1e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017

best variational

-0.51238

DMRG

best projected

-0.51287(3)

ph-AFQMC

best approximate

-0.5119131

PC-NEVPT2

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.51238best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.51237	1.1e-5	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.50426	8.1e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.46959	4.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.51287best projected	0	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.51260	2.7e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.51255	3.2e-4	5.2e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.51249	3.8e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.51240	4.7e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.51218	6.9e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.51126	1.6e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5119131best approximate	0	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5119057	7.5e-6	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.5113827	5.3e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4991910	1.3e-2	n/a	approximate	GW	Motta et al. (2017)	2017
-0.4935376	1.8e-2	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.5150225

MRCI

best projected

-0.51580(5)

ph-AFQMC

best approximate

-0.514026

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5150225best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.5049822	1.0e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4709806	4.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.51580best projected	0	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.51577tied with best projected at 2σ	3.4e-5	n/a	projected	DMET	Motta et al. (2017)	2017
-0.51544	3.6e-4	7.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.51515	6.5e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.51382	2.0e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.514026best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.513880	1.5e-4	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.513863	1.6e-4	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017

best variational

-0.51448

DMRG

best projected

-0.51507(3)

ph-AFQMC

best approximate

-0.513382

PC-NEVPT2

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.51448best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.51437	1.1e-4	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.50484	9.6e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.47070	4.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.51507best projected	0	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.51499	7.9e-5	n/a	projected	DMET	Motta et al. (2017)	2017
-0.51471	3.6e-4	4.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.51446	6.1e-4	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.51318	1.9e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.513382best approximate	0	n/a	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.513367	1.5e-5	n/a	approximate	SC-NEVPT2	Motta et al. (2017)	2017
-0.513367	1.5e-5	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.497207	1.6e-2	n/a	approximate	GF2	Motta et al. (2017)	2017

best variational

-0.514968(3)

VMC (JAGP)

best projected

-0.51558(1)

LR-DMC (LDA determinant)

best extrapolated

-0.51612(9)

DMET

best approximate

-0.5143(1)

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.514968best variational	0	3.0e-6	variational	VMC (JAGP)	Motta et al. (2017)	2017
-0.513869	1.1e-3	6.0e-6	variational	VMC (SJ)	Motta et al. (2017)	2017
-0.51558best projected	0	1.1e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)	2017
-0.51557tied with best projected at 2σ	1.1e-5	7.0e-6	projected	LR-DMC (AGP)	Motta et al. (2017)	2017
-0.51612best extrapolated	0	9.0e-5	extrapolated	DMET	Motta et al. (2017)	2017
-0.51569	4.3e-4	9.0e-5	extrapolated	ph-AFQMC	Motta et al. (2017)	2017
-0.51568tied with best extrapolated at 2σ	4.4e-4	1.4e-4	extrapolated	SBDMRG	Motta et al. (2017)	2017
-0.51554	5.8e-4	5.0e-5	extrapolated	MRCI-F12+Q	Motta et al. (2017)	2017
-0.51549	6.3e-4	8.0e-5	extrapolated	MRCI+Q	Motta et al. (2017)	2017
-0.51407	2.1e-3	1.0e-4	extrapolated	UCCSD	Motta et al. (2017)	2017
-0.50504	1.1e-2	7.0e-6	extrapolated	HF	Motta et al. (2017)	2017
-0.47109	4.5e-2	1.3e-5	extrapolated	HF	Motta et al. (2017)	2017
-0.5143best approximate	0	1.0e-4	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5141tied with best approximate at 2σ	2.3e-4	8.0e-5	approximate	PC-NEVPT2	Motta et al. (2017)	2017
-0.5140tied with best approximate at 2σ	2.4e-4	8.0e-5	approximate	SC-NEVPT2	Motta et al. (2017)	2017

exact

-0.4818701

FCI

best variational

-0.4818701

MRCI

best projected

-0.4818701

MRCI+Q

best approximate

-0.4809595

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4818701exact	0	n/a	exact	FCI	Motta et al. (2017)	2017
-0.4818701	0	n/a	exact	FCI	Li et al. (2023)	2023
-0.4818701best variational	0	n/a	variational	MRCI	Motta et al. (2017)	2017
-0.4818699	1.8e-7	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.4818690	1.1e-6	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.4785920	3.3e-3	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.4760350	5.8e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.4104930	7.1e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.6644594	−1.8e-1	n/a	projected below exact by > 2σ	RCCSD	Motta et al. (2017)	2017
-0.4866000	−4.7e-3	n/a	projected below exact by > 2σ	CCSDT	Low et al. (2019)	2019
-0.4862000	−4.3e-3	n/a	projected below exact by > 2σ	MkMRCCSD	Low et al. (2019)	2019
-0.4820000	−1.3e-4	2.0e-5	projected below exact by > 2σ	ph-AFQMC	Motta et al. (2017)	2017
-0.4819818	−1.1e-4	n/a	projected below exact by > 2σ	SEET	Motta et al. (2017)	2017
-0.4818701best projected	0	n/a	projected	MRCI+Q	Motta et al. (2017)	2017
-0.4816875	1.8e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.4814200	4.5e-4	n/a	projected	CCSDTQ	Low et al. (2019)	2019
-0.4809518	9.2e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4808925	9.8e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.4808186	1.1e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.6682346	−1.9e-1	n/a	approximate below exact by > 2σ	RCCSD(T)	Motta et al. (2017)	2017
-0.4967080	−1.6e-2	n/a	approximate below exact by > 2σ	CCSD(T)	Li et al. (2023)	2023
-0.4893000	−8.3e-3	n/a	approximate below exact by > 2σ	MkMRCCSD(T)	Low et al. (2019)	2019
-0.4809595best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4762711	4.7e-3	n/a	approximate	GF2	Motta et al. (2017)	2017
-0.4437050	3.7e-2	n/a	approximate	GW	Motta et al. (2017)	2017
-0.4425500	3.8e-2	n/a	approximate	GF2	Motta et al. (2017)	2017

exact

-0.4790989

FCI

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4790989exact	0	n/a	exact	FCI	Stair & Evangelista (2020)		2020

best variational

-0.5268575

VQE

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5268575best variational	0	n/a	variational	VQE	Li et al. (2023)	tencent-quantum-lab/TenCirChem	2023

exact

-0.5420192

FCI

best variational

-0.5420125

VMC (RBM)

best approximate

-0.5419892

CCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5420192exact	0	n/a	exact	FCI	Li et al. (2023)	2023
-0.5420125best variational	0	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.5409100	1.1e-3	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.5419892best approximate	0	n/a	approximate	CCSD(T)	Li et al. (2023)	2023

exact

-0.5377347

Huang et al. (2026)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5377347exact	0	n/a	exact	ED	Huang et al. (2026)		2026

exact

-0.4819042

FCI

best variational

-0.4819025

VMC (RBM)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4819042exact	0	n/a	exact	FCI	Li et al. (2023)	2023
-0.4819025best variational	0	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.4709842	1.1e-2	n/a	variational	VMC (RBM)	Li et al. (2023)	2023
-0.4989908	n/a	n/a	approximate below exact by > 2σ	CCSD(T)	Li et al. (2023)	2023

best variational

-0.525915

VQE

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.525915best variational	0	n/a	variational	VQE	Li et al. (2023)	tencent-quantum-lab/TenCirChem	2023

best variational

-0.5252269

VQE

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5252269best variational	0	n/a	variational	VQE	Li et al. (2023)	tencent-quantum-lab/TenCirChem	2023

best projected

-0.481978(1)

FCIQMC

Guther et al. (2020)

ghb24/NECI_STABLE

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.481978best projected	0	1.0e-6	projected	FCIQMC	Guther et al. (2020)	ghb24/NECI_STABLE	2020

best projected

-0.357541(9)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.357541best projected	0	9.1e-6	projected	ph-AFQMC	Motta et al. (2017)		2017

best projected

-0.51444(1)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.51444best projected	0	1.4e-5	projected	ph-AFQMC	Motta et al. (2017)		2017

best projected

-0.54115(2)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.54115best projected	0	1.8e-5	projected	ph-AFQMC	Motta et al. (2017)		2017

best projected

-0.50541(2)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50541best projected	0	2.3e-5	projected	ph-AFQMC	Motta et al. (2017)		2017

best variational

-0.3969058

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3969058best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.3958294	1.1e-3	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.3937633

DMRG

best projected

-0.39379(3)

ph-AFQMC

best approximate

-0.3936663

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.3937633best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.3716534	2.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.3711191	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.39379best projected	0	2.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.39307	7.2e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.39275	1.0e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.3936663best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.3933774	2.9e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.3948131

best projected

-0.42184(7)

ph-AFQMC

best approximate

-0.421883

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.3948131best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.3933991	1.4e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.42184best projected	0	7.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.42062	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.421883best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.3898388

best projected

-0.41760(3)

ph-AFQMC

best approximate

-0.41743

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.3898388best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.3892642	5.7e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.41760best projected	0	3.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.41660	1.0e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.41602	1.6e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.41743best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.42157(2)

VMC (SJ)

best projected

-0.42510(3)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.42157best variational	0	1.5e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.42510best projected	0	3.3e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.3518877

DMRG

best projected

-0.3528238

DMET

best approximate

-0.35206

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.3518877best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.3437885	8.1e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.3437885	8.1e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.3528238best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.3519200	9.0e-4	2.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.3517106	1.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.3517106	1.1e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.3512330	1.6e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.3497105	3.1e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.35206best approximate	0	n/a	approximate	GW	Motta et al. (2017)	2017
-0.35186	2.0e-4	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.35186	2.0e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.4739482

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4739482best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.4738362	1.1e-4	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.4891083

DMRG

best projected

-0.48927(3)

ph-AFQMC

best approximate

-0.489002

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4891083best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.4663163	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4662985	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.48927best projected	0	2.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.48841	8.6e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.48832	9.5e-4	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.48606	3.2e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.489002best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.488939	6.3e-5	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.4736828

best projected

-0.50143(5)

ph-AFQMC

best approximate

-0.5011587

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4736828best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4736257	5.7e-5	n/a	variational	HF	Motta et al. (2017)	2017
-0.50143best projected	0	5.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.50031	1.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5011587best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.4731441

best projected

-0.50030(3)

ph-AFQMC

best approximate

-0.4999623

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4731441best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4731052	3.9e-5	n/a	variational	HF	Motta et al. (2017)	2017
-0.50030best projected	0	2.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.49916	1.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.49907	1.2e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4999623best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.50020(1)

VMC (SJ)

best projected

-0.50177(2)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50020best variational	0	1.2e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.50177best projected	0	1.6e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.461805

DMRG

best projected

-0.4627503

DMET

best approximate

-0.4617621

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.461805best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.452303	9.5e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.452303	9.5e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.4627503best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4618400	9.1e-4	1.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.4615555	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.4615555	1.2e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4610035	1.7e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.4596374	3.1e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4617621best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.4617621tied with best approximate at 2σ	<1e-7	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4617233	3.9e-5	n/a	approximate	GW	Motta et al. (2017)	2017

best variational

-0.5155844

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5155844best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5153165	2.7e-4	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5344613

DMRG

best projected

-0.5354635

DMET

best approximate

-0.5343077

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5344613best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5113981	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5111476	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5354635best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5345433	9.2e-4	2.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5336360	1.8e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5334170	2.0e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5316955	3.8e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5343077best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5341497	1.6e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5154895

best projected

-0.54253(5)

ph-AFQMC

best approximate

-0.542323

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5154895best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5152228	2.7e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.54253best projected	0	5.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.54143	1.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.54140	1.1e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.542323best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5152041

best projected

-0.54186(3)

ph-AFQMC

best approximate

-0.5414947

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5152041best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5149397	2.6e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.54186best projected	0	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.54064	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.54043	1.4e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.53964	2.2e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5414947best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.54142(1)

VMC (SJ)

best projected

-0.54276(1)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.54142best variational	0	9.9e-6	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.54276best projected	0	1.4e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.5132063

DMRG

best projected

-0.5140977

DMET

best approximate

-0.5131409

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5132063best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5023686	1.1e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5020872	1.1e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5140977best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5131800	9.2e-4	1.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5128768	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5126303	1.5e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5123124	1.8e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5110453	3.1e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5131409best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5129869	1.5e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5127267	4.1e-4	n/a	approximate	GW	Motta et al. (2017)	2017

best variational

-0.5337486

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5337486best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5329271	8.2e-4	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5542583

DMRG

best projected

-0.55440(3)

ph-AFQMC

best approximate

-0.5540527

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5542583best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5312590	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5304660	2.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.55440best projected	0	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.55330	1.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.55295	1.4e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.55194	2.5e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5540527best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5537406	3.1e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5336765

best projected

-0.55999(7)

ph-AFQMC

best approximate

-0.5599073

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5336765best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5328553	8.2e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.55999best projected	0	7.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.55894	1.0e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.55864	1.4e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5599073best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5334553

best projected

-0.55942(3)

ph-AFQMC

best approximate

-0.559162

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5334553best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5326362	8.2e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.55942best projected	0	3.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.55824	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.55789	1.5e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.55711	2.3e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.559162best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.559065(9)

VMC (SJ)

best projected

-0.56038(1)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.559065best variational	0	9.3e-6	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.56038best projected	0	1.4e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.534978

DMRG

best projected

-0.5357627

DMET

best approximate

-0.534889

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.534978best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.522957	1.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.521928	1.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5357627best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5349500	8.1e-4	1.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5345609	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5340680	1.7e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5339711	1.8e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5328204	2.9e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.534889best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.534467	4.2e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.533873	1.0e-3	n/a	approximate	GW	Motta et al. (2017)	2017

best variational

-0.5394784

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5394784best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5377888	1.7e-3	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.560521

DMRG

best projected

-0.5616303

DMET

best approximate

-0.560279

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.560521best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.537893	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.536243	2.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5616303best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5605700	1.1e-3	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5594507	2.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5590185	2.6e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5586046	3.0e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5583058	3.3e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.560279best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.559817	4.6e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5394138

best projected

-0.56530(5)

ph-AFQMC

best approximate

-0.564994

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5394138best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5377247	1.7e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.56530best projected	0	5.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.56396	1.3e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.56360	1.7e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.564994best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5392194

best projected

-0.56451(3)

ph-AFQMC

best approximate

-0.564239

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5392194best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5375333	1.7e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.56451best projected	0	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.56325	1.3e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.56283	1.7e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.56238	2.1e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.564239best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.564180(9)

VMC (SJ)

best projected

-0.56550(1)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.564180best variational	0	8.9e-6	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.56550best projected	0	1.4e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.5409897

DMRG

best projected

-0.5416268

DMET

best approximate

-0.5408894

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5409897best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5278635	1.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5255659	1.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5416268best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5409833	6.4e-4	1.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5404839	1.1e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5398662	1.8e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5398010	1.8e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5388130	2.8e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5408894best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5402033	6.9e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5389333	2.0e-3	n/a	approximate	GW	Motta et al. (2017)	2017

best variational

-0.5386818

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5386818best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5357502	2.9e-3	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5595467

DMRG

best projected

-0.55961(2)

ph-AFQMC

best approximate

-0.55928

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5595467best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5375521	2.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5346660	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.55961best projected	0	2.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.55838	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.55793	1.7e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.55790	1.7e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.55790	1.7e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.55928best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.55868	6.0e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5386235

best projected

-0.56379(4)

ph-AFQMC

best approximate

-0.5634263

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5386235best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5356926	2.9e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.56379best projected	0	3.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.56232	1.5e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.56209	1.7e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5634263best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5384493

best projected

-0.56295(3)

ph-AFQMC

best approximate

-0.5626683

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5384493best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5355216	2.9e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.56295best projected	0	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.56160	1.3e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.56115	1.8e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.56111	1.8e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5626683best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.562636(9)

VMC (SJ)

best projected

-0.56403(1)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.562636best variational	0	9.3e-6	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.56403best projected	0	1.4e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.5385523

DMRG

best projected

-0.5390239

DMET

best approximate

-0.5384874

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5385523best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5244789	1.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5201690	1.8e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5390239best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5385467	4.8e-4	1.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5379790	1.0e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5373282	1.7e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5371188	1.9e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5363129	2.7e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5384874best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5375114	9.8e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5350933	3.4e-3	n/a	approximate	GW	Motta et al. (2017)	2017

best variational

-0.5292216

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5292216best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5222793	6.9e-3	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5482932

DMRG

best projected

-0.5493137

DMET

best approximate

-0.5480643

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5482932best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5284163	2.0e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5215079	2.7e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5493137best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5484233	8.9e-4	2.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5477207	1.6e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5470327	2.3e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5470300	2.3e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5464818	2.8e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5480643best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5471538	9.1e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5291749

best projected

-0.55215(4)

ph-AFQMC

best approximate

-0.5517193

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5291749best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5222337	6.9e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.55215best projected	0	3.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.55084	1.3e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.55045	1.7e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5517193best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.529024

best projected

-0.55142(2)

ph-AFQMC

best approximate

-0.5509443

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.529024best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.522083	6.9e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.55142best projected	0	2.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.55007	1.4e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.54974	1.7e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.54937	2.1e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5509443best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.550876(9)

VMC (SJ)

best projected

-0.55248(2)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.550876best variational	0	8.6e-6	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.55248best projected	0	1.7e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.5231183

DMRG

best projected

-0.523325

DMET

best approximate

-0.5239338

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5231183best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5083289	1.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4965191	2.7e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.523325best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.523130	2.0e-4	1.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.522999	3.3e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.521994	1.3e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.521316	2.0e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.520629	2.7e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5239338best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5216103	2.3e-3	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5150367	8.9e-3	n/a	approximate	GW	Motta et al. (2017)	2017

best variational

-0.5183556

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5183556best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5047565	1.4e-2	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5340762

DMRG

best projected

-0.5347214

SEET

best approximate

-0.5327924

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5340762best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5175791	1.6e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5039095	3.0e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5347214best projected	0	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5343367	3.8e-4	2.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5331455	1.6e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5323249	2.4e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5327924best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5183116

best projected

-0.53788(4)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5183116best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5047117	1.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53788best projected	0	4.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.53705	8.3e-4	n/a	projected	DMET	Motta et al. (2017)	2017

best variational

-0.5181643

best projected

-0.53718(3)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5181643best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5045474	1.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53718best projected	0	2.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.53626	9.2e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.53506	2.1e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017

best variational

-0.536326(9)

VMC (SJ)

best projected

-0.53821(2)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.536326best variational	0	9.5e-6	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.53821best projected	0	2.0e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.5054037

DMRG

best projected

-0.5055314

DMET

best approximate

-0.5037865

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5054037best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.4924335	1.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4669831	3.8e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5055314best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5054933	3.8e-5	1.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5047729	7.6e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5036471	1.9e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5027644	2.8e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5037865best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4897667	1.4e-2	n/a	approximate	GW	Motta et al. (2017)	2017

best variational

-0.5102735

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5102735best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.4873343	2.3e-2	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5216948

DMRG

best projected

-0.5240882

SEET

best approximate

-0.5205262

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5216948best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5094912	1.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4862468	3.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5240882best projected	0	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5224454	1.6e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5217367	2.4e-3	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5212581	2.8e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5202610	3.8e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5205262best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5102287

best projected

-0.52512(7)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5102287best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4872783	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.52512best projected	0	7.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.52504tied with best projected at 2σ	8.4e-5	n/a	projected	DMET	Motta et al. (2017)	2017

best variational

-0.5100848

best projected

-0.52443(4)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5100848best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4870715	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.52443best projected	0	3.8e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.52422	2.1e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.52272	1.7e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017

best variational

-0.523410(9)

VMC (SJ)

best projected

-0.52555(2)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.523410best variational	0	8.7e-6	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.52555best projected	0	2.0e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.4913033

DMRG

best projected

-0.4914582

SEET

best approximate

-0.4900449

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4913033best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.4820305	9.3e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.4377174	5.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4914582best projected	0	n/a	projected	SEET	Motta et al. (2017)	2017
-0.4914567tied with best projected at 2σ	1.5e-6	1.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.4914392	1.9e-5	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4900038	1.5e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4890372	2.4e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4900449best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4653600	2.5e-2	n/a	approximate	GW	Motta et al. (2017)	2017

best variational

-0.5053753

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5053753best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.4714314	3.4e-2	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.512651

DMRG

best projected

-0.5128862

DMET

best approximate

-0.511785

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.512651best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.504610	8.0e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.470041	4.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5128862best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5128533tied with best projected at 2σ	3.3e-5	2.4e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5116523	1.2e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.511785best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5053287

best projected

-0.5162413

DMET

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5053287best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4713471	3.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5162413best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5157867	4.5e-4	7.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017

best variational

-0.5051879

best projected

-0.5154642

DMET

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5051879best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4710791	3.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5154642best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5151133	3.5e-4	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5136503	1.8e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017

best variational

-0.513577(9)

VMC (SJ)

best projected

-0.51601(3)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.513577best variational	0	9.4e-6	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.51601best projected	0	2.6e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.4820203

DMRG

best projected

-0.4828246

SEET

best approximate

-0.4812442

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year
-0.4820203best variational	0	n/a	variational	DMRG	Motta et al. (2017)		2017
-0.4763935	5.6e-3	n/a	variational	HF	Motta et al. (2017)		2017
-0.4113200	7.1e-2	n/a	variational	HF	Motta et al. (2017)		2017
-0.4828246best projected	0	n/a	projected	SEET	Motta et al. (2017)		2017
-0.4821867	6.4e-4	6.7e-6	projected	ph-AFQMC	Motta et al. (2017)		2017
-0.4821097	7.1e-4	n/a	projected	DMET	Motta et al. (2017)		2017
-0.4819720	8.5e-4	3.1e-5	projected	FCIQMC	Guther et al. (2020)	ghb24/NECI_STABLE	2020
-0.4812359	1.6e-3	n/a	projected	UCCSD	Motta et al. (2017)		2017
-0.4805859	2.2e-3	n/a	projected	DMET	Motta et al. (2017)		2017
-0.4812442best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)		2017
-0.4442067	3.7e-2	n/a	approximate	GW	Motta et al. (2017)		2017

best variational

-0.3930718

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.3930718best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.3920485	1.0e-3	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.388254

DMRG

best projected

-0.38822(2)

ph-AFQMC

best approximate

-0.3882394

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.388254best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.365552	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.364446	2.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.38822best projected	0	1.8e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.38707	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.38698	1.2e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.3882394best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.3878618	3.8e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.3909264

best projected

-0.4169616

RCCSD

best approximate

-0.418261

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.3909264best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.3896584	1.3e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.4169616best projected	0	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.418261best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.3867182

best projected

-0.41352(4)

ph-AFQMC

best approximate

-0.4133358

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.3867182best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.3849004	1.8e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.41352best projected	0	4.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.41193	1.6e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.4133358best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.41856(3)

VMC (SJ)

best projected

-0.42197(3)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.41856best variational	0	2.8e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.42197best projected	0	3.4e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.3456814

LDMRG

best projected

-0.3466732

DMET

best approximate

-0.345728

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.3456814best variational	0	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.3456812	2.0e-7	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.3456804	1.0e-6	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.3456430	3.8e-5	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.3453520	3.3e-4	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.3372976	8.4e-3	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.3372975	8.4e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.3466732best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.3457040	9.7e-4	2.0e-6	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.3454434	1.2e-3	n/a	projected	CCSD	Hachmann et al. (2006)	2006
-0.3454434	1.2e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.3449205	1.8e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.3431425	3.5e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.345728best approximate	0	n/a	approximate	GW	Motta et al. (2017)	2017
-0.345645	8.3e-5	n/a	approximate	CCSD(T)	Hachmann et al. (2006)	2006
-0.345645	8.3e-5	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.344527	1.2e-3	n/a	approximate	MP2	Hachmann et al. (2006)	2006

best variational

-0.4724546

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.4724546best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.4712956	1.2e-3	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.486182

DMRG

best projected

-0.48637(1)

ph-AFQMC

best approximate

-0.4860532

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.486182best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.463172	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.463004	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.48637best projected	0	1.2e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.48540	9.7e-4	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.48523	1.1e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.48282	3.5e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4860532best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.4859160	1.4e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.471144

best projected

-0.49888(3)

ph-AFQMC

best approximate

-0.4983418

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.471144best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.470371	7.7e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.49888best projected	0	3.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.49741	1.5e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.4983418best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.4700515

best projected

-0.49746(4)

ph-AFQMC

best approximate

-0.4971284

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4700515best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4698476	2.0e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.49746best projected	0	4.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.49625	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.4971284best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.49748(1)

VMC (SJ)

best projected

-0.49913(4)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.49748best variational	0	1.4e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.49913best projected	0	3.7e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.458953

LDMRG

best projected

-0.4599375

DMET

best approximate

-0.4588914

CCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.458953best variational	0	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.458953	<1e-6	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.458952	<1e-6	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.458930	2.3e-5	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.458743	2.1e-4	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.449361	9.6e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.449225	9.7e-3	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.4599375best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4589500	9.9e-4	1.4e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.4586276	1.3e-3	n/a	projected	CCSD	Hachmann et al. (2006)	2006
-0.4584908	1.4e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4580748	1.9e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.4564522	3.5e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4588914best approximate	0	n/a	approximate	CCSD(T)	Hachmann et al. (2006)	2006
-0.4588030	8.8e-5	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4587720	1.2e-4	n/a	approximate	GW	Motta et al. (2017)	2017
-0.4572620	1.6e-3	n/a	approximate	MP2	Hachmann et al. (2006)	2006

best variational

-0.5142633

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5142633best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5137476	5.2e-4	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5331854

DMRG

best projected

-0.5342916

DMET

best approximate

-0.5330286

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5331854best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5100440	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5095481	2.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5342916best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5333860	9.1e-4	1.8e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5322822	2.0e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5320568	2.2e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5301283	4.2e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5330286best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5328110	2.2e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5141705

best projected

-0.5401476

RCCSD

best approximate

-0.5411192

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5141705best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5136561	5.1e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.5401476best projected	0	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5411192best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5138868

best projected

-0.54063(3)

ph-AFQMC

best approximate

-0.540299

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5138868best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5133749	5.1e-4	n/a	variational	HF	Motta et al. (2017)	2017
-0.54063best projected	0	3.2e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.53937	1.3e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.53816	2.5e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.540299best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.53996(2)

VMC (SJ)

best projected

-0.54153(2)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.53996best variational	0	1.6e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.54153best projected	0	2.1e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.5118756

LDMRG

best projected

-0.5127902

DMET

best approximate

-0.5117824

CCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5118756best variational	0	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5118754	2.0e-7	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5118752	4.0e-7	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5118612	1.4e-5	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5117384	1.4e-4	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5011782	1.1e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5005952	1.1e-2	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.5127902best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5118660	9.2e-4	6.0e-6	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5114558	1.3e-3	n/a	projected	CCSD	Hachmann et al. (2006)	2006
-0.5111777	1.6e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5109038	1.9e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5094159	3.4e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5117824best approximate	0	n/a	approximate	CCSD(T)	Hachmann et al. (2006)	2006
-0.5115376	2.4e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5113300	4.5e-4	n/a	approximate	GW	Motta et al. (2017)	2017
-0.5094898	2.3e-3	n/a	approximate	MP2	Hachmann et al. (2006)	2006

best variational

-0.5332496

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5332496best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5321503	1.1e-3	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5307409

best projected

-0.5548843

DMET

best approximate

-0.5535398

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5307409best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5296729	1.1e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.5548843best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5539140	9.7e-4	1.4e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5527072	2.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5524484	2.4e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5511663	3.7e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5535398best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5532482	2.9e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5331783

best projected

-0.558395

RCCSD

best approximate

-0.5594386

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5331783best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5320796	1.1e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.558395best projected	0	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5594386best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5329572

best projected

-0.55895(3)

ph-AFQMC

best approximate

-0.5587018

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5329572best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5318609	1.1e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.55895best projected	0	3.2e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.55770	1.2e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.55639	2.6e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5587018best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.55836(1)

VMC (SJ)

best projected

-0.55992(2)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.55836best variational	0	1.5e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.55992best projected	0	2.3e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.5343888

LDMRG

best projected

-0.5351831

DMET

best approximate

-0.5342628

CCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5343888best variational	0	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5343886	2.0e-7	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5343886	2.0e-7	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5343798	9.0e-6	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5342994	8.9e-5	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5226038	1.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5212450	1.3e-2	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.5351831best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5343760	8.1e-4	1.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5338686	1.3e-3	n/a	projected	CCSD	Hachmann et al. (2006)	2006
-0.5334875	1.7e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5332892	1.9e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5319681	3.2e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5342628best approximate	0	n/a	approximate	CCSD(T)	Hachmann et al. (2006)	2006
-0.5338717	3.9e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.5332560	1.0e-3	n/a	approximate	GW	Motta et al. (2017)	2017
-0.5310826	3.2e-3	n/a	approximate	MP2	Hachmann et al. (2006)	2006

best variational

-0.5393799

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5393799best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5374127	2.0e-3	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.560418

DMRG

best projected

-0.5615634

DMET

best approximate

-0.5601304

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.560418best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.537787	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.535862	2.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5615634best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5604890	1.1e-3	1.0e-5	projected	ph-AFQMC	Shee et al. (2018)	2018
-0.5604820	1.1e-3	1.6e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5604750	1.1e-3	1.2e-5	projected	ph-AFQMC	Shee et al. (2018)	2018
-0.5602350	1.3e-3	1.2e-5	projected	ph-AFQMC	Shee et al. (2018)	2018
-0.5602110	1.4e-3	1.4e-5	projected	ph-AFQMC	Shee et al. (2018)	2018
-0.5592242	2.3e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5589306	2.6e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5582362	3.3e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5601304best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5597484	3.8e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5393155

best projected

-0.56515(3)

ph-AFQMC

best approximate

-0.564877

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5393155best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5373494	2.0e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.56515best projected	0	3.4e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.56376	1.4e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.564877best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5391208

best projected

-0.56451(4)

ph-AFQMC

best approximate

-0.5641164

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5391208best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5371582	2.0e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.56451best projected	0	4.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.56304	1.5e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.56203	2.5e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5641164best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.56381(1)

VMC (SJ)

best projected

-0.56543(2)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.56381best variational	0	9.9e-6	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.56543best projected	0	2.1e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.540773

LDMRG

best projected

-0.5414071

DMET

best approximate

-0.540629

CCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.540773best variational	0	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.540773	<1e-6	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.540773	<1e-6	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.540768	5.0e-6	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.540716	5.7e-5	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.527934	1.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.525320	1.5e-2	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.5414071best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5407760	6.3e-4	6.0e-6	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5401530	1.3e-3	n/a	projected	CCSD	Hachmann et al. (2006)	2006
-0.5396656	1.7e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5395431	1.9e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5383638	3.0e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.540629best approximate	0	n/a	approximate	CCSD(T)	Hachmann et al. (2006)	2006
-0.540063	5.7e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.538722	1.9e-3	n/a	approximate	GW	Motta et al. (2017)	2017
-0.536230	4.4e-3	n/a	approximate	MP2	Hachmann et al. (2006)	2006

best variational

-0.5387831

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5387831best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5355882	3.2e-3	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5376519

best projected

-0.560789

DMET

best approximate

-0.5593002

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5376519best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5345063	3.1e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.560789best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.559718	1.1e-3	1.6e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.558330	2.5e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.558005	2.8e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.557765	3.0e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5593002best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5588094	4.9e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5387247

best projected

-0.56380(3)

ph-AFQMC

best approximate

-0.5634712

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5387247best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5355314	3.2e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.56380best projected	0	2.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.56228	1.5e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5634712best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5385504

best projected

-0.56316(5)

ph-AFQMC

best approximate

-0.5626926

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5385504best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5353607	3.2e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.56316best projected	0	4.6e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.56156	1.6e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.56096	2.2e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5626926best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.56242(1)

VMC (SJ)

best projected

-0.56409(2)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.56242best variational	0	1.3e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.56409best projected	0	2.3e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.5385218

DMRG

best projected

-0.5389803

DMET

best approximate

-0.538418

CCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5385218best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5385218tied with best variational at 2σ	<1e-7	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5385192	2.6e-6	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5384862	3.6e-5	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5247554	1.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5201640	1.8e-2	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.5389803best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5385120	4.7e-4	1.8e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5378298	1.2e-3	n/a	projected	CCSD	Hachmann et al. (2006)	2006
-0.5371942	1.8e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5371744	1.8e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5360719	2.9e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.538418best approximate	0	n/a	approximate	CCSD(T)	Hachmann et al. (2006)	2006
-0.537583	8.3e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.535096	3.3e-3	n/a	approximate	GW	Motta et al. (2017)	2017
-0.532322	6.1e-3	n/a	approximate	MP2	Hachmann et al. (2006)	2006

best variational

-0.5294429

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5294429best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.5223006	7.1e-3	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5484576

DMRG

best projected

-0.549566

DMET

best approximate

-0.5481804

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5484576best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5286408	2.0e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5215376	2.7e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.549566best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.548628	9.4e-4	1.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.547076	2.5e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.547044	2.5e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.546697	2.9e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5481804best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017
-0.5473802	8.0e-4	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5293962

best projected

-0.5505126

RCCSD

best approximate

-0.5518596

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5293962best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5222554	7.1e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.5505126best projected	0	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5518596best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5292454

best projected

-0.55145(4)

ph-AFQMC

best approximate

-0.5510824

RCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5292454best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5221053	7.1e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.55145best projected	0	4.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.55008	1.4e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.54980	1.7e-3	n/a	projected	RCCSD	Motta et al. (2017)	2017
-0.5510824best approximate	0	n/a	approximate	RCCSD(T)	Motta et al. (2017)	2017

best variational

-0.55049(1)

VMC (SJ)

best projected

-0.55262(3)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.55049best variational	0	1.3e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.55262best projected	0	2.5e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.5232114

LDMRG

best projected

-0.5234051

DMET

best approximate

-0.521806

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5232114best variational	0	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5232112	2.0e-7	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5232106	8.0e-7	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5231984	1.3e-5	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.5086805	1.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4967152	2.6e-2	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.5234051best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5231880	2.2e-4	1.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5219818	1.4e-3	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5215140	1.9e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5205328	2.9e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.521806best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.515194	6.6e-3	n/a	approximate	GW	Motta et al. (2017)	2017
-0.512092	9.7e-3	n/a	approximate	MP2	Hachmann et al. (2006)	2006

best variational

-0.518544

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.518544best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.504830	1.4e-2	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.51777

best projected

-0.5352079

DMET

best approximate

-0.5329892

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.51777best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.50399	1.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5352079best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5344620	7.5e-4	1.2e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5332151	2.0e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5325150	2.7e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5329892best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5185002

best projected

-0.53798(3)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5185002best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5047861	1.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53798best projected	0	2.7e-5	projected	ph-AFQMC	Motta et al. (2017)	2017

best variational

-0.5183529

best projected

-0.53742(2)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5183529best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.5046234	1.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.53742best projected	0	2.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.53633	1.1e-3	n/a	projected	DMET	Motta et al. (2017)	2017

best variational

-0.53563(1)

VMC (SJ)

best projected

-0.53834(3)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.53563best variational	0	1.3e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.53834best projected	0	3.0e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.505496

LDMRG

best projected

-0.5056322

DMET

best approximate

-0.503953

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.505496best variational	0	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.505496	<1e-6	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.505496	<1e-6	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.505492	3.6e-6	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.492684	1.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.467216	3.8e-2	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.5056322best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5055300	1.0e-4	1.4e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5048644	7.7e-4	n/a	projected	SEET	Motta et al. (2017)	2017
-0.5038132	1.8e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5026845	2.9e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.503953best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.489934	1.4e-2	n/a	approximate	GW	Motta et al. (2017)	2017
-0.487122	1.7e-2	n/a	approximate	MP2	Hachmann et al. (2006)	2006

best variational

-0.5103961

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5103961best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.4874118	2.3e-2	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5217914

DMRG

best projected

-0.5226823

DMET

best approximate

-0.5206612

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5217914best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.5096145	1.2e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.4863413	3.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5226823best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5218620	8.2e-4	1.4e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5213583	1.3e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5203920	2.3e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5206612best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5103515

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5103515best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.4873572	2.3e-2	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5102075

best projected

-0.52450(4)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5102075best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4871531	2.3e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.52450best projected	0	4.4e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.52432	1.8e-4	n/a	projected	DMET	Motta et al. (2017)	2017

best variational

-0.52221(2)

VMC (SJ)

best projected

-0.52570(4)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.52221best variational	0	1.8e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.52570best projected	0	3.7e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.4913656

DMRG

best projected

-0.4916637

SEET

best approximate

-0.4901495

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4913656best variational	0	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.4913656tied with best variational at 2σ	<1e-7	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.4913646	1.0e-6	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.4821720	9.2e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.4379266	5.3e-2	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.4916637best projected	0	n/a	projected	SEET	Motta et al. (2017)	2017
-0.4915281	1.4e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4914660	2.0e-4	1.0e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.4901080	1.6e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4889695	2.7e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4901495best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4654980	2.5e-2	n/a	approximate	GW	Motta et al. (2017)	2017
-0.4640822	2.6e-2	n/a	approximate	MP2	Hachmann et al. (2006)	2006

best variational

-0.5054446

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5054446best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.4714792	3.4e-2	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5046794

best projected

-0.5134833

DMET

best approximate

-0.5118654

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5046794best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4701290	3.5e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5134833best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5130101	4.7e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5129260	5.6e-4	1.6e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.5117310	1.8e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.5118654best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017

best variational

-0.5053981

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.5053981best variational	0	n/a	variational	HF	Motta et al. (2017)		2017
-0.4714235	3.4e-2	n/a	variational	HF	Motta et al. (2017)		2017

best variational

-0.5052571

best projected

-0.5156009

DMET

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.5052571best variational	0	n/a	variational	HF	Motta et al. (2017)	2017
-0.4711566	3.4e-2	n/a	variational	HF	Motta et al. (2017)	2017
-0.5156009best projected	0	n/a	projected	DMET	Motta et al. (2017)	2017
-0.5151880	4.1e-4	4.3e-5	projected	ph-AFQMC	Motta et al. (2017)	2017

best variational

-0.51192(1)

VMC (SJ)

best projected

-0.51616(7)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.51192best variational	0	1.3e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.51616best projected	0	7.1e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.4820554

LDMRG

best projected

-0.4831221

SEET

best approximate

-0.4813012

UCCSD(T)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4820554best variational	0	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.4820552	2.0e-7	n/a	variational	DMRG	Motta et al. (2017)	2017
-0.4820550	4.0e-7	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.4764653	5.6e-3	n/a	variational	HF	Motta et al. (2017)	2017
-0.4114858	7.1e-2	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.4831221best projected	0	n/a	projected	SEET	Motta et al. (2017)	2017
-0.4822126	9.1e-4	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4821680	9.5e-4	1.4e-5	projected	ph-AFQMC	Motta et al. (2017)	2017
-0.4812927	1.8e-3	n/a	projected	UCCSD	Motta et al. (2017)	2017
-0.4805521	2.6e-3	n/a	projected	DMET	Motta et al. (2017)	2017
-0.4813012best approximate	0	n/a	approximate	UCCSD(T)	Motta et al. (2017)	2017
-0.4459522	3.5e-2	n/a	approximate	MP2	Hachmann et al. (2006)	2006
-0.4443080	3.7e-2	n/a	approximate	GW	Motta et al. (2017)	2017

best variational

-0.4749942

LDMRG

best approximate

-0.4302988

MP2

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.4749942best variational	0	n/a	variational	LDMRG	Hachmann et al. (2006)	2006
-0.3791190	9.6e-2	n/a	variational	HF	Hachmann et al. (2006)	2006
-0.4302988best approximate	0	n/a	approximate	MP2	Hachmann et al. (2006)	2006

best projected

-0.34303(1)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.34303best projected	0	1.4e-5	projected	ph-AFQMC	Motta et al. (2017)		2017

best projected

-0.511254(9)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.511254best projected	0	8.6e-6	projected	ph-AFQMC	Motta et al. (2017)		2017

best projected

-0.54073(1)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.54073best projected	0	1.1e-5	projected	ph-AFQMC	Motta et al. (2017)		2017

best projected

-0.50560(1)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50560best projected	0	1.1e-5	projected	ph-AFQMC	Motta et al. (2017)		2017

best variational

-0.41649(2)

VMC (SJ)

best projected

-0.42018(3)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.41649best variational	0	1.9e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.42018best projected	0	3.2e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.49544(1)

VMC (SJ)

best projected

-0.49896(7)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.49544best variational	0	1.2e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.49896best projected	0	6.9e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best variational

-0.41616(2)

VMC (SJ)

best projected

-0.41967(4)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.41616best variational	0	1.9e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.41967best projected	0	3.7e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best projected

-0.34087(1)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.34087best projected	0	1.5e-5	projected	ph-AFQMC	Motta et al. (2017)		2017

best variational

-0.49576(1)

VMC (SJ)

best projected

-0.49844(4)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.49576best variational	0	1.1e-5	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.49844best projected	0	3.7e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best projected

-0.51125(1)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.51125best projected	0	1.2e-5	projected	ph-AFQMC	Motta et al. (2017)		2017

best variational

-0.563316(7)

VMC (SJ)

best projected

-0.56538(1)

LR-DMC (LDA determinant)

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.563316best variational	0	6.5e-6	variational	VMC (SJ)	Motta et al. (2017)		2017
-0.56538best projected	0	1.3e-5	projected	LR-DMC (LDA determinant)	Motta et al. (2017)		2017

best projected

-0.54069(2)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.54069best projected	0	1.9e-5	projected	ph-AFQMC	Motta et al. (2017)		2017

best projected

-0.50565(2)

ph-AFQMC

E/N (Ha)	distance to class best	σ	bound type	method	source	code	year	comment
-0.50565best projected	0	2.0e-5	projected	ph-AFQMC	Motta et al. (2017)		2017

Hydrogen sheet#

1 instances, energies as E/N (Ha)

lattice

instance

value

energy

method

source

code

energies

best variational

-0.52710(7)

VMC (JAGP)

Genovese et al. (2019)

best projected

-0.52812(5)

LR-DMC (JAGP)

Genovese et al. (2019)

E/N (Ha)	distance to class best	σ	bound type	method	source	year
-0.52710best variational	0	7.5e-5	variational	VMC (JAGP)	Genovese et al. (2019)	2019
-0.52687tied with best variational at 2σ	2.3e-4	1.0e-4	variational	VMC (JAGP)	Genovese et al. (2019)	2019
-0.51735	9.8e-3	1.0e-4	variational	VMC (SJ)	Genovese et al. (2019)	2019
-0.52812best projected	0	5.0e-5	projected	LR-DMC (JAGP)	Genovese et al. (2019)	2019