How these numbers were read
Where each number below was read, and how it was checked.
0.56850(3) — FCIQMC (initiator (n_add = 3); extrapolated: 1/M → 0...
Checked 2026-10-19 · source text of arXiv:1201.4691 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5325(4) (total, Ha)
Table I, rs=1.0 column, row M=infinity; sources/1201.4691.txt line 14842; printed correlation energy -0.5325(4) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Tables I and II; AIP copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.56856(2) — CCSDT (initiator stochastic coupled cluster at the...
Checked 2026-10-19 · source text of arXiv:1511.05752 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5317(3) (total, Ha)
Table II, row rs=1.0, column E_CCSDT; sources/1511.05752.txt line 605; printed correlation energy -0.5317(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Table II; AIP copy not read; unit and cell fixed by its FCIQMC column, which reprints arXiv:1201.4691's complete-basis values (-0.5969, -0.5325, -0.4447) for 14 electrons in a simple cubic cell | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.56856(3) — FCIQMC (initiator (n_add = 3), run at 1850 spin orbitals;...
Checked 2026-10-19 · source text of arXiv:1201.4691 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5316(4) (total, Ha)
Table II, rs=1.0, N=14, column Ecorr (a.u.); sources/1201.4691.txt line 21001; printed correlation energy -0.5316(4) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Tables I and II; AIP copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.56858(1) — FCIQMC ((i)FCIQMC; initiator used for M > 66 at rs=1.0 (txt...
Checked 2026-10-19 · source text of arXiv:1706.09923 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5313(2)
Table I, row FCIQMC, rs=1.0 a0 (footnote i); sources/1706.09923.txt line 310; printed in Ha, total; printed correlation energy -0.5313(2), E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Eq. (7) (txt line 154-159): 'H = sum_k 1/2 (k^2 + V_M) c+c + ...', with 'V_M the Madelung constant that does not affect the correlation energy'; cubic box of length L; no Ewald-sum statement; no Hartree-Fock energy printed. Only correlation energies are printed, so the convention cannot be checked against a printed HF value.
0.56859 — TC-DCD (correlator cutoff k_c = 1 × 2π/L; extrapolated: 1/M...
Checked 2026-10-17 · source text of arXiv:2103.03176 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 0.56859
Table I, row rs=1.0, column TC-DCD; sources/2103.03176.txt line 378; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.
0.56860(1) — CCSDTQ (coupled cluster Monte Carlo (HANDE), non-initiator;...
Checked 2026-10-19 · source text of arXiv:1706.09923 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5311(2)
Table I, row CCSDTQ, rs=1.0 a0 (own value); sources/1706.09923.txt line 308; printed in Ha, total; printed correlation energy -0.5311(2), E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Eq. (7) (txt line 154-159): 'H = sum_k 1/2 (k^2 + V_M) c+c + ...', with 'V_M the Madelung constant that does not affect the correlation energy'; cubic box of length L; no Ewald-sum statement; no Hartree-Fock energy printed. Only correlation energies are printed, so the convention cannot be checked against a printed HF value.
0.56861(1) — Transcorrelated FCIQMC (FCIQMC on the transcorrelated...
Checked 2026-10-19 · source text of arXiv:1712.07524 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5309(2)
Table 1, N=14, rs=1.0, column FCIQMC-TC; sources/1712.07524.txt line 793; printed in Ha, total; printed correlation energy -0.5309(2), E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Not stated: grep for Madelung and Ewald finds nothing. Only correlation energies are printed (Table 1), so the convention is moot for the numbers, but the HF energy of the same systems is not printed either. Interaction Fourier transform w(k) = 4 pi / k^2 for k != 0, 0 for k = 0 (Eq. 28, txt line 595-598).
0.56863(1) — CCSDT (coupled cluster Monte Carlo (HANDE), non-initiator;...
Checked 2026-10-19 · source text of arXiv:1706.09923 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5307(2)
Table I, row CCSDT, rs=1.0 a0 (own value); sources/1706.09923.txt line 307; printed in Ha, total; printed correlation energy -0.5307(2), E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Eq. (7) (txt line 154-159): 'H = sum_k 1/2 (k^2 + V_M) c+c + ...', with 'V_M the Madelung constant that does not affect the correlation energy'; cubic box of length L; no Ewald-sum statement; no Hartree-Fock energy printed. Only correlation energies are printed, so the convention cannot be checked against a printed HF value.
0.56864(4) — FCIQMC (initiator (n_add = 3), 2368 spin orbitals)
Checked 2026-10-19 · source text of arXiv:1201.4691 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5305(5) (total, Ha)
Table I, rs=1.0 column, row M=2368; sources/1201.4691.txt line 14841; printed correlation energy -0.5305(5) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Tables I and II; AIP copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.56866(2) — ph-AFQMC (phaseless AFQMC with a single-determinant RHF...
Checked 2026-10-19 · source text of arXiv:1905.04361 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5302(3)
Table III, rs=1.0, M=1189, column ph-AFQMC; sources/1905.04361.txt line 493; printed in Ha, total; printed correlation energy -0.5302(3), E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Eq. (19) (txt line 210): H = T + Vee + E_M; txt lines 232-237: 'the Madelung energy E_M is included to account for the self-interaction of the Ewald sum under periodic boundary conditions. For simplicity we use the formula proposed by Schoof and co-workers' E_M ~ -2.837297 (3/4pi)^(1/3) N^(2/3)/rs (Eq. 22, txt line 238-239). So the Madelung term is included, but through the approximate closed form (Ref 76: T. Schoof, S. Groth, J. Vorberger, M. Bonitz, PRL 115, 130402 (2015)), not through a stated Ewald sum. No Hartree-Fock energy is printed. Reader's own check (python, scratch-R8/hf.py, NOT QM
0.56869(6) — ph-AFQMC (phaseless AFQMC with a single-determinant RHF...
Checked 2026-10-19 · source text of arXiv:1905.04361 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5298(8)
Table III, rs=1.0, M=2109, column ph-AFQMC; sources/1905.04361.txt line 494; printed in Ha, total; printed correlation energy -0.5298(8), E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Eq. (19) (txt line 210): H = T + Vee + E_M; txt lines 232-237: 'the Madelung energy E_M is included to account for the self-interaction of the Ewald sum under periodic boundary conditions. For simplicity we use the formula proposed by Schoof and co-workers' E_M ~ -2.837297 (3/4pi)^(1/3) N^(2/3)/rs (Eq. 22, txt line 238-239). So the Madelung term is included, but through the approximate closed form (Ref 76: T. Schoof, S. Groth, J. Vorberger, M. Bonitz, PRL 115, 130402 (2015)), not through a stated Ewald sum. No Hartree-Fock energy is printed. Reader's own check (python, scratch-R8/hf.py, NOT QM
0.56872(2) — FCIQMC (initiator (n_add = 3), 1850 spin orbitals)
Checked 2026-10-19 · source text of arXiv:1201.4691 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5294(3) (total, Ha)
Table I, rs=1.0 column, row M=1850; sources/1201.4691.txt line 14840; printed correlation energy -0.5294(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Tables I and II; AIP copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.568851(1) — FermiNet (16 determinants)
Checked 2026-10-16 · source text of arXiv:2604.15888 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 7.96391(2)
Table III (SM S3.D), rs=1, column E' n_det=16; sources/2604.15888.txt line 1324; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.
0.568904(2) — FermiNet (16 dense determinants, 4 layers 256/32)
Checked 2026-10-19 · source text of arXiv:2202.05183 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = −0.52682(3) (total, Ha)
Table I, row 'ndet = 16', column rs=1.0; sources/2202.05183.txt line 136; printed correlation energy −0.52682(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Table I and Supplementary Table III; APS copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.56891 — TC-CCD (correlator cutoff k_c = 1 × 2π/L; extrapolated: 1/M...
Checked 2026-10-17 · source text of arXiv:2103.03176 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 0.56891
Table I, row rs=1.0, column TC-CCD; sources/2103.03176.txt line 378; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.
0.56893(1) — FCIQMC (initiator (n_add = 3), 778 spin orbitals)
Checked 2026-10-19 · source text of arXiv:1201.4691 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5265(2) (total, Ha)
Table I, rs=1.0 column, row M=778; sources/1201.4691.txt line 14839; printed correlation energy -0.5265(2) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Tables I and II; AIP copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.568956(5) — WAP-net (n_d = 1)
Checked 2026-10-16 · source text of arXiv:2202.04622 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 1.137912(9)
Table III column 2 (WAP-Net nd=1), block Ne = 14 (paramagnetic), row rs = 1.0; sources/2202.04622.txt line 517; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.
0.568965(5) — WAP-net (n_d = 8)
Checked 2026-10-16 · source text of arXiv:2202.04622 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 1.13793(1)
Table III column 3 (WAP-Net nd=8), block Ne = 14 (paramagnetic), row rs = 1.0; sources/2202.04622.txt line 517; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.
0.568967(6) — MP-NQS (plane-wave orbitals)
Checked 2026-10-16 · source text of arXiv:2305.07240 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 0.568967(6)
Table I (Appendix G), N=14 unpolarized, rs=1, column MP-NQS; sources/2305.07240.txt line 662; printed in Ha per electron; version read: arXiv text, Appendix G Tables I-V; APS copy not read | Ha per electron, simple cubic cell; Eq. 13 gives the Ewald sum and 'const.'. The WAP-net values it quotes equal arXiv:2202.04622's Table III (Madelung included) / 2 to 5e-7, and its own N = 14, rs = 1 energy sits 0.0376 Ha below QMBL's HF energy, as theirs does.
0.568975(5) — Fixed-node DMC (trial state: iterative backflow)
Checked 2026-10-16 · source text of arXiv:2202.04622 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 1.13795(1)
Table III column EIBDMC, block Ne = 14 (paramagnetic), row rs = 1.0; sources/2202.04622.txt line 517; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.
0.568979(5) — FermiNet (4 determinants, Gaussian basis transformation)
Checked 2026-10-16 · source text of arXiv:2604.15888 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 7.96570(7)
Table III (SM S3.D), rs=1, column E n_det=4; sources/2604.15888.txt line 1324; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.
0.568979(4) — FermiNet (4 determinants)
Checked 2026-10-16 · source text of arXiv:2604.15888 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 7.96571(5)
Table III (SM S3.D), rs=1, column E' n_det=4; sources/2604.15888.txt line 1324; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.
0.568986(2) — FermiNet (1 dense determinant, 4 layers 256/32)
Checked 2026-10-19 · source text of arXiv:2202.05183 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = −0.52568(3) (total, Ha)
Table I, row 'ndet = 1', column rs=1.0; sources/2202.05183.txt line 135; printed correlation energy −0.52568(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Table I and Supplementary Table III; APS copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.568993(2) — FermiNet (16 block determinants, 4 layers 256/32)
Checked 2026-10-19 · source text of arXiv:2202.05183 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = −0.52558(3) (total, Ha)
Table III (SI), Block determinants, ndet=16, rs=1.0; sources/2202.05183.txt line 673; printed correlation energy −0.52558(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Table I and Supplementary Table III; APS copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.569006(7) — Slater-Jastrow-backflow (single determinant)
Checked 2026-10-19 · source text of arXiv:2202.05183 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = −0.5254(1) (total, Ha)
Table I, row 'SJB VMC', column rs=1.0; sources/2202.05183.txt line 132; printed correlation energy −0.5254(1) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Table I and Supplementary Table III; APS copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.569015(1) — FermiNet (1 determinant)
Checked 2026-10-16 · source text of arXiv:2604.15888 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 7.96621(2)
Table III (SM S3.D), rs=1, column E' n_det=1; sources/2604.15888.txt line 1324; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.
0.569016(4) — FermiNet (1 determinant, Gaussian basis transformation)
Checked 2026-10-16 · source text of arXiv:2604.15888 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 7.96622(6)
Table III (SM S3.D), rs=1, column E n_det=1; sources/2604.15888.txt line 1324; printed in Ha, total; version read: arXiv text with its Supplemental Material; no journal version (Crossref) | Total energies in Hartree (captions 'Total energies, in Hartree'), divided by N; the SM's Ewald sum includes the self-image terms. QMBL's HF check: N = 14, rs = 1, sc: E/N = 0.56902 is 0.0375 Ha below QMBL's HF energy 0.6065343, as arXiv:2202.04622's are.
0.569027(2) — FermiNet (1 block determinant, 4 layers 256/32)
Checked 2026-10-19 · source text of arXiv:2202.05183 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = −0.52510(3) (total, Ha)
Table III (SI), Block determinants, ndet=1, rs=1.0; sources/2202.05183.txt line 672; printed correlation energy −0.52510(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Table I and Supplementary Table III; APS copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.56909 — DCD (extrapolated: 1/M → 0 (complete basis))
Checked 2026-10-17 · source text of arXiv:2103.03176 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 0.56909
Table I, row rs=1.0, column DCD; sources/2103.03176.txt line 378; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.
0.569160(5) — Iterative backflow (single determinant)
Checked 2026-10-16 · source text of arXiv:2202.04622 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 1.13832(1)
Table III column EIBVMC, block Ne = 14 (paramagnetic), row rs = 1.0; sources/2202.04622.txt line 517; printed in Ry per electron; version read: arXiv:2202.04622v3 text (title 'Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas'); APS copy not read | Table III in Ry per electron (converted × 1/2); Ewald sum with the Madelung term N v_M added (text); simple cubic cell. QMBL's HF check: at rs = 1, N = 14 the energies sit 0.0376 Ha per electron below QMBL's HF energy 0.6065343, a correlation energy; without the Madelung term they would sit 0.365 Ha higher.
0.569470(7) — FCIQMC (initiator (n_add = 3), 358 spin orbitals)
Checked 2026-10-19 · source text of arXiv:1201.4691 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5189(1) (total, Ha)
Table I, rs=1.0 column, row M=358; sources/1201.4691.txt line 14838; printed correlation energy -0.5189(1) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Tables I and II; AIP copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.56948(4) — ph-AFQMC (phaseless AFQMC with a single-determinant RHF...
Checked 2026-10-19 · source text of arXiv:1905.04361 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5187(6)
Table III, rs=1.0, M=179, column ph-AFQMC; sources/1905.04361.txt line 492; printed in Ha, total; printed correlation energy -0.5187(6), E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Eq. (19) (txt line 210): H = T + Vee + E_M; txt lines 232-237: 'the Madelung energy E_M is included to account for the self-interaction of the Ewald sum under periodic boundary conditions. For simplicity we use the formula proposed by Schoof and co-workers' E_M ~ -2.837297 (3/4pi)^(1/3) N^(2/3)/rs (Eq. 22, txt line 238-239). So the Madelung term is included, but through the approximate closed form (Ref 76: T. Schoof, S. Groth, J. Vorberger, M. Bonitz, PRL 115, 130402 (2015)), not through a stated Ewald sum. No Hartree-Fock energy is printed. Reader's own check (python, scratch-R8/hf.py, NOT QM
0.56971(2) — CCSD (initiator stochastic coupled cluster at the...
Checked 2026-10-19 · source text of arXiv:1511.05752 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.5155(3) (total, Ha)
Table II, row rs=1.0, column E_CCSD; sources/1511.05752.txt line 605; printed correlation energy -0.5155(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Table II; AIP copy not read; unit and cell fixed by its FCIQMC column, which reprints arXiv:1201.4691's complete-basis values (-0.5969, -0.5325, -0.4447) for 14 electrons in a simple cubic cell | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.56975 — CCD (extrapolated: 1/M → 0 (complete basis))
Checked 2026-10-17 · source text of arXiv:2103.03176 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. 0.56975
Table I, row rs=1.0, column CCD; sources/2103.03176.txt line 378; printed in Ha per electron; version read: arXiv text, Tables I and II; APS copy not read | 'Total energy (a.u./electron), including the Madelung constant' (Table captions), 14 and 54 electrons in a simple cubic cell; the CC energies are extrapolated to the complete basis (linear in 1/M, Sec. IV). At N = 54, rs = 1 the DCD value agrees with arXiv:0801.0518's backflow DMC to 1e-4 Ha.
0.569784(6) — CCSD (coupled cluster Monte Carlo (HANDE), non-initiator;...
Checked 2026-10-19 · source text of arXiv:1706.09923 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.51450(9)
Table I, row CCSD, rs=1.0 a0 (own value); sources/1706.09923.txt line 306; printed in Ha, total; printed correlation energy -0.51450(9), E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Eq. (7) (txt line 154-159): 'H = sum_k 1/2 (k^2 + V_M) c+c + ...', with 'V_M the Madelung constant that does not affect the correlation energy'; cubic box of length L; no Ewald-sum statement; no Hartree-Fock energy printed. Only correlation energies are printed, so the convention cannot be checked against a printed HF value.
0.56982 — CCD (full CCD (driver, ladders, rings, crossed-rings...
Checked 2026-10-19 · source text of arXiv:1310.6806 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.514
Table III, rs=1.0, column CCD; sources/1310.6806.txt line 493; printed in Ha, total; printed correlation energy -0.514, E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Sec. II (txt line 64-81): HF eigenvalues with the zero-momentum integral given by 'vM, the Madelung constant ... defined uniquely for a cell geometry and box length, and here we calculate it to be vM L ~ 2.8372'. No Ewald-sum statement beyond that. The paper prints correlation energies only, which do not depend on the Madelung term, and no Hartree-Fock energy.
0.570754(6) — FCIQMC (initiator (n_add = 3), 186 spin orbitals)
Checked 2026-10-19 · source text of arXiv:1201.4691 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.50093(9) (total, Ha)
Table I, rs=1.0 column, row M=186; sources/1201.4691.txt line 14837; printed correlation energy -0.50093(9) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Tables I and II; AIP copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.5708673(1) — MP2 (extrapolated: 1/M → 0 (complete basis))
Checked 2026-10-19 · source text of arXiv:1202.4990 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.499338(2) (total, Ha)
Table I, rs=1.0; sources/1202.4990.txt line 8296; printed correlation energy -0.499338(2) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Table I; APS copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).
0.573598(6) — FCIQMC (initiator (n_add = 3), 114 spin orbitals)
Checked 2026-10-19 · source text of arXiv:1201.4691 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading
Reported as. E_c = -0.46111(9) (total, Ha)
Table I, rs=1.0 column, row M=114; sources/1201.4691.txt line 14836; printed correlation energy -0.46111(9) Ha for 14 electrons; E = E_HF + E_c with E_HF = 0.606534328824 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Tables I and II; AIP copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).