How these numbers were read
Where each number below was read, and how it was checked.
3.41226(2) — 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 = -0.5969(3) (total, Ha)
Table I, rs=0.5 column, row M=infinity; sources/1201.4691.txt line 14842; printed correlation energy -0.5969(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.41229(1) — 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 = -0.5965(2) (total, Ha)
Table II, row rs=0.5, column E_CCSDT; sources/1511.05752.txt line 603; printed correlation energy -0.5965(2) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.41233(5) — 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 = -0.5959(7) (total, Ha)
Table II, rs=0.5, N=14, column Ecorr (a.u.); sources/1201.4691.txt line 20998; printed correlation energy -0.5959(7) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.412397(3) — FCIQMC (direct linear 1/M fit including spin orbitals up to...
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 = -0.59497(4)
Sec. VI Discussion, text; sources/1706.09923.txt line 293; printed in Ha, total; printed correlation energy -0.59497(4), E = E_HF + E_c with E_HF = 3.45489439316 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.
3.41241(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 = -0.5948(2)
Table 1, N=14, rs=0.5, column FCIQMC-TC; sources/1712.07524.txt line 791; printed in Ha, total; printed correlation energy -0.5948(2), E = E_HF + E_c with E_HF = 3.45489439316 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).
3.412418(6) — FCIQMC ((i)FCIQMC; initiator used for M > 358 at rs=0.5...
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 = -0.59467(9)
Table I, row FCIQMC, rs=0.5 a0 (footnote g); sources/1706.09923.txt line 310; printed in Ha, total; printed correlation energy -0.59467(9), E = E_HF + E_c with E_HF = 3.45489439316 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.
3.412419(6) — 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 = -0.59465(8)
Table I, row CCSDTQ, rs=0.5 a0 (own value); sources/1706.09923.txt line 308; printed in Ha, total; printed correlation energy -0.59465(8), E = E_HF + E_c with E_HF = 3.45489439316 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.
3.412425(5) — 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 = -0.59457(7)
Table I, row CCSDT, rs=0.5 a0 (own value); sources/1706.09923.txt line 307; printed in Ha, total; printed correlation energy -0.59457(7), E = E_HF + E_c with E_HF = 3.45489439316 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.
3.41244 — 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. 3.41244
Table I, row rs=0.5, column TC-DCD; sources/2103.03176.txt line 377; 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.
3.41247(3) — 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 = -0.5939(4) (total, Ha)
Table I, rs=0.5 column, row M=2368; sources/1201.4691.txt line 14841; printed correlation energy -0.5939(4) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.41249(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 = -0.5936(3) (total, Ha)
Table I, rs=0.5 column, row M=1850; sources/1201.4691.txt line 14840; printed correlation energy -0.5936(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.41252 — 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. 3.41252
Table I, row rs=0.5, column DCD; sources/2103.03176.txt line 377; 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.
3.41253(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 = -0.5931(6)
Table II, rs=0.5, M=2109, column ph-AFQMC; sources/1905.04361.txt line 523; printed in Ha, total; printed correlation energy -0.5931(6), E = E_HF + E_c with E_HF = 3.45489439316 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
3.41257(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 = -0.5926(8)
Table II, rs=0.5, M=1213, column ph-AFQMC; sources/1905.04361.txt line 521; printed in Ha, total; printed correlation energy -0.5926(8), E = E_HF + E_c with E_HF = 3.45489439316 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
3.41257(3) — 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 = -0.5925(4)
Table II, rs=0.5, M=1419, column ph-AFQMC; sources/1905.04361.txt line 522; printed in Ha, total; printed correlation energy -0.5925(4), E = E_HF + E_c with E_HF = 3.45489439316 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
3.41258 — 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. 3.41258
Table I, row rs=0.5, column TC-CCD; sources/2103.03176.txt line 377; 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.
3.41260(1) — 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 = -0.5921(2)
Table II, rs=0.5, M=1189, column ph-AFQMC; sources/1905.04361.txt line 520; printed in Ha, total; printed correlation energy -0.5921(2), E = E_HF + E_c with E_HF = 3.45489439316 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
3.41261(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 = -0.5920(8)
Table II, rs=0.5, M=925, column ph-AFQMC; sources/1905.04361.txt line 519; printed in Ha, total; printed correlation energy -0.5920(8), E = E_HF + E_c with E_HF = 3.45489439316 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
3.412684(4) — 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 = −0.59094(6) (total, Ha)
Table I, row 'ndet = 16', column rs=0.5; sources/2202.05183.txt line 136; printed correlation energy −0.59094(6) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.412773(7) — 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 = -0.5897(1) (total, Ha)
Table II, row rs=0.5, column E_CCSD; sources/1511.05752.txt line 603; printed correlation energy -0.5897(1) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.412779(4) — 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 = −0.58962(6) (total, Ha)
Table III (SI), Block determinants, ndet=16, rs=0.5; sources/2202.05183.txt line 673; printed correlation energy −0.58962(6) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.41278 — 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. 3.41278
Table I, row rs=0.5, column CCD; sources/2103.03176.txt line 377; 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.
3.41280(2) — 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 = -0.5893(3) (total, Ha)
Table I, rs=0.5 column, row M=778; sources/1201.4691.txt line 14839; printed correlation energy -0.5893(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.412827(4) — 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 = −0.58895(6) (total, Ha)
Table I, row 'ndet = 1', column rs=0.5; sources/2202.05183.txt line 135; printed correlation energy −0.58895(6) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.412847(4) — CCSD (CCMC non-initiator, linear fit in 1/M, three points...
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 = -0.58866(5)
Fig. 1 caption, linear fit; sources/1706.09923.txt line 201; printed in Ha, total; printed correlation energy -0.58866(5), E = E_HF + E_c with E_HF = 3.45489439316 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.
3.412859(4) — 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 = -0.58850(6)
Table I, row CCSD, rs=0.5 a0 (own value); sources/1706.09923.txt line 306; printed in Ha, total; printed correlation energy -0.58850(6), E = E_HF + E_c with E_HF = 3.45489439316 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.
3.412860(5) — CCSD (CCMC non-initiator, cubic fit in 1/M, one point...
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 = -0.58848(7)
Fig. 1 caption, cubic fit; sources/1706.09923.txt line 204; printed in Ha, total; printed correlation energy -0.58848(7), E = E_HF + E_c with E_HF = 3.45489439316 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.
3.412872(5) — 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 = −0.58831(7) (total, Ha)
Table III (SI), Block determinants, ndet=1, rs=0.5; sources/2202.05183.txt line 672; printed correlation energy −0.58831(7) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.41289(1) — 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 = -0.5881(2)
Table II, rs=0.5, M=389, column ph-AFQMC; sources/1905.04361.txt line 518; printed in Ha, total; printed correlation energy -0.5881(2), E = E_HF + E_c with E_HF = 3.45489439316 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
3.4128944 — 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 = -0.588
Table III, rs=0.5, column CCD; sources/1310.6806.txt line 488; printed in Ha, total; printed correlation energy -0.588, E = E_HF + E_c with E_HF = 3.45489439316 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.
3.4129101(7) — Fixed-node DMC (trial state: Slater-Jastrow-backflow;...
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 = −0.58778(1) (total, Ha)
Table I, row 'SJB DMC', column rs=0.5; sources/2202.05183.txt line 133; printed correlation energy −0.58778(1) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.4130201(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 = −0.58624(1) (total, Ha)
Table I, row 'SJB VMC', column rs=0.5; sources/2202.05183.txt line 132; printed correlation energy −0.58624(1) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.41349(2) — 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 = -0.5797(3) (total, Ha)
Table I, rs=0.5 column, row M=358; sources/1201.4691.txt line 14838; printed correlation energy -0.5797(3) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.41351(1) — 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 = -0.5794(2)
Table II, rs=0.5, M=179, column ph-AFQMC; sources/1905.04361.txt line 517; printed in Ha, total; printed correlation energy -0.5794(2), E = E_HF + E_c with E_HF = 3.45489439316 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
3.41379139(7) — 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 = -0.575442(1) (total, Ha)
Table I, rs=0.5; sources/1202.4990.txt line 8295; printed correlation energy -0.575442(1) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.41495(1) — 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 = -0.5592(2)
Table II, rs=0.5, M=93, column ph-AFQMC; sources/1905.04361.txt line 516; printed in Ha, total; printed correlation energy -0.5592(2), E = E_HF + E_c with E_HF = 3.45489439316 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
3.414973(7) — 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 = -0.5589(1) (total, Ha)
Table I, rs=0.5 column, row M=186; sources/1201.4691.txt line 14837; printed correlation energy -0.5589(1) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).
3.417944(7) — 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 = -0.5173(1)
Table II, rs=0.5, M=57, column ph-AFQMC; sources/1905.04361.txt line 515; printed in Ha, total; printed correlation energy -0.5173(1), E = E_HF + E_c with E_HF = 3.45489439316 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
3.417973(7) — 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 = -0.5169(1) (total, Ha)
Table I, rs=0.5 column, row M=114; sources/1201.4691.txt line 14836; printed correlation energy -0.5169(1) Ha for 14 electrons; E = E_HF + E_c with E_HF = 3.45489439316 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).