How these numbers were read
Where each number below was read, and how it was checked.
-0.01429(3) — ph-AFQMC (RHF trial, time step 0.005 a.u., 2880 walkers;...
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. -0.01429(3)
Table V, rs=2.0, column ph-AFQMC; sources/1905.04361.txt line 677; printed in Ha per electron; 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
-0.014046(8) — 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. −0.014046(8)
Table II (Appendix G), N=54 unpolarized, rs=2, column MP-NQS; sources/2305.07240.txt line 679; 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.
-0.013966(9) — Fixed-node DMC (trial state: Slater-Jastrow-backflow;...
Checked 2026-10-17 · source text of arXiv:0801.0518 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. −0.013966(9)
Table I, rs=2.0, row BF, column ED; sources/0801.0518.txt line 256; printed in Ha per electron; version read: arXiv text, Table I; APS copy not read | Ha per electron, 54 electrons (27 + 27) in a simple cubic cell. The paper's Hartree-Fock energies (VMC of the plane-wave determinant) match QMBL's HF energy within their error bars at all six rs, e.g. 0.5689(4) against 0.569245 at rs = 1 (checks/heg-hf/convention-check-2026-10-17.json).
-0.01390(1) — MP-NQS (Gaussian orbitals on bcc sites)
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. −0.01390(1)
Table II (Appendix G), N=54 unpolarized, rs=2, column MP-NQS (Gauss); sources/2305.07240.txt line 679; 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.
-0.013840(1) — DeepSolid (1 determinant, 3 layers 256/32)
Checked 2026-10-16 · source text of arXiv:2203.15472 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. -0.013840(1)
Supplementary Table 11, row rs=2, column 'Net'; sources/2203.15472.txt line 1015; printed in Ha per electron; version read: arXiv:2203.15472v2 text, Supplementary Table 11; Nature Communications copy not read | Ha per electron, 54-electron closed-shell gas in a simple cubic cell (27 + 27); QMBL's HF check: at rs = 0.5 the energy 3.221226 sits 0.044 Ha below QMBL's HF energy 3.2653295.
-0.01382(2) — Slater-Jastrow-backflow (homogeneous backflow)
Checked 2026-10-17 · source text of arXiv:0801.0518 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. −0.01382(2)
Table I, rs=2.0, row BF; sources/0801.0518.txt line 256; printed in Ha per electron; version read: arXiv text, Table I; APS copy not read | Ha per electron, 54 electrons (27 + 27) in a simple cubic cell. The paper's Hartree-Fock energies (VMC of the plane-wave determinant) match QMBL's HF energy within their error bars at all six rs, e.g. 0.5689(4) against 0.569245 at rs = 1 (checks/heg-hf/convention-check-2026-10-17.json).
-0.01379 — TC-DCD (correlator cutoff k_c = 2 × 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. -0.01379
Table II, row rs=2.0, column TC-DCD; sources/2103.03176.txt line 391; 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.
-0.01326(2) — Fixed-node DMC (trial state: Slater-Jastrow)
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. −0.01326(2)
Table II (Appendix G), N=54 unpolarized, rs=2, column FN-DMC; sources/2305.07240.txt line 679; 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.
-0.01324 — TC-CCD (correlator cutoff k_c = 2 × 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. -0.01324
Table II, row rs=2.0, column TC-CCD; sources/2103.03176.txt line 391; 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.
-0.01311(2) — Fixed-node DMC (trial state: Slater-Jastrow; extrapolated:...
Checked 2026-10-17 · source text of arXiv:0801.0518 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. −0.01311(2)
Table I, rs=2.0, row SJ, column ED; sources/0801.0518.txt line 254; printed in Ha per electron; version read: arXiv text, Table I; APS copy not read | Ha per electron, 54 electrons (27 + 27) in a simple cubic cell. The paper's Hartree-Fock energies (VMC of the plane-wave determinant) match QMBL's HF energy within their error bars at all six rs, e.g. 0.5689(4) against 0.569245 at rs = 1 (checks/heg-hf/convention-check-2026-10-17.json).
-0.01286 — 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. -0.01286
Table II, row rs=2.0, column DCD; sources/2103.03176.txt line 391; 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.
-0.01252(3) — Slater-Jastrow (three-electron Jastrow)
Checked 2026-10-17 · source text of arXiv:0801.0518 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. −0.01252(3)
Table I, rs=2.0, row SJ3; sources/0801.0518.txt line 255; printed in Ha per electron; version read: arXiv text, Table I; APS copy not read | Ha per electron, 54 electrons (27 + 27) in a simple cubic cell. The paper's Hartree-Fock energies (VMC of the plane-wave determinant) match QMBL's HF energy within their error bars at all six rs, e.g. 0.5689(4) against 0.569245 at rs = 1 (checks/heg-hf/convention-check-2026-10-17.json).
-0.01246(3) — Slater-Jastrow
Checked 2026-10-17 · source text of arXiv:0801.0518 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. −0.01246(3)
Table I, rs=2.0, row SJ; sources/0801.0518.txt line 254; printed in Ha per electron; version read: arXiv text, Table I; APS copy not read | Ha per electron, 54 electrons (27 + 27) in a simple cubic cell. The paper's Hartree-Fock energies (VMC of the plane-wave determinant) match QMBL's HF energy within their error bars at all six rs, e.g. 0.5689(4) against 0.569245 at rs = 1 (checks/heg-hf/convention-check-2026-10-17.json).
-0.01162 — 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. -0.01162
Table II, row rs=2.0, column CCD; sources/2103.03176.txt line 391; 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.
-0.0112326 — 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 = -1.620
Table II, rs=2.0, column CCD; sources/1310.6806.txt line 462; printed in Ha, total; printed correlation energy -1.620, E = E_HF + E_c with E_HF = 0.0187673646843 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.
0.0186(2) — Hartree-Fock (plane-wave determinant, VMC estimate)
Checked 2026-10-17 · source text of arXiv:0801.0518 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. 0.0186(2)
Table I, rs=2.0, row HF; sources/0801.0518.txt line 253; printed in Ha per electron; version read: arXiv text, Table I; APS copy not read | Ha per electron, 54 electrons (27 + 27) in a simple cubic cell. The paper's Hartree-Fock energies (VMC of the plane-wave determinant) match QMBL's HF energy within their error bars at all six rs, e.g. 0.5689(4) against 0.569245 at rs = 1 (checks/heg-hf/convention-check-2026-10-17.json).