How these numbers were read
Where each number below was read, and how it was checked.
-0.0552180(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. -0.110436(1)
Table III column EIBDMC, block Ne = 14 (paramagnetic), row rs = 10.0; sources/2202.04622.txt line 520; 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.
-0.0552126(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. −0.0552126(6)
Table I (Appendix G), N=14 unpolarized, rs=10, column MP-NQS; sources/2305.07240.txt line 665; 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.
-0.0552038(3) — 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. -0.1104076(6)
Table III column 3 (WAP-Net nd=8), block Ne = 14 (paramagnetic), row rs = 10.0; sources/2202.04622.txt line 520; 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.
-0.0552025(3) — 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. -0.1104049(6)
Table III column 2 (WAP-Net nd=1), block Ne = 14 (paramagnetic), row rs = 10.0; sources/2202.04622.txt line 520; 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.
-0.0551799(2) — FermiNet (16 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. -0.772519(3)
Table III (SM S3.D), rs=10, column E n_det=16; sources/2604.15888.txt line 1327; 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.
-0.0551786(3) — FermiNet (16 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. -0.772501(4)
Table II (SM S3.B), rs=10, column E'' n_det=16; sources/2604.15888.txt line 1170; 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.
-0.0551699(2) — 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. -0.772378(3)
Table III (SM S3.D), rs=10, column E' n_det=16; sources/2604.15888.txt line 1327; 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.
-0.0551615(3) — 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. -0.1103229(7)
Table III column EIBVMC, block Ne = 14 (paramagnetic), row rs = 10.0; sources/2202.04622.txt line 520; 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.
-0.0551086(3) — 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. -0.771521(4)
Table II (SM S3.B), rs=10, column E'' n_det=4; sources/2604.15888.txt line 1169; 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.
-0.0551037(3) — 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. -0.771452(4)
Table III (SM S3.D), rs=10, column E n_det=4; sources/2604.15888.txt line 1327; 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.
-0.05509 — TC-DCD (correlator cutoff k_c = √2 × 2π/L; extrapolated:...
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. -0.05509
Table I, row rs=10.0, column TC-DCD; sources/2103.03176.txt line 381; 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.
-0.0550894(2) — 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. -0.771252(3)
Table III (SM S3.D), rs=10, column E n_det=1; sources/2604.15888.txt line 1327; 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.
-0.0550893(3) — 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. -0.771250(4)
Table II (SM S3.B), rs=10, column E'' n_det=1; sources/2604.15888.txt line 1168; 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.
-0.0550869(3) — 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. -0.771216(4)
Table III (SM S3.D), rs=10, column E' n_det=4; sources/2604.15888.txt line 1327; 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.
-0.0550698(2) — 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. -0.770977(3)
Table III (SM S3.D), rs=10, column E' n_det=1; sources/2604.15888.txt line 1327; 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.
-0.0542 — TC-CCD (correlator cutoff k_c = √2 × 2π/L; extrapolated:...
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. -0.05420
Table I, row rs=10.0, column TC-CCD; sources/2103.03176.txt line 381; 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.
-0.05289 — 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. -0.05289
Table I, row rs=10.0, column DCD; sources/2103.03176.txt line 381; 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.
-0.0519395(4) — 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 = -0.163951(6) (total, Ha)
Table I, rs=10.0; sources/1202.4990.txt line 8300; printed correlation energy -0.163951(6) Ha for 14 electrons; E = E_HF + E_c with E_HF = -0.0402287252155 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).
-0.0513716 — 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 = -0.156
Table III, rs=10.0, column CCD; sources/1310.6806.txt line 502; printed in Ha, total; printed correlation energy -0.156, E = E_HF + E_c with E_HF = -0.0402287252155 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.
-0.05137 — 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. -0.05137
Table I, row rs=10.0, column CCD; sources/2103.03176.txt line 381; 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.