{ "model": "HEG3D", "lattice": "sc", "n_sites": 54, "boundary": "P", "params": { "N_up": 27, "N_dn": 27, "rs": 2, "twist": "Gamma" }, "instance_id": "HEG3D/sc_54_P_27_27_2", "rows": [ { "energy": -0.758484, "sigma": 0.000432, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "MP-NQS", "method_detail": "plane-wave orbitals", "method_as_published": "MP-NQS (plane-wave orbitals)", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "G. Pescia, J. Nys, J. Kim, A. Lovato & G. Carleo, Message-passing neural quantum states for the homogeneous electron gas, Phys. Rev. B 110, 035108 (2024), arXiv:2305.07240, doi:10.1103/PhysRevB.110.035108", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": -0.7506, "sigma": 0.00054, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "MP-NQS", "method_detail": "Gaussian orbitals on bcc sites", "method_as_published": "MP-NQS (Gaussian orbitals on bcc sites)", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "G. Pescia, J. Nys, J. Kim, A. Lovato & G. Carleo, Message-passing neural quantum states for the homogeneous electron gas, Phys. Rev. B 110, 035108 (2024), arXiv:2305.07240, doi:10.1103/PhysRevB.110.035108", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": -0.71604, "sigma": 0.00108, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "Fixed-node DMC", "method_detail": "trial state: Slater-Jastrow", "method_as_published": "FN-DMC (Slater-Jastrow trial state)", "family": "DMC", "bound_type": "projected", "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)", "reference": "G. Pescia, J. Nys, J. Kim, A. Lovato & G. Carleo, Message-passing neural quantum states for the homogeneous electron gas, Phys. Rev. B 110, 035108 (2024), arXiv:2305.07240, doi:10.1103/PhysRevB.110.035108", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": -0.74736, "sigma": 0.000054, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "DeepSolid", "method_detail": "1 determinant, 3 layers 256/32", "method_as_published": "DeepSolid (1 determinant)", "family": "other NQS", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "X. Li, Z. Li & J. Chen, Ab initio calculation of real solids via neural network ansatz, Nat. Commun. 13, 7895 (2022), arXiv:2203.15472, doi:10.1038/s41467-022-35627-1", "peer_reviewed": true, "source": "sweep-allresults-2026-10-16", "provenance": "primary", "verified": { "checked_on": "2026-10-16", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": 1.0044, "sigma": 0.0108, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "Hartree-Fock", "method_detail": "plane-wave determinant, VMC estimate", "method_as_published": "VMC of the Hartree-Fock determinant", "family": "mean field", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "P. López Ríos, A. Ma, N. D. Drummond, M. D. Towler & R. J. Needs, Inhomogeneous backflow transformations in quantum Monte Carlo calculations, Phys. Rev. E 74, 066701 (2006), arXiv:0801.0518, doi:10.1103/PhysRevE.74.066701", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": -0.67284, "sigma": 0.00162, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "Slater-Jastrow", "method_detail": "", "method_as_published": "VMC, SJ", "family": "classic VMC", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "P. López Ríos, A. Ma, N. D. Drummond, M. D. Towler & R. J. Needs, Inhomogeneous backflow transformations in quantum Monte Carlo calculations, Phys. Rev. E 74, 066701 (2006), arXiv:0801.0518, doi:10.1103/PhysRevE.74.066701", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": -0.70794, "sigma": 0.00108, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "Fixed-node DMC", "method_detail": "trial state: Slater-Jastrow; extrapolated: Δτ → 0", "method_as_published": "DMC, SJ nodes", "family": "DMC", "bound_type": "projected", "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)", "reference": "P. López Ríos, A. Ma, N. D. Drummond, M. D. Towler & R. J. Needs, Inhomogeneous backflow transformations in quantum Monte Carlo calculations, Phys. Rev. E 74, 066701 (2006), arXiv:0801.0518, doi:10.1103/PhysRevE.74.066701", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": -0.67608, "sigma": 0.00162, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "Slater-Jastrow", "method_detail": "three-electron Jastrow", "method_as_published": "VMC, SJ3", "family": "classic VMC", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "P. López Ríos, A. Ma, N. D. Drummond, M. D. Towler & R. J. Needs, Inhomogeneous backflow transformations in quantum Monte Carlo calculations, Phys. Rev. E 74, 066701 (2006), arXiv:0801.0518, doi:10.1103/PhysRevE.74.066701", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": -0.74628, "sigma": 0.00108, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "Slater-Jastrow-backflow", "method_detail": "homogeneous backflow", "method_as_published": "VMC, BF", "family": "classic VMC", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "P. López Ríos, A. Ma, N. D. Drummond, M. D. Towler & R. J. Needs, Inhomogeneous backflow transformations in quantum Monte Carlo calculations, Phys. Rev. E 74, 066701 (2006), arXiv:0801.0518, doi:10.1103/PhysRevE.74.066701", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": -0.754164, "sigma": 0.000486, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "Fixed-node DMC", "method_detail": "trial state: Slater-Jastrow-backflow; extrapolated: Δτ → 0", "method_as_published": "DMC, BF nodes", "family": "DMC", "bound_type": "projected", "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)", "reference": "P. López Ríos, A. Ma, N. D. Drummond, M. D. Towler & R. J. Needs, Inhomogeneous backflow transformations in quantum Monte Carlo calculations, Phys. Rev. E 74, 066701 (2006), arXiv:0801.0518, doi:10.1103/PhysRevE.74.066701", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": -0.62748, "sigma": null, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "CCD", "method_detail": "extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCD, complete-basis limit", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "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", "note": "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.", "secondary_of": null } }, { "energy": -0.69444, "sigma": null, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "DCD", "method_detail": "extrapolated: 1/M → 0 (complete basis)", "method_as_published": "DCD, complete-basis limit", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "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", "note": "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.", "secondary_of": null } }, { "energy": -0.71496, "sigma": null, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "TC-CCD", "method_detail": "correlator cutoff k_c = 2 × 2π/L; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "TC-CCD (k_c = 2), complete-basis limit", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "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", "note": "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.", "secondary_of": null } }, { "energy": -0.74466, "sigma": null, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "TC-DCD", "method_detail": "correlator cutoff k_c = 2 × 2π/L; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "TC-DCD (k_c = 2), complete-basis limit", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "K. Liao, T. Schraivogel, H. Luo, D. Kats & A. Alavi, Towards efficient and accurate ab initio solutions to periodic systems via transcorrelation and coupled cluster theory, Phys. Rev. Research 3, 033072 (2021), arXiv:2103.03176, doi:10.1103/PhysRevResearch.3.033072", "peer_reviewed": true, "source": "sweep-allresults-2026-10-17", "provenance": "primary", "verified": { "checked_on": "2026-10-17", "method": "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", "note": "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.", "secondary_of": null } }, { "energy": -0.77166, "sigma": 0.00162, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "ph-AFQMC", "method_detail": "RHF trial, time step 0.005 a.u., 2880 walkers; basis M=1419 (Table V caption: 'Both ph-AFQMC and i-FCIQMC numbers are obtained from M = 1419", "method_as_published": "RHF+ph-AFQMC [RHF trial, time step 0.005 a.u., 2880 walkers; basis M=1419 (Table V caption: 'Both ph-AFQMC and i-FCIQMC numbers are obtained from M = 1419] (arXiv:1905.04361)", "family": "AFQMC / GFMC", "bound_type": "projected", "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)", "reference": "Joonho Lee, Fionn D. Malone, Miguel A. Morales, An Auxiliary-Field Quantum Monte Carlo Perspective on the Ground State of the Dense Uniform Electron Gas: An Investigation with Hartree-Fock Trial Wavefunctions, J. Chem. Phys. 151, 064122, arXiv:1905.04361, doi:10.1063/1.5109572", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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", "secondary_of": null } }, { "energy": -0.606562307048, "sigma": null, "energy_variance": null, "dof": 54, "einf": null, "v_score": null, "method": "CCD", "method_detail": "full CCD (driver, ladders, rings, crossed-rings, mosaics); equals CCSD in the HEG; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCD [full CCD (driver, ladders, rings, crossed-rings, mosaics); equals CCSD in the HEG; extrapolated: 1/M → 0 (complete basis)] (arXiv:1310.6806)", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "James J. Shepherd, Thomas M. Henderson, and Gustavo E. Scuseria, Coupled Cluster Channels in the Homogeneous Electron Gas, J. Chem. Phys. 140, 124102, arXiv:1310.6806, doi:10.1063/1.4867783", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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", "note": "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.", "secondary_of": null } } ], "url": "https://qmbl.org/i/HEG3D/sc_54_P_27_27_2/", "per_site_divisor": 54, "per_site_label": "E/N (Ha)", "record": { "energy": -0.77166, "sigma": 0.00162, "method": "ph-AFQMC", "method_detail": "RHF trial, time step 0.005 a.u., 2880 walkers; basis M=1419 (Table V caption: 'Both ph-AFQMC and i-FCIQMC numbers are obtained from M = 1419", "reference": "Joonho Lee, Fionn D. Malone, Miguel A. Morales, An Auxiliary-Field Quantum Monte Carlo Perspective on the Ground State of the Dense Uniform Electron Gas: An Investigation with Hartree-Fock Trial Wavefunctions, J. Chem. Phys. 151, 064122, arXiv:1905.04361, doi:10.1063/1.5109572", "bound_type": "projected", "energy_per_site": -0.01429 }, "no_record_reason": null }