{ "model": "HEG3D", "lattice": "sc", "n_sites": 14, "boundary": "P", "params": { "N_up": 7, "N_dn": 7, "rs": 0.5, "twist": "Gamma" }, "instance_id": "HEG3D/sc_14_P_7_7_0.5", "rows": [ { "energy": 47.77892, "sigma": null, "energy_variance": null, "dof": 14, "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": "3.41278", "note": "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.", "secondary_of": null } }, { "energy": 47.77528, "sigma": null, "energy_variance": null, "dof": 14, "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": "3.41252", "note": "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.", "secondary_of": null } }, { "energy": 47.77612, "sigma": null, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "TC-CCD", "method_detail": "correlator cutoff k_c = 1 × 2π/L; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "TC-CCD (k_c = 1), 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": "3.41258", "note": "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.", "secondary_of": null } }, { "energy": 47.77416, "sigma": null, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "TC-DCD", "method_detail": "correlator cutoff k_c = 1 × 2π/L; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "TC-DCD (k_c = 1), 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": "3.41244", "note": "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.", "secondary_of": null } }, { "energy": 47.7822815043, "sigma": 0.00000994, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "Slater-Jastrow-backflow", "method_detail": "single determinant", "method_as_published": "SJB-VMC (N = 14 table)", "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": "G. Cassella, H. Sutterud, S. Azadi, N. D. Drummond, D. Pfau, J. S. Spencer & W. M. C. Foulkes, Discovering Quantum Phase Transitions with Fermionic Neural Networks, Phys. Rev. Lett. 130, 036401 (2023), arXiv:2202.05183, doi:10.1103/PhysRevLett.130.036401", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7807415043, "sigma": 0.00000994, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "Fixed-node DMC", "method_detail": "trial state: Slater-Jastrow-backflow; extrapolated: Δτ → 0", "method_as_published": "SJB-DMC (N = 14 table)", "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. Cassella, H. Sutterud, S. Azadi, N. D. Drummond, D. Pfau, J. S. Spencer & W. M. C. Foulkes, Discovering Quantum Phase Transitions with Fermionic Neural Networks, Phys. Rev. Lett. 130, 036401 (2023), arXiv:2202.05183, doi:10.1103/PhysRevLett.130.036401", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7795715043, "sigma": 0.0000602, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FermiNet", "method_detail": "1 dense determinant, 4 layers 256/32", "method_as_published": "FermiNet (1 dense determinant, N = 14 table)", "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. Cassella, H. Sutterud, S. Azadi, N. D. Drummond, D. Pfau, J. S. Spencer & W. M. C. Foulkes, Discovering Quantum Phase Transitions with Fermionic Neural Networks, Phys. Rev. Lett. 130, 036401 (2023), arXiv:2202.05183, doi:10.1103/PhysRevLett.130.036401", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7775815042, "sigma": 0.0000602, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FermiNet", "method_detail": "16 dense determinants, 4 layers 256/32", "method_as_published": "FermiNet (16 dense determinants, N = 14 table)", "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. Cassella, H. Sutterud, S. Azadi, N. D. Drummond, D. Pfau, J. S. Spencer & W. M. C. Foulkes, Discovering Quantum Phase Transitions with Fermionic Neural Networks, Phys. Rev. Lett. 130, 036401 (2023), arXiv:2202.05183, doi:10.1103/PhysRevLett.130.036401", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7802115042, "sigma": 0.00007, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FermiNet", "method_detail": "1 block determinant, 4 layers 256/32", "method_as_published": "FermiNet (1 block determinant, N = 14 table)", "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. Cassella, H. Sutterud, S. Azadi, N. D. Drummond, D. Pfau, J. S. Spencer & W. M. C. Foulkes, Discovering Quantum Phase Transitions with Fermionic Neural Networks, Phys. Rev. Lett. 130, 036401 (2023), arXiv:2202.05183, doi:10.1103/PhysRevLett.130.036401", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7789015042, "sigma": 0.0000602, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FermiNet", "method_detail": "16 block determinants, 4 layers 256/32", "method_as_published": "FermiNet (16 block determinants, N = 14 table)", "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. Cassella, H. Sutterud, S. Azadi, N. D. Drummond, D. Pfau, J. S. Spencer & W. M. C. Foulkes, Discovering Quantum Phase Transitions with Fermionic Neural Networks, Phys. Rev. Lett. 130, 036401 (2023), arXiv:2202.05183, doi:10.1103/PhysRevLett.130.036401", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.8516215043, "sigma": 0.0000994, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FCIQMC", "method_detail": "initiator (n_add = 3), 114 spin orbitals", "method_as_published": "i-FCIQMC (M = 114 spin orbitals)", "family": "FCIQMC / CC", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "J. J. Shepherd, G. H. Booth & A. Alavi, Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models, J. Chem. Phys. 136, 244101 (2012), arXiv:1201.4691, doi:10.1063/1.4720076", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.8096215043, "sigma": 0.0000994, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FCIQMC", "method_detail": "initiator (n_add = 3), 186 spin orbitals", "method_as_published": "i-FCIQMC (M = 186 spin orbitals)", "family": "FCIQMC / CC", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "J. J. Shepherd, G. H. Booth & A. Alavi, Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models, J. Chem. Phys. 136, 244101 (2012), arXiv:1201.4691, doi:10.1063/1.4720076", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7888215042, "sigma": 0.000294, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FCIQMC", "method_detail": "initiator (n_add = 3), 358 spin orbitals", "method_as_published": "i-FCIQMC (M = 358 spin orbitals)", "family": "FCIQMC / CC", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "J. J. Shepherd, G. H. Booth & A. Alavi, Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models, J. Chem. Phys. 136, 244101 (2012), arXiv:1201.4691, doi:10.1063/1.4720076", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7792215043, "sigma": 0.000294, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FCIQMC", "method_detail": "initiator (n_add = 3), 778 spin orbitals", "method_as_published": "i-FCIQMC (M = 778 spin orbitals)", "family": "FCIQMC / CC", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "J. J. Shepherd, G. H. Booth & A. Alavi, Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models, J. Chem. Phys. 136, 244101 (2012), arXiv:1201.4691, doi:10.1063/1.4720076", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7749215042, "sigma": 0.000294, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FCIQMC", "method_detail": "initiator (n_add = 3), 1850 spin orbitals", "method_as_published": "i-FCIQMC (M = 1850 spin orbitals)", "family": "FCIQMC / CC", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "J. J. Shepherd, G. H. Booth & A. Alavi, Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models, J. Chem. Phys. 136, 244101 (2012), arXiv:1201.4691, doi:10.1063/1.4720076", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7746215043, "sigma": 0.000406, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FCIQMC", "method_detail": "initiator (n_add = 3), 2368 spin orbitals", "method_as_published": "i-FCIQMC (M = 2368 spin orbitals)", "family": "FCIQMC / CC", "bound_type": "variational", "bound_type_reason": "variational ansatz at a stated size; energy is an upper bound (assigned during source reading)", "reference": "J. J. Shepherd, G. H. Booth & A. Alavi, Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models, J. Chem. Phys. 136, 244101 (2012), arXiv:1201.4691, doi:10.1063/1.4720076", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7716215042, "sigma": 0.000294, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FCIQMC", "method_detail": "initiator (n_add = 3); extrapolated: 1/M → 0 (complete basis)", "method_as_published": "i-FCIQMC, 1/M extrapolation", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "J. J. Shepherd, G. H. Booth & A. Alavi, Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models, J. Chem. Phys. 136, 244101 (2012), arXiv:1201.4691, doi:10.1063/1.4720076", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7726215043, "sigma": 0.0007, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FCIQMC", "method_detail": "initiator (n_add = 3), run at 1850 spin orbitals; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "i-FCIQMC, single-point basis-limit estimate (run at M = 1850)", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "J. J. Shepherd, G. H. Booth & A. Alavi, Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models, J. Chem. Phys. 136, 244101 (2012), arXiv:1201.4691, doi:10.1063/1.4720076", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7930795042, "sigma": 9.94e-7, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "MP2", "method_detail": "extrapolated: 1/M → 0 (complete basis)", "method_as_published": "MP2, 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": "J. J. Shepherd, A. Grüneis, G. H. Booth, G. Kresse & A. Alavi, Convergence of many-body wave-function expansions using a plane-wave basis: From homogeneous electron gas to solid state systems, Phys. Rev. B 86, 035111 (2012), arXiv:1202.4990, doi:10.1103/PhysRevB.86.035111", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7788215043, "sigma": 0.0000994, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "CCSD", "method_detail": "initiator stochastic coupled cluster at the infinite-population limit; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCSD (initiator stochastic CC), 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": "J. S. Spencer & A. J. W. Thom, Developments in stochastic coupled cluster theory: The initiator approximation and application to the uniform electron gas, J. Chem. Phys. 144, 084108 (2016), arXiv:1511.05752, doi:10.1063/1.4942173", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.7720215042, "sigma": 0.000196, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "CCSDT", "method_detail": "initiator stochastic coupled cluster at the infinite-population limit; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCSDT (initiator stochastic CC), 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": "J. S. Spencer & A. J. W. Thom, Developments in stochastic coupled cluster theory: The initiator approximation and application to the uniform electron gas, J. Chem. Phys. 144, 084108 (2016), arXiv:1511.05752, doi:10.1063/1.4942173", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } }, { "energy": 47.8512215042, "sigma": 0.0000994, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "ph-AFQMC", "method_detail": "phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag", "method_as_published": "RHF+ph-AFQMC [phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag] (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": "E_c = -0.5173(1)", "note": "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", "secondary_of": null } }, { "energy": 47.8093215041, "sigma": 0.000196, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "ph-AFQMC", "method_detail": "phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag", "method_as_published": "RHF+ph-AFQMC [phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag] (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": "E_c = -0.5592(2)", "note": "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", "secondary_of": null } }, { "energy": 47.7891215042, "sigma": 0.000196, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "ph-AFQMC", "method_detail": "phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag", "method_as_published": "RHF+ph-AFQMC [phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag] (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": "E_c = -0.5794(2)", "note": "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", "secondary_of": null } }, { "energy": 47.7804215042, "sigma": 0.000196, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "ph-AFQMC", "method_detail": "phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag", "method_as_published": "RHF+ph-AFQMC [phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag] (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": "E_c = -0.5881(2)", "note": "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", "secondary_of": null } }, { "energy": 47.7765215042, "sigma": 0.000798, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "ph-AFQMC", "method_detail": "phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag", "method_as_published": "RHF+ph-AFQMC [phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag] (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": "E_c = -0.5920(8)", "note": "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", "secondary_of": null } }, { "energy": 47.7764215041, "sigma": 0.000196, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "ph-AFQMC", "method_detail": "phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag", "method_as_published": "RHF+ph-AFQMC [phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag] (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": "E_c = -0.5921(2)", "note": "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", "secondary_of": null } }, { "energy": 47.7759215042, "sigma": 0.000798, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "ph-AFQMC", "method_detail": "phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag", "method_as_published": "RHF+ph-AFQMC [phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag] (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": "E_c = -0.5926(8)", "note": "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", "secondary_of": null } }, { "energy": 47.7760215043, "sigma": 0.000406, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "ph-AFQMC", "method_detail": "phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag", "method_as_published": "RHF+ph-AFQMC [phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag] (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": "E_c = -0.5925(4)", "note": "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", "secondary_of": null } }, { "energy": 47.7754215042, "sigma": 0.000602, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "ph-AFQMC", "method_detail": "phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag", "method_as_published": "RHF+ph-AFQMC [phaseless AFQMC with a single-determinant RHF trial, time step 0.005 a.u., 2880 walkers (txt line 325-327); calculated with the PAUXY packag] (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": "E_c = -0.5931(6)", "note": "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", "secondary_of": null } }, { "energy": 47.7800215042, "sigma": 0.0000602, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "CCSD", "method_detail": "coupled cluster Monte Carlo (HANDE), non-initiator; level CCSD; ion: CCSD fitted in 1/M with chosen polynomial order, higher levels by ing l; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCSD [coupled cluster Monte Carlo (HANDE), non-initiator; level CCSD; ion: CCSD fitted in 1/M with chosen polynomial order, higher levels by ing l; extrapolated: 1/M → 0 (complete basis)] (arXiv:1706.09923)", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "Verena A. Neufeld and Alex J. W. Thom, A study of the dense Uniform Electron Gas with high orders of Coupled Cluster, J. Chem. Phys. 147, 194105, arXiv:1706.09923, doi:10.1063/1.5003794", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": 47.7739515042, "sigma": 0.00007, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "CCSDT", "method_detail": "coupled cluster Monte Carlo (HANDE), non-initiator; level CCSDT; ion: CCSD fitted in 1/M with chosen polynomial order, higher levels by ing ; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCSDT [coupled cluster Monte Carlo (HANDE), non-initiator; level CCSDT; ion: CCSD fitted in 1/M with chosen polynomial order, higher levels by ing ; extrapolated: 1/M → 0 (complete basis)] (arXiv:1706.09923)", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "Verena A. Neufeld and Alex J. W. Thom, A study of the dense Uniform Electron Gas with high orders of Coupled Cluster, J. Chem. Phys. 147, 194105, arXiv:1706.09923, doi:10.1063/1.5003794", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": 47.7738715042, "sigma": 0.0000798, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "CCSDTQ", "method_detail": "coupled cluster Monte Carlo (HANDE), non-initiator; level CCSDTQ; ion: CCSD fitted in 1/M with chosen polynomial order, higher levels by ing; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCSDTQ [coupled cluster Monte Carlo (HANDE), non-initiator; level CCSDTQ; ion: CCSD fitted in 1/M with chosen polynomial order, higher levels by ing; extrapolated: 1/M → 0 (complete basis)] (arXiv:1706.09923)", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "Verena A. Neufeld and Alex J. W. Thom, A study of the dense Uniform Electron Gas with high orders of Coupled Cluster, J. Chem. Phys. 147, 194105, arXiv:1706.09923, doi:10.1063/1.5003794", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": 47.7738515043, "sigma": 0.0000896, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FCIQMC", "method_detail": "(i)FCIQMC; initiator used for M > 358 at rs=0.5 (txt line 253-255); CBS value estimated as footnote g; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "FCIQMC [(i)FCIQMC; initiator used for M > 358 at rs=0.5 (txt line 253-255); CBS value estimated as footnote g; extrapolated: 1/M → 0 (complete basis)] (arXiv:1706.09923)", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "Verena A. Neufeld and Alex J. W. Thom, A study of the dense Uniform Electron Gas with high orders of Coupled Cluster, J. Chem. Phys. 147, 194105, arXiv:1706.09923, doi:10.1063/1.5003794", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": 47.7798615042, "sigma": 0.0000504, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "CCSD", "method_detail": "CCMC non-initiator, linear fit in 1/M, three points excluded (rejected by the paper: disagrees with quadratic fit within 2 sigma); extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCSD [CCMC non-initiator, linear fit in 1/M, three points excluded (rejected by the paper: disagrees with quadratic fit within 2 sigma); extrapolated: 1/M → 0 (complete basis)] (arXiv:1706.09923)", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "Verena A. Neufeld and Alex J. W. Thom, A study of the dense Uniform Electron Gas with high orders of Coupled Cluster, J. Chem. Phys. 147, 194105, arXiv:1706.09923, doi:10.1063/1.5003794", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": 47.7800415042, "sigma": 0.00007, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "CCSD", "method_detail": "CCMC non-initiator, cubic fit in 1/M, one point excluded (agrees with the quadratic fit within 2 sigma); extrapolated: 1/M → 0 (complete basis)", "method_as_published": "CCSD [CCMC non-initiator, cubic fit in 1/M, one point excluded (agrees with the quadratic fit within 2 sigma); extrapolated: 1/M → 0 (complete basis)] (arXiv:1706.09923)", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "Verena A. Neufeld and Alex J. W. Thom, A study of the dense Uniform Electron Gas with high orders of Coupled Cluster, J. Chem. Phys. 147, 194105, arXiv:1706.09923, doi:10.1063/1.5003794", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": 47.7735515041, "sigma": 0.0000406, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "FCIQMC", "method_detail": "direct linear 1/M fit including spin orbitals up to M = 4218; shown by the paper to be too negative; extrapolated: 1/M → 0 (complete basis)", "method_as_published": "iFCIQMC [direct linear 1/M fit including spin orbitals up to M = 4218; shown by the paper to be too negative; extrapolated: 1/M → 0 (complete basis)] (arXiv:1706.09923)", "family": "FCIQMC / CC", "bound_type": "extrapolated", "bound_type_reason": "zero-variance or bond-dimension extrapolation; not an upper bound (assigned during source reading)", "reference": "Verena A. Neufeld and Alex J. W. Thom, A study of the dense Uniform Electron Gas with high orders of Coupled Cluster, J. Chem. Phys. 147, 194105, arXiv:1706.09923, doi:10.1063/1.5003794", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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.", "secondary_of": null } }, { "energy": 47.7805215042, "sigma": null, "energy_variance": null, "dof": 14, "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 = -0.588", "note": "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.", "secondary_of": null } }, { "energy": 47.7737215042, "sigma": 0.000196, "energy_variance": null, "dof": 14, "einf": null, "v_score": null, "method": "Transcorrelated FCIQMC", "method_detail": "FCIQMC on the transcorrelated Hamiltonian H_TC = exp(-tau) H exp(tau) with the basis-adapted correlation factor of Eq. (22), three-body term", "method_as_published": "FCIQMC-TC [FCIQMC on the transcorrelated Hamiltonian H_TC = exp(-tau) H exp(tau) with the basis-adapted correlation factor of Eq. (22), three-body term] (arXiv:1712.07524)", "family": "FCIQMC / CC", "bound_type": "projected", "bound_type_reason": "projection (GFMC/fixed-node) on a trial state; not a strict variational bound (assigned during source reading)", "reference": "Hongjun Luo and Ali Alavi, Combining the Transcorrelated method with Full Configuration Interaction Quantum Monte Carlo: application to the homogeneous electron gas, J. Chem. Theory Comput. 14, 1403-1411, arXiv:1712.07524, doi:10.1021/acs.jctc.7b01257", "peer_reviewed": true, "source": "sweep-allresults-2026-10-19", "provenance": "primary", "verified": { "checked_on": "2026-10-19", "method": "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)", "note": "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).", "secondary_of": null } } ], "url": "https://qmbl.org/i/HEG3D/sc_14_P_7_7_0.5/", "per_site_divisor": 14, "per_site_label": "E/N (Ha)", "record": { "energy": 47.7716215042, "sigma": 0.000294, "method": "FCIQMC", "method_detail": "initiator (n_add = 3); extrapolated: 1/M → 0 (complete basis)", "reference": "J. J. Shepherd, G. H. Booth & A. Alavi, Investigation of the full configuration interaction quantum Monte Carlo method using homogeneous electron gas models, J. Chem. Phys. 136, 244101 (2012), arXiv:1201.4691, doi:10.1063/1.4720076", "bound_type": "extrapolated", "energy_per_site": 3.4122586788714284 }, "no_record_reason": null }