{
  "model": "HEG3D",
  "lattice": "sc",
  "n_sites": 14,
  "boundary": "P",
  "params": {
    "N_up": 7,
    "N_dn": 7,
    "rs": 3,
    "twist": "Gamma"
  },
  "instance_id": "HEG3D/sc_14_P_7_7_3",
  "rows": [
    {
      "energy": -1.01579094295,
      "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)",
      "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)] (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 = -0.3590(2)",
        "note": "Table III, rs=3.0, M=81, column ph-AFQMC; sources/1905.04361.txt line 500; printed in Ha, total; printed correlation energy -0.3590(2), E = E_HF + E_c with E_HF = -0.0469136387818 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": -1.02909094295,
      "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)",
      "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)] (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 = -0.3723(4)",
        "note": "Table III, rs=3.0, M=179, column ph-AFQMC; sources/1905.04361.txt line 501; printed in Ha, total; printed correlation energy -0.3723(4), E = E_HF + E_c with E_HF = -0.0469136387818 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": -1.02929094294,
      "sigma": 0.000504,
      "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)",
      "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)] (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 = -0.3725(5)",
        "note": "Table III, rs=3.0, M=925, column ph-AFQMC; sources/1905.04361.txt line 502; printed in Ha, total; printed correlation energy -0.3725(5), E = E_HF + E_c with E_HF = -0.0469136387818 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": -0.996290942945,
      "sigma": 0.0000994,
      "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 = -0.3395(1)",
        "note": "Table I, row CCSD, rs=3.0 a0 (own value); sources/1706.09923.txt line 306; printed in Ha, total; printed correlation energy -0.3395(1), E = E_HF + E_c with E_HF = -0.0469136387818 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": -1.03479094295,
      "sigma": 0.000294,
      "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 = -0.3780(3)",
        "note": "Table I, row CCSDT, rs=3.0 a0 (own value); sources/1706.09923.txt line 307; printed in Ha, total; printed correlation energy -0.3780(3), E = E_HF + E_c with E_HF = -0.0469136387818 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": -1.04009094295,
      "sigma": 0.000294,
      "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 = -0.3833(3)",
        "note": "Table I, row CCSDTQ, rs=3.0 a0 (own value); sources/1706.09923.txt line 308; printed in Ha, total; printed correlation energy -0.3833(3), E = E_HF + E_c with E_HF = -0.0469136387818 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": -1.04049094294,
      "sigma": 0.000294,
      "energy_variance": null,
      "dof": 14,
      "einf": null,
      "v_score": null,
      "method": "CCSDTQ5",
      "method_detail": "coupled cluster Monte Carlo (HANDE), non-initiator; level CCSDTQ5; ion: CCSD fitted in 1/M with chosen polynomial order, higher levels by in; extrapolated: 1/M → 0 (complete basis)",
      "method_as_published": "CCSDTQ5 [coupled cluster Monte Carlo (HANDE), non-initiator; level CCSDTQ5; ion: CCSD fitted in 1/M with chosen polynomial order, higher levels by in; 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 = -0.3837(3)",
        "note": "Table I, row CCSDTQ5, rs=3.0 a0 (own value); sources/1706.09923.txt line 309; printed in Ha, total; printed correlation energy -0.3837(3), E = E_HF + E_c with E_HF = -0.0469136387818 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": -0.995790942945,
      "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 = -0.339",
        "note": "Table III, rs=3.0, column CCD; sources/1310.6806.txt line 495; printed in Ha, total; printed correlation energy -0.339, E = E_HF + E_c with E_HF = -0.0469136387818 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_14_P_7_7_3/",
  "per_site_divisor": 14,
  "per_site_label": "E/N (Ha)",
  "record": {
    "energy": -1.04049094294,
    "sigma": 0.000294,
    "method": "CCSDTQ5",
    "method_detail": "coupled cluster Monte Carlo (HANDE), non-initiator; level CCSDTQ5; ion: CCSD fitted in 1/M with chosen polynomial order, higher levels by in; extrapolated: 1/M → 0 (complete basis)",
    "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",
    "bound_type": "extrapolated",
    "energy_per_site": -0.07432078163857143
  },
  "no_record_reason": null
}