{
  "model": "Hchain",
  "lattice": "chain",
  "n_sites": 50,
  "boundary": "O",
  "params": {
    "N_up": 25,
    "N_dn": 25,
    "R": 2.4,
    "basis": "cc-pVTZ"
  },
  "instance_id": "Hchain/chain_50_O_R2.4_ccpvtz",
  "rows": [
    {
      "energy": -27.5726,
      "sigma": 0.002,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "ph-AFQMC",
      "ansatz": null,
      "method_detail": "",
      "method_as_published": "AFQMC [phaseless]",
      "family": "AFQMC / GFMC",
      "bound_type": "projected",
      "bound_type_reason": "AFQMC, fixed-node or lattice-regularised DMC, coupled cluster, MRCI+Q or an embedding method; not a bound (RULES.md 13.4; assigned during source reading)",
      "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059",
      "peer_reviewed": true,
      "source": "track3-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0; source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading",
        "reported_as": "-27.5726 0.0020 (total for N = 50; second number the stated uncertainty)",
        "note": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/AFQMC_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "arXiv:1705.01608v2 (6 Nov 2017, sources/1705.01608.txt and .pdf) and journal PRX 7, 031059 (sources/1705.01608-PhysRevX.7.031059.txt); dataset github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183, raw files re-fetched from raw.githubusercontent.com (all HTTP 200) and compared with the committed TSV; node scripts compare.mjs, gap.mjs, others.mjs in this folder",
          "location": "dataset file N_50_OBC/R_2.4/AFQMC_basis-TZ",
          "reported_as": "-27.5726 0.0020",
          "conversion": "-27.5726 Eh total (file stores the total, nuclear repulsion included); per atom -27.5726 / 50 = -0.55145200; sigma 0.002 total = 0.0000400000 per atom",
          "note": "mechanical match: raw GitHub file = committed TSV = reported_as; eps*N and sigma*N reproduce the file to 1e-9; N_up = N_dn = N/2, OBC chain, basis token matches the file's basis key; method AFQMC phaseless, projected, sampled (RULES §13.4); no DMRG or FCI on this instance to test against; number printed only in the dataset; the paper's tables print H10 and TDL values only (searched both texts for the total and the 5-decimal per-atom value: only coincidental TDL-table matches); no duplicate row on the instance (no other AFQMC row in the sweep file; track 3 has no data/Hchain files)",
          "secondary_of": null,
          "source_entry": "h-motta17-afqmc-c2#48 (qmbl-verify 2026-10-23/24, verified)"
        }
      }
    },
    {
      "energy": -27.504012,
      "sigma": null,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "DMET",
      "ansatz": null,
      "method_detail": "fragment of 2 atoms",
      "method_as_published": "DMET [fragment of 2 atoms]",
      "family": "other",
      "bound_type": "projected",
      "bound_type_reason": "AFQMC, fixed-node or lattice-regularised DMC, coupled cluster, MRCI+Q or an embedding method; not a bound (RULES.md 13.4; assigned during source reading)",
      "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059",
      "peer_reviewed": true,
      "source": "track3-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0; source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading",
        "reported_as": "-27.504012 (total for N = 50)",
        "note": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/DMET_2_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183a5a2dd2a471bbde3f3c4952cc3d2432ea (commit 2017-10-09 by the first author), fetched fresh from raw.githubusercontent.com on 2026-10-24 and compared with sources/1705.01608-data-b99a183.tsv; method text: PRX 7, 031059 journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2 text, Appendix A 3 a",
          "location": "file N_50_OBC/R_2.4/DMET_2_basis-TZ (single number, total energy in Hartree with nuclear repulsion)",
          "reported_as": "-27.504012 (total, Hartree, N = 50)",
          "conversion": "-27.504012 / 50 = -0.5500802400 Ha per atom; stored eps x N = -27.504012 (difference 0.0e+0)",
          "note": "N = 50, open chain, R = 2.4 bohr, cc-pVTZ, N_up = N_dn = 25, DMET[2] with FCI solver; bound_type projected (RULES 13.4); no sigma (deterministic). Number first printed in the dataset; not printed in the journal or arXiv v2 tables (text search of both). No other row with this value on the instance; data/Hchain does not exist (track 3 held), so no cross-batch duplicate.",
          "secondary_of": null,
          "source_entry": "h-motta17-dmet-c2#59 (qmbl-verify 2026-10-23/24, verified)"
        }
      },
      "sampled": false,
      "corrections": [
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-27.504012 (total for N = 50)",
          "location": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/DMET_2_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference",
          "checked_on": "2026-10-20",
          "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).",
          "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json"
        }
      ]
    },
    {
      "energy": -27.55412,
      "sigma": null,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "RCCSD(T)",
      "ansatz": null,
      "method_detail": "",
      "method_as_published": "RCCSD(T)",
      "family": "FCIQMC / CC",
      "bound_type": "approximate",
      "bound_type_reason": "finite-order perturbation theory, GW, or a perturbative correction to coupled cluster (track 3, 2026-10-21); error of unknown sign (RULES.md 13.4; assigned during source reading)",
      "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059",
      "peer_reviewed": true,
      "source": "track3-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0; source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading",
        "reported_as": "-27.55412 (total for N = 50)",
        "note": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/RCCSD(T)_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "PRX 7, 031059 (2017) journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2 text (sources/1705.01608.txt, v2 stamp read from the PDF with pypdf); data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183, files re-fetched from GitHub (sources/1705.01608-data-raw-misc-1.json in the run folder), identical to the committed TSV; compared by script (tsvcheck.mjs, fetch_raw.mjs)",
          "location": "data repository file N_50_OBC/R_2.4/RCCSD(T)_basis-TZ (the paper prints no finite-basis H50 value in Tables II-VI; Appendix A 1 a names the H50 cc-pVTZ/cc-pVQZ RCCSD and RCCSD(T) runs: 'H50 with cc-pVTZ and cc-pVQZ basis with this implementation [PySCF]')",
          "reported_as": "-27.55412 (total, Hartree)",
          "conversion": "none: the file is the total for N = 50 with nuclear repulsion (Table II STO-6G H10 FCI convention, App. B)",
          "note": "Value identical to the raw GitHub file and the TSV; N = 50, OBC (N_50_OBC), R = 2.4 bohr, basis cc-pVTZ from the file name suffix, N_up = N_dn = 25 ('We only consider spin-unpolarized systems, with N_up = N_dn = N/2'); bound_type approximate per RULES.md §13.4 (CCSD(T) provisional approximate, 2026-10-21); RHF reference; no exact row exists on this instance, so the 2026-10-24 ruling gives no below-reference flag; sigma null correct (deterministic, no stated uncertainty).",
          "secondary_of": null,
          "source_entry": "h-motta17-misc-1#32 (qmbl-verify 2026-10-23/24, verified)"
        }
      },
      "sampled": false,
      "corrections": [
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-27.55412 (total for N = 50)",
          "location": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/RCCSD(T)_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference",
          "checked_on": "2026-10-20",
          "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).",
          "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json"
        }
      ]
    },
    {
      "energy": -27.48998,
      "sigma": null,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "RCCSD",
      "ansatz": null,
      "method_detail": "",
      "method_as_published": "RCCSD",
      "family": "FCIQMC / CC",
      "bound_type": "projected",
      "bound_type_reason": "AFQMC, fixed-node or lattice-regularised DMC, coupled cluster, MRCI+Q or an embedding method; not a bound (RULES.md 13.4; assigned during source reading)",
      "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059",
      "peer_reviewed": true,
      "source": "track3-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0; source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading",
        "reported_as": "-27.48998 (total for N = 50)",
        "note": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/RCCSD_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "PRX 7, 031059 (2017) journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2 text (sources/1705.01608.txt, v2 stamp read from the PDF with pypdf); data repository github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183, files re-fetched from GitHub (sources/1705.01608-data-raw-misc-1.json in the run folder), identical to the committed TSV; compared by script (tsvcheck.mjs, fetch_raw.mjs)",
          "location": "data repository file N_50_OBC/R_2.4/RCCSD_basis-TZ (the paper prints no finite-basis H50 value in Tables II-VI; Appendix A 1 a names the H50 cc-pVTZ/cc-pVQZ RCCSD and RCCSD(T) runs: 'H50 with cc-pVTZ and cc-pVQZ basis with this implementation [PySCF]')",
          "reported_as": "-27.48998 (total, Hartree)",
          "conversion": "none: the file is the total for N = 50 with nuclear repulsion (Table II STO-6G H10 FCI convention, App. B)",
          "note": "Value identical to the raw GitHub file and the TSV; N = 50, OBC (N_50_OBC), R = 2.4 bohr, basis cc-pVTZ from the file name suffix, N_up = N_dn = 25 ('We only consider spin-unpolarized systems, with N_up = N_dn = N/2'); bound_type projected per RULES.md §13.4 (full CCSD projected); RHF reference; no exact row exists on this instance, so the 2026-10-24 ruling gives no below-reference flag; sigma null correct (deterministic, no stated uncertainty).",
          "secondary_of": null,
          "source_entry": "h-motta17-misc-1#44 (qmbl-verify 2026-10-23/24, verified)"
        }
      },
      "sampled": false,
      "corrections": [
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-27.48998 (total for N = 50)",
          "location": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/RCCSD_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference",
          "checked_on": "2026-10-20",
          "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).",
          "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json"
        }
      ]
    },
    {
      "energy": -26.1052665,
      "sigma": null,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "HF",
      "ansatz": null,
      "method_detail": "restricted",
      "method_as_published": "RHF",
      "family": "mean field",
      "bound_type": "variational",
      "bound_type_reason": "the energy of a stated wave function (Hartree-Fock, DMRG at a stated bond dimension, MRCI, VMC, a neural-network state); an upper bound in the instance's basis (RULES.md 13.4; assigned during source reading)",
      "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059",
      "peer_reviewed": true,
      "source": "track3-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0; source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading",
        "reported_as": "-26.1052665 (total for N = 50)",
        "note": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/RHF_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX commit b99a183 (raw files re-fetched 2026-10-24 into sources/hydrogen-benchmark-PRX-b99a183-rhf/, content-identical (after trimming the trailing newline) to sources/1705.01608-data-b99a183.tsv); paper read as journal text PRX 7, 031059 and arXiv:1705.01608v2",
          "location": "dataset file N_50_OBC/R_2.4/RHF_basis-TZ",
          "reported_as": "-26.1052665 (file content, Hartree, total for N = 50; no error bar in the file)",
          "conversion": "stored as the total: -26.1052665; per atom -26.1052665 / 50 = -0.522105330",
          "note": "TSV and raw file content agree; instance N = 50, open chain, R = 2.4 bohr, cc-pVTZ (README: TZ = cc-pVTZ), N_up = N_dn = 25 (closed-shell RHF of the neutral chain); total in Hartree with nuclear repulsion (dataset convention, checked on H10 STO-6G RHF against pyscf to 3e-6 and on H50 STO-6G against Hachmann 2006 E_RHF totals); RHF lies above UHF in the same basis and below the next-smaller basis; bound_type variational, sigma null, peer_reviewed true; number first printed in the dataset (paper prints no finite-N RHF for N = 30/50), so dataset citation is right. Basis increments per atom are family-consistent with N = 10/30/50.",
          "secondary_of": null,
          "source_entry": "h-motta17-rhf-c2#55 (qmbl-verify 2026-10-23/24, verified)"
        }
      },
      "sampled": false,
      "corrections": [
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-26.1052665 (total for N = 50)",
          "location": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/RHF_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference",
          "checked_on": "2026-10-20",
          "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).",
          "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json"
        }
      ]
    },
    {
      "energy": -26.46227,
      "sigma": null,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "HF",
      "ansatz": null,
      "method_detail": "unrestricted",
      "method_as_published": "UHF",
      "family": "mean field",
      "bound_type": "variational",
      "bound_type_reason": "the energy of a stated wave function (Hartree-Fock, DMRG at a stated bond dimension, MRCI, VMC, a neural-network state); an upper bound in the instance's basis (RULES.md 13.4; assigned during source reading)",
      "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059",
      "peer_reviewed": true,
      "source": "track3-2026-10-20",
      "provenance": "primary",
      "verified": {
        "checked_on": "2026-10-20",
        "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0; source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading",
        "reported_as": "-26.462270 (total for N = 50)",
        "note": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/UHF_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.",
        "secondary_of": null,
        "second_read": {
          "checked_on": "2026-10-24",
          "scope": "value",
          "method": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX at b99a183 (data commit d54c7fa by the first author, 2017-10-09; b99a183 is a README update minutes later and still HEAD on 2026-10-24); raw UHF files re-fetched 2026-10-24 into sources/hydrogen-benchmark-PRX-b99a183-uhf/ and sources/1705.01608-data-raw-uhf-c2.json, identical to sources/1705.01608-data-b99a183.tsv for all 70 files; paper read as journal text PRX 7, 031059 (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2 text",
          "location": "dataset file N_50_OBC/R_2.4/UHF_basis-TZ",
          "reported_as": "-26.462270 (file content, Hartree, total for N = 50; no error bar in the file)",
          "conversion": "stored as the total: -26.462270; per atom -26.462270 / 50 = -0.529245400",
          "note": "TSV and raw file agree; instance N = 50, open chain, R = 2.4 bohr, cc-pVTZ (README: TZ = cc-pVTZ), N_up = N_dn = 25 (paper: N_up = N_dn = N/2); total in Hartree with nuclear repulsion (dataset convention: N_10 R_1.8 UHF_basis-STO -5.27744870209 / 10 = -0.527745 = Table II UHF column, journal and arXiv v2); UHF 7.140 mEh per atom below RHF of the same basis and below the next-smaller basis; bound_type variational (Table I: HF variational 'Yes'; RULES §13.4), sigma null (file holds one number), peer_reviewed true, number first printed in the dataset (the paper prints finite-N UHF only for H10), so the dataset citation is right; no duplicate on the instance (no other UHF row; data/ has no Hchain directory). Cross-check: a 3-point exponential CBS fit of the TZ/QZ/5Z files, (E50 - E30)/20, reproduces Table VI's TDL UHF column to <= 2.6e-5 Eh per atom at every R >= 1.4; end shift E50/50 - E30/30 is basis-independent at this R (STO -0.35, DZ -0.22, TZ -0.22, QZ -0.22, 5Z -0.22 mEh).",
          "secondary_of": null,
          "source_entry": "h-motta17-uhf-c2#60 (qmbl-verify 2026-10-23/24, verified)"
        }
      },
      "sampled": false,
      "corrections": [
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-26.462270 (total for N = 50)",
          "location": "dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_50_OBC/R_2.4/UHF_basis-TZ in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference",
          "checked_on": "2026-10-20",
          "reason": "Deterministic, not a Monte Carlo estimate, as the track-3 reader recorded it (pass row `sampled`); the method string alone reads the other way (units.mjs, isSampled).",
          "source_entry": "passes/track3/sweep-rows-2026-10-20-hydrogen.json"
        }
      ]
    }
  ],
  "url": "https://qmbl.org/i/Hchain/chain_50_O_R2.4_ccpvtz/",
  "per_site_divisor": 50,
  "per_site_label": "E/N (Ha)",
  "best": {
    "exact": null,
    "variational": {
      "energy": -26.46227,
      "sigma": null,
      "method": "HF",
      "ansatz": null,
      "method_detail": "unrestricted",
      "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059",
      "bound_type": "variational",
      "energy_per_site": -0.5292454
    },
    "projected": {
      "energy": -27.5726,
      "sigma": 0.002,
      "method": "ph-AFQMC",
      "ansatz": null,
      "method_detail": "",
      "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059",
      "bound_type": "projected",
      "energy_per_site": -0.551452
    },
    "extrapolated": null,
    "approximate": {
      "energy": -27.55412,
      "sigma": null,
      "method": "RCCSD(T)",
      "ansatz": null,
      "method_detail": "",
      "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059",
      "bound_type": "approximate",
      "energy_per_site": -0.5510824
    },
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -27.5726,
    "sigma": 0.002,
    "method": "ph-AFQMC",
    "ansatz": null,
    "method_detail": "",
    "reference": "M. Motta, D. M. Ceperley, G. K.-L. Chan, J. A. Gomez, E. Gull, S. Guo, C. A. Jiménez-Hoyos, T. N. Lan, J. Li, F. Ma, A. J. Millis, N. V. Prokof’ev, U. Ray, G. E. Scuseria, S. Sorella, E. M. Stoudenmire, Q. Sun, I. S. Tupitsyn, S. R. White, D. Zgid & S. Zhang, Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods, Phys. Rev. X 7, 031059 (2017), arXiv:1705.01608, doi:10.1103/PhysRevX.7.031059",
    "bound_type": "projected",
    "energy_per_site": -0.551452
  },
  "no_record_reason": null
}