{
  "model": "Hchain",
  "lattice": "chain",
  "n_sites": 50,
  "boundary": "O",
  "params": {
    "N_up": 25,
    "N_dn": 25,
    "R": 1.4,
    "basis": "cc-pV5Z"
  },
  "instance_id": "Hchain/chain_50_O_R1.4_ccpv5z",
  "rows": [
    {
      "energy": -25.68738031,
      "sigma": null,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "HF",
      "ansatz": null,
      "method_detail": "restricted, basis vectors with overlap eigenvalue below 1e-7 removed (near linear dependence; Appendix A.1)",
      "method_as_published": "RHF [basis vectors with overlap eigenvalue below 1e-7 removed (near linear dependence; Appendix A.1)]",
      "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": "-25.68738031 (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_1.4/RHF_basis-5Z 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
      },
      "sampled": false,
      "corrections": [
        {
          "field": "method_detail",
          "from": "",
          "to": "basis vectors with overlap eigenvalue below 1e-7 removed (near linear dependence; Appendix A.1)",
          "checked_on": "2026-10-24",
          "reported_as": "For the largest basis sets cc-pVTZ, cc-pVQZ, and cc-pV5Z at geometries R < 1.6 aB and cc-pVDZ at R < 1.4 aB, the Gaussian basis is nearly linearly dependent. We remove linearly dependent vectors with an overlap threshold of 10^-7. Although a smaller threshold could be used in the Hartree-Fock calculation, changing the energy by ~10^-6 EHa per atom, we find the resulting CCSD calculations with smaller thresholds to be numerically unstable.",
          "location": "PRX 7, 031059, Appendix A.1 (coupled cluster), p. 031059-13; same text arXiv v2 line 790-800 of sources/1705.01608.txt; main text Sec. V A: 'To deal with basis-set linear dependence, which becomes relevant at the shortest bond lengths and largest basis sets, we apply a threshold to eigenvalues of the overlap matrix.'",
          "version_read": "journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2; identical",
          "conversion": "none",
          "reason": "R = 1.4 bohr, cc-pV5Z: inside the paper's stated linear-dependence window, so the energy is for the cc-pVxZ space with near-null vectors removed (paper: about 1e-6 Eh per atom effect on HF). The row should say so; value unchanged. The paper states the threshold in the CC subsection, whose RHF references the dataset RHF files most plausibly are.",
          "source_entry": "h-motta17-rhf-c2#31 (qmbl-verify 2026-10-23/24, correction; skeptic upheld)"
        },
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-25.68738031 (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_1.4/RHF_basis-5Z 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": -25.713163,
      "sigma": null,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "HF",
      "ansatz": null,
      "method_detail": "unrestricted, basis vectors with overlap eigenvalue below 1e-7 removed (near linear dependence; Appendix A.1)",
      "method_as_published": "UHF [basis vectors with overlap eigenvalue below 1e-7 removed (near linear dependence; Appendix A.1)]",
      "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": "-25.713163 (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_1.4/UHF_basis-5Z 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
      },
      "sampled": false,
      "corrections": [
        {
          "field": "method_detail",
          "from": "",
          "to": "basis vectors with overlap eigenvalue below 1e-7 removed (near linear dependence; Appendix A.1)",
          "checked_on": "2026-10-24",
          "reported_as": "For the largest basis sets cc-pVTZ, cc-pVQZ, and cc-pV5Z at geometries R < 1.6 aB and cc-pVDZ at R < 1.4 aB, the Gaussian basis is nearly linearly dependent. We remove linearly dependent vectors with an overlap threshold of 10^-7. Although a smaller threshold could be used in the Hartree-Fock calculation, changing the energy by ~10^-6 EHa per atom, we find the resulting CCSD calculations with smaller thresholds to be numerically unstable.",
          "location": "PRX 7, 031059, Appendix A 1 a (coupled cluster), p. 031059-13 (journal text lines 767-778); arXiv v2 text lines 790-800 (same sentences, past tense); main text Sec. IV C: 'To deal with basis-set linear dependence, which becomes relevant at the shortest bond lengths and largest basis sets, we apply a threshold to eigenvalues of the overlap matrix.'",
          "version_read": "journal text (sources/1705.01608-PhysRevX.7.031059.txt) and arXiv:1705.01608v2 (sources/1705.01608.txt); same statement",
          "conversion": "none",
          "reason": "R = 1.4 bohr, cc-pV5Z: inside the paper's stated linear-dependence window, so the UHF energy is for the cc-pVxZ space with near-null overlap vectors removed (paper: about 1e-6 Eh per atom effect on Hartree-Fock). The row should say so; value unchanged (located: dataset file N_50_OBC/R_1.4/UHF_basis-5Z = -25.713163, identical to reported_as). The threshold is stated in the CC subsection, whose UHF references (UCCSD) the dataset UHF files most plausibly are. Same proposal as group h-motta17-rhf-c2 for the RHF files.",
          "source_entry": "h-motta17-uhf-c2#36 (qmbl-verify 2026-10-23/24, correction; skeptic upheld)"
        },
        {
          "field": "sampled",
          "to": false,
          "reported_as": "-25.713163 (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_1.4/UHF_basis-5Z 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_R1.4_ccpv5z/",
  "per_site_divisor": 50,
  "per_site_label": "E/N (Ha)",
  "best": {
    "exact": null,
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      "energy": -25.713163,
      "sigma": null,
      "method": "HF",
      "ansatz": null,
      "method_detail": "unrestricted, basis vectors with overlap eigenvalue below 1e-7 removed (near linear dependence; Appendix A.1)",
      "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": -0.51426326
    },
    "projected": null,
    "extrapolated": null,
    "approximate": null,
    "below_exact": []
  },
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  "record": {
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    "method_detail": "unrestricted, basis vectors with overlap eigenvalue below 1e-7 removed (near linear dependence; Appendix A.1)",
    "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",
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  },
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}