{
  "model": "Hchain",
  "lattice": "chain",
  "n_sites": 50,
  "boundary": "O",
  "params": {
    "N_up": 25,
    "N_dn": 25,
    "R": 2.4,
    "basis": "none"
  },
  "instance_id": "Hchain/chain_50_O_R2.4_none",
  "rows": [
    {
      "energy": -27.630757495,
      "sigma": 0.00127205,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "LR-DMC",
      "ansatz": "LDA determinant",
      "method_detail": "cc-pVTZ trial basis",
      "method_as_published": "LR-DMC [LDA trial state, cc-pVTZ trial basis]",
      "family": "DMC",
      "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": "-27.6307574949652 1.272046395697757E-003 (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/LRDMC_LDA_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 b99a183: raw file fetched from raw.githubusercontent.com and compared byte-for-byte (trimmed) with the committed sources/1705.01608-data-b99a183.tsv; node",
          "location": "dataset file N_50_OBC/R_2.4/LRDMC_LDA_basis-TZ (number first printed in the dataset; the paper shows N > 10 LR-DMC only in figures and TDL fits, Table VI)",
          "reported_as": "-27.6307574949652 1.272046395697757E-003 (total for N = 50; second number the uncertainty)",
          "conversion": "total as printed: -27.6307574949652 Ha; per atom -27.6307574949652/50 = -0.5526151498993039 (stored eps identical); sigma 0.001272046395697757 Ha total, 0.000025440927913955143 per atom (stored identical)",
          "note": "Instance chain, open boundary (dataset folder N_50_OBC; Table III is the finite H10 molecule), basis-free (real-space fixed-node LR-DMC, RULES 13.1), neutral S_z = 0 by RULES 13.1 default (no other sector stated). bound_type projected per RULES 13.4 (lattice-regularised DMC); the paper presents the a -> 0 limit of the lattice regularisation (Appendix A 2 b), i.e. the fixed-node energy. Trial state LDA Slater determinant/AGP with Jastrow, determinant basis cc-pVTZ per the dataset file name (basis-TZ, README 'TZ : cc-pVTZ'). Not a record row; no other LR-DMC row or same-number row on this instance in passes/track3 (data/Hchain does not exist, track 3 held). Per-atom value consistent with the N-trend at this R (N = 10, 30, 50, ... approach the Table VI TDL value).",
          "secondary_of": null,
          "source_entry": "h-motta17-lr-dmc#49 (qmbl-verify 2026-10-23/24, verified)"
        }
      }
    },
    {
      "energy": -27.5246051831,
      "sigma": 0.000658697,
      "energy_variance": null,
      "dof": 50,
      "einf": null,
      "v_score": null,
      "method": "VMC",
      "ansatz": "SJ",
      "method_detail": "LDA determinant, cc-pVTZ trial basis",
      "method_as_published": "VMC [LDA determinant with Jastrow factor, cc-pVTZ trial basis]",
      "family": "classic VMC",
      "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": "-27.5246051831444 6.586973342786051E-004 (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/VMC_LDA_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: file fetched fresh from raw.githubusercontent.com at commit b99a183 and at master, byte-compared with sources/1705.01608-data-b99a183.tsv (check_dataset.mjs); paper read for conventions (journal text + arXiv v2)",
          "location": "dataset file N_50_OBC/R_2.4/VMC_LDA_basis-TZ (no finite-N value for N = 50 located in the paper's Tables I-VI; the paper prints finite-N energies for H10 only, and VMC(LDA) at the TDL in Table VI)",
          "reported_as": "-27.5246051831444 6.586973342786051E-004 (file content: total energy in Hartree for N = 50, then its uncertainty)",
          "conversion": "total stored as is (-27.5246051831444 Ha); eps = -27.5246051831444/50 = -0.5504921037; sigma 6.586973342786051E-004/50 = 1.317395e-5 per atom (row eps and sigma_per_site agree to 0 and <=2e-19)",
          "note": "chain of N = 50 atoms, open (finite molecule), R = 2.4 bohr, N_up = N_dn = 25 (paper Sec. II: \"We only consider spin-unpolarized systems, with N_up = N_dn = N/2\"), continuum all-electron Hamiltonian Eq. (1) with nuclear repulsion -> basis = none (RULES 13.1); bound_type variational (RULES 13.4); peer_reviewed (PRX 7, 031059). File content totals: N = 10 files reproduce Table III per-atom values x 10, and the error column is the total-energy error (N = 10: dataset sigma/10 reproduces the printed (n)). VMC lies 2.123 mHa/atom above the same paper's LR-DMC(LDA) on this instance (variational ordering holds). No duplicate row on this instance.",
          "secondary_of": null,
          "source_entry": "h-motta17-vmc#49 (qmbl-verify 2026-10-23/24, verified)"
        }
      }
    }
  ],
  "url": "https://qmbl.org/i/Hchain/chain_50_O_R2.4_none/",
  "per_site_divisor": 50,
  "per_site_label": "E/N (Ha)",
  "best": {
    "exact": null,
    "variational": {
      "energy": -27.5246051831,
      "sigma": 0.000658697,
      "method": "VMC",
      "ansatz": "SJ",
      "method_detail": "LDA determinant, cc-pVTZ trial basis",
      "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": -0.550492103662
    },
    "projected": {
      "energy": -27.630757495,
      "sigma": 0.00127205,
      "method": "LR-DMC",
      "ansatz": "LDA determinant",
      "method_detail": "cc-pVTZ trial basis",
      "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": -0.5526151499
    },
    "extrapolated": null,
    "approximate": null,
    "below_exact": []
  },
  "no_best_reason": null,
  "record": {
    "energy": -27.630757495,
    "sigma": 0.00127205,
    "method": "LR-DMC",
    "ansatz": "LDA determinant",
    "method_detail": "cc-pVTZ trial basis",
    "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": -0.5526151499
  },
  "no_record_reason": null
}