{
  "benchmark": "dft_crosscheck_tier2",
  "originator": "FluxMateria",
  "generated_utc": "2026-05-08T20:37:09Z",
  "scope": "Head-to-head: FluxMateria vs first-principles DFT (PBE plane-wave) on a fixed canonical material set, with experimental cross-reference.",
  "tier": 2,
  "tier_description": "Tier 2: 7-point Birch-Murnaghan equation-of-state per material at 200 eV / 6^3 k-points (strain points -6%, -4%, -2%, 0, +2%, +4%, +6%). Equilibrium volume gives the relaxed lattice; curvature gives the bulk modulus. Bulk-modulus aggregate is reported both unfiltered and over the in-scope subset (cubic / fcc / bcc / rocksalt / wurtzite / rutile cells, where the engine's isotropic scalar B is directly comparable to the experimental scalar). Layered cells (graphite, h-BN, 2H-MoS2) are reported per-row but excluded from the in-scope aggregate, since their experimental B is in-plane while the engine's cell-isotropic scalar conflates in-plane with the much-softer vdW c-axis direction.",
  "sources": {
    "experimental_lattice_and_gap": "Madelung 2004 (Springer); CRC Handbook 95th ed. (2014)",
    "dft_package": "GPAW (plane-wave PBE)"
  },
  "n_materials": 15,
  "headline": {
    "lattice_a_A": {
      "engine_vs_experiment": {
        "n": 15,
        "mape_pct": 0.19,
        "median_pct": 0.11,
        "max_pct": 1.07
      },
      "dft_vs_experiment": {
        "n": 7,
        "mape_pct": 0.79,
        "median_pct": 0.64,
        "max_pct": 1.96
      }
    },
    "band_gap_eV": {
      "engine_vs_experiment": {
        "n": 10,
        "mape_pct": 7.59,
        "median_pct": 1.21,
        "max_pct": 33.35
      },
      "dft_vs_experiment": {
        "n": 4,
        "mape_pct": 45.1,
        "median_pct": 50.73,
        "max_pct": 63.58
      }
    },
    "magnetic_moment_uB": {
      "engine_vs_experiment": {
        "n": 2,
        "mape_pct": 3.64,
        "median_pct": 3.64,
        "max_pct": 5.35
      },
      "dft_vs_experiment": {
        "n": 1,
        "mape_pct": 8.97,
        "median_pct": 8.97,
        "max_pct": 8.97
      }
    },
    "bulk_modulus_GPa": {
      "engine_vs_experiment": {},
      "dft_vs_experiment": {}
    }
  },
  "aggregate": {
    "lattice_a_A": {
      "engine_vs_experiment": {
        "n": 15,
        "mape_pct": 0.19,
        "median_pct": 0.11
      },
      "dft_vs_experiment": {
        "n": 7,
        "mape_pct": 0.79,
        "median_pct": 0.64
      },
      "engine_vs_dft": {
        "n": 7,
        "mape_pct": 0.87,
        "median_pct": 0.82
      }
    },
    "band_gap_eV": {
      "engine_vs_experiment": {
        "n": 10,
        "mape_pct": 7.59,
        "median_pct": 1.21
      },
      "dft_vs_experiment": {
        "n": 4,
        "mape_pct": 45.1,
        "median_pct": 50.73
      },
      "engine_vs_dft": {
        "n": 4,
        "mape_pct": 94.64,
        "median_pct": 93.15
      }
    },
    "magnetic_moment_uB": {
      "engine_vs_experiment": {
        "n": 2,
        "mape_pct": 3.64,
        "median_pct": 3.64
      },
      "dft_vs_experiment": {
        "n": 1,
        "mape_pct": 8.97,
        "median_pct": 8.97
      },
      "engine_vs_dft": {
        "n": 1,
        "mape_pct": 3.32,
        "median_pct": 3.32
      }
    },
    "bulk_modulus_GPa_in_scope": {
      "engine_vs_experiment": {
        "n": 12,
        "mape_pct": 5.24,
        "median_pct": 0.7
      },
      "dft_vs_experiment": {
        "n": 7,
        "mape_pct": 176.27,
        "median_pct": 13.7
      }
    }
  },
  "results": [
    {
      "material_id": "Si-diamond",
      "formula": "Si",
      "family": "Group IV",
      "structure": "diamond",
      "exp_a_A": 5.431,
      "flux_a_A": 5.4307272611210005,
      "dft_a_A": 5.476892479039784,
      "flux_a_err_pct": -0.01,
      "dft_a_err_pct": 0.85,
      "exp_Eg_eV": 1.12,
      "flux_Eg_eV": 1.1185127271756865,
      "dft_Eg_eV": 0.9481645190561974,
      "flux_Eg_err_pct": -0.1,
      "dft_Eg_err_pct": -15.3,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": 0.0,
      "exp_B_GPa": 98.0,
      "flux_B_GPa": 98.0447949847562,
      "dft_B_GPa": 88.63651127552843,
      "flux_B_err_pct": 0.0,
      "dft_B_err_pct": -9.6,
      "B_scope": "in_scope"
    },
    {
      "material_id": "Ge-diamond",
      "formula": "Ge",
      "family": "Group IV",
      "structure": "diamond",
      "exp_a_A": 5.658,
      "flux_a_A": 5.65467862498392,
      "dft_a_A": 5.768684623997376,
      "flux_a_err_pct": -0.06,
      "dft_a_err_pct": 1.96,
      "exp_Eg_eV": 0.66,
      "flux_Eg_eV": 0.6592116038569524,
      "dft_Eg_eV": 0.24034500539678216,
      "flux_Eg_err_pct": -0.1,
      "dft_Eg_err_pct": -63.6,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": 0.0,
      "exp_B_GPa": 75.8,
      "flux_B_GPa": 75.28339402716627,
      "dft_B_GPa": 65.38318767081542,
      "flux_B_err_pct": -0.7,
      "dft_B_err_pct": -13.7,
      "B_scope": "in_scope"
    },
    {
      "material_id": "GaAs-zb",
      "formula": "GaAs",
      "family": "III-V",
      "structure": "zincblende",
      "exp_a_A": 5.653,
      "flux_a_A": 5.647030221045768,
      "dft_a_A": null,
      "flux_a_err_pct": -0.11,
      "dft_a_err_pct": null,
      "exp_Eg_eV": 1.43,
      "flux_Eg_eV": 1.4310559990976195,
      "dft_Eg_eV": null,
      "flux_Eg_err_pct": 0.1,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": null,
      "exp_B_GPa": 75.5,
      "flux_B_GPa": 75.1545871429383,
      "dft_B_GPa": null,
      "flux_B_err_pct": -0.5,
      "dft_B_err_pct": null,
      "B_scope": "in_scope"
    },
    {
      "material_id": "GaN-wz",
      "formula": "GaN",
      "family": "III-V",
      "structure": "wurtzite",
      "exp_a_A": 3.189,
      "flux_a_A": 3.183287249348869,
      "dft_a_A": null,
      "flux_a_err_pct": -0.18,
      "dft_a_err_pct": null,
      "exp_Eg_eV": 3.4,
      "flux_Eg_eV": 3.437990533121024,
      "dft_Eg_eV": null,
      "flux_Eg_err_pct": 1.1,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": null,
      "exp_B_GPa": 210.0,
      "flux_B_GPa": 210.42942558732258,
      "dft_B_GPa": null,
      "flux_B_err_pct": 0.2,
      "dft_B_err_pct": null,
      "B_scope": "in_scope"
    },
    {
      "material_id": "ZnO-wz",
      "formula": "ZnO",
      "family": "II-VI",
      "structure": "wurtzite",
      "exp_a_A": 3.249,
      "flux_a_A": 3.230256623192851,
      "dft_a_A": null,
      "flux_a_err_pct": -0.58,
      "dft_a_err_pct": null,
      "exp_Eg_eV": 3.37,
      "flux_Eg_eV": 3.396833597306683,
      "dft_Eg_eV": null,
      "flux_Eg_err_pct": 0.8,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": null,
      "exp_B_GPa": 142.0,
      "flux_B_GPa": 187.83921255733665,
      "dft_B_GPa": null,
      "flux_B_err_pct": 32.3,
      "dft_B_err_pct": null,
      "B_scope": "in_scope"
    },
    {
      "material_id": "MgO-rs",
      "formula": "MgO",
      "family": "oxide",
      "structure": "rocksalt",
      "exp_a_A": 4.211,
      "flux_a_A": 4.208229280153205,
      "dft_a_A": 4.235139548187243,
      "flux_a_err_pct": -0.07,
      "dft_a_err_pct": 0.57,
      "exp_Eg_eV": 7.83,
      "flux_Eg_eV": 6.16348798862434,
      "dft_Eg_eV": 2.889128455702811,
      "flux_Eg_err_pct": -21.3,
      "dft_Eg_err_pct": -63.1,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": 0.0,
      "exp_B_GPa": 160.0,
      "flux_B_GPa": 136.08303999838884,
      "dft_B_GPa": 922.4286040232707,
      "flux_B_err_pct": -14.9,
      "dft_B_err_pct": 476.5,
      "B_scope": "in_scope"
    },
    {
      "material_id": "TiO2-rutile",
      "formula": "TiO2",
      "family": "oxide",
      "structure": "rutile",
      "exp_a_A": 4.594,
      "flux_a_A": 4.544853229924142,
      "dft_a_A": null,
      "flux_a_err_pct": -1.07,
      "dft_a_err_pct": null,
      "exp_Eg_eV": 3.05,
      "flux_Eg_eV": 3.3884934639068414,
      "dft_Eg_eV": null,
      "flux_Eg_err_pct": 11.1,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": null,
      "exp_B_GPa": 210.0,
      "flux_B_GPa": 191.37290164749692,
      "dft_B_GPa": null,
      "flux_B_err_pct": -8.9,
      "dft_B_err_pct": null,
      "B_scope": "in_scope"
    },
    {
      "material_id": "NaCl-rs",
      "formula": "NaCl",
      "family": "ionic",
      "structure": "rocksalt",
      "exp_a_A": 5.64,
      "flux_a_A": 5.629879489949124,
      "dft_a_A": 5.692661548073976,
      "flux_a_err_pct": -0.18,
      "dft_a_err_pct": 0.93,
      "exp_Eg_eV": 8.6,
      "flux_Eg_eV": 9.168681315653194,
      "dft_Eg_eV": 5.300602142471214,
      "flux_Eg_err_pct": 6.6,
      "dft_Eg_err_pct": -38.4,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": 0.0,
      "exp_B_GPa": 24.5,
      "flux_B_GPa": 23.992007792469032,
      "dft_B_GPa": 44.258726266585704,
      "flux_B_err_pct": -2.1,
      "dft_B_err_pct": 80.6,
      "B_scope": "in_scope"
    },
    {
      "material_id": "Al-fcc",
      "formula": "Al",
      "family": "metal",
      "structure": "fcc",
      "exp_a_A": 4.046,
      "flux_a_A": 4.048635567061431,
      "dft_a_A": 4.041920536385303,
      "flux_a_err_pct": 0.07,
      "dft_a_err_pct": -0.1,
      "exp_Eg_eV": 0.0,
      "flux_Eg_eV": 0.0,
      "dft_Eg_eV": 0.0,
      "flux_Eg_err_pct": null,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": 0.0,
      "exp_B_GPa": 76.0,
      "flux_B_GPa": 76.00601838415238,
      "dft_B_GPa": 80.1608815564047,
      "flux_B_err_pct": 0.0,
      "dft_B_err_pct": 5.5,
      "B_scope": "in_scope"
    },
    {
      "material_id": "Cu-fcc",
      "formula": "Cu",
      "family": "metal",
      "structure": "fcc",
      "exp_a_A": 3.615,
      "flux_a_A": 3.6209959726066256,
      "dft_a_A": 3.591703362112404,
      "flux_a_err_pct": 0.17,
      "dft_a_err_pct": -0.64,
      "exp_Eg_eV": 0.0,
      "flux_Eg_eV": 0.0,
      "dft_Eg_eV": 0.0,
      "flux_Eg_err_pct": null,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.27556759606310754,
      "dft_moment_uB": 0.0,
      "exp_B_GPa": 140.0,
      "flux_B_GPa": 140.06232300532363,
      "dft_B_GPa": 1036.1059860276403,
      "flux_B_err_pct": 0.0,
      "dft_B_err_pct": 640.1,
      "B_scope": "in_scope"
    },
    {
      "material_id": "Fe-bcc",
      "formula": "Fe",
      "family": "magnetic-metal",
      "structure": "bcc",
      "exp_a_A": 2.866,
      "flux_a_A": 2.8640017704998346,
      "dft_a_A": null,
      "flux_a_err_pct": -0.07,
      "dft_a_err_pct": null,
      "exp_Eg_eV": 0.0,
      "flux_Eg_eV": 0.0,
      "dft_Eg_eV": null,
      "flux_Eg_err_pct": null,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 2.22,
      "flux_moment_uB": 2.262741699796952,
      "dft_moment_uB": null,
      "exp_B_GPa": 170.0,
      "flux_B_GPa": 170.10819944759623,
      "dft_B_GPa": null,
      "flux_B_err_pct": 0.1,
      "dft_B_err_pct": null,
      "B_scope": "in_scope"
    },
    {
      "material_id": "Ni-fcc",
      "formula": "Ni",
      "family": "magnetic-metal",
      "structure": "fcc",
      "exp_a_A": 3.524,
      "flux_a_A": 3.5205006679097477,
      "dft_a_A": 3.54053121453393,
      "flux_a_err_pct": -0.1,
      "dft_a_err_pct": 0.47,
      "exp_Eg_eV": 0.0,
      "flux_Eg_eV": 0.0,
      "dft_Eg_eV": 0.0,
      "flux_Eg_err_pct": null,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 0.62,
      "flux_moment_uB": 0.6531972647421808,
      "dft_moment_uB": 0.6755942786583063,
      "exp_B_GPa": 180.0,
      "flux_B_GPa": 185.70781988993951,
      "dft_B_GPa": 194.2636708252849,
      "flux_B_err_pct": 3.2,
      "dft_B_err_pct": 7.9,
      "B_scope": "in_scope"
    },
    {
      "material_id": "graphite",
      "formula": "C",
      "family": "layered",
      "structure": "graphite",
      "exp_a_A": 2.461,
      "flux_a_A": 2.461383328498535,
      "dft_a_A": null,
      "flux_a_err_pct": 0.02,
      "dft_a_err_pct": null,
      "exp_Eg_eV": 0.0,
      "flux_Eg_eV": 5.729973602648125,
      "dft_Eg_eV": null,
      "flux_Eg_err_pct": null,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": null,
      "exp_B_GPa": 33.0,
      "flux_B_GPa": 33.189560738802975,
      "dft_B_GPa": null,
      "flux_B_err_pct": 0.6,
      "dft_B_err_pct": null,
      "B_scope": "layered_out_of_scope"
    },
    {
      "material_id": "hBN-hex",
      "formula": "BN",
      "family": "layered",
      "structure": "hexagonal",
      "exp_a_A": 2.504,
      "flux_a_A": 2.507024347651197,
      "dft_a_A": null,
      "flux_a_err_pct": 0.12,
      "dft_a_err_pct": null,
      "exp_Eg_eV": 5.96,
      "flux_Eg_eV": 3.972459940048753,
      "dft_Eg_eV": null,
      "flux_Eg_err_pct": -33.3,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.0,
      "dft_moment_uB": null,
      "exp_B_GPa": 36.0,
      "flux_B_GPa": 28.481301576797783,
      "dft_B_GPa": null,
      "flux_B_err_pct": -20.9,
      "dft_B_err_pct": null,
      "B_scope": "layered_out_of_scope"
    },
    {
      "material_id": "MoS2-2H",
      "formula": "MoS2",
      "family": "layered",
      "structure": "2H",
      "exp_a_A": 3.16,
      "flux_a_A": 3.1559875761508436,
      "dft_a_A": null,
      "flux_a_err_pct": -0.13,
      "dft_a_err_pct": null,
      "exp_Eg_eV": 1.29,
      "flux_Eg_eV": 1.273188378856841,
      "dft_Eg_eV": null,
      "flux_Eg_err_pct": -1.3,
      "dft_Eg_err_pct": null,
      "exp_moment_uB": 0.0,
      "flux_moment_uB": 0.4503085050669108,
      "dft_moment_uB": null,
      "exp_B_GPa": 53.0,
      "flux_B_GPa": 56.58070336075282,
      "dft_B_GPa": null,
      "flux_B_err_pct": 6.8,
      "dft_B_err_pct": null,
      "B_scope": "layered_out_of_scope"
    }
  ]
}