{
  "analytic_components": {
    "electron_repulsion": 1.0546875,
    "kinetic": 2.84765625,
    "nuclear_attraction": -6.75,
    "potential": -5.6953125,
    "total": -2.84765625,
    "virial_residual": 0.0,
    "zeta": 1.6875
  },
  "curve_points": 501,
  "dependencies": "Python standard library only",
  "implementation": "CPython",
  "license": "MIT",
  "model": "two hydrogenic 1s orbitals with common exponent zeta",
  "nuclear_charge": 2.0,
  "numeric_components": {
    "electron_repulsion": 1.0546874999058498,
    "kinetic": 2.847656249491589,
    "nuclear_attraction": -6.749999999397438,
    "potential": -5.695312499491589,
    "total": -2.84765625,
    "virial_residual": -5.084110910047457e-10,
    "zeta": 1.6874999998493596
  },
  "outputs": [
    "variational-helium-energy-curve.csv",
    "variational-helium-summary.csv",
    "variational-helium-metadata.json"
  ],
  "platform": "Windows-11-10.0.26200-SP0",
  "python": "3.12.13",
  "random_seed": null,
  "units": "Hartree atomic units",
  "validation": {
    "analytic_virial_residual_Eh": 0.0,
    "energy_absolute_error_Eh": 0.0,
    "energy_agreement": true,
    "finite_difference_gradient_Eh": 0.0,
    "hartree_fock_improves_trial": true,
    "numeric_iterations": 68,
    "optimization_lowers_full_H": true,
    "stationary_finite_difference": true,
    "variational_upper_bound": true,
    "virial_stationarity": true,
    "zeta_absolute_error": 1.5064038905165944e-10,
    "zeta_agreement": true
  },
  "zeta_interval": [
    0.5,
    3.0
  ]
}