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Physics simulations

Materials Atlas · physics workbench

Model. Compare. Investigate.

Work from molecular geometry, crystal structure, processing conditions or a material stack. Inspect the physics, compare calculated results, and turn uncertainty into the next research question.

Research with AI →Metal equations of state →Methods & scientific foundations →
01 Define the system02 Review the method03 Calculate & check04 Compare & decide
Define your calculation

Molecular electronic structure

Compute a closed-shell molecule's mean-field energy, orbitals and forces from its geometry.

Scientific inputs
Method scope & sources

Small closed-shell molecules containing H through Ne with RHF or PBE and a declared basis.

  • Fixed nuclei at the supplied geometry
  • Closed-shell spin-zero state
  • Finite basis and mean-field approximation; no dispersion correction or thermochemical correction

PySCF molecular calculations ↗

Edit calculation inputs ↓
Calculated result

Hydrogen · RHF / STO-3G

Model calculation
Electronic plus nuclear total energy-1.1168Hartree
Number of electrons2
Dipole magnitude2.8219E-15Debye
Maximum atomic force magnitude1.4233eV/Å
Highest occupied orbital energy-15.743eV
Lowest unoccupied orbital energy18.263eV
Orbital energy (eV)
18.26309.76120.251.25970.5-7.24180.75-15.7431
Orbital index (zero-based)
Molecular orbital energies
Orbital index (zero-based): 0 · Orbital energy: -15.743 eV

Interpret the result

  • Isolated all-electron closed-shell molecule in the Born–Oppenheimer approximation.
  • Coordinates in Å, energy in Hartree, force in eV/Å. Same method, basis and charge-state conventions are required for energy differences.
  • Fixed SCF tolerance 1e−10 Hartree; 80 cycles; one computational thread; 512 MB nominal engine memory.

Orbital gap is not a measured optical gap or a bulk band gap.

Single-point geometry: nonzero forces are expected; no geometry optimization or finite-temperature free energy is implied.

STO-3G is a minimal basis; use a larger basis and method comparison before quantitative chemical conclusions.

Restricted Hartree–Fock omits electron correlation and is unreliable for bond breaking and strongly correlated states.

Numerical checks & provenance
Density-matrix electron count4.4409E-16 ≤ 1E-7 electrons
Occupied-orbital SCF gradient4.4409E-16 ≤ 1E-5 Hartree
Net force under rigid translation1.1102E-16 ≤ 1E-7 Hartree/Bohr

Passing these checks verifies the stated numerical properties. Agreement with experiment requires a separate, condition-matched comparison.

Input SHA-256: 5a19a0727aed246bfac84eb2372be6fa0240446f5b4159515d5b423e318f684c
Runner SHA-256: f27376d0f80371a1da4c926f1a21d43d841802e9f87bac7e876738ea78181e3d
atlas 1 · python 3.14.10 · numpy 2.5.4 · scipy 1.18.1 · pyscf 2.15.0
Calculated 11/12/2026, 2:03:22 AM · 0.45397 s

Test the explanation

Compare a numerical refinement or a different physical assumption. Agreement within one model does not establish agreement with experiment.

Build the investigation

Bring the observable, conditions and result into a research plan with competing hypotheses and a test that can distinguish them.

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