CogLabThe Cognition Lab

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

Periodic electronic structure

Calculate a small periodic cell with PBE and compare denser real-space and k-point sampling.

Scientific inputs
Method scope & sources

Neutral closed-shell cells containing H through Ar with fixed PBE and GTH-PBE pseudopotentials.

  • Fixed periodic geometry and a localized Gaussian basis
  • Sampling convergence is measured against the chosen tolerance
  • No magnetic state, geometry relaxation, excited-state or experimental accuracy claim

PySCF periodic DFT ↗

Edit calculation inputs ↓
Calculated result

Silicon · periodic PBE

Model calculation
Refined periodic total energy-7.7883Hartree/cell
Refined periodic energy per atom-105.97eV/atom
Primitive input cell volume40.026ų/cell
Gap across sampled Kohn–Sham orbitals2.1209eV
Energy change on mesh refinement1.0143E-5eV/atom
Energy change on reciprocal-grid refinement1.0312eV/atom
Energy per atom (eV/atom)
-104.930-105.190.5-105.451-105.711.5-105.972
Refinement stage
Numerical settings refinement
Refinement stage: 0 · Energy per atom: -104.93 eV/atom

Interpret the result

  • Three-dimensional periodic neutral closed-shell system with a Gaussian GTH basis and GTH-PBE pseudopotential.
  • PBE Kohn–Sham DFT using PySCF FFT density fitting; lattice vectors and Cartesian positions in Å.
  • Three separate SCF calculations refine real-space mesh and reciprocal sampling; no relaxation is performed.

The final result uses the refined settings; a small two-grid difference is a sensitivity check, not proof of complete basis or Brillouin-zone convergence.

PBE/GTH energy and sampled orbital gap are model predictions; no experimental band-gap accuracy, forces, stress or finite-temperature behavior is implied.

This closed-shell insulating-state recipe has no spin polarization or metallic occupation smearing.

Reciprocal sampling sensitivity 1.03116 eV/atom exceeds the requested 0.01 eV/atom target. Increase k-grid before quantitative use.

Numerical checks & provenance
Periodic density-matrix electron count5.3291E-15 ≤ 1E-6 electrons
Periodic occupied-orbital SCF gradient2.4991E-10 ≤ 0.0001 Hartree

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

Input SHA-256: 49c0190594a757a036be5266b170a032e8beb0a1dbf17a0174369973f7d4b7c4
Runner SHA-256: f27376d0f80371a1da4c926f1a21d43d841802e9f87bac7e876738ea78181e3d
atlas 1 · python 3.14.10 · numpy 2.5.4 · scipy 1.18.1 · pyscf 2.15.0 · ase 3.29.0
Calculated 11/12/2026, 2:03:43 AM · 18.271 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.

Investigate this result →