QUANTAATOMIC WORKBENCH
MOLECULAR DFT01 / 03

Matter,
from the inside.

Explore the field. Change the bond.
Let the equations answer.

H₂
Hydrogen2 nuclei · 2 electrons
Total energy—Eₕ
ρ(r)
Electron densityPBE / def2-SVP · all-electron
↔ Drag to orbit · Scroll to scale
THE PHYSICS BEHIND THE FIELD

Computed. Inspectable.

The shapes come from wavefunctions and electron density. The dots sample probability; they are not orbiting electrons.

Molecules

PySCF solves self-consistent, all-electron Kohn–Sham DFT with PBE or PBE0, a def2-SVP basis, grid level 3 and a 10⁻⁹ Eₕ energy tolerance. Nuclei are fixed classical particles; all molecules are isolated, neutral, closed-shell singlets. “Find minimum” varies a single symmetric bond length, keeping angles fixed (water: 104.5°). Forces are calculated analytically.

DFT is approximate. Finite basis errors and electron correlation limitations matter, especially for stretched bonds. The Kohn–Sham gap is not an experimental excitation energy. This app does not calculate bulk phases, temperature, solvent or nuclear quantum motion.

Hydrogen orbitals

Normalized analytic solutions of the nonrelativistic Coulomb Schrödinger equation with an infinitely heavy proton. 1s, 2s, real 2pₓ and 3dₓᵧ states. Colors encode wavefunction sign, not electric charge.

Quantum spins

Two spin-½ particles, starting in |↑↓⟩. The state evolves through numerical diagonalization of H/h = Δ(S₁z − S₂z)/2 + J S₁·S₂ + Ω(S₁x + S₂x), followed by exp(−i2πHt/h). Frequencies are in Hz, time in seconds; display playback runs at 0.2×. Bloch arrows show each reduced state. Shorter arrows indicate a mixed reduced state. Entropy measures entanglement for this pure joint state. No relaxation or environmental noise.

Rendering & headset

Density is evaluated on a 48³ grid in bohr. A deterministic probability sample, interpolated isosurface or z section displays the field. Surface thresholds are relative to the grid maximum; these are not fixed-probability boundaries. Nuclei are enlarged markers. Quest uses WebXR immersive-ar, with a transparent background. Point and trigger/pinch to select, squeeze to move, thumbstick to rotate or scale. Use the floating controls for models, solve, minimum and exit.

PySCF DFT ↗Quantum ESPRESSO ↗Spinach ↗Meta mixed reality ↗

This app runs PySCF and its own stated spin Hamiltonian. It does not run VASP, CP2K, Quantum ESPRESSO or Spinach.