⚛️ Molecular Orbital Theory Lab

About this simulation

Molecular orbital (MO) theory says that when two atoms bond, their atomic orbitals don't just overlap — they mathematically combine (LCAO) into brand-new molecular orbitals that span the whole molecule. Every combination produces one lower-energy bonding orbital (constructive overlap, extra electron density between the nuclei) and one higher-energy antibonding orbital (destructive overlap, a node between the nuclei) marked with an asterisk (*).

How it works

• Electrons fill the energy ladder from the bottom up (Aufbau principle), obeying the Pauli exclusion principle (max 2 per orbital, opposite spins).
• Degenerate orbitals (the π pair) each get one electron before any pairing occurs — Hund's rule — which is exactly why O₂ ends up with two unpaired electrons.
• Bond order = (bonding electrons − antibonding electrons) / 2. A bond order of 0 means the molecule doesn't exist as a stable species — this is why He₂ falls apart.
• Any orbital with unpaired electrons makes the molecule paramagnetic (weakly attracted into a magnetic field); fully paired molecules are diamagnetic.
• For Li₂–N₂ the σ2p orbital sits above the π2p pair; for O₂, F₂ and Ne₂ increased 2s–2p mixing drops below that threshold and σ2p sits below π2p — the ladder automatically reorders.

Controls

• Molecule — pick a homonuclear diatomic from H₂ to Ne₂.
• Bond length — stretch or compress the internuclear distance to see how orbital lobes overlap.
• Cloud pulse speed — animation rate of the orbital electron-density clouds.
• Show electron spin arrows — toggle ↑↓ spin markers on filled orbitals.
• ↺ Replay filling — restarts the electron-by-electron fill animation. Drag to rotate, scroll to zoom.

Did you know?

O₂ is one of the only common gases visibly attracted to a strong magnet — pour liquid oxygen between the poles of a magnet and it clings there — a direct, everyday consequence of the two unpaired electrons molecular orbital theory predicts in its π2p* orbitals, something the older Lewis-structure model completely misses.