Two atomic 1s orbitals (LCAO basis) combine into molecular orbitals. The bonding combination
φ+ = N(1s_A + 1s_B) piles electron density between the nuclei; the antibonding combination
φ− = N(1s_A − 1s_B) creates a node between them and pushes density outward.
ψ± = (1s_A ± 1s_B) / √(2 ± 2S)
S(r) = e^(-ζr)(1 + ζr + ζ²r²/3)
Bond order = (n_bonding − n_antibonding) / 2
- Bonding / Antibonding toggle — switches between the constructive (φ+) and destructive (φ−) LCAO combination.
- Bond length r — internuclear separation; changes overlap S and where the density cloud concentrates.
- Electron count N — how many electrons fill the shown orbital (0–4), scaling cloud opacity and binding energy.
- Basis set spread ζ — orbital exponent; larger ζ contracts each atomic orbital, smaller ζ makes diffuse clouds that overlap more.
- Cloud density — number of Monte Carlo-sampled points rendered as the |ψ|² probability cloud (visual resolution only).
Real-world use: this LCAO/Hartree-Fock picture underlies computational tools (Gaussian, ORCA, Psi4) used
in drug design to predict how molecules bind to protein targets, and in materials science to screen
candidate catalysts before synthesis.