Molecular Orbital Formation from s and p Orbitals

How orbital shape decides bond symmetry. Compare s–s, s–p and p–p overlap, and σ (head-on) against π (side-on).

Overlap

s + s

symmetry about the bond axis

σ: cylindrically symmetric, no nodal plane containing the axis

overlap integral (rel. to max over all 4 types)

1.00

on-site energy

Separation R 4.00 Å

Bonding orbital, in phase ψ = s_A + s_B

Antibonding orbital, out of phase ψ = s_A − s_B

positive phase negative phase nodal surface (ψ = 0)

MO energy-level diagram schematic: splitting ∝ overlap S(R)

Overlap integral vs separation ∫ψ_Aψ_B dτ, scaled to the max over all four types