Undergraduate · 15 min

Hybrid orbitals and delocalization

Render sp, sp² and sp³ lobes in 3D, then connect each hybridization to geometry, resonance and the CIP stakes of stereoisomerism.

Goal

Recognise a carbon’s hybridization from its geometry (sp³ tetrahedral, sp² planar, sp linear) and use it to judge where resonance or hyperconjugation can operate.

Apparatus and reagents

The orbital viewer below; examples $\ce{CH4}$ , $\ce{C2H4}$ , $\ce{C2H2}$ and the allyl cation.

Procedure

Set type = 2 (sp³) and rotate: count the four equivalent lobes pointing to tetrahedron corners.
Set type = 1 (sp²): three lobes lie in a plane at 120°; the unused p orbital sticks out perpendicular.
Set type = 0 (sp): two lobes opposite at 180°, two perpendicular p orbitals — the recipe for triple bonds.
Assign the hybridization of every carbon in $\ce{CH2=CH-CH2+}$ and state where the empty p orbital must sit for resonance.

What to observe

sp³ lobes reach 109.5°; sp² lobes are coplanar at 120°; sp lobes are collinear at 180° — the mixing ratio n s + m p dictates the angle.
An sp² carbon always keeps a free p orbital; alignment of neighbouring p orbitals is exactly what resonance and hyperconjugation need.

Explanation

Hybridization is a bookkeeping of the valence basis: mixing one s with k p orbitals gives k+1 equivalent lobes whose geometry minimises repulsion — and leaves 3−k pure p orbitals. The leftover p system explains resonance ( $\ce{CH2=CH-CH2+}$ ↔ $\ce{+CH2-CH=CH2}$ ) and hyperconjugation (σ C–H donation into an adjacent p or π* orbital), the same electronic bookkeeping behind the CIP description of stereogenic centres.

History of the experiment

Pauling introduced orbital hybridization in 1931 to reconcile valence-bond theory with the tetrahedral carbon — the same picture that makes resonance bookkeeping possible.

Chemists behind it

Linus Pauling