Hybridisation and Molecular Orbitals

Two Ways to Explain a Bond

Valence bond theory says a bond is the overlap of two atomic orbitals, each contributing one electron. Head-on overlap along the internuclear axis makes a sigma bond; sideways overlap of parallel $p$ orbitals makes a pi bond, which has a nodal plane through the axis.

Pure atomic orbitals give the wrong shapes, carbon's $2s^2 2p^2$ would predict two bonds at $90^\circ$, not four at $109.5^\circ$. Hybridisation mixes them into equivalent hybrids:

The count is simple: the number of hybrid orbitals equals the number of electron domains. So a single bond is one sigma; a double bond is one sigma plus one pi; a triple bond is one sigma plus two pi. In ethene each carbon is $sp^2$, leaving one unhybridised $p$ orbital on each to form the pi bond, and because pi overlap is destroyed by twisting, the double bond cannot rotate.

Molecular orbital theory takes a different route: atomic orbitals combine into orbitals belonging to the whole molecule. Two atomic orbitals give one bonding MO (lower energy, electron density between the nuclei) and one antibonding MO (higher energy, with a node between them). Electrons fill these by the same rules as atoms, and

$$\text{bond order} = \tfrac{1}{2}(N_{\text{bonding}} - N_{\text{antibonding}})$$

A bond order of zero means no bond, which is exactly why $\mathrm{He_2}$ does not exist. MO theory also predicts what valence bond theory cannot: $\mathrm{O_2}$ has two unpaired electrons in degenerate antibonding orbitals and is therefore paramagnetic, it sticks to a magnet, which a Lewis structure with a tidy double bond would never suggest.

Common pitfall: thinking hybridisation is something an atom physically does before bonding. It is a mathematical recombination of orbitals chosen to match the observed geometry, the shape is the evidence, and the hybrid is the description.