Valence bond theory and hybridisation

Valence bond theory explains bonds through overlap of atomic orbitals. A bond forms when a half-filled orbital of one atom overlaps with a half-filled orbital of another, and the two electrons pair up with opposite spins. The greater the overlap, the stronger the bond. As two hydrogen atoms approach, the energy falls to a minimum of –435.8 kJ mol⁻¹ at a distance of 74 pm: the bond length of H₂.

Overlap can happen in two ways:

• σ (sigma) bond: head-on overlap along the line joining the two nuclei (the internuclear axis): s with s, s with p, or p with p end-on. It is strong.
• π (pi) bond: sideways overlap of two parallel p orbitals, above and below the axis. It is weaker.

So a single bond is one σ; a double bond is σ + π; a triple bond is σ + 2π. In ethene, H₂C=CH₂, there are 5 σ bonds (four C–H and one C–C) and 1 π bond.

Valence bond theory alone cannot explain why, for example, all four bonds of methane are identical. Hybridisation solves this: atomic orbitals of similar energy on the same atom mix to form the same number of new, identical hybrid orbitals, which point in definite directions:

• sp: one s + one p → 2 hybrids at 180° (linear): BeCl₂, ethyne (C₂H₂).
• sp²: one s + two p → 3 hybrids at 120° (trigonal planar): BCl₃, ethene (C₂H₄).
• sp³: one s + three p → 4 hybrids at 109.5° (tetrahedral): CH₄; also NH₃ and H₂O, where some hybrids hold lone pairs.

Atoms with d orbitals can form more hybrids: sp³d (trigonal bipyramidal, PCl₅, whose axial bonds are longer than its equatorial ones, because they suffer more repulsion), sp³d² (octahedral, SF₆) and dsp² (square planar).

A quick way to find the hybridisation of an atom: count its σ bonds plus its lone pairs. 2 means sp, 3 means sp², 4 means sp³. An atom's hybridisation can change in a reaction: boron in BF₃ is sp², but when BF₃ bonds to ammonia (F₃B·NH₃), it becomes sp³. Likewise aluminium is sp² in AlCl₃ and sp³ in AlCl₄⁻.