Molecular orbital theory and hybridisation

The simple picture of a covalent bond as "two atoms sharing an electron pair" is a useful shorthand, but molecular orbital theory gives a more complete quantum-mechanical account of what actually happens: when atoms approach each other, their atomic orbitals combine (mathematically, as linear combinations) to produce new orbitals — molecular orbitals — that are no longer localised on a single atom but extend over the whole molecule. For two atomic orbitals combining, exactly two molecular orbitals result, and they are not equivalent to each other. The bonding molecular orbital results from atomic orbitals combining in phase, concentrating electron density in the region between the two nuclei, and its energy is lower than that of the original atomic orbitals — electrons placed in this orbital are more stable than they would be in separate atoms, which is exactly what makes bond formation energetically favourable. The antibonding molecular orbital results from the atomic orbitals combining out of phase, producing a node (a region of zero electron density) between the nuclei, and its energy is correspondingly higher than the original atomic orbitals. Whether a bond forms, and how strong it is, depends on how many electrons occupy the bonding versus antibonding orbitals — filling only the bonding orbital gives a strong bond, while equal occupation of bonding and antibonding orbitals gives no net bonding at all, exactly why some diatomic combinations of atoms simply do not form stable molecules.

Molecular orbital theory, built from combining orbitals across the whole molecule, does not by itself explain a separate observation: many atoms form a specific number of bonds in a specific three-dimensional arrangement that does not obviously match the shapes of their unhybridised atomic orbitals. Carbon's unhybridised orbitals are one spherical 2s orbital and three dumbbell-shaped 2p orbitals oriented along perpendicular axes — a lopsided, non-equivalent set — yet carbon in methane forms four completely equivalent bonds pointed toward the corners of a tetrahedron. Hybridisation resolves this by treating the relevant atomic orbitals on a single atom as mixing together mathematically into a new set of equivalent hybrid orbitals with a specific geometry: mixing one s and three p orbitals produces four equivalent sp3 hybrids in a tetrahedral arrangement, matching methane's observed geometry exactly; mixing one s and two p orbitals produces three equivalent sp2 hybrids in a trigonal planar arrangement, matching the geometry seen around a carbon in a double bond; mixing one s and one p orbital produces two equivalent sp hybrids in a linear arrangement, matching the geometry around a carbon in a triple bond. Hybridisation and molecular orbital theory are not competing explanations of the same phenomenon but complementary tools operating at different scales: hybridisation reshapes an individual atom's orbitals to match observed local geometry, while molecular orbital theory describes how orbitals on different atoms combine to actually form bonds — a full molecular orbital treatment of a polyatomic molecule typically builds molecular orbitals from hybridised atomic orbitals as its starting point.