1.11 : MO Theory and Covalent Bonding

The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while out-of-phase waves produce nodes or regions of no electron density.

The in-phase combination of two atomic s orbitals on adjacent atoms produces a lower energy σs bonding molecular orbital in which most of the electron density is directly between the nuclei. The out-of-phase addition produces a higher energy σs* antibonding molecular orbital, in which there is a node between the nuclei.

Similarly, the wave function of p orbitals gives rise to two lobes with opposite phases. When p orbitals overlap end to end, they create σ and σ* orbitals. The side-by-side overlap of two p orbitals generates π bonding and π* antibonding molecular orbitals.

The filled molecular orbital diagram shows the number of electrons in bonding and antibonding molecular orbitals. An electron contributes to a bonding interaction only if it occupies a bonding orbital. The net contribution of the electrons to the bond strength of a molecule is determined from the bond order, which is calculated as follows:

The bond order is a guide to the strength of a covalent bond; a bond between two given atoms becomes stronger as the bond order increases. If the distribution of electrons in the molecular orbitals yields a bond order of zero, a stable bond does not form.

The molecular orbital theory is also useful for polyatomic molecules. The Lewis model of benzene (C₆H₆), which has a planar hexagonal structure with sp² hybridized carbon atoms, cannot accurately represent its delocalized electrons. However, the molecular orbital theory assigns those electrons to three π bonding molecular orbitals covering the entire carbon ring. This results in a fully occupied (6 electrons) set of bonding molecular orbitals that endow the benzene ring with additional thermodynamic and chemical stability.