Localized Molecular Orbitals

Localized molecular orbitals are molecular orbitals which are concentrated in a limited spatial region of a molecule, for example a specific bond or a lone pair on a specific atom. They can be used to relate molecular orbital calculations to simple bonding theories, and also to speed up post-Hartree–Fock electronic structure calculations by taking advantage of the local nature of electron correlation.

Standard ab initio quantum chemistry methods lead to delocalized orbitals which in general extend over an entire molecule and have the symmetry of the molecule. Localized orbitals may then be found as linear combinations of the delocalized orbitals, given by an appropriate unitary transformation.

In the water molecule for example, ab initio calculations show bonding character primarily in two molecular orbitals, each with electron density equally distributed among the two O-H bonds. The localized orbital corresponding to one O-H bond is the sum of these two delocalized orbitals, and the localized orbital for the other O-H bond is their difference; as per Valence bond theory. Similarly, molecular orbital calculations show two nonbonding valence-shell orbitals: a roughly sp2 hybrid orbital in the plane of the molecule and a pure p orbital perpendicular to this plane. The roughly tetrahedral sp3 hybrids of valence bond theory for the lone pairs can be compared to the sum and the difference of these nonbonding orbitals.