Localized orbitals

The molecular orbitals generated by diagonalization are normally delocalized over the system. By using a unitary transform of the occupied M.O.s, it is possible to generate a set of molecular orbitals which are localized on from one up to three centers.

These localized M.O.s are not eigenvectors of the Hamiltonian, nor are their energies eigenvalues. However, localized orbitals can be equated with the single, double, triple, and delocalized $\pi$ -bonds of classical organic chemistry.