Localization of molecular orbitals within the RHF method

The canonical MOs derived from the RHF method are usually delocalized over the whole molecule, i.e. their amplitudes are significant for all atoms in the molecule. This applies, however, mainly to high energy MOs, which exhibit a similar AO amplitude for most atoms. Yet the canonical MOs of the inner shells are usually very well localized. The canonical MOs are occupied, as usual, by putting two electrons on each low lying orbital (the Pauli exclusion principle). 

pictui,. obtaLivjd is m conuast to chcniical intuition, which indicates that the electron pairs are localized within the chemical bonds, free electron pairs and inner atomic shells. The picture which agrees with intuition may be obtained after the localization of the MOs. 

The new orbitals do not satisfy the Fock equations (830), these are satisfied by eanonical orbitals only. 

The localized orbitals (being some other orthonormal basis set in the space spanned by the canonical orbitals) satisfy the Fock equation (8.18) with the off-diagonal Lagrange multipliers. 

Unfortunately, the view to which chemists get used, i.e. the chemical bonds between pairs of atoms, lone electron pairs, iimer shells, can be derived in an infinite 

---