Non-orthogonal localized orbitals and orthogonal atomic hybrids derived from Mullikenʹs population analysis

The construction of non-orthogonal localized molecular orbitals (Wannier functions of extended systems) with maximal degree of localization according to the Magnasco-Perico localization criterion derived from Mullikenʹs population analysis is discussed and several forms of the equations giving these orbitals are presented. A partial orthogonality property of these orbitals permits an easy determination of the effective orthogonal atomic orbitals characterizing the actual state of the atom in the molecule; this helps to find connections between large-scale ab initio SCF calculations and traditional atomic orbital concepts. Calculations indicate full agreement with the traditional AO picture: for all ‘ordinary’ compounds one gets as many molecular orbitals appreciably localized on the given atom as are contained in the classical ‘minimal basis’ for that atom.