NONORTHOGONAL LOCALIZED ORBITALS AND ORTHOGONAL ATOMIC HYBRIDS DERIVED FROM MULLIKENS POPULATION ANALYSIS

The construction of non-orthogonal localized molecular orbitals (Wanni er functions of extended systems) with maximal degree of localization according to the Magnasco-Perico localization criterion derived from M ulliken's population analysis is discussed and several forms of the eq uations giving these orbitals are presented. A partial orthogonality p roperty of these orbitals permits an easy determination of the effecti ve orthogonal atomic orbitals characterizing the actual state of the a tom in the molecule; this helps to find connections between large-scal e 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 appre ciably localized on the given atom as are contained in the classical ' minimal basis' for that atom.