A method is presented for expressing the occupied self-consistent-field (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic minimal-basis-set orbitals that deviate as little as possible from free-atom SCF minimal-basis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the free-atom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed "quasiatomic minimal-basis-sets" is independent of the calculational atomic orbital basis used. The resulting resolution of molecular orbitals in terms of quasiatomic minimal basis set orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimal-basis orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence orbitals, which are useful for calculating electron correlation and the interpretation of reactions. The method is applicable to Kohn-Sham density functional theory orbitals and is easily generalized to valence MCSCF orbitals.

The method, introduced in the preceding paper, for recasting molecular self-consistent field (SCF) or density functional theory (DFT) orbitals in terms of intrinsic minimal bases of quasiatomic orbitals, which differ only little from the optimal free-atom minimal-basis orbitals, is used to elucidate the bonding in several silicon clusters. The applications show that the quasiatomic orbitals deviate from the minimal-basis SCF orbitals of the free atoms by only very small deformations and that the latter arise mainly from bonded neighbor atoms. The Mulliken population analysis in terms of the quasiatomic minimal-basis orbitals leads to a quantum mechanical interpretation of small-ring strain in terms of antibonding encroachments of localized molecular-orbitals and identifies the origin of the bond-stretch isomerization in Si4H6. In the virtual SCF/DFT orbital space, the method places the qualitative notion of virtual valence orbitals on a firm basis and provides an unambiguous ab initio identification of the frontier orbitals.

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