Deduction of the Zero Differential Overlap Approximation from an Orthogonal Atomic Orbital Basis

Abstract

The validity of the zero differential overlap approximation is investigated by means of a systematic expansion in terms of a parameter of the order of magnitude of a typical overlap integral between neighboring atoms. The terms of the Fock operator in a basis of orthogonal atomic orbitals can be arranged after different orders of the parameter. It is demonstrated that, by inclusion of second-order terms, the conditions imposed by the zero differential overlap approximation are automatically fulfilled. Moreover, all the basic integrals are shown to be transferable in the first order and all but W in the second order. The connection with the ω technique in the Hückel method is also given. A numerical application has been made to ethylene and benzene.