Zero Differential Overlap in ϕ-Electron Theories

Abstract

The Pariser-Parr-Pople method includes two essential simplifications in comparison to the full self-consistent linear combination of atomic orbitals-molecular orbital (LCAO-MO) π-electron method. The first simplification is the zero differential overlap (ZDO) assumption, which implies a drastic reduction of the number of integrals. The second simplification is that the values of the remaining integrals are determined in a more or less empirical way. In this chapter, only the first of these steps is discussed. It also provides a review of the self-consistent field method. The assumptions typical for the ZDO approximation are also given. To investigate the order of this approximation in the orthogonalized atomic orbitals (OAO) basis an expansion method is introduced. The expansion parameter H core is chosen to be essentially the overlap integral between adjacent atoms. It is clarified that the OAO's are almost as well localized as the AO's. The matrix elements of the different terms in the Fock operator are expanded in the parameter ɛ. The chapter also discusses the connection of the Hiickel method with the Pariser-Parr-Pople method. Two features are especially stressed, viz. the connection with the ω technique and the difference between Hückel parameters pertinent to spectral features on one hand and to the total energy on the other hand. It is pointed out that the matrix elements between nonadjacent atoms ought to be included in a consistent first-order approximation.