General approach for the construction of hybrid orbitals

Abstract

A general approach to construct hybrid orbitals based on the projection of both the subspace of atomic orbitals and the subspace of hybrid orbitals is presented. It is shown that the projection must be associated with a chain of groups to ensure the independence of the method with respect to the selected coordinate system. The eigenfunction method to obtain symmetry projected functions turns out to be the natural projection technique to establish the present approach. The proposed method allows construction of hybrid orbitals in a systematic and general way, even in the hypothetical case where irreducible representations are contained more than once in the reduction of the space of hybrid orbitals. To illustrate our approach, a hybridization d 2sp3 for octahedral molecules is discussed. © 2005 Wiley Periodicals, Inc.