The structure and transformation properties of correlation functions for open shell states of molecules in non-orthogonal ao as well as in MO bases

Abstract

A rigorous derivation of many-electron correlation functions for constructing the exact wave function for open shell molecules is given. These correlation functions are formally projections from the exact many-particle wave function and as such are particular realizations of applying Sinanoǧlu's Partial Orthogonalization Method. Correlation functions are derived for both an orthonormal set of (molecular) orbitals and a non-orthogonal set of (atomic) orbitals which provide alternative, but equivalent descriptions of a molecule in the independent particle picture. The transformations between the “molecular orbital” and “atomic orbital” correlation functions are considered. Simplifications of these relations for closed shell systems are presented; these in turn lead to new types of correlation functions for open shells. These new correlation functions are generalizations of those originally introduced by Silverstone and Sinanoǧlu and are susceptible to direct physical interpretation in terms of excitations from the independent particle “open shell” sea. The results given here, especially those on the non-orthogonal AO basis should be useful for semiempirical molecular correlation energy methods, as well as in CI studies.