Generalizations of the direct CI method based on the graphical unitary group approach. I. Single replacements from a complete CI root function of any spin, first order wave functions

Abstract

The direct CI method is generalized to the class of wave functions, denoted as first order wave functions. With a first order wave function is meant a complete CI expansion in a small internal valence space and single excitations outside this space. The wave function can have any spin. The formalism of the graphical unitary group approach of Paldus and Shavitt is used to reduce the coupling coefficients of the direct CI method to expressions involving the internal space only. The necessary formula tape is therefore reduced drastically in size. An approximate and much faster method is suggested for very large CI expansions, based on the neglect of certain integrals. The method is applied to the singlet–triplet splitting of dioxymethane, CH2O2, which is a proposed intermediate in the ozonolysis of ethylene. The calculations predicts the 1A1 to be the ground state, but the splitting between 1A1 and 3B2 is calculated to be very small, 2.0 kcal/mole, in the best calculations reported here.