The Theory of Pair-Correlated Wave Functions

Abstract

This chapter presents simple and unified treatment of correlated pair theories, paying particular attention to spin-coupling requirements. The theory of pair-correlated wave functions may be derived easily from the group function approach, one electronic group being a pair of electrons and the other being the remaining (N-2) electrons. There is a nontrivial spin-coupling problem when it is required that the correlated wave function shall remain an exact eigenfunction of the total spin operators. This difficulty has been resolved in a simple way, applicable even in the general case of an “open-shell” system with a nonsinglet ground state. The basic single determinant wave function used as the zero-order approximation in the perturbation calculation, may be, conveniently optimized without relaxing spin eigenfunction requirements by introducing a single model Hamiltonian containing suitable projection operators. The eigenfunctions of this operator are the exact SCF functions for both the closed and open shells. On exciting electrons two at a time from the basic determinant to correlated pair functions, which are strong orthogonal to single determinant wave function the variational equation for the second-order energy separates into a set of two electron equations, one for each pair function. The fact that these equations are uncoupled is a result of the strong-orthogonality condition, a constraint, which is equivalent to disregarding a possible contribution from single excitations. The effects of admitting single and multiple excitations and using a basic function, which is constructed from a finite orbital basis, and is therefore not exact, are also discussed in the chapter.