A local energy method based on the reduced density matrix equations

Abstract

In the Frost local energy method a “best” wavefunction is determined by minimizing the variance of the local energy. Certain simplifications in Frost's method may be obtained by working with the hierarchy equations for reduced density matrices which are obtained by successive integrations over the Schrödinger equation. We define a reduced local energy matrix which is a function of only two variables, in contrast to Frost's local energy which is a function of the number of particles in the system. Considering the Hartree-Fock case a procedure for obtaining a “best” reduced density matrix by minimizing the variance of the reduced local energy matrix is presented. This results in a set of iterative matrix equations for the determination of the normalized idempotent density matrix. Our results which are based on one equation in two variables are compared to the related efforts of Scott who worked directly with the N orbital energies of the Hartree-Fock equations.