Alternative Technique for the Constrained Variational Problem Based on an Asymptotic Projection Method: I. Basics

Abstract

An alternative approach to problems in quantum chemistry which can be written as an eigenvalue equation with orthogonality restrictions imposed on eigenvectors is reviewed. The basic tenets of a simply implemented asymptotic projection method for taking the necessary orthogonality constraints into account are presented. The eigenvalue equation for a modified operator is derived and the equivalence of the original and modified problem is rigorously demonstrated. The asymptotic projection method is compared with the conventional approach to constrained variational problems based on the elimination of off-diagonal Lagrange multipliers and with other methods. A general procedure for application of the method to excited state problems is demonstrated by means of calculations of excited state energies and excitation energies for the one-electron molecular systems, H 2 + and H 3 ++ .