Relation between Bounds on the Overlap and on the Second-Order Perturbation Energy

Abstract

Bounds on the overlap integral between an approximation and the exact wavefunctions are shown to follow from bounds on the second-order perturbation energy. Thus the Eckart lower bound on the overlap is a special case of the Unsöld approximation. Also, the generalized Hylleraase variational principle leads to the James-Coolidge and Wang upper bounds on the overlap.