Perturbation Theory of the Constrained Variational Method in Molecular Quantum Mechanics

Abstract

The variational problem of minimizing the energy of a trial wavefunction which is constrained to give the known theoretical or experimental expectation value of an operator is discussed. A perturbation approach is developed, which leads to simple equations for estimating the effect of the constraint on the expectation values of other operators, and the increase in energy due to the constraint. It is shown that for hypervirial operators the constraint procedure for satisfying the corresponding hypervirial theorem leads to equal and opposite results from the variational procedure. The equations are compared with those of a conventional perturbation treatment, which tends to support the constraint procedure. The theory is extended to cover the effect of constraints on second-order properties and multiple constraints. The perturbation equations are applied to Robinson's (1957) calculations on the lithium hydride molecule, previously discussed by Rasiel and Whitman (1965).