Methods for solving constrained SCF-LCAO-MO equations.

Abstract

When the variational procedure of the SCF-LCAO-MO approximation for a closed-shell ground state is modified so as to include as constraint the expectation value of an operator of the form ℳ = ∑ℳ _i + ∑∑ℳ _ij , the result is a set of modified SCF-LCAO-MO equations. Various methods for solving these constrained orbital equations are investigated. These are the third-order perturbation approach developed in a previous paper, a perturbation-iteration procedure, and the parameterization technique. The methods are applied to a calculation on the ground state of the N ₂ molecule. As a starting point for the calculation the LCAO-MO wave function of Scherr is taken. This wave function is then constrained to satisfy the molecular virial theorem in one case and to reproduce the experimental value of the molecular quadrupole moment in another. The numerical results obtained by the various methods of solution are compared. It is found that all of the three methods can be recommended but it is believed that in most cases the parameterization technique, when based on the first-order perturbation approach, is to be preferred.