Generalized Perturbation Method Employing Nonorthogonal Functions

Abstract

A method is developed for solving second‐order perturbation problems without explicit knowledge of the higher molecular states. This method involves, in principle, a transformation of basis from the set of orthonormalized eigenfunctions of the unperturbed molecular Hamiltonian to an arbitrary set of functions not, in general, either normalized or mutually orthogonal, but of such symmetry that perturbation matrix elements connecting them to the ground state do not vanish. If the new basis is chosen expediently, convergence to second‐order eigenvalues may be attained with a small number of functions. The method is related to the conventional perturbation and variational approaches. As an illustration, the perturbed harmonic oscillator is treated.