Derivative Numerov–Cooley theory. A method for finding vibrational state properties of diatomic molecules

Abstract

The difference equation method for finding one-dimensional vibrational state wave functions and energies which is usually referred to as the Numerov–Cooley method has been extended to molecular properties which are defined as energy derivatives. By straightforward differentiation of the Schrödinger equation with respect to embedded parameters, for instance, electric field components, a difference equation procedure has been developed that finds derivative vibrational wave functions and derivatives of the electronic–vibrational state energies of diatomic molecules. Representative test calculations are reported.