The Calculation of Zero-Point Energies of Molecules by Perturbation Methods

Two methods are proposed for calculating zero-point energies of molecules. The first makes use of the fact that one can easily write down the quantum mechanical HAMILTONian for a vibrating system. The zero-point energy can then be obtained by a perturbation scheme without solving the secular equation. The second method requires a knowledge of the normal modes and frequencies of a reference molecule, but then enables one to calculate isotope effects by a perturbation scheme. The methods are applied to some examples and the convergence of the perturbation series is investigated. The approximate validity of the law of the mean for the isotope effect on zero-point energies is explored within the framework of the methods.