Estimation of Vibrational Frequencies and Vibrational Densities of States in Isotopically Substituted Nonlinear Triatomic Molecules

Abstract

For use in unimolecular reactions, a simple method is introduced for obtaining the unknown vibration frequencies of the many asymmetric isotopomers of a molecule from those of the symmetric ones. The method is illustrated for a triatomic molecule XYZ, ozone. It is based on the neglect of a single G matrix element in the GF expression for XYZ, yielding for it a block-factored expression of the XYX type for the frequencies of all the isotopomers XYZ. It agrees with available data to the accuracy needed, a few cm^(-1). The first-order perturbation vanishes. (The zeroth-order case is not a symmetric molecule since it contains all three masses.) A simple second-order perturbation result for the GF matrix using data for one asymmetric isotopomer then provides agreement to about 1 cm^(-1). The virtues of the method are its simplicity, transparency, and novelty, though normally one would use much more general methods such as ASYM 20 or 40. The method itself is not restricted to triatomic molecules.