Estimation of vibrational frequencies and vibrational densities of states in isotopically substituted nonlinear triatomic molecules

For use in unimolecular reactions, a simple method is introduced for obtain ing the unknown vibration frequencies: of the many asymmetric isotopomers o f a molecule from those of the symmetric ones. The method is illustrated fo r 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-facto red expression of the XYX type for the frequencies of all the isotopomers X YZ. 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 symmetr ic molecule since it contains all three masses.) PL Simple second-order per turbation 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 i ts simplicity, transparency, and,novelty, though normally one would use muc h more general methods such as ASYM 20 or 40. The method itself is not rest ricted to triatomic molecules.