Vibrational Analysis of Substituted and Perturbed Molecules. I. The Exact Isotope Rule for Molecules

Abstract

The Green's function and partitioning techniques developed for treating the lattice‐impurity problem have been applied to molecular systems. The vibrational frequencies of isotopically substituted molecules are obtained exactly and explicitly without recourse to a force constant model. It is shown that the mixing of the symmetry coordinates of the unperturbed molecule is determined uniquely from the experimental frequencies. The usual product rule is obtained; however, it does not involve the moments of inertia. The more general problem involving changes in the bond strength is formally presented. Explicit expressions for the vibrational frequencies for any isotopic substitution of a nonlinear XY₂ molecule are derived. Numerical results for H₂O and H₂S are given.