VIBRATIONAL ANALYSIS OF SUBSTITUTED AND PERTURBED MOLECULES. I. EXACT ISOTOPE RULES FOR MOLECULES

Abstract

Green's function and partitioning techniques are applied to molecular systems. A general theory is developed which results in exact and explicit formulas for the vibrational frequencies of isotopically substituted molecules without recourse to a force constant model. The construction of the Green's function from the symmetry coordinates and experimental frequencies is discussed. It is shown that the mixing of the symmetry coordinates of the unperturbed molecules is determined uniquely from the experimental data. The product rule obtained does not involve the moments of inertia and in many cases depends only upon mass ratios.