Compliance Matrix and Molecular Vibrations

Abstract

It is shown that treatment of the molecular vibration problem in the form | F^—1G^—1—λ^—1E | =0 has certain advantages when the data from vibrational spectroscopy are to be combined with information from mean amplitudes of vibration or centrifugal distortion toward the end of determining a complete quadratic potential function. The matrix F^—1=C is a compliance matrix; its elements presumably have as much physical significance as those of F. Some new isotopic sum rules are formulated, appropriate to the compliance scheme, but they are not nearly so general as those involving the λ's. Linear molecules are discussed, and some numerical examples are given for nonlinear XY₂ and XY₄.