The determination of the redundancy relations among the bending coordinates around a central atom

Abstract

The redundancy relations among thc bending coordinates around a central atom have been derived to second order approximation by means of spherical trigonometry. The formalism derived here is not always applicable. A numerical result is more easily obtained by means of the formalism given here than in the generally applicable methods proposed by Crawfordl and Cihla and Pliva z. IntroductionIn solving the normal coordinate problem of the vibrational motions in a molecule one tries to connect the vibrational potential energy function V, with the vibrational parameters 1. V, may be developed quite generally as a power series of the internal displacement coordinates Si 3 * 4 :