Role of redundant coordinates in evaluating skeletal force constants in simple cyclic systems

Abstract

The treatment of redundant vibrational coordinates and their effect on force field determinations often presents difficulties for the vibrational spectroscopist. W hiffen [17], for example, approached the redundancy problem in the force field for the planar vibrations of benzene by transforming a set of redundant internal valence force constants ƒ ij , to a non-redundant set of tilde force constants ƒ ij , where ƒ ij represents appropriate linear combinations of the original ƒ ij . We use the concept of tilde force constants to eliminate the redundancies among the internal valence displacement coordinates in cyclopropane C 3H 6 and phosphorus P 4 and to clarify the precise meaning of the resulting skeletal force constants for these systems.