Group Theory and Normal Modes

Abstract

This article—which is tutorial in its approach—gives explicit directions for determining the normal modes of a symmetrical vibrating system through the use of group theory. The example considered is the planar, homonuclear, equilateral molecule. The eigenvalues are first determined from the secular equation by a numerical, empirical method. After a brief review of the applicable concepts from group theory, it is shown how the projection operator method may be used to solve the same problem in a direct way.