Other Applications

Abstract

In this chapter we outline an application of the Fourier transform in the selection of the so-called normal modes in molecular spectroscopy, e.g., [15, p. 138], [16, p.184]. Although the Fourier transforms appear, implicitly, in [17, p.239], their usefulness in sorting out the distinct vibrational modes is not made explicit. The need for a detailed analysis of the modes comes from the fact that a typical action of a space group on the molecular framework is not transitive. Therefore, the irreducible representations appear with extramultiplicities in the factorization of the space group representation. By isolating the symmetry orbits, and thus retaining the transitivity, the separation of the modes appearswith less effort. The joint vibrational scheme is then obtaining by matching the transforms according to the irreducible representations.