Decomposition of Molecules with n-Fold Symmetry

Abstract

In Chapter 1 we developed graph theoretical methods for the facile solution of HMO parameters of conjugated polyenes with eight or less carbon vertices without having to expand their secular determinants. Also, it was shown that knowledge of some eigenvalues through other means, such as embedding, permitted us to solve even larger molecular polyenes for their HMO parameters. In this chapter, we will show how to decompose or fragment larger symmetrical molecular graphs into smaller subgraphs. The eigenvalues of these subgraphs then can be obtained by the methods discussed in Chapter 1. The collection of eigenvalues for these subgraphs will be eigenvalues of the precursor molecular graph. Mirror plane fragmentation of molecules having at least one mirror plane of symmetry (e.g., C _2v and D _2h) is the most general decomposition method.