ChemInform Abstract: Molecular Topology and Approximate Normal Modes: Ethane and Cyclopropane.

Abstract

Abstract It is shown that approximate normal modes in terms of two parameters can be predicted for ethane and cyclopropane from molecular topology. The complete GF matrices of the molecules are simplified to block diagonal form where each block involves local symmetry coordinates of a single type. Vibrational frequencies calculated from these simplified matrices agree well with the frequencies resulting from diagonalization of the completed GF matrices. It is seen that each block of the simplified matrices is of the form GF = α E + β A , where E is an identity matrix and A is a CC bond adjacency matrix in the case of CC stretches and a carbon atom adjacency matrix in the case of CH stretches and bends. Thus, normal coordinates and vibrational frequencies in terms of the parameters α and β can be found from the diagonalization of adjacency matrices.