Harmonie Force Fields and Bond Orders for Naphthalene, Anthracene, Biphenylene and Perylene with Mean Amplitudes for Perylene

Abstract

Complete normal coordinate analyses were performed for naphthalene, anthracene, biphenylene and perylene, starting from a simple force field with seven adjustable force constants. A relationship between bond orders and carbon-carbon stretching force constants was deduced from: (a) bond distances as a function of bond orders, (b) a version of Badger's rule relating stretching force constants to the bond distances. The relationship was used to modify the initial seven-parameter force field, and the vibrational frequencies calculated from both the initial and modified force fields are discussed. In general the simple force field approximation produces sets of frequencies in remarkably good agreement with experimental assignments. The force field approximation failed badly when applied to benzene. No obvious explanation was found for this unexpected feature, which makes it worth while to continue the investigations. The mean amplitudes of vibration were calculated. For perylene an account of the complete set of mean amplitudes is given for the first time.