Density of levels in vibrational spectra of molecules

Density distribution of the discrete spectrum of a Hamiltonian which represents a system of N-coupled oscillators and, hence may describe molecular vibrations in the local mode approximation, is analyzed. The spectral density moments are expressed as linear combinations of products of coefficients which depend on the molecular topology (analogs of the propagation coefficients in the statistical theory of nuclear and atomic spectra) and of one-particle moments describing individual bonds and interactions between them. The dependence of the first three moments of the energy-level density on the structural parameters of the molecule is discussed. Detailed expressions for several special cases are derived. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63 : 835–842, 1997