Energy level distributions in spectra of coupled harmonic oscillators

Abstract The spectral density distribution of a hamiltonian which represents a system of N coupled harmonic oscillators, and hence may approximately describe molecular vibrations in the local mode picture, is analyzed. The spectral density moments are expressed as linear combination of products of coefficients which depend on the molecular structure and of one-particle moments describing individual bonds and interactions between them. Detailed expressions for linear and tetrahedral molecules are analyzed. Moreover, general formulae for matrix elements of powers of momentum in the harmonic oscillator basis are given.