The spectral density distribution of a Hamiltonian which represents a system of N coupled Morse 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 are analyzed for linear and tetrahedral molecules. Moreover a comparison with the case of coupled harmonic oscillators is given.
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