Skewness and kurtosis of level distributions in vibrational spectra. Coupled Morse oscillators

The skewness and kurtosis of the spectral density distribution of a Hamiltonian, which represents a system of N coupled Morse oscillators and, hence, describes molecular vibrations in the local mode approximation are derived. Detailed expressions are given for N=2 case and for various structures with N=3,6. The effect of the values of coupling constants on both statistical functions is analyzed. A comparison with the well-known Morse oscillator spectrum is given.