Overtone vibrations of molecules

A vibrational equation for overtones is derived by applying the direct multiplication of matrices in the framework of the molecular vibration theory. The relationships determining the characteristics of the overtone vibration mode and expressions describing the changes in the structural and geometric molecular parameters are obtained by solving the deduced equation. The electro-optical parameters of the overtones 2ν_s, 3ν_s, 4ν_s, and 5ν_s(s=3, 4) of a methane molecule are calculated from the deduced relationships using the semiempirical quantum-mechanical CNDO/2 method and numerical differentiation with cubic spline functions.