In this paper we provide an extension of the theoretical study of nonradiative decay of a single vibronic level of a large molecule. We have derived theoretical expressions for the dependence of the electronic relaxation rate on the excess vibrational energy in the excited electronic state of a "harmonic molecule" which is characterized by displaced and frequency modified potential surfaces. The simple case of displaced potential surfaces was handled by relating the potential surfaces via a simple displacement operator. To handle frequency changes in optical selection we have applied Feynman's operator techniques to disentangle exponential operators which involve nonlinear terms. The role of frequency changes in optical selection experiments was elucidated.