Application of the Franck-Condon principle to the XY₂ molecule

A method is presented for the determination of the excited state structure of a bent XY₂ molecule by an application of the Franck-Condon principle. The data required are the frequencies of vibration of the ground and excited states, the peak molecular extinction coefficients of a few selected vibronic bands, and the ground state structural parameters. The method is illustrated by calculating the structure of the excited states of the 3800A and the 2300A absorption systems of the sulfur dioxide molecule and the 3500A absorption system of the chlorine dioxide molecule. The most important feature of the proposed method is that it allows the n-dimensional Condon overlap integral to be treated as n one-dimensional integrals, where n is the number of totally symmetrical modes of vibration. In the case of the XY₂ molecule n= 2. A measure of the accuracy of this method is obtained by comparing results of the one-dimensional calculations with those of the more exact n-dimensional calculations