Classical trajectory calculation of the benzene overtone spectra

A quasi-classical trajectory method is used to calculate line widths for CH(D) overtone states in benzene. The potential energy function used for the trajectories is derived in part from ab initio calculations. An important potential property is the attenuation of a CCH(D) bend force constant as the CH(D) bond is extended. The probability P(n,t) of populating the initially prepared overtone state |n〉 versus time is calculated for both CH and CD overtone states. All the CD states in C₆D₆ and the high-energy CH states in C₆H₆ decay nonexponentially. Absorption envelopes are determined from the Fourier transform of the square-root of the P(n,t) probabilities. The line widths vary from 30 to 110 cm^-1 and are somewhat smaller for the CD overtones. Comparisons are made between the calculated and experimental line widths.