A statistical wave function model for C–H/C–D overtone linewidths: Application to C6H6, C6D6, C6HD5, C6HF5

A simple quantitative model calculation is presented for C–H overtone spectra in polyatomic systems. The model employs a realistic force field Hamiltonian that includes the structure of all modes. The physical basis for the linewidths is a centrifugal coupling to the CCH in-plane wag motions, as first suggested by Sibert, Reinhardt, and Hynes. To avoid exhaustive analysis of the full coupled-mode problem, approximate solutions for the eigenstates are constructed, using a statistical assumption on the wave functions in terms of their expansion coefficients in the decoupled mode basis. The results yield a simple physical interpretation for the observed isotope effects, the fluctuations in linewidth with the quantum number, the anomalously narrow lines of C6HF5, etc. Calculations are presented for the linewidths of C6H6, C6HD5, C6D6, and good agreement with the experiment is found. The statistical assumption for calculation of the density of effectively coupled states appears to be adequate for problems of this type.