A statistical wave function model for C-H/C-D overtone linewidths: Application to C₆H₆, C₆D₆, C ₆HD₅, 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, C ₆D₆, 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.