Collisional energy exchange in highly vibrationally excited molecules: The biased random walk model

A theory is developed for collisional energy exchange between a large highly vibrationally excited molecule and a rare gas, based on a diffusive motion for the internal energy of the molecule during the collision. The model is developed from a number of general trends deduced from the corpus of reliable experimental data and from trajectory studies. Since ‘‘energy diffusion’’ must be restricted to satisfy microscopic reversibility, one obtains a Smoluchowski equation for the distribution function for energy transfer in terms of one quantity s=(collision duration)1/2 × (‘‘energy diffusion coefficient’’)1/2. An expression for s is obtained (using linear response theory) in terms of properties such as the vibrational frequencies of the molecule. The simple model, with no adjustable parameters, is able to fit to ∼40% a very wide range of data: Some 50 experiments, with temperatures ranging from 300–1200 K and molecules ranging from haloethanes to C10–hydrocarbons. The model is improved by an empirical statistical treatment, and then offers a reliable means of estimating collisional energy transfer properties for rare gas/highly vibrationally excited molecule systems.