Cross sections for rotational energy transfer: An information-theoretic synthesis

State-to-state cross sections are readily computed by combining the capabilities of the classical trajectories method with an information-theoretic ("surprisal") synthesis. The method is illustrated by an application to rotational energy transfer in several systems, (Ar+N₂, Li ⁺+H₂, Li⁺+D₂, H+CO). It is shown that by using classical trajectories to compute a single moment of the distribution of final rotational energy (for a given initial rotational energy) and then maximizing the entropy of the distribution subject to the given value of the moment one can obtain a good prediction of the distribution. Invoking microscopic reversibility, the entire matrix of state-to-state, σ(j-j′), rotational energy transfer cross sections (at the given total energy) is then determined. More averaged quantities, such as the cross sections for inelastic collisions σ(j), are thereby easily obtained. When a realistic potential energy surface is not available or when one requires a simple but reliable prediction, the synthesis can be based on invoking a sum rule. Here the moment of the distribution is not computed via classical trajectories but is expressed as a simple function of the initial conditions. It is shown that available cross sections often satisfy the simplest possible sum rule and hence a synthesis can be readily carried out where the only inputs are the total energy and the rotational constant of the diatomic molecule. The distribution of final rotational states predicted in this way is independent of the nature of the collision partner. The method is illustrated by applications to H+CO, Ar+N₂, Li⁺+H₂, He+HD, H+H₂, and H+D₂. Results for the distribution of final rotational state and the dependnece of the cross section on the initial rotational state and on the collision energy are in very good accord with classical trajectory and with quantal close-coupling computations.