Exchange Reactions with Activation Energy. I. Simple Barrier Potential for (H, H2)

A quasiclassical procedure for the examination of the collision dynamics of atom—diatomic-molecule reactions with activation energy is introduced. By means of Monte Carlo averages over a large number of appropriately chosen three-dimensional classical trajectories, the total reaction cross section (Sr) and other reaction attributes can be determined as a function of the initial relative velocity (Vr) and the initial molecular rotation-vibration state (J, ν). The method is applied to the exchange reaction resulting from a hydrogen atom and a hydrogen molecule moving on a simple barrier potential of the London—Eyring—Polanyi—Sato type. It is found that Sr is a monotonically increasing function of relative velocity that rises smoothly from a threshold at ∼0.9×106 cm/sec to its asymptotic value of ∼4.5a02 at ∼1.8×106 cm/sec. The zero-point vibrational energy of the molecule contributes to the energy required for reaction, but the rotational energy does not. The reaction probability, which depends on VR, ν, and J, is found to be a smoothly decreasing function of the impact parameter (b) with a maximum of ∼0.6 for b=0 at high velocities. By integration of Sr over the distributions of VR, ν, and J corresponding to temperatures between 300° and 1000°K, a rate constant that can be fitted to an expression of the form K(T)=ATα exp—Ea°/RT is obtained, where A, Ea°, and α(α=1.1762) are constants. This temperature dependence is analyzed and contrasted with the results obtained from an absolute rate theory treatment based on the same surface. A detailed examination of the collision trajectories shows no evidence for a long-lived ``collision complex''; instead the results are best represented by a direct interaction model with an interaction time on the order of that required for the atom to pass unimpeded by the molecule. For reactive collisions, the transition configuration is nonlinear with average angles of 170° for VR=0.93×106 cm/sec and 150° for VR=1.30×106 cm/sec; for nonreactive collisions, the average angle is between 95° and 125°, but has no simple relation to VR.