Broken Path Model of Reactive Collisions: Application to Collinear (H, H2)

Abstract

Within the context of the collinear $\mathrm{H}+{\mathrm{H}}_2$ reaction, an approximate technique for reactive scattering on realistic potential surfaces is presented. Essentially, the broken path model provides a novel framework for the derivation of propagation matrices. The model is constructed by segmenting the potential surface into rectangular or pie‐shaped regions. In each region, the potential is approximated by two simple analytical functions associated with translational and vibrational motions. Local Cartesian coordinates are defined in each region. Since adjacent local coordinate axes are offset and at angles to each other, the asymptotic regions are connected by a ``broken path.'' The potential approximations and coordinate system allow us to solve a set of uncoupled Schrödinger equations for translation of the wavefunction across a box. Coupling occurs at the boundaries where matching of the wavefunctions and normal gradients is required. Propagation matrices are defined for each box; they include both translation and connection into the next region. A set of propagation matrices transforms the wavefunction from the initial to final asymptotic regions. Calculations are presented to show the effects of small variations in the model, the influence of closed channels, and nonadiabaticity. We find that sensitivity to variation in region size and potential approximations increases as the total energy increases. However, deviations are reduced if we employ all channels required for convergence. The importance of closed channels and nonadiabatic effects are seen by comparing results from adiabatic (one channel studies) and nonadiabatic calculations. In addition, if reaction path curvature, which contributes to nonadiabaticity, is neglected, the accuracy of the results is reduced. For all our calculations we use the exact reaction probability as a test of our accuracy.