Comparison of quantum mechanical and quasiclassical scattering as a function of surface topology

Abstract

All-channel, time-dependent quantum mechanically computed total reaction probabilities for collinear A+BC→AB+C reactions have been compared with quasiclassical trajectory results on three hypothetical LEPS-type potential-energy surfaces. Each surface had identical reactant and product limits and barrier height but differed in the location of the saddle point. In all calculations the atomic masses were taken to be 1 amu to maximize possible quantum effects. Quantum and quasiclassically computed total reaction probabilities are found to be in reasonable accord, except near threshold, for reactions taking place on symmetric potential-energy surfaces analogous to that for the (H+H₂) exchange reaction. If the surface symmetry is removed by displacing the saddle point into the exit channel, however, the extent of agreement between quantal and quasiclassical results is drastically reduced. At an energy of 1.5 kcal/mole above threshold, the quasiclassical reaction probability is over five times the quantal result. Even at energies 7.5 kcal/mole in excess of threshold, the quasiclassical to quantum mechanical ratio is 2. The extent of agreement between the two calculations is also reduced if the surface symmetry is removed by moving the saddle point into the entrance channel, although the effect is smaller than for displacement into the exit channel. Both quasiclassical and quantal calculations predict a large increase in reaction probability for asymmetric surfaces with the barrier in the exit channel whenever the total energy is preferentially partitioned in BC vibration. These results indicate that approximate scattering theories are best tested by investigation of systems with low reduced mass moving on asymmetric potential-energy surfaces with the saddle point located in the product channel.