Classical S matrix: numerical applications to classically allowed chemical reactions

The classical S matrix theory (a theory in which all degrees of freedom are treated semiclassically) developed by Miller and Marcus is applied to the collinear H + H₂ reaction on a model potential energy surface. The classical, primitive, and uniform approximations and the initial value representation integral expression for the classical S matrix are calculated for total energies in the range 15-30 kcal/mole and compared to the exact quantum mechardeal calculations of Diestler. We choose a potential energy surface for which the quasiclassical reaction probability is unity over an energy range of 6 kcal/mole in order to make the test of theory particularly meaningful. It is seen that the classical S matrix theory is in very poor agreement with the quantum mechanical results for the reaction probabilities, although the semiclassical results for reactions producing vibrationally excited products are better behaved than those for reactions producing ground state products. The collision lifetimes and the stationary trajectories show no indication at all that the semiclassical calculations include a mechanism which could account for the 75% oscillation in the quantum mechanical P^R_0-0.