Semiclassical collision theory in the initial value representation: Efficient numerics and reactive formalism

Two contributions to semiclassical mechanics, within the initial value representation, are presented. The first is the introduction of an efficient integration scheme, based upon number theoretic lattices, which allows the effective evaluation of S matrix elements despite highly oscillatory integrands. Applications to collinear H+H2 and three-dimensional He+H2 inelastic scattering show good agreement with quantum results for both classically allowed and tunneling transitions with relatively few trajectories. The second contribution is the derivation of an initial value integral representation for reactive scattering using the idea of asymptotic equivalence with the classical-limit formulas. The result is a generally useful formula, requiring only real valued trajectories, for reactive scattering above and below the classical reaction threshold.