A novel discrete variable representation for quantum mechanical reactive scattering via the <i>S</i>-matrix Kohn method

TLDR

The S‑matrix Kohn variational method for quantum reactive scattering was introduced by Zhang, Chu, and Miller in 1988. The study introduces a novel discrete variable representation to serve as the L2 basis for the S‑matrix Kohn variational method in quantum reactive scattering. The DVR constructs a universal kinetic‑energy matrix with a diagonal potential‑energy matrix, adapts grid points via energy truncation to the shape of any potential surface, and can also be applied to quantum eigenvalue problems. Benchmark tests on H+H₂→H₂+H and Cl+HCl→ClH+Cl demonstrate that the DVR achieves converged reaction probabilities with only modestly more grid points than previous methods, accurately captures heavy‑light‑heavy dynamics, and, due to its sparse Hamiltonian, promises to extend the S‑matrix Kohn approach to more complex reactions.

Abstract

A novel discrete variable representation (DVR) is introduced for use as the L2 basis of the S-matrix version of the Kohn variational method [Zhang, Chu, and Miller, J. Chem. Phys. 88, 6233 (1988)] for quantum reactive scattering. (It can also be readily used for quantum eigenvalue problems.) The primary novel feature is that this DVR gives an extremely simple kinetic energy matrix (the potential energy matrix is diagonal, as in all DVRs) which is in a sense ‘‘universal,’’ i.e., independent of any explicit reference to an underlying set of basis functions; it can, in fact, be derived as an infinite limit using different basis functions. An energy truncation procedure allows the DVR grid points to be adapted naturally to the shape of any given potential energy surface. Application to the benchmark collinear H+H2→H2+H reaction shows that convergence in the reaction probabilities is achieved with only about 15% more DVR grid points than the number of conventional basis functions used in previous S-matrix Kohn calculations. Test calculations for the collinear Cl+HCl→ClH+Cl reaction shows that the unusual dynamical features of heavy+light-heavy reactions are also well described by this approach. Since DVR approaches avoid having to evaluate integrals in order to obtain the Hamiltonian matrix and since a DVR Hamiltonian matrix is extremely sparse, this DVR version of the S-matrix Kohn approach should make it possible to deal with more complex chemical reactions than heretofore possible.