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

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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. 8 8, 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.