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

Abstract

Articles you may be interested inCombining the discrete variable representation with the Smatrix Kohn method for quantum reactive scattering J. Chem. Phys. 99, 9681 (1993) 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 CI + HCI ..... ClH + CI reaction shows that the unusual dynamical features of heavy + lightheavy 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.

Gross-Pitaevskii equation for Bose particles in a double-well potential: Two-mode models and beyond

“…9. Here, z c values from (32) and (34) have been restated in terms of ∆n c using (10) in order to compare with TDGPE results. For bothḡ = 3.0 and 10.0, when V b is high enough, there is good agreement between VTM and TDGPE results.…”

“…This scaling will be used throughout this paper, and in particular in all the figures. To obtain numerical values for the overlap integrals γ ij , where i, j = ±, we solved (5) using the DVR method [33,34] with increasingly finer mesh, with iterations for each mesh to make the Φ ± functions and the the nonlinear term self-consisent. Values for the γ ij are shown as a function of barrier height, V b , for σ=1.5, for gN =1, 10 and 100, in Fig.…”

Rotational excitation and de-excitation of HF molecules by He atoms

“…At each point of the propagation grid the matrix elements of the potential were evaluated by expanding the potential in Legendre polynomials retaining terms up to l = 6 on a grid of 8 points used to calculate the Gauss Hermite quadrature of the vibrational part of the integral. A Discrete Variable Representation (DVR) along the Gauss Hermite grid of the diatomic rovibrational wave functions was calculated by solving the exact diatomic equations using the diatomic potential described in our previous work ) and a Finite Basis Representation (FBR) of 150 imaginary exponential wave functions as described for example by Colbert & Miller (1982).…”

Program for quantum wave-packet dynamics with time-dependent potentials

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