An application of distributed approximating functional-wavelets to reactive scattering

Abstract

A newly developed distributed approximating functional (DAF)-wavelet, the Dirichlet–Gabor DAF-wavelet (DGDW), is applied in a calculation of the state-to-state reaction probabilities for the three-dimensional (3-D) (J=0)H+H2 reaction, using the time-independent wave-packet reactant-product decoupling (TIWRPD) method. The DGDWs are reconstructed from a rigorous mathematical sampling theorem, and are shown to be DAF-wavelet generalizations of both the sine discrete variable representation (sinc-DVR) and the Fourier distributed approximating functionals (DAFs). An important feature of the generalized sinc-DVR representation is that the grid points are distributed at equally spaced intervals and the kinetic energy matrix has a banded, Toeplitz structure. Test calculations show that, in accordance with mathematical sampling theory, the DAF-windowed sinc-DVR converges much more rapidly and to higher accuracy with bandwidth, 2W+1. The results of the H+H2 calculation are in very close agreement with the results of previous TIWRPD calculations, demonstrating that the DGDW representation is an accurate and efficient representation for use in FFT wave-packet propagation methods, and that, more generally, the theory of wavelets and related techniques have great potential for the study of molecular dynamics.