AN APPLICATION OF DISTRIBUTED APPROXIMATING FUNCTIONAL-WAVELETS TO REACTIVE SCATTERING

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+H-2 reaction, using the time-independent wave-packet react ant-product decoupling (TIWRPD) method. The DGDWs are reconstructed fr om a rigorous mathematical sampling theorem, and are shown to be DAF-w avelet generalizations of both the sine discrete variable representati on (sinc-DVR) and the Fourier distributed approximating functionals (D AFs). An important feature of the generalized sinc DVR representation is thar the grid points are distributed at equally spaced intervals an d the kinetic energy matrix has a banded, Toeplitz structure. Test cal culations show that, in accordance with mathematical sampling theory, the DAF-windowed sinc-DVR converges much more rapidly and to higher ac curacy with bandwidth, 2W+1. The results of the H+H-2 calculation are in very close agreement with the results of previous TIWRPD calculatio ns, demonstrating that the DGDW representation is an accurate and effi cient representation for use in FFT wave-packet propagation methods, a nd that, more generally, the theory of wavelets and related techniques have great potential for the study of molecular dynamics. (C) 1998 Am erican Institute of Physics.