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! (J50)H1H2 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, 2W11. The results of the H1H2 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. © 1998 American Institute of Physics. @S0021-9606~98!02114-X#