We implemented Eq. (18) and used it, along with real wave packet propagation, to calculate total reaction probabilities for the three-dimensional D + H DH + H reaction with total angular momentum J=0. The Liu-Siegbahn-Truhlar-Horowitz (LSTH) potential energy surface[17,18,19] was used. For comparison, we also present results from a real wave packet propagation combined with the asymptotic product analysis method.
The asymptotic product analysis results are based on the same grids and parameters as given in Ref. . Thus, we outline only a few key aspects. Product (DH+H) Jacobi coordinates were employed for the real wave packet propagation, with 80 evenly spaced grid points from 0.15 a.u. to 12.0 a.u. in the R and r coordinates, and 50 Legendre polynomials ( ) for . Product analysis was performed at = 6.5 a.u. The results, labeled ``G-BK'' in Table 1 are simply the sum of all the possible state-to-state probabilities. For the flux calculations we implemented Eq. (18). These calculations were carried out in reactant (D+H2) Jacobi coordinates Ra, ra and . 80 evenly spaced grid points in Ra from 0.15 to 12 a.u. were employed. It suffices for the diatomic coordinate ra to employ 59 grid points 0.5 to 9.5 a.u. The degree of freedom was expanded in 25 even (jI = 0,2,...,48) Legendre polynomials. The flux was calculated at the surface defined by ra = 6.0 a.u. (The reactant coordinate propagation, owing to the diatomic symmetry and to the smaller ra grid is significantly more efficient.) The total reaction probability denoted by ``flux'' in Table 1 represents the result. 1000 iterations of Eq. (14) suffices to converge the reaction probabilities. Table 1 shows that the agreement between the results from the flux and earlier G-BK approaches is excellent.