A procedure for the transformation from reactant to product Jacobi coordinates is proposed, which is designed for the extraction of state-to-state reaction probabilities using a time-dependent method in a body-fixed frame. The method consists of several steps which involve a negligible extra computational time as compared with the propagation. Several intermediate coordinates are used, in which the efficiency depends on the masses of the atoms involved in the reaction. A detailed study of the relative efficiency of using reactant and product Jacobi coordinates is presented for several systems, and simple arguments are found depending on the masses of the atoms involved in the reaction. It is found that the proposed method is, in general, more efficient than the use of product Jacobi coordinates, specially for nonzero total angular momentum. State-to-state reaction probabilities are obtained for Li+FH-->LiF+H and F+HO-->FH+O collisions for several total angular momenta.

The state-to-state differential cross sections for some atom + diatom reactions have been calculated using a new wave packet code, MAD-WAVE3, which is described in some detail and uses either reactant or product Jacobi coordinates along the propagation. In order to show the accuracy and efficiency of the coordinate transformation required when using reactant Jacobi coordinates, as recently proposed [ J. Chem. Phys. 2006 , 125 , 054102 ], the method is first applied to the H + D(2) reaction as a benchmark, for which exact time-independent calculations are also performed. It is found that the use of reactant coordinates yields accurate results, with a computational effort slightly lower than that when using product coordinates. The H(+) + D(2) reaction, with the same masses but a much deeper insertion well, is also studied and exhibits a completely different mechanism, a complex-forming one which can be treated by statistical methods. Due to the longer range of the potential, product Jacobi coordinates are more efficient in this case. Differential cross sections for individual final rotational states of the products are obtained based on exact dynamical calculations for some selected total angular momenta, combined with the random phase approximation to save the high computational time required to calculate all partial waves with very long propagations. The results obtained are in excellent agreement with available exact time-independent calculations. Finally, the method is applied to the Li + HF system for which reactant coordinates are very well suited, and quantum differential cross sections are not available. The results are compared with recent quasiclassical simulations and experimental results [J. Chem. Phys. 2005, 122, 244304]. Furthermore, the polarization of the product angular momenta is also analyzed as a function of the scattering angle.