Coordinate transformation methods to calculate state-to-state reaction probabilities with wave packet treatments

Abstract

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.

Accurate time dependent wave packet calculations for the N + OH reaction

“…For this kind of systems, it has been demonstrated that it is more efficient to use reactant Jacobi coordinates. 28 The present state-to-state reaction probabilities are calculated using a wave packet method, with the code MADWAVE3 recently reported by Zanchet et al 29 The MADWAVE3 codes based on wave packet method have been well documented in the literature 9,29 and only the details relevant to the present work will be given here. In the present calculations, the initial wave packet is located in the asymptotic reactant channel where there is no influence of the interaction potential, and the propagation grid scheme is defined using the same reactant Jacobi coordinates.…”

“…4, the CS results are compared with CC results with increasing the number of 's for the case of J = 20. The fast convergence with the increase of helicity functions indicates that the use of reactant Jacobi coordinates, as expected for the mass combination, 28 The use of product Jacobi coordinates would require the inclusion of a higher number of 's, making the calculation of state-to-state probabilities very difficult. Figure 5 shows the total reaction probability as a function of J (i.e., opacity function), calculated at four specific collision energies by means of the WP method and QCT approach.…”

Extraction of state-to-state reactive scattering attributes from wave packet in reactant Jacobi coordinates

“…The kth Chebyshev propagation state on the projection plane, ⌿ v ,j ,K J⑀ ͑k ; R 0 ͒, can be calculated on the potential optimized discrete variable representation ͑PODVR͒ and Gauss-Legendre quadrature grids by a collocation method 51,19 or by the coordinate transformation method 26 at each propagation step. The energy resolved scattering wave function ⌽ v j K J⑀ ͑E͒ in the BF frame can be obtained by a discrete Fourier transform,…”

“…In this paper, we first compare the two RCB wave packet methods, introduced by us 20 and by Gómez-Carrasco and Roncero, 26 for studying the A + BC→ AB+ C, AC+ B type reaction at the state-to-state level, using the H + HD reaction as an example. These RCB methods were implemented with the efficient and accurate Chebyshev propagator.…”

“…25 The L-shaped grid method saves a large number of grid points, as compared with a conventional rectangular grid, which makes this RCB wave packet method particularly attractive and presents an efficient alternative to the PCB approaches. [14][15][16] In 2006, Gómez-Carrasco and Roncero 26 developed an coordinate transform method to extract state-to-state information in one product channel, 27 also from the TDWP propagated in reactant Jacobi coordinates. By careful numerical testing with several reactive scattering systems, these authors reached a conclusion that their RCB method is generally more efficient than the PCB method, especially for J Ͼ 0 cases.…”