Further partitioning of the reactant-product decoupling equations of state-to-state reactive scattering and their solution by the time-independent wave-packet method

Abstract

The reactant-product decoupling (RPD) equations are a rigorous formulation of state-to-state reactive scattering recently introduced by Peng and Zhang. For an N-arrangement reaction there are a total of N RPD equations, each of which describes the dynamics in just one region of coordinate space. One of the regions (the r-region) encloses the reactant channel and the strong interaction region; each of the other N−1 regions encloses one of the product channels. In this paper we develop a suggestion later made by Kouri and co-workers: that the original RPD equations can be further partitioned into a set of new RPD equations, in which the original r-region is now partitioned into three regions—two enclosing the reactant channel, and one enclosing the strong interaction region. After introducing the new RPD equations, we derive the time-independent wave-packet (TIW) form of the equations, and show how to solve them using an extended version of the Chebyshev propagator. We test the new RPD equations (and the method) by calculating state-to-state reaction probabilities and inelastic probabilities for the three-dimensional (J = 50) H+H2 reaction.

State-to-state reaction probabilities within the quantum transition state framework

“…10-13) typically transform between reactant and product coordinate systems while propagating using reactantproduct decoupling schemes. 48,49 In the present approach, initial wave packets representing the vibrational state of the activated complex are obtained by diagonalization of the thermal flux operator. These initial wave packets are then transformed into reactant and product coordinate systems.…”

Quantum wave packet dynamics with trajectories: Implementation with distributed approximating functionals

“…Another way to handle this problem is to introduce reactant-product decoupling ͑RPD͒ into the particle calculations. 44,45 RPD permits the solution of the scattering equations in just one region of coordinate space at a time.…”

Coriolis coupling effects in the calculation of state-to-state integral and differential cross sections for the H+D2 reaction

“…The RPD approaches [29][30][31][32] introduce partitioning/absorbing potentials which decouple the Schrödinger equation. The wavepacket propagation can then be carried out separately for reactants and for products using the Jacobi coordinates appropriate for each channel.…”

“…Chebyshev and split-operator propagators are the two most commonly used schemes in the RPD method. [29][30][31][32] The Chebyshev real wavepacket method [33][34][35][36][37][38][39] usually employs product Jacobi coordinates to evolve the real part of the wavepacket with Chebyshev iterations, thus providing an efficient and convenient approach to the calculation of S ͑scattering͒ matrix elements.…”

“…In state-of-the-art theory, in addition to the timeindependent quantum mechanical approaches, 27,28 timedependent wavepacket quantum methods such as the reactant-product decoupling ͑RPD͒ method, [29][30][31][32] the Chebyshev real wavepacket method, [33][34][35][36][37][38][39] the coordinate transformation method, 40 etc., have been developed and applied in the recent state-to-state calculations on triatomic systems. The RPD approaches [29][30][31][32] introduce partitioning/absorbing potentials which decouple the Schrödinger equation.…”