Coordinate Problem Cracking by Using Only the Reactant Jacobi Coordinates: A New Quantum Wave Packet Method for Product State-Resolved Reactive Scattering Calculations

Abstract

In the traditional concept, the Jacobi coordinates of the reactants cannot be efficient for calculating product state-resolved information of a reactive scattering process with a quantum wave packet method. This so-called coordinate problem is cracked in this work but by using only the reactant Jacobi coordinate. In the proposed method, the grid points in all three degrees of freedom (including the angular one using the Lagrange interpolation polynomials method) are optimally selected according to the shape of the potential energy surface (PES), so only the necessary grid points (the smallest number of grid points) within the range need to be retained in the calculations. Therefore, the numerical efficiency of the method is comparable to the most efficient ones with the domain decomposition technique or domain decoupling technique, where the optimized coordinates are used in each domain, such as the previous interaction-asymptotic region decomposition (IARD) method, especially when a long-range interaction potential is involved in the calculations. The reaction between F and H₂ with J = 0, which involves long-range resonance states and some states of product with extremely slow translational energy, thus requiring a huge grid range in the calculation, is taken as the numerical example to demonstrate the numerical performance and efficiency of the proposed method. This method is uniformly stable, unlike the previous IARD method, and is expected to be very attractive in a reactive scattering calculation for reactions involving a long-range interaction potential.