Coupled 3D Time-Dependent Wave-Packet Approach in Hyperspherical coordinates: application to the adiabatic singlet-state(1¹A') D⁺ + H₂ reaction

Abstract

We explore a coupled three-dimensional (3D) time-dependent wave packet formalism in hyperspherical coordinates for a 4D reactive scattering problem on the lowest adiabatic singlet surface (1¹A′) of the D⁺ + H₂ reaction. The coupling among the wavepackets arises through quantization of the rotation matrix, which represents the orientation of the three particles in space. The required transformation from Jacobi to hyperspherical coordinates and vice versa during initialization and projection of the wave packet on the asymptotic state(s), and the coupled equations of motion, are briefly discussed. With the long-range potential known to contribute significantly on the D⁺ + H₂ system, we demonstrate the workability of our approach, where the convergence profiles of the reaction probability for the reactive noncharge transfer (RNCT) process [D⁺ + H₂(v=0, j=0,1) → HD(v′,j′) + H⁺] are shown for three different collisional energies (1.7, 2.1, and 2.5 eV) with respect to the helicity (K) and total angular momentum (J) quantum numbers. The calculated reactive cross-section is presented as a function of the collision energy for two different initial states of the diatom (v = 0, j = 0, 1).