A time-dependent quantum wavepacket method on stair-shaped grids for reactive scattering using the hyperspherical coordinates

Development of efficient numerical methods for quantum reactive scattering process by using time-dependent quantum wavepacket method is always necessary in the field of quantum chemistry, due to the complexity of the system, and the large computational efforts required. To perform quantum reactive scattering calculation in hyperspherical coordinates, as the hyper-radial (ρ) increases, the potential well along the angular degree of the freedom (χ) becomes narrower and narrower, which thus requires denser and denser grid points for well describing the diatomic vibrational motion. This makes the time dependent wavepacket packet calculations prohibitively difficult using hyperspherical coordinate when the reaction involves long range interaction potential or requires long absorption potential. In this study, we developed a stair-shaped grid based quantum wavepacket method to overcome this difficulty. In this method, the hyper-radial is partitioned into multidomains in the form of a stair-shape. In each domain, different grid point numbers could be applied for the angular degree of the freedom (χ). In this way, the computational effort could be saved. For numerical example, the stair-shaped grid based quantum wavepacket method is applied to compute the total reaction probability of the F+HCl (v0,j0)→ HF+Cl reaction , which involves long range interaction potential. The results are compared with those calculated with the reactant coordinate-based (RCB) Jacobi coordinate and Interaction Asymptotic Region Decomposition (IARD) method. [Display omitted] •This study introduces a novel stair-shaped grid-based quantum wavepacket method for efficient quantum reactive scattering calculations.•The method addresses computational challenges in hyperspherical coordinates with increasing hyper-radial, demanding denser grid points. Especially for reactive systems with long-range interaction potential.•By partitioning the hyper-radial into stair-shaped domains with variable grid points in kinematics angle, the method optimizes computational resources.•The approach is applied to calculate the total reaction probability for the F+HCl (v0,j0)→ HF+Cl reaction, featuring a long-range interaction potential.•Comparative analysis with established methods, such as reactant coordinate-based method and the Interaction Asymptotic Region Decomposition method, underscores the accuracy and efficiency of the proposed stair-shaped grid-based quantum wavepacket method.