Higher-order split operator schemes for solving the Schrödinger equation in the time-dependent wave packet method: applications to triatomic reactive scattering calculations

Abstract

The efficiency of the numerical propagators for solving the time-dependent Schrödinger equation in the wave packet approach to reactive scattering is of vital importance. In this Perspective, we first briefly review the propagators used in quantum reactive scattering calculations and their applications to triatomic reactions. Then we present a detailed comparison of about thirty higher-order split operator propagators for solving the Schrödinger equation with their applications to the wave packet evolution within a one-dimensional Morse potential, and the total reaction probability calculations for the H + HD, H + NH, H + O(2), and F + HD reactions. These four triatomic reactions have quite different dynamic characteristics and thus provide a comprehensive picture of the relative advantages of these higher-order propagation methods for describing reactive scattering dynamics. Our calculations reveal that the most often used second-order split operator method is typically more efficient for a direct reaction, particularly for those involving flat potential energy surfaces. However, the optimal higher-order split operator methods are more suitable for a reaction with resonances and intermediate complexes or a reaction experiencing potential energy surface with fluctuations of considerable amplitude. Three 4th-order and one 6th-order split operator methods, which are most efficient for solving reactive scattering in various conditions among the tested ones, are recommended for general applications. In addition, a brief discussion on the relative performance between the Chebyshev real wave packet method and the split operator method is given. The results in this Perspective are expected to stimulate more applications of (high-order) split operators to the quantum reactive scattering calculation and other related problems.

Communication: Rigorous quantum dynamics of O + O2 exchange reactions on an ab initio potential energy surface substantiate the negative temperature dependence of rate coefficients

“…The wave packet was propagated using an efficient high-order split operator method, 34 which allows a large time step of 120 a.u. The PES used in the calculation is that of Dawes et al, 22 which includes an analytical form developed by Lepers et al 35 to better describe the asymptotic regions.…”

Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems

“…However, the scaling of the error with ∆t is improved over the common naive practice. Another local approach with improved scaling is to use a high order splitting method [44].…”

Time-dependent wave packet dynamics of H2 + D2 reaction

“…The second-order operator can be expressed as [88,89,90,91,92]. Given an integrator S 2k (∆t) of order 2k, then a composition…”