Capturing quantum effects with quasi-classical trajectories in the D + H +3 → H2D+ + H reaction

Abstract

We present quasi-classical trajectory (QCT) cross sections, rate constants, and product state distributions for the D + H⁺₃ → H₂D⁺ + H reaction. Using the same H⁺₄ potential surface, the rate constants obtained from several QCT-based methods correcting for zero-point effects by Gaussian binning the product H₂D⁺ are compared to ring polymer molecular dynamics (RPMD) rate constants [Bulut et al., J. Phys. Chem. A, 2019, 123, 8766] which include quantum effects and to recent experimentally derived rate constants [Bowen et al., J. Chem. Phys., 2021, 154, 084307]. QCT with standard binning predicts rate constants that increase slowly as the temperature decreases from 1500 to 100 K. In contrast, the RPMD rate constants decrease rapidly with decreasing temperature. By 100 K, the QCT standard binning rate constant is more than 3 orders of magnitude larger than the RPMD rate constant. We show that QCT with Gaussian binning and proper normalization captures the zero-point effects and reproduces the RPMD rate constants over a large temperature range. Furthermore, the simple technique of counting only reactive trajectories with vibrational energy above the product zero-point energy matches the RPMD results well down to ∼300 K. The present Gaussian binned rate constants are in fair agreement with new experimentally derived rate constants from 100 to 1500 K. However, because the Gaussian binned rate constants do not include tunneling, important at lower temperatures, and the RPMD and experimentally derived rate constants have significant differences, the roles of the competing effects of zero-point energy, internal excitation of the H⁺₃, and quantum tunneling are not simple and require further study for a consistent picture of the dynamics. Since rate constants for complex forming reactions, such as the title reaction, are difficult to converge with RPMD, alternative QCT-based methods, which include quantum effects and in addition provide product state distributions as described here, are highly desirable.