Surface Hopping with Reliable Wave Function by Introducing Auxiliary Wave Packets to Trajectory Branching

Abstract

It is well-known that the widely utilized fewest switches surface hopping method suffers from the severe overcoherence problem, and thus adiabatic populations calculated by wave functions are generally inferior to those based on active states. More importantly, to achieve a complete description of nonadiabatic dynamics, the density matrix is essential. In this paper, we present an auxiliary branching corrected surface hopping (A-BCSH) method that introduces auxiliary wave packets (WPs) on the adiabatic potential energy surfaces for trajectory branching. Both rapid and gradual separation of WP components on different surfaces are characterized, and thus the correct decoherence time along each trajectory is captured. As demonstrated in the three standard Tully models, A-BCSH exhibits excellent internal consistency. Namely, close adiabatic populations are obtained based on both wave functions and active states. In particular, A-BCSH successfully obtains a reliable time-dependent spatial distribution of the density matrix, which relies only on electronic wave functions. Due to its high performance, our A-BCSH method provides a new and highly promising perspective on further development of more consistent surface hopping with reliable wave function.

Detailed Complementary Consistency: Wave Function Tells Particle How to Hop, Particle Tells Wave Function How to Collapse

“…The FSSH hopping probabilities are defined along each trajectory to ensure that the fraction of trajectories on each surface at any time follows the statistical populations based on wave functions. Although the FSSH results have shown good detailed balance, , the detailed internal consistency is not guaranteed due to the presence of frustrated hops and lack of decoherence. − Recently, we proposed the auxiliary branching corrected surface hopping (A-BCSH) and the auxiliary branching corrected mean field (A-BCMF) methods, which have achieved significantly better accuracy and consistency simultaneously compared to FSSH, implying a possible intrinsic connection between accuracy and detailed internal consistency in mixed quantum-classical dynamics.…”