Exact-Factorization-Based Surface Hopping for Multistate Dynamics

Abstract

A surface-hopping algorithm recently derived from the exact factorization approach, SHXF [Ha et al. J. Phys. Chem. Lett. 2018, 9, 1097], introduces an additional term in the electronic equation of surface hopping that couples electronic states through the quantum momentum. This term not only provides a first-principles description of decoherence, but here we show it is crucial to accurately capture nonadiabatic dynamics when more than two states are occupied at any given time. Using a vibronic coupling model of the uracil cation, we show that the lack of this term in traditional surface-hopping methods, including those with decoherence corrections, leads to failure to predict the dynamics through a three-state intersection, while SHXF performs similarly to the multiconfiguration time-dependent Hartree quantum dynamics benchmark.

Exact Factorization Adventures: A Promising Approach for Non-bound States

“…The most practical impact of the XF approach so far has been in the development of rigorous MQC methods, and CTMQC and SHXF have both successfully predicted dynamics in a number of complex situations [26,[128][129][130][131][132][133][134], giving improved results from first-principles compared to traditional MQC methods [135]. These methods involve computing a term that depends on the nuclear quantum momentum, for which three different implementations exist.…”

“…( 12), in a surface-hopping scheme [21,22] where the nuclei evolve on a single BO surface at any time, making hops between them according to a stochastic algorithm. This XF-based surfacehopping (SHXF) has been applied to a range of complex systems, from organic molecules to molecular motors [130][131][132][133][134][135]. Part of what has made SHXF able to treat such large systems, is that the quantum momentum term is computed via auxiliary trajectories thus enabling an independent trajectory scheme; these auxiliary trajectories approximately mimic the local coupling of a trajectory to nearby ones.…”

“…But its role goes beyond just decoherence. It was recently shown to be crucial to describe processes where multiple electronic states are simultaneously coupled in some regions of the nuclear configuration space via non-adiabatic coupling [135].…”

Exact Factorization Adventures: A Promising Approach for Non-Bound States

“…Another approach is to use the electronic equation derived from XF, i.e., Equation ( 12), in a surface-hopping scheme [21,22] where the nuclei evolve on a single BO surface at any time, making hops between them according to a stochastic algorithm. This XF-based surface-hopping (SHXF) has been applied to a range of complex systems, from organic molecules to molecular motors [131][132][133][134][135][136]. Part of what has made SHXF able to treat such large systems, is that the quantum momentum term is computed via auxiliary trajectories thus enabling an independent trajectory scheme; these auxiliary trajectories approximately mimic the local coupling of a trajectory to nearby ones.…”

“…A significant improvement over traditional MQC methods was recently found in ref. [136]: here, the quantum-momentum term has a role that goes beyond just decoherence. It was shown to be crucial to describe processes where multiple electronic states are simultaneously coupled in some regions of the nuclear configuration space via non-adiabatic coupling.…”