Analysis of the Trajectory Surface Hopping Method from the Markov State Model Perspective

Abstract

We analyze the applicability of the seminal fewest switches surface hopping (FSSH) method of Tully to modeling quantum transitions between electronic states that are not coupled directly, in the processes such as Auger recombination. We address the known deficiency of the method to describe such transitions by introducing an alternative definition for the surface hopping probabilities, as derived from the Markov state model perspective. We show that the resulting transition probabilities simplify to the quantum state populations derived from the time-dependent Schrodinger equation, reducing to the rapidly switching surface hopping approach of Tully and Preston. The resulting surface hopping scheme is simple and appeals to the fundamentals of quantum mechanics. The computational approach is similar to the FSSH method of Tully, yet it leads to a notably different performance. We demonstrate that the method is particularly accurate when applied to superexchange modeling. We further show improved accuracy of ...