A Simple Solution to the Trivial Crossing Problem in Surface Hopping.

Surface hopping studies on supramolecular and nanoscale systems suffer severely from the trivial crossing problem, arising due to high density of adiabatic potential energy surfaces. We present a straightforward solution to the problem by introducing a self-consistency test to the well-known fewest switches surface hopping (FSSH) procedure. If the test is failed, the hopping probabilities are corrected with a simple procedure. The novel self-consistent fewest switches surface hopping (SC-FSSH) approach is applied to the Holstein Hamiltonian to study the time-dependence of the electron population. Already in the five-state system, SC-FSSH allows us to reduce the simulation time 10(4)-fold to achieve the FSSH accuracy. The reliable performance and simple formulation of SC-FSSH greatly expands the applicability range of the surface hopping method.