Solution for the Trivial Crossing Problem in Surface Hopping Simulations by the Classification on Excited States

In this article, we study excited-state relaxation dynamics in single conjugated polymer chains with surface hopping simulations and propose a solution for the encountered trivial crossing problem. By analyzing the transition density matrices, we find that all excited states can be divided into two types. The surface hopping simulations show that the two types of excited states do not interact each other (the nonadiabatic couplings between them are negligible), indicating that the trivial crossings only occur between different types of excited state. The two types of excited state separately span two uncoupled subspaces, and we can let the system evolve only in one of the subspaces. In such a way, the trivial crossings between different types of excited states are completely eliminated. Moreover, this method greatly reduces the computational cost of surface hopping simulations.