State-pairwise decoherence times for nonadiabatic dynamics on more than two electronic states

Independent trajectory (IT) nonadiabatic molecular dynamics simulation methods are powerful tools for modeling processes involving transitions between electronic states. Incorporation and refinement of decoherence corrections into popular IT methods, e.g., Ehrenfest dynamics and trajectory surface hopping, is an important means of improving their accuracies. In this work, we identify a new challenge in the development of such decoherence corrections; when a system exists in a coherent superposition of three or more electronic states, coherences may decay unphysically when the decoherence correction is based on decoherence times assigned on a state-wise basis. As a solution, we introduce decoherence corrected Ehrenfest schemes based on decoherence times assigned on a state-pairwise basis. By application of these methods to a set of very simple one-dimensional model problems, we show that one of these state-pairwise methods ("collapse to a block") correctly describes the loss of coherence between all pairs of states in our multistate model problems, whereas a method based on a state-wise description of coherence loss does not. The new one-dimensional models introduced here can serve as useful tests for other decoherence correction schemes.