Analysis of the Geometrical Evolution in On-the-Fly Surface-Hopping Nonadiabatic Dynamics with Machine Learning Dimensionality Reduction Approaches: Classical Multidimensional Scaling and Isometric Feature Mapping

On-the-fly trajectory-based nonadiabatic dynamics simulation has become an important approach to study ultrafast photochemical and photophysical processes in recent years. Because a large number of trajectories are generated from the dynamics simulation of polyatomic molecular systems with many degrees of freedom, the analysis of simulation results often suffers from the large amount of high-dimensional data. It is very challenging but meaningful to find dominating active coordinates from very complicated molecular motions. Dimensionality reduction techniques provide ideal tools to realize this purpose. We apply two dimensionality reduction approaches (classical multidimensional scaling and isometric feature mapping) to analyze the results of the on-the-fly surface-hopping nonadiabatic dynamics simulation. Two representative model systems, CH₂NH₂⁺ and the phytochromobilin chromophore model, are chosen to examine the performance of these dimensionality reduction approaches. The results show that these approaches are very promising, because they can extract the major molecular motion from complicated time-dependent molecular evolution without preknown knowledge.