Accurate trajectory surface hopping simulations are often limited by the high cost of electronic structure calculations, particularly when many trajectories are required to obtain statistically meaningful nonadiabatic dynamics. These simulations require smooth potential energy surfaces and nuclear gradients, which DFT/MRCI and other stochastic approaches cannot provide. Therefore, we develop Gaussian process regression (GPR) surrogate models for on-the-fly molecular dynamics, with the goal of enabling efficient nonadiabatic trajectory surface hopping on expensive electronic structure surfaces.

Initially, we apply the GPR framework to the simpler case of ground-state dynamics, before extending this approach to surface hopping. We utilise a Bayesian Committee Machine framework, which aggregates multiple independently trained GPR surrogates to enable efficient, highly accurate predictions. We test this approach on ground-state hydrogen peroxide dynamics, as well as excited-state surface hopping dynamics in ammonia using model potentials.

These results show that GPR-based surrogate models can reproduce key features of both ground state and nonadiabatic dynamics while substantially reducing the number of direct surface evaluations required. As well as providing a method to perform dynamics using electronic structure methods where gradients are unavailable or expensive, this approach produces a highly efficient trained potential energy surface for subsequent simulations and analysis.