Mixed Quantum–Classical Dynamics with Machine Learning-Based Potentials via Wigner Sampling

Machine learning-based approaches for surface hopping (SH) offer the prospect of SH simulations with ab initio accuracy, but with a computational cost more similar to classical molecular dynamics simulations. However, such approaches in the adiabatic basis are difficult due to the need to fit a machine learning model to reproduce the nonadiabatic coupling, which rapidly changes in the vicinity of a conical intersection. Previous approaches have typically dealt with this difficulty by either computing the hopping probabilities using methods that do not require the explicit nonadiabatic coupling or by employing adaptive sampling. In this study, we introduce a new approach using a simple modification of Wigner sampling to generate appropriate training data. Test SH simulations on the two-state spin-boson Hamiltonian system show that Wigner sampling with an appropriately selected data set can reduce the size of the training data set by up to a factor of 7.5 per degree of freedom compared to previously linear sampling-based approaches.