Neural networks and kernel ridge regression for excited states dynamics of CH 2 NH 2+ : From single-state to multi-state representations and multi-property machine learning models

Excited-state dynamics simulations are a powerful tool to investigate photo-induced reactions of molecules and materials and provide complementary information to experiments. Since the applicability of these simulation techniques is limited by the costs of the underlying electronic structure calculations, we develop and assess different machine learning models for this task. The machine learning models are trained on ab initio calculations for excited electronic states, using the methylenimmonium cation (CH2NH$_2^+$) as a model system. Two distinct strategies for modeling excited state properties are tested in this work. The first strategy is to treat each state separately in a kernel ridge regression model and all states together in a multiclass neural network. The second strategy is to instead encode the state as input into the model, which is tested with both models. Numerical evidence suggests that using the state as input yields the best performance. An important goal for excited-state machine learning models is their use in dynamics simulations, which needs not only state-specific information but also couplings, i.e. properties involving pairs of states. Accordingly, we investigate how well machine learning models can predict the couplings. Furthermore, we explore how combining all properties in a single neural network affects the accuracy. Finally, machine learning predicted energies, forces, and couplings are used to carry out excited-state dynamics simulations. Results demonstrate the scopes and possibilities of machine learning to model excited-state properties.