Nonadiabatic Dynamics Algorithms with Only Potential Energies and Gradients: Curvature-Driven Coherent Switching with Decay of Mixing and Curvature-Driven Trajectory Surface Hopping

Direct dynamics by mixed quantum–classical nonadiabatic methods is an important tool for understanding processes involving multiple electronic states. Very often, the computational bottleneck of such direct simulation comes from electronic structure theory. For example, at every time step of a trajectory, nonadiabatic dynamics requires potential energy surfaces, their gradients, and the matrix elements coupling the surfaces. The need for the couplings can be alleviated by employing the time derivatives of the wave functions, which can be evaluated from overlaps of electronic wave functions at successive timesteps. However, evaluation of overlap integrals is still expensive for large systems. In addition, for electronic structure methods for which the wave functions or the coupling matrix elements are not available, nonadiabatic dynamics algorithms become inapplicable. In this work, building on recent work by Baeck and An, we propose new nonadiabatic dynamics algorithms that only require adiabatic potential energies and their gradients. The new methods are named curvature- driven coherent switching with decay of mixing (κCSDM) and curvature-driven trajectory surface hopping (κTSH). We show how powerful these new methods are in terms of computer time and good agreement with methods employing nonadiabatic coupling vectors computed in conventional ways. The lowering of the computational cost will allow longer nonadiabatic trajectories and greater ensemble averaging to be affordable, and the ability to calculate the dynamics without electronic structure coupling matrix elements extends the dynamics capability to new classes of electronic structure methods.

Forecasting Nonadiabatic Dynamics using Hybrid Convolutional Neural Network/Long Short-Term Memory Network

Modeling nonadiabatic dynamics in complex molecular or condensed-phase systems has been challenging especially for the long-time dynamics. In this work, we propose a time series machine learning scheme based on the hybrid convolutional neural network/long short-term memory (CNN-LSTM) framework for predicting the long-time quantum behavior given only the short-time dynamics. This scheme takes advantage of both the powerful local feature extraction ability of CNN and the long-term global sequential pattern recognition ability of LSTM. With feature fusion of individually trained CNN-LSTM models for the quantum population and coherence dynamics, the proposed scheme is shown to have high accuracy and robustness in predicting the linearized semiclassical and symmetrical quasiclassical mapping dynamics of various spin-boson models with learning time up to 0.3 ps. Furthermore, if the hybrid network has learned the dynamics of a system, this knowledge is transferable that could significantly enhance the accuracy in predicting the dynamics of a similar system. The hybrid CNN-LSTM network is thus believed to have high predictive power in forecasting the nonadiabatic dynamics in realistic charge and energy transfer processes in photoinduced energy conversion.