High-Dimensional Neural Network Potentials for Organic Reactions and an Improved Training Algorithm

Artificial neural networks (NNs) represent a relatively recent approach for the prediction of molecular potential energies, suitable for simulations of large molecules and long time scales. By using NNs to fit electronic structure data, it is possible to obtain empirical potentials of high accuracy combined with the computational efficiency of conventional force fields. However, as opposed to the latter, changing bonding patterns and unusual coordination geometries can be described due to the underlying flexible functional form of the NNs. One of the most promising approaches in this field is the high-dimensional neural network (HDNN) method, which is especially adapted to the prediction of molecular properties. While HDNNs have been mostly used to model solid state systems and surface interactions, we present here the first application of the HDNN approach to an organic reaction, the Claisen rearrangement of allyl vinyl ether to 4-pentenal. To construct the corresponding HDNN potential, a new training algorithm is introduced. This algorithm is termed "element-decoupled" global extended Kalman filter (ED-GEKF) and is based on the decoupled Kalman filter. Using a metadynamics trajectory computed with density functional theory as reference data, we show that the ED-GEKF exhibits superior performance - both in terms of accuracy and training speed - compared to other variants of the Kalman filter hitherto employed in HDNN training. In addition, the effect of including forces during ED-GEKF training on the resulting potentials was studied.