Energy- and Local-Gradient-Based Neural Network Method for Accurately Describing Long-Range Interaction: Application...

The long-range interaction plays an important role in theoretically describing ion-molecule reaction. However, most energy-based neural network fitting methods usually introduce spurious long-range interactions. In this work, we propose an energy- and local-gradient-based neural network (ELGNN) method to fit potential energy surfaces (PESs). K-means clustering is employed to divide the whole configuration space into three regions: reactant asymptotic region, interaction region, and product asymptotic region. In the interaction region, only the energies of sampled points are computed, while in the asymptotic regions, the gradients of partially sampled configurations are calculated as well, and both the energies and energy gradients (if necessary) are used to fit long-range interactions. These regions are joined together by switching functions. The ELGNN method is first applied to fit the PES of the H₂ + CO⁺ reaction, which has significant long-range interactions. It is found that the ELGNN method works better than the energy-based NN method in describing long-range interactions. The dynamics and kinetics of the reaction are then investigated on the new PES.