Symmetry-Adapted High Dimensional Neural Network Representation of Electronic Friction Tensor of Adsorbates on Metals

TL;DR

This paper introduces a symmetry-adapted neural network method to accurately and efficiently represent the electronic friction tensor in metal-adsorbate systems, enabling large-scale nonadiabatic molecular dynamics simulations.

Contribution

We develop a novel neural network framework that preserves tensor symmetry and positive semidefiniteness for electronic friction tensors, applicable to diverse surface-adsorbate systems.

Findings

Accurately models the electronic friction tensor for H2+Ag(111).

Enables large-scale nonadiabatic molecular dynamics simulations.

Maintains symmetry and physical properties of the tensor.

Abstract

Nonadiabatic effects in chemical reaction at metal surfaces, due to excitation of electron-hole pairs, stand at the frontier of the studies of gas-surface reaction dynamics. However, the first principles description of electronic excitation remains challenging. In an efficient molecular dynamics with electronic friction (MDEF) method, the nonadiabatic couplings are effectively included in a so-called electronic friction tensor (EFT), which can be computed from first-order time-dependent perturbation theory (TDPT) in terms of density functional theory (DFT) orbitals. This second-rank tensor depends on adsorbate position and features a complicated transformation with regard to the intrinsic symmetry operations of the system. In this work, we develop a new symmetry-adapted neural network representation of EFT, based on our recently proposed embedded atom neural network (EANN) framework. Inspired by the derivation of the nonadiabatic coupling matrix, we represent the tensorial friction by the first and second derivatives of multiple outputs of NNs with respect to atomic Cartesian coordinates. This rigorously preserves the positive semidefiniteness, directional property, and correct symmetry-equivariance of EFT. Unlike previous methods, our new approach can readily include both molecular and surface degrees of freedom, regardless of the type of surface. Tests on the H2+Ag(111) system show that this approach yields an accurate, efficient, and continuous representation of EFT, making it possible to perform large scale TDPT-based MDEF simulations to study both adiabatic and nonadiabatic energy dissipation in a unified framework.