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

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.

Determining the Effect of Hot Electron Dissipation on Molecular Scattering Experiments at Metal Surfaces

“… 40 This allows us to largely reduce errors in the description of the adiabatic PES and to focus on scrutinizing the quality of nonadiabatic description at a level that was not possible before. By combining this highly accurate PES with a faithful multidimensional EANN representation of the full-rank ODF EFT derived by time-dependent perturbation theory, 41 in the present work, we study systematically the influence of EF on the state-to-state scattering dynamics of NO from Au(111) (see Figure 1 for a schematic system definition). Impressively, incorporating both molecular and surface DOFs, the MDEF(ODF) model allows a quantitatively correct description of the single quantum vibrational relaxation dynamics of NO( v i = 3) and NO( v i = 2) and their dependence on translational energy.…”

Chemical dynamics from the gas‐phase to surfaces

“…For the latter, we require demonstrably correct theoretical methods for electronically nonadiabatic dynamics. Current friction approaches while improving 314 are unlikely to be sufficient as they rely on a weak coupling approximation and are likely not applicable to problems that exhibit strong and localized nonadiabaticity, such as electron transfer. IESH still represents a fruitful avenue of future study and improvement 316 .…”

“…294 Recently, a symmetry-adapted neural network representation of the electronic friction tensor has been developed and promises to render ODF calculations quite practical. 314…”

Machine Learning for Electronically Excited States of Molecules

“… 180 − 185 In solid state physics for example, the electronic states are usually treated as continua. The density of states at the Fermi level, 186 band gaps, 187 − 189 and electronic friction tensors 125 , 190 , 191 have been described with ML models to date, and especially the electronic friction tensor is useful to study the indirect effects of electronic excitations in materials. 192 − 197 Electron transfer processes as a result of electron–hole-pair excitations can be further investigated along with multiquantum vibrational transitions by discretizing the continuum of electronic states and fitting them (often manually) to reproduce experimental or quantum chemical data in a model Hamiltonian.…”