Efficient Sampling for Machine Learning Electron Density and Its Response in Real Space

Electron density is a fundamental quantity that can in principle determine all ground state electronic properties of a given system. Although machine learning (ML) models for electron density based on either an atom-centered basis or a real-space grid have been proposed, the demand for a number of high-order basis functions or grid points is enormous. In this work, we propose an efficient grid-point sampling strategy that combines targeted sampling favoring a large density and a screening of grid points associated with linearly independent atomic features. This new sampling strategy is integrated with a field-induced recursively embedded atom neural network model to develop a real-space grid-based ML model for the electron density and its response to an electric field. This approach is applied to a QM9 molecular data set, a H2O/Pt(111) interfacial system, an Au(100) electrode, and an Au nanoparticle under an electric field. The number of training points is found to be much smaller than previous models, while yielding comparably accurate predictions for the electron density of the entire grid. The resultant machine-learned electron density model enables us to properly partition partial charge onto each atom and analyze the charge variation upon proton transfer in the H2O/Pt(111) system. The machine-learning electronic response model allows us to predict charge transfer and the electrostatic potential change induced by an electric field applied to an Au(100) electrode or an Au nanoparticle.

On the quantum dynamical treatment of surface vibrational modes for reactive scattering of H2 from Cu(111) at 925 K

We construct the effective Hartree potential for H2 on Cu(111) as introduced in our earlier work [Dutta et al., J. Chem. Phys. 154, 104103 (2021), and Dutta et al., J. Chem. Phys. 157, 194112 (2022)] starting from the same gas-metal interaction potential obtained for 0 K. Unlike in that work, we now explicitly account for surface expansion at 925 K and investigate different models to describe the surface vibrational modes: (i) a cluster model yielding harmonic normal modes at 0 K and (ii) slab models resulting in phonons at 0 and 925 K according to the quasi-harmonic approximation-all consistently calculated at the density functional theory level with the same exchange-correlation potential. While performing dynamical calculations for the H2(v = 0, j = 0)-Cu(111) system employing Hartree potential constructed with 925 K phonons and surface temperature, (i) the calculated chemisorption probabilities are the highest compared to the other approaches over the energy domain and (ii) the threshold for the reaction probability is the lowest, in close agreement with the experiment. Although the survival probabilities (v' = 0) depict the expected trend (lower in magnitude), the excitation probabilities (v' = 1) display a higher magnitude since the 925 K phonons and surface temperature are more effective for the excitation process compared to the phonons/normal modes obtained from the other approaches investigated to describe the surface.

Investigating the Eley-Rideal recombination of hydrogen atoms on Cu (111) via a high-dimensional neural network potential energy surface

As a prototypical system for studying the Eley-Rideal (ER) mechanism at the gas-surface interface, the reaction between incident H/D atoms and pre-covered D/H atoms on Cu (111) has attracted much experimental and theoretical interest. Detailed final state-resolved experimental data have been available for about thirty-years, leading to the discovery of many interesting dynamical features. However, previous theoretical models have suffered from reduced-dimensional approximations and/or omitting energy transfer to surface phonons and electrons, or the high cost of on-the-fly ab initio molecular dynamics, preventing quantitative comparisons with experimental data. Herein, we report the first high-dimensional neural network potential (NNP) for this ER reaction based on first-principles calculations including all molecular and surface degrees of freedom. Thanks to the high efficiency of this NNP, we are able to perform extensive quasi-classical molecular dynamics simulations with the inclusion of the excitation of low-lying electron-hole pairs (EHPs), which generally yield good agreement with various experimental results. More importantly, the isotopic and/or EHP effects in total reaction cross-sections and distributions of the product energy, scattering angle, and individual ro-vibrational states have been more clearly shown and discussed. This study sheds valuable light on this important ER prototype and opens a new avenue for further investigations of ER reactions using various initial conditions, surface temperatures, and coverages in the future.

First-Principles Insights into Adiabatic and Nonadiabatic Vibrational Energy-Transfer Dynamics during Molecular Scattering from Metal Surfaces: The Importance of Surface Reactivity

Energy transfer is ubiquitous during molecular collisions and reactions at gas-surface interfaces. Of particular importance is vibrational energy transfer because of its relevance to bond forming and breaking. In this Perspective, we review recent first-principles studies on vibrational energy-transfer dynamics during molecular scattering from metal surfaces at the state-to-state level. Taking several representative systems as examples, we highlight the intrinsic correlation between vibrational energy transfer in nonreactive scattering and surface reactivity and how it operates in both electronically adiabatic and nonadiabatic pathways. Adiabatically, the presence of a dissociation barrier softens a bond in the impinging molecule and increases its couplings with other molecular modes and surface phonons. In the meantime, the stronger interaction between the molecule and the surface also changes the electronic structure at the barrier, resulting in an increase of nonadiabatic effects. We further discuss future prospects toward a more quantitative understanding of this important surface dynamical process.

REANN: A PyTorch-based end-to-end multi-functional deep neural network package for molecular, reactive, and periodic systems

In this work, we present a general purpose deep neural network package for representing energies, forces, dipole moments, and polarizabilities of atomistic systems. This so-called recursively embedded atom neural network model takes advantages of both the physically inspired atomic descriptor based neural networks and the message-passing based neural networks. Implemented in the PyTorch framework, the training process is parallelized on both the central processing unit and the graphics processing unit with high efficiency and low memory in which all hyperparameters can be optimized automatically. We demonstrate the state-of-the-art accuracy, high efficiency, scalability, and universality of this package by learning not only energies (with or without forces) but also dipole moment vectors and polarizability tensors in various molecular, reactive, and periodic systems. An interface between a trained model and LAMMPs is provided for large scale molecular dynamics simulations. We hope that this open-source toolbox will allow for future method development and applications of machine learned potential energy surfaces and quantum-chemical properties of molecules, reactions, and materials.