The Development Of Atomistic Neural Network Model And Its Applications In The Gas-Surface Reactions

Chemical reactions occurring at gas-solid interfaces are driving forces for many interfacial physical chemistry processes,such as heterogeneous catalysis.Molecular dynamics simulation is an important theoretical tool for understanding the gas-surface reaction at the microscopic level.The atomic motions are subject to the quantum mechanics,in principle,one can first separate the nuclear motion and electron motion,and then calculate the potential energy at a set of fixed configurations using first principle calculations to construct a potential energy surface(PES)for the nuclear motion.PES plays a key role in molecular dynamics simulation.Ideally,such a PES needs to cover not only molecular configurations from the asymptote to strongly interacting regions on the surface,but also extensive surface configurations that can be sampled at a given surface temperature.This means that the PES suited for gas-surface reactions would include both features of the anisotropic molecular systems and the periodic condensed phase systems.In addition,the PES should not only be accurate but also be required to be efficient enough to afford large scale molecular dynamics simulations.In this paper,we have constructed a reactive PES describing the interaction of CO2 with a movable Ni(100)surface using our implementation of modified Behler-Parrinello atomistic neural network(BPNN).We have devoted our efforts to improving the machine learning model in accuracy and efficiency and proposed the embedded atom neural network(EANN),piecewise EANN and recursively EANN.These models can accurately represent the adiabatic interactions of gas surface reaction.Besides representing energy,we have extended the models to the symmetry-adapted representation of the electronic friction tensor,and these models were employed to study the scattering process of NO on Au(111)surface.With these well-defined models,we have investigated the energy conversion of NO on Au(111)surface in a unified framework.BPNN realizes linear scaling with respect to system size and is a promoting approach to construct high dimensional PES.Here,a very small portion of existing direct dynamics data were reused to construct accurate reactive PES describing the interaction of CO2 with a movable Ni(100)surface using our implementation of BPNN.We proposed a unified strategy to investigate gaseous and gas-surface reactions,performing hundreds of direct dynamics trajectories,followed by low cost and high quality simulations on full-dimensional analytical PESs.Due to the explicit calculation of angular symmetry functions,the computational cost of BPNN is proportional to the square of the number of neighbor atoms.Inspired by the famous embedded atom method,we have developed the EANN model by constructing the embedded density via the square of the linear combination of Gaussian-type orbitals and representing the complex relationship between the embedded density vector and atomic energy using neural networks.EANN is highly efficient as it implicitly contains three-body information without an explicit summation of conventional costly angular descriptors.To further increase this efficiency,we proposed a piecewise EANN model with piecewise switching function based descriptors,resulting in a more favorable linear scaling with respect to the number of neighboring atoms.Furthermore,we further improved the evaluation of the embedded density descriptor of EANN and assign the orbital coefficient as a quantity dependent on its own local environment inspired by quantum chemistry.The orbital coefficients can be updated in a recursive manner and we thus named the new model recursively EANN.We have formally proven that this model can efficiently incorporate complete many-body correlations without explicitly computing high-order terms.The design of this model has provided an easy and general way to update local many-body descriptors to a message-passing form without changing their basic structures.(piecewise/recursively)EANN model has been able to construct an accurate and efficient representation of the gas-surface interaction,which can describe the energy conversion between the gas and the surface.However,the gaseous species on the metal surface can dissipate their energy not only by exciting lattice vibrations but also through electron-hole pair excitations(EHPs).We employed the molecular dynamics with electronic friction to describe EHPs and the electronic friction tensor is employed to approximate this non-adiabatic effect.The orbital dependent electronic friction tensor(ODF)can be computed from first-order time-dependent perturbation theory in terms of Kohn-Sham orbitals.We have developed a new symmetry-adapted neural network representation of ODF,based on our recently proposed EANN.The ODF can be expressed by the summation of the inner product between different order gradients(first and second)matrices and their transposes.This model rigorously preserves the positive semidefiniteness,directional property,and correct symmetry-equivariance of ODF.With well-defined ML models for energy and ODF,we were able to perform a comprehensive quantitative analysis of the performance of adiabatic and nonadiabatic molecular dynamics in describing vibrational state-to-state scattering of NO on Au(111)and compared directly to experimental results.This allows us to investigate the true failure of the MDEF model.