High-dimensional neural-network potentials for multicomponent systems: Applications to zinc oxide

We construct a full-dimensional ab initio neural network potential energy surface (PES) for the isomerization system of the formic acid dimer (FAD). This is based upon ab initio calculations using the DLPNO-CCSD(T) approach with the aug-cc-pVTZ basis set, performed at over 14000 symmetry-unique geometries. An accurate fit to the obtained energies is generated using a general neural network fitting procedure combined with the fundamental invariant method, and the overall energy-weighted root-mean-square fitting error is about 6.4 cm-1. Using this PES, we present a multidimensional quantum dynamics study on tunneling splittings with an efficient theoretical scheme developed by our group. The ground-state tunneling splitting of FAD calculated with a four-mode coupled method is in good agreement with the most recent experimental measurements. The PES can be applied for further dynamics studies. The effectiveness of the present scheme for constructing a high-dimensional PES is demonstrated, and this scheme is expected to be feasible for larger molecular systems.

Representing high-dimensional potential-energy surfaces for reactions at surfaces by neural networks

Machine learning approaches have been promising in constructing high-dimensional potential energy surfaces (PESs) for molecules and materials. Neural networks (NNs) are one of the most popular such tools because of its simplicity and efficiency. The training algorithm for NNs becomes essential to achieve a fast and accurate fit with numerous data. The Levenberg-Marquardt (LM) algorithm has been recognized as one of the fastest and robust algorithms to train medium sized NNs and widely applied in recent NN based high quality PESs. However, when the number of ab initio data becomes large, the efficiency of LM is limited, making the training time consuming. Extreme learning machine (ELM) is a recently proposed algorithm which determines the weights and biases of a single hidden layer NN by a linear solution and is thus extremely fast. It, however, does not produce sufficiently small fitting error because of its random nature. Taking advantages of both algorithms, we report a generalized hybrid algorithm in training multilayer NNs. Tests on H+H2 and CH4+Ni(111) systems demonstrate the much higher efficiency of this hybrid algorithm (ELM-LM) over the original LM. We expect that ELM-LM will find its widespread applications in building up high-dimensional NN based PESs.

A new potential energy surface (PES) and dynamical study of the reactive process of H2CO + OH toward the formation of HCO + H2O and HCOOH + H are presented. In this work, a source of spurious long range interactions in symmetry adapted neural network (NN) schemes is identified, which prevents their direct application for low temperature dynamical studies. For this reason, a partition of the PES into a diabatic matrix plus a NN many-body term has been used, fitted with a novel artificial neural network scheme that prevents spurious asymptotic interactions. Quasi-classical trajectory (QCT) and ring polymer molecular dynamics (RPMD) studies have been carried on this PES to evaluate the rate constant temperature dependence for the different reactive processes, showing good agreement with the available experimental data. Of special interest is the analysis of the previously identified trapping mechanism in the RPMD study, which can be attributed to spurious resonances associated with excitations of the normal modes of the ring polymer.

To investigate the state-to-state dynamics of the P(D2) + H2(XΣg+1)(v = 0, j = 0) reaction, we reconstructed the PH2(X2B1) potential energy surface (PES) using the permutation invariant polynomial neural network (PIP-NN) method based on 40 595 abinitio points. The aug-cc-pVQZ basis sets with Davidson correction were employed throughout the calculations. The reference wave function for the multi-reference configuration interaction calculations was constructed from a full valence complete-active-space self-consistent field wave function. To achieve higher PES accuracy, the double many-body expansion-scaled external correlation (DMBE-SEC) method was applied to extrapolate to the one-electron complete basis set limit, yielding a total root-mean square deviation of 2.4meV for the final NN-PES. Based on the refined PH2(X2B1) NN-PES, geometries, energies, and harmonic frequencies of stationary points were obtained and analyzed in detail, showing excellent agreement with other theoretical results. Subsequently, quantum time-dependent wave packet(TDWP) and quasi-classical trajectory (QCT) methods were utilized to compute reaction probability, integral cross section (ICS), differential cross section (DCS), product rovibrational distribution, and rate constant on the developed NN-PES. The TDWP results reveal rich resonant structures, while the QCT calculations provide a qualitatively correct description of the coarse-grained reaction cross sections. These results also demonstrate a threshold-type microscopic reaction mechanism characterized by dominant forward-backward scattering, attributable to long-lived collision complex formation. Collectively, these findings provide fundamental mechanistic insights into the microscopic reaction mechanism and dynamics of phosphorus chemistry in interstellar environments.

The rate coefficients of the barrierless O(1D) + CH4 reaction are determined both theoretically and experimentally at 50-296 K. For the calculations, ring polymer molecular dynamics (RPMD) simulations are performed on the basis of a new neural network potential energy surface (PES) in the reactant asymptotic part. Only the reactant asymptotic part of the PES is constructed because of its barrierless and exothermic properties. Experimentally, the reaction rate coefficients are measured using a supersonic flow reactor. Pulsed laser photolysis of O3 molecules is used as the source of O(1D) atoms, which are detected directly through vacuum ultraviolet laser induced fluorescence at 115 nm. The branching ratio for H atom production is measured by comparing the H atom yields of the O(1D) + CH4 and O(1D) + H2 reactions. At T ≥ 75 K, good agreement between theoretical and experimental rate coefficients is found, while at 50 K, the larger difference is discussed in detail.

Liquid iron is the major component of planetary cores. Its structure and dynamics under high pressure and temperature is of great significance in studying geophysics and planetary science. However, for experimental techniques, it is still difficult to generate and probe such a state of matter under extreme conditions, while for theoretical method like molecular dynamics simulation, the reliable estimation of dynamic properties requires both large simulation size and <i>ab initio</i> accuracy, resulting in unaffordable computational costs for traditional method. Owing to the technical limitation, the understanding of such matters remains limited. In this work, combining molecular dynamics simulation, we establish a neural network potential energy surface model to study the static and dynamic properties of liquid iron at its extreme thermodynamic state close to core-mantle boundary. The implementation of deep neural network extends the simulation scales from one hundred atoms to millions of atoms within quantum accuracy. The estimated static and dynamic structure factor show good consistency with all available X-ray diffraction and inelastic X-ray scattering experimental observations, while the empirical potential based on embedding-atom-method fails to give a unified description of liquid iron across a wide range of thermodynamic conditions. We also demonstrate that the transport property like diffusion coefficient exhibits a strong size effect, which requires more than at least ten thousands of atoms to give a converged value. Our results show that the combination of deep learning technology and molecular modelling provides a way to describe matter realistically under extreme conditions.

A high dimensional and accurate atomistic neural network potential energy surface (ANN-PES) that describes the interaction between one O2 molecule and a highly oriented pyrolytic graphite (HOPG) surface has been constructed using the open-source package (aenet). The validation of the PES is performed by paying attention to static characteristics as well as by testing its performance in reproducing previous ab initio molecular dynamics simulation results. Subsequently, the ANN-PES is used to perform quasi-classical molecular dynamics calculations of the alignment-dependent scattering of O2 from HOPG. The results are obtained for 200 meV O2 molecules with different initial alignments impinging with a polar incidence angle with respect to the surface normal of 22.5° on a thermalized (110 and 300 K) graphite surface. The choice of these initial conditions in our simulations is made to perform comparisons to recent experimental results on this system. Our results show that the scattering of O2 from the HOPG surface is a rather direct process, that the angular distributions are alignment dependent, and that the final translational energy of end-on molecules is around 20% lower than that of side-on molecules. Upon collision with the surface, the molecules that are initially aligned perpendicular to the surface become highly rotationally excited, whereas a very small change in the rotational state of the scattered molecules is observed for the initial parallel alignments. The latter confirms the energy transfer dependence on the stereodynamics for the present system. The results of our simulations are in overall agreement with the experimental observations regarding the shape of the angular distributions and the alignment dependence of the in-plane reflected molecules.

The classical interchange (permutation) of atoms of similar identity does not have an effect on the overall potential energy. In this study, we present feed-forward neural network structures that provide permutation symmetry to the potential energy surfaces of molecules. The new feed-forward neural network structures are employed to fit the potential energy surfaces for two illustrative molecules, which are H(2)O and ClOOCl. Modifications are made to describe the symmetric interchange (permutation) of atoms of similar identity (or mathematically, the permutation of symmetric input parameters). The combined-function-derivative approximation algorithm (J. Chem. Phys. 2009, 130, 134101) is also implemented to fit the neural-network potential energy surfaces accurately. The combination of our symmetric neural networks and the function-derivative fitting effectively produces PES fits using fewer numbers of training data points. For H(2)O, only 282 configurations are employed as the training set; the testing root-mean-squared and mean-absolute energy errors are respectively reported as 0.0103 eV (0.236 kcal/mol) and 0.0078 eV (0.179 kcal/mol). In the ClOOCl case, 1693 configurations are required to construct the training set; the root-mean-squared and mean-absolute energy errors for the ClOOCl testing set are 0.0409 eV (0.943 kcal/mol) and 0.0269 eV (0.620 kcal/mol), respectively. Overall, we find good agreements between ab initio and NN prediction in term of energy and gradient errors, and conclude that the new feed-forward neural-network models advantageously describe the molecules with excellent accuracy.

Previous experimental and theoretical studies have shown that direct reactive systems typically exhibit backward-peaked differential cross sections (DCS) at relatively low collision energies, while complex-forming reactive systems tend to display forward-backward symmetric DCS. Is this a universal phenomenon in all direct reactions, especially those proceeding through non-collinear transition states? In this work, we developed the quantum wave packet method to calculate the full-dimensional state-to-state DCSs for the title exchange reaction with D2O in the ground rovibrational state on a highly accurate neural network potential energy surface. For the first time, we obtain a sideward-scattered angle distribution just above the threshold, which directly reflects the C3V transition state geometry of this reaction. As the collision energy increases, the DCS broadens and undergoes a series of notable changes, culminating in the dominance of backward scattering at E c = 1.4 eV, accompanied by an early-sideward scattering peak. Although trajectory analysis can explain most of the DCS variations, significant differences persist between the quantum and quasiclassical trajectory DCSs, arising from quantum interference between the contributions from low and high partial waves. Additionally, the collision energy dependent DCSs at the scattering angle of 107° exhibit two clear step-like features around E c = 0.91 and 1.16 eV, which can be attributed to the shape resonance states trapped in the C3V well. In the energy region considered here, the majority of the available energy goes into the translational motion of the products, and the reaction exhibits low vibrational mode-specific behavior.

Two-dimensional (2D) layered metal–organic frameworks (MOFs) are gaining attention due to their unique structural and electronic properties with promising applications in compact electronic device fabrication. Long-time and large-scale molecular dynamics simulations of these materials can enhance and expedite the mapping out of their structure–property–function relationships for these applications. To make such simulations more feasible, herein, we construct a high-dimensional committee neural network potential (CNNP) for archetypal 2D MOFs Ni3(HIB)2 and Ni3(HITP)2 where HIB = hexaiminobenzene and HITP = hexaiminotriphenylene. We harness the power of active learning and committee neural networks to obtain a CNNP model by using only hundreds of snapshots from ab initio molecular dynamics (AIMD) trajectories. The developed CNNP model allows for simulations of thousands of atoms over extended time scales, which is typically unfeasible with AIMD simulations while maintaining the accuracy of the reference data. Our stable MD simulations based on the developed CNNP model reveal the flexible nature of the studied 2D MOFs at room temperature, including puckered layers, as opposed to the planar ones from 0 K electronic structure calculations. Furthermore, our model demonstrates transferability between bulk and monolayers, as well as different organic linkers. As the first model of its kind, we show that the high-dimensional CNNP models could be a reliable and effective approach for future studies on 2D MOFs.

We analyzed the dynamics of N atom scattering from N -covered Ag(1 1 1), using the generalized Langevin oscillator (GLO) method and a three-dimensional neural network potential energy surface. Two values for the mass of the surface oscillator were considered in the GLO model to account for the energy exchange with the surface, i.e., that of Ag and that of N. For these mass values different trends were found for the dependence of the ratio of the average final divided by the average initial translational energy on the scattering angle. Using the nitrogen mass gives a trend closer to the experimental results for the dependence of the energy of the in-plane scattered atoms on the scattering angle, but worse agreement with experiment for the angular distribution of the in-plane scattered atoms. Two different algorithms are applied to integrate the stochastic equations of motion in the presence of energy dissipation. Our calculations show that a trivially extended Bulirsch-Stoer algorithm is more efficient than an algorithm based on a Langevin Liouville operator splitting technique, in that it yields the same results with a much larger time step.

Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calculations, and thus enable molecular dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the atomic positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as molecules, crystalline and amorphous solids, and liquids.

While the underlying potential energy surface (PES) determines the structure and other properties of a material, it has been frustrating to predict new materials from theory even with the advent of supercomputing facilities. The accuracy of the PES and the efficiency of PES sampling are two major bottlenecks, not least because of the great complexity of the material PES. This work introduces a "Global-to-Global" approach for material discovery by combining for the first time a global optimization method with neural network (NN) techniques. The novel global optimization method, named the stochastic surface walking (SSW) method, is carried out massively in parallel for generating a global training data set, the fitting of which by the atom-centered NN produces a multi-dimensional global PES; the subsequent SSW exploration of large systems with the analytical NN PES can provide key information on the thermodynamics and kinetics stability of unknown phases identified from global PESs. We describe in detail the current implementation of the SSW-NN method with particular focuses on the size of the global data set and the simultaneous energy/force/stress NN training procedure. An important functional material, TiO2, is utilized as an example to demonstrate the automated global data set generation, the improved NN training procedure and the application in material discovery. Two new TiO2 porous crystal structures are identified, which have similar thermodynamics stability to the common TiO2 rutile phase and the kinetics stability for one of them is further proved from SSW pathway sampling. As a general tool for material simulation, the SSW-NN method provides an efficient and predictive platform for large-scale computational material screening.

This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.