Neural Network Potential Energy Surface Research Articles

Computational determination of the S1(Ã1A″) absorption spectra of HONO and DONO using full-dimensional neural network potential energy surfaces.

The Ã1A″ ← X̃1A' absorption spectra of HONO and DONO were simulated by a full six-dimensional quantum mechanical method based on the newly constructed potential energy surfaces for the ground and excited electronic states, which were represented by the neural network method utilizing over 36 000 abinitio energy points calculated at the multireference configuration interaction level with Davidson correction. The absorption spectrum of HONO/DONO comprises a superposition of the spectra from two isomers, namely, trans- and cis-HONO/DONO, due to their coexistence in the ground X̃1A' state. Our calculated spectra of both HONO and DONO were found to be in fairly good agreement with the experiment, including the energy positions and widths of the peaks. The dominant progression was assigned to the N=O stretch mode (20n) associated with trans-HONO/DONO, which can be attributed to the promotion of an electron to the π* orbital of N=O. Specifically, the resonances with higher vibrational quanta were found to be in the domain of the Feshbach-type resonances. The assignments of the spectra and mode specificity therein are discussed.

Quantum study of the CH3+ photodissociation in full-dimensional neural network potential energy surfaces.

C H 3 + , a cornerstone intermediate in interstellar chemistry, has recently been detected for the first time by using the James Webb Space Telescope. The photodissociation of this ion is studied here. Accurate explicitly correlated multi-reference configuration interaction abinitio calculations are done, and full-dimensional potential energy surfaces are developed for the three lower electronic states, with a fundamental invariant neural network method. The photodissociation cross section is calculated using a full-dimensional quantum wave packet method in heliocentric Radau coordinates. The wave packet is represented in angular and radial grids, allowing us to reduce the number of points physically accessible, requiring to push up the spurious states appearing when evaluating the angular kinetic terms, through projection technique. The photodissociation spectra, when employed in astrochemical models to simulate the conditions of the Orion bar, result in a lesser destruction of CH3+ compared to that obtained when utilizing the recommended values in the kinetic database for astrochemistry.

Understanding the Photoinduced Desorption and Oxidation of CO on Ru(0001) Using a Neural Network Potential Energy Surface.

The study of ultrafast photoinduced dynamics of adsorbates on metal surfaces requires thorough investigation of laser-excited electrons and, in many cases, the highly excited surface lattice. While ab initio molecular dynamics with electronic friction and thermostats (Te, Tl)-AIMDEF addresses such complex modeling, it imposes severe computational costs, hindering quantitative comparison with experimental desorption probabilities. In order to bypass this limitation, we utilize the embedded atom neural network method to construct a potential energy surface (PES) for the coadsorption of CO and O on Ru(0001). Our results demonstrate that this PES not only reproduces the short-time ab initio dynamics but is also able to yield statistically significant data for long lasting trajectories that correlate well with experimental findings. Furthermore, the analysis of the laser-induced dynamics reveals the existence of a dynamic trapping state that acts as a precursor for CO desorption, and it is not observed under thermal conditions. Altogether, our results validate the underlying theoretical framework, providing robust support for the description of not only the photoinduced desorption but also the oxidation of CO in terms of nonequilibrated but thermal hot electrons and phonons.

A globally accurate neural network potential energy surface and quantum dynamics study of Mg+(2S) + H2 → MgH+ + H reaction

A globally accurate ground-state MgH2+ potential energy surface (PES) is constructed by neural network method based on 12,056 high-level ab initio points. On the PES, the dynamics calculations of the Mg+(2S) + H2/HD (v0 = 0, j0 = 0) reaction are performed using the time-dependent wave packet method. The branching ratio (MgD+/MgH+) in the Mg+ + HD reaction is much larger than one in most studied collision energies. The dynamics results imply that the title reaction follows the complex-forming mechanism near the threshold, and the direct abstraction process gradually plays the dominant role as the collision energy increases.

Multicoverage Study of Femtosecond Laser-Induced Desorption of CO from Pd(111).

We study the strong coverage dependence of the femtosecond laser-induced desorption of CO from Pd(111) using molecular dynamics simulations that consistently include the effect of the laser-induced hot electrons on both the adsorbates and surface atoms. Adiabatic forces are obtained from a multicoverage neural network potential energy surface that we construct using data from density functional theory calculations for 0.33 and 0.75 monolayer (ML). Our molecular dynamics simulations performed for these two trained coverages and an additional intermediate coverage of 0.60 ML reproduce well the peculiarities of the experimental findings. The performed simulations also permit us to disentangle the relative role played by the excited electrons and phonons on the desorption process and discover interesting properties of the reaction dynamics as the relevance that the precursor physisorption well acquires during the dynamics as coverage increases.

A neural network potential energy surface assisted molecular dynamics study on the pyrolysis behavior of two spiro-hydrocarbons.

Spiro-hydrocarbons are potentially a type of novel alternative jet fuel due to their high density and net heat of combustion. In this work, the pyrolysis study of two spiro-hydrocarbons (spiro[cyclopropane-1,6'-tricyclo[3.2.1.02,4]octane] (C10H14) as Fuel 1 and spiro[bicyclo[2.2.1]heptane-2,1'-cyclopropane] (C9H14) as Fuel 2) is performed via molecular dynamics (MD) simulations, with a neural network potential energy surface (NNPES), deep potential (DP) model, adopted. The data set for the DP model of each fuel is constructed after 31 and 27 iterations, respectively. The high precision of the DP model is demonstrated, and the temperature transferability of each model is observed. The overall pyrolysis performance is evaluated with the fuel decomposition rate, showing that both fuels have comparable gas-reactivity to commercial aviation fuels, such as JP-10. The reaction networks of initial pyrolysis for Fuels 1 and 2 are constructed, and the contribution of each pathway is discussed. Fuel 1 tends to form an unsaturated six-membered ring structure, while Fuel 2 generates unsaturated open-chain hydrocarbons. Further analyses of the MD results provide time-evolution information on each component in the pyrolysis species pool. Compared to Fuel 1, the initial pyrolysis of Fuel 2 leads to more hydrogen, alkenes, and alkanes, as well as fewer monocyclic aromatic hydrocarbons (MAHs), demonstrating a reduced tendency for afterward coking. This work might contribute to the development of the mechanism of the two spiro-hydrocarbons and guide the research of other similar structural fuels.

A neural network potential energy surface of the Li3 system and quantum dynamics studies for the 7Li + 6Li2 → 6Li7Li + 6Li reaction.

A high-precision global potential energy surface (PES) of the Li3 system is constructed based on high-level ab initio calculations, and the root-mean-square error is 5.54 cm-1. The short-range of the PES is fitted by the fundamental invariant neural network (FI-NN) method, while the long-range uses a function with an accurate asymptotic potential energy form, and the two regions are connected by a switching function. Based on the new PES, the statistical quantum-mechanical (SQM) and the time-dependent wave packet (TDWP) methods are used to study the dynamics of 7Li + 6Li2 (v = 0, j = 0) → 6Li7Li + 6Li reactions in the low collision energy region (10-11 to 10-3 cm-1) and the high collision energy region (8 to 800 cm-1), respectively. In the high collision energy region, the calculation results of the SQM method and the TDWP method are inconsistent, indicating that the reaction dynamics does not follow the statistical behavior in the high collision energy region. In addition, we found that the Coriolis coupling effect plays an important role in this reaction. The symmetric forward-backward scattering in the total DCS indicates that the reaction follows the complex-forming reaction mechanism.

Full-scale ab initio simulations of laser-driven atomistic dynamics

The coupling of excited states and ionic dynamics is the basic and challenging point for the materials response at extreme conditions. In the laboratory, the intense laser produces transient nature and complexity with highly nonequilibrium states, making it extremely difficult and interesting for both experimental measurements and theoretical methods. With the inclusion of laser-excited states, we extend an ab initio method into the direct simulations of whole laser-driven microscopic dynamics from solid to liquid. We construct the framework of combining the electron-temperature-dependent deep neural-network potential energy surface with a hybrid atomistic-continuum approach, controlling non-adiabatic energy exchange and atomistic dynamics, which enables consistent interpretation of experimental data. By large-scale ab initio simulations, we demonstrate that the nonthermal effects introduced by hot electrons play a dominant role in modulating the lattice dynamics, thermodynamic pathway, and structural transformation. We highlight that the present work provides a path to realistic computational studies of laser-driven processes, thus bridging the gap between experiments and simulations.

Quantum and classical molecular dynamics for H atom scattering from graphene.

This work presents systematic comparisons between classical molecular dynamics (cMD) and quantum dynamics (QD) simulations of 15-dimensional and 75-dimensional models in their description of H atom scattering from graphene. We use an experimentally validated full-dimensional neural network potential energy surface of a hydrogen atom interacting with a large cell of graphene containing 24 carbon atoms. For quantum dynamics simulations, we apply Monte Carlo canonical polyadic decomposition to transform the original potential energy surface (PES) into a sum of products form and use the multi-layer multi-configuration time-dependent Hartree method to simulate the quantum scattering of a hydrogen or deuterium atom with an initial kinetic energy of 1.96 or 0.96 eV and an incident angle of 0°, i.e., perpendicular to the graphene surface. The cMD and QD initial conditions have been carefully chosen in order to be as close as possible. Our results show little differences between cMD and QD simulations when the incident energy of the H atom is equal to 1.96 eV. However, a large difference in sticking probability is observed when the incident energy of the H atom is equal to 0.96 eV, indicating the predominance of quantum effects. To the best of our knowledge, our work provides the first benchmark of quantum against classical simulations for a system of this size with a realistic PES. Additionally, new projectors are implemented in the Heidelberg multi-configuration time-dependent Hartree package for the calculation of the atom scattering energy transfer distribution as a function of outgoing angles.

The Identity of Nickel Peroxide as a Nickel Superoxyhydroxide for Enhanced Electrocatalysis.

Nickel peroxides are a class of stoichiometric oxidants that can selectively oxidize various organic compounds, but their molecular level structure remained elusive until now. Herein, we utilized structural prediction using the Stochastic Surface Walking method based on a neural network potential energy surface and advanced characterization using the as-synthesized nickel peroxide to unravel its chemical identity as the bridging superoxide containing nickel hydroxide, or nickel superoxyhydroxide. Superoxide incorporation tunes the local chemical environment of nickel and oxygen beyond the conventional Bode plot, offering a 6.4-fold increase in the electrocatalytic activity of urea oxidation. A volcanic dependence of the activity on the oxygen equivalents leads to the proposed active site of the Ni(OO)(OH)Ni five-membered ring. This work not only unveils the possible structures of nickel peroxides but also emphasizes the significance of tailoring the oxygen environment for advanced catalysis.

An Ab Initio Neural Network Potential Energy Surface for the Dimer of Formic Acid and Further Quantum Tunneling Dynamics.

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.

Multifidelity Neural Network Formulations for Prediction of Reactive Molecular Potential Energy Surfaces

This paper focuses on the development of multifidelity modeling approaches using neural network surrogates, where training data arising from multiple model forms and resolutions are integrated to predict high-fidelity response quantities of interest at lower cost. We focus on the context of quantum chemistry and the integration of information from multiple levels of theory. Important foundations include the use of symmetry function-based atomic energy vector constructions as feature vectors for representing structures across families of molecules and single-fidelity neural network training capabilities that learn the relationships needed to map feature vectors to potential energy predictions. These foundations are embedded within several multifidelity topologies that decompose the high-fidelity mapping into model-based components, including sequential formulations that admit a general nonlinear mapping across fidelities and discrepancy-based formulations that presume an additive decomposition. Methodologies are first explored and demonstrated on a pair of simple analytical test problems and then deployed for potential energy prediction for C5H5 using B2PLYP-D3/6-311++G(d,p) for high-fidelity simulation data and Hartree-Fock 6-31G for low-fidelity data. For the common case of limited access to high-fidelity data, our computational results demonstrate that multifidelity neural network potential energy surface constructions achieve roughly an order of magnitude improvement, either in terms of test error reduction for equivalent total simulation cost or reduction in total cost for equivalent error.

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.

A neural network potential energy surface for the Li + LiNa → Li2 + Na reaction and quantum dynamics study from ultracold to thermal energies.

An improved fundamental invariant neural network (FI-NN) approach for representing a potential energy surface (PES) involving permutation symmetry is introduced in this work. In this approach, FIs are regarded as symmetric neurons, thus avoiding complex preprocessing of training set data, especially when the training set contains gradient data. In this work, the improved FI-NN method, combined with simultaneous fitting of the energy and gradient strategy, is used for constructing a global accurate PES of a Li2Na system (root-mean-square error of 12.20 cm-1). The potential energies and the corresponding gradients are calculated by a UCCSD(T) method with effective core potentials. Based on the new PES, the vibrational energy levels and the corresponding wave functions of Li2Na molecules are calculated using an accurate quantum mechanics method. To accurately describe the cold or ultracold reaction dynamics of the Li + LiNa(v = 0, j = 0) → Li2(v', j') + Na reaction, the long-range region of the PES in both the reactant and product asymptotes is represented by an asymptotically correct form. A statistical quantum model (SQM) is used to study the dynamics of the ultracold Li + LiNa reaction. The calculated results are in good agreement with the exact quantum dynamics results (B. K. Kendrick, J. Chem. Phys., 2021, 154, 124303), which indicates that the dynamics of the ultracold Li + LiNa reaction can be well described by the SQM approach. The time-dependent wave packet calculations are performed for the Li + LiNa reaction at thermal energies, and the characteristic of differential cross-sections confirms that the reaction follows the complex-forming reaction mechanism.

Full-dimensional neural network potential energy surface and dynamics of the CH2OO + H2O reaction.

An accurate global full-dimensional machine learning-based potential energy surface (PES) of the simplest Criegee intermediate (CH2OO) reaction with water monomer was developed based on the high level of extensive CCSD(T)-F12a/aug-cc-pVTZ calculations. This analytical global PES not only covers the regions of reactants to hydroxymethyl hydroperoxide (HMHP) intermediates, but also different end product channels, which facilities both the reliable and efficient kinetics and dynamics calculations. The rate coefficients calculated by the transition state theory with the interface to the full-dimensional PES agree well with the experimental results, indicating the accuracy of the current PES. Extensive quasi-classical trajectory (QCT) calculations were performed both from the bimolecular reaction CH2OO + H2O and from HMHP intermediate on the new PES. The product branching ratios of hydroxymethoxy radical (HOCH2O, HMO) + OH radical, formaldehyde (CH2O) + H2O2 and formic acid (HCOOH) + H2O were calculated. The reaction yields dominantly HMO + OH, because of the barrierless pathway from HMHP to this channel. The computed dynamical results for this product channel show the total available energy was deposited into the internal rovibrational excitation of HMO, and the energy release in OH and translational energy is limited. The large amount of OH radical found in the current study implies that the CH2OO + H2O reaction can provide crucially OH yield in Earth's atmosphere.

Large scale and quantum accurate molecular dynamics simulation: Liquid iron under extreme condition

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.

Three-dimensional Langevin dynamics of N atom scattering from N-covered Ag(1 1 1)

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.

Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning.

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD(T) calculations at the same cost as a Hartree-Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH5+, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C2H5+, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH5+ and C2H5+ the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C2H5+ was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C2H5+.

Transferable Neural Network Potential Energy Surfaces for Closed-Shell Organic Molecules: Extension to Ions.

Transferable high dimensional neural network potentials (HDNNPs) have shown great promise as an avenue to increase the accuracy and domain of applicability of existing atomistic force fields for organic systems relevant to life science. We have previously reported such a potential (Schrödinger-ANI) that has broad coverage of druglike molecules. We extend that work here to cover ionic and zwitterionic druglike molecules expected to be relevant to drug discovery research activities. We report a novel HDNNP architecture, which we call QRNN, that predicts atomic charges and uses these charges as descriptors in an energy model that delivers conformational energies within chemical accuracy when measured against the reference theory it is trained to. Further, we find that delta learning based on a semiempirical level of theory approximately halves the errors. We test the models on torsion energy profiles, relative conformational energies, geometric parameters, and relative tautomer errors.

Ab initio neural network MD simulation of thermal decomposition of a high energy material CL-20/TNT.

CL-20 (2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane, also known as HNIW) is one of the most powerful energetic materials. However, its high sensitivity to environmental stimuli greatly reduces its safety and severely limits its application. In this work, ab initio based neural network potential (NNP) energy surfaces for both β-CL-20 and CL-20/TNT co-crystals were constructed. To accurately simulate the thermal decomposition processes of these two crystal systems, reactive molecular dynamics simulations based on the NNPs were performed. Many important intermediate species and their associated reaction paths during the decomposition had been identified in the simulations and the direct results on detonation temperatures of both systems were provided. The simulations also showed clearly that 2,4,6-trinitrotoluene (TNT) molecules in the co-crystal act as a buffer to slow down the chain reactions triggered by nitrogen dioxide and this effect is more significant at lower temperatures. Specifically, the addition of TNT molecules in the CL-20/TNT co-crystal introduces intermolecular hydrogen bonds between CL-20 and TNT molecules in the system, thereby increasing the thermal stability of the co-crystal. The current reactive molecular dynamics simulation is performed based on the NNP which helps in accelerating the speed of ab initio molecular dynamics (AIMD) simulation by more than 3 orders of magnitude while preserving the accuracy of density functional theory (DFT) calculations. This enabled us to perform longer-time simulations at more realistic temperatures that traditional AIMD methods cannot achieve. With the advantage of the NNP in its powerful fitting ability and transferability, the NNP-based MD simulation can be widely applied to energetic material systems.