Machine learning product state distributions from initial reactant states for a reactive atom–diatom collision system

High-Energy Reaction Dynamics of N3

The atom-exchange and atomization dissociation dynamics for the N(4S) + N2(1Σg+) reaction are studied using a reproducing kernel Hilbert space (RKHS)-based, global potential energy surface (PES) at the MRCI-F12/aug-cc-pVTZ-F12 level of theory (MRCI, multireference configuration interaction). For the atom exchange reaction (NANB + NC → NANC + NB), computed thermal rates and their temperature dependence from quasi-classical trajectory (QCT) simulations agree to within error bars with the available experiments. Companion QCT simulations using a recently published CASPT2-based PES confirm these findings. For the atomization reaction, leading to three N(4S) atoms, the computed rates from the RKHS-PES overestimate the experimentally reported rates by 1 order of magnitude, whereas those from the permutationally invariant polynomial (PIP)-PES agree favorably, and the T dependence of both computations is consistent with the experiment. These differences can be traced back to the different methods and basis sets used. The lifetime of the metastable N3 molecule is estimated to be ∼200 fs depending on the initial state of the reactants. Finally, neural-network-based exhaustive state-to-distribution models are presented using both PESs for the atom exchange reaction. These models will be instrumental for a broader exploration of the reaction dynamics of air.

Exhaustive State-to-State Cross Sections and Rate Coefficients for Inelastic N2-N2 Collisions using QCT Combined with Neural Network Models

Using the quasi-classical trajectory method, we systematically studied the state-to-state vibrational relaxation process of N2(v1) + N2(v2) collisions over a wide temperature range (5000-30,000 K). Different temperature dependencies of the single- and multiquantum VV and VT events in various (v1,v2) collisions are captured, with the dominant channel being related to the initial vibrational energy levels (vmax = 50). At a specified relative translational energy, there is a monotonic relationship of the VT cross sections with the vibrational energy level, particularly in high-energy collisions. Additionally, we constructed well-trained neural network models (R-values reaching 0.99) using limited quasi-classical trajectory (QCT) data sets, which can be used to predict the state-to-state cross sections and rate coefficients of the VV processes N2(v1) + N2(v2) → N2(v1 - Δv) + N2(v2 + Δv) and VT processes N2(v1) + N2(v2) → N2(v1 - Δv) + N2(v2) (Δv = ±1, ±2, ±3) for collisions with arbitrary initial vibrational states. This work not only significantly reduces computational resources but also serves as a reference for the study of the state-to-state dynamics of all four-atom collision systems in hypersonic flows.

Gaussian Process Regression for State-to-State Integral Cross Sections: The Case of the O + O2 Collision Dissociation Reactions

Research on hypersonic vehicles has become increasingly important worldwide in recent years. However, accurately simulating the dynamics of the nonequilibrium high-temperature reactions that are in the hypersonic flow around the vehicles presents a significant challenge as a large number of states and transitions are accessible even for the smallest atom-diatom reaction systems. It is quite difficult, sometimes even impossible, to exhaustively investigate all relevant combinations or determine high-dimensional analytical representations for the state-to-state reaction probabilities. In this study, we used Gaussian process regression (GPR) to fit a model based on only 807 QCT data for training. The confidence interval of the GPR prediction and the Kullback-Leibler (KL) divergence were used to help minimize the sampling amount of data for fitting the converged GPR model. The model aims to predict the state-to-state integral cross section (ICS) of the O + O2 → 3O dissociation reaction under random initial conditions (Et, v, j). In total, it took almost a month to obtain this converged GPR model, but it took only a few seconds to predict the ICS value for any initial condition. For 330 initial conditions not included in the training set, the mean-square error (MSE) between the QCT-calculated ICSs and the GPR-predicted ones is only 0.08 Å2 and the R2 is 0.9986, indicating that the GPR model can replace the direct expensive QCT calculation with high accuracy. Finally, we calculated the equilibrium dissociation rate coefficients based on the StS ICS values predicted by the GPR model, and the results were in good agreement with available experimental and theoretical results. Thus, this study provides an effective and accurate approach to the extensive direct state-to-state reaction dynamic calculations.

Dissociation cross sections and rates in O2 + N collisions: molecular dynamics simulations combined with machine learning

The collision-induced dissociation reaction of O2 (v, j) + N, a fundamental process in nonequilibrium air flows around reentry vehicles, has been studied systematically by applying molecular dynamics simulations on the 2A', 4A' and 6A' potential energy surfaces of NO2 in a wide temperature range. In particular, we have directly investigated the role of the 6A' surface in this process and discussed the applicability of the simplified approximate rate models proposed by Esposito et al. and Andrienko et al. based on the lowest two surfaces. The present work indicates that the state-selected dissociation of O2 + N is dominated by the 6A' surface for all except for the low-lying O2 states. Furthermore, a complete database of rovibrationally detailed cross sections and rate coefficients is a prerequisite for modeling the relevant nonequilibrium air flows in spacecraft reentry. Here, the combination of the quasi-classical trajectory (QCT) and the neural network (NN) has been proposed to predict all state-selected dissociation cross sections and further construct dissociation parameter sets. All NN-based models established in this work accurately reproduce the results calculated from QCT simulations over a wide range of rovibrational quantum numbers with R2 > 0.99. Compared with the explicit QCT simulations, the computational requirement for predicting cross sections and rates based on the NN models significantly reduces. Finally, thermal equilibrium rate coefficients computed from NN models match remarkably well the available theoretical and experimental results in the whole temperature range explored.

Classification of the HCN isomerization reaction dynamics in Ar buffer gas via machine learning

The effect of the presence of Ar on the isomerization reaction HCN ⇄ CNH is investigated via machine learning. After the potential energy surface function is developed based on the CCSD(T)/aug-cc-pVQZ level ab initio calculations, classical trajectory simulations are performed. Subsequently, with the aim of extracting insights into the reaction dynamics, the obtained reactivity, that is, whether the reaction occurs or not under a given initial condition, is learned as a function of the initial positions and momenta of all the atoms in the system. The prediction accuracy of the trained model is greater than 95%, indicating that machine learning captures the features of the phase space that affect reactivity. Machine learning models are shown to successfully reproduce reactivity boundaries without any prior knowledge of classical reaction dynamics theory. Subsequent analyses reveal that the Ar atom affects the reaction by displacing the effective saddle point. When the Ar atom is positioned close to the N atom (resp. the C atom), the saddle point shifts to the CNH (HCN) region, which disfavors the forward (backward) reaction. The results imply that analyses aided by machine learning are promising tools for enhancing the understanding of reaction dynamics.

Efficient quasi-classical trajectory calculations by means of neural operator architectures

An accurate description of non-equilibrium chemistry relies on rovibrational state-to-state (StS) kinetics data, which can be obtained through the quasi-classical trajectory (QCT) method for high-energy collisions. However, these calculations still represent one of the major computational bottlenecks in predictive simulations of non-equilibrium reacting gases. This work addresses this limitation by proposing SurQCT, a novel machine learning-based surrogate for efficiently and accurately predicting StS chemical reaction rate coefficients. The QCT emulator is constructed using three independent components: two deep operator networks (DeepONets) for inelastic and exchange processes and a feed-forward neural network (FNN) for the dissociation reactions. SurQCT is tested on the O₂ + O system, showing a computational speed-up of 85%. Furthermore, we carry out a StS master equation analysis of an isochoric, isothermal heat bath simulation at various temperatures to study how the predicted rate coefficients impact the accuracy of multiple quantities of interest (QoIs) at the kinetics level (e.g., global quasi-steady state (QSS) dissociation rate coefficients and energy relaxation times). For all these QoIs, the master equation analysis relying on SurQCT data shows an accuracy within 15% across the entire temperature regime.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Combining Machine Learning and Spectroscopy to Model Reactive Atom + Diatom Collisions

The prediction of product translational, vibrational, and rotational energy distributions for arbitrary initial conditions for reactive atom + diatom collisions is of considerable practical interest in atmospheric re-entry. Because of the large number of accessible states, determination of the necessary information from explicit (quasi-classical or quantum) dynamics studies is impractical. Here, a machine-learned (ML) model based on translational energy and product vibrational states assigned from a spectroscopic, ro-vibrational coupled energy expression based on the Dunham expansion is developed and tested quantitatively. All models considered in this work reproduce final state distributions determined from quasi-classical trajectory (QCT) simulations with R² ∼ 0.98. As a further validation, thermal rates determined from the machine-learned models agree with those from explicit QCT simulations and demonstrate that the atomistic details are retained by the machine learning which makes them suitable for applications in more coarse-grained simulations. More generally, it is found that ML is suitable for designing robust and accurate models from mixed computational/experimental data which may also be of interest in other areas of the physical sciences.

Transfer Learning Approach to Multitarget Temperature-Dependent Reaction Rate Prediction

Accurate prediction of temperature-dependent reaction rate constants of organic compounds is of great importance to both atmospheric chemistry and combustion science. Extensive work has been done on developing automated mechanism generation systems but the lack of quality reaction rate data remains a huge bottleneck in the application of highly detailed mechanisms. Machine learning prediction models have been recently adopted to alleviate the data gap in thermochemistry and have great potential to do the same for kinetic data with the recent release of quality reaction rate data compilations. The ultimate goal is to formulate easily accessible, general-purpose, temperature-dependent, and multitarget models for the prediction of reaction rates. To that end, we propose a model that depends on the well-known Morgan fingerprints as well as learned representations transferred from the QM9 data set. We propose the use of an Arrhenius-based loss where predictions of the three modified-Arrhenius parameters (A, n, and B = E_a/R) are given instead of the direct prediction of reaction rate constants. Our model is >35% more accurate compared to a baseline model of feed forward network (FFN) on Morgan fingerprints.

Rovibrational-Specific QCT and Master Equation Study on N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) Systems in High-Energy Collisions

This work presents a detailed investigation of the energy-transfer and dissociation mechanisms in N₂(X¹Σ_g⁺) + O(³P) and NO(X²Π) + N(⁴S) systems using rovibrational-specific quasiclassical trajectory (QCT) and master equation analyses. The complete set of state-to-state kinetic data, obtained via QCT, allows for an in-depth investigation of the Zel'dovich mechanism leading to the formation of NO molecules at microscopic and macroscopic scales. The master equation analysis demonstrates that the low-lying vibrational states of N₂ and NO have dominant contributions to the NO formation and the corresponding extinction of N₂ through the exchange process. For the considered temperature range, it is found that nearly 50% of the dissociation processes for N₂ and NO molecules occur in the quasi-steady-state (QSS) regime, while for the Zel'dovich reaction, the distribution of the reactants does not reach the QSS conditions. Furthermore, using the QSS approximation to model the Zel'dovich mechanism leads to overestimating NO production by more than a factor of 4 in the high-temperature range. The breakdown of this well-known approximation has profound consequences for the approaches that heavily rely on the validity of QSS assumption in hypersonic applications. Finally, the investigation of the rovibrational state population dynamics reveals substantial similarities among different chemical systems for the energy-transfer and the dissociation processes, providing promising physical foundations for the use of reduced-order strategies in other chemical systems without significant loss of accuracy.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.