Machine learning-enabled prediction of nonequilibrium reaction dynamics: A mixed Gaussian process regression-neural network framework for O + O2 state-to-state dissociation kinetics.

We carry out quantum scattering dynamics and quasi-classical trajectory (QCT) calculations for the reactive collision in the ground (12A″) and first excited (12A′) potential energy surface. We calculate the reaction probabilities of and reaction for total angular momentum J = 0. The results calculated by QCT are consistent with those from quantum mechanical wave packet. Using the QCT method, we generate in the center-of-mass frame the product state-resolved integral cross-sections (ICSs); two commonly used generalized polarization-dependent differential cross-sections (PDDCSs), (2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt); and three angular distributions of the product rotational vectors, P(θr), P(ϕr), and P(θr, ϕr). We discuss the influence on the scalar and vector properties of the potential energy surface, the collision energy, and the isotope mass. Since there are deep potential wells in these two potential energy surfaces, their kinetic characteristics are similar to each other and the isotopic effect is not obvious. However, the well depths and configurations of the two potential energy surfaces are different, so the effects of isotopic substitution on the integral cross-section and the rotational polarization of product are different.

A detailed study of the proton exchange reaction H(+) + D(2)(v = 0, j = 0) --> HD + D(+) on its ground 1(1)A' potential energy surface has been carried out using 'exact' close-coupled quantum mechanical wavepacket (WP-EQM), quasi-classical trajectory (QCT), and statistical quasi-classical trajectory (SQCT) calculations for a range of collision energies starting from the reaction threshold to 1.3 eV. The WP-EQM calculations include all total angular momenta up to J(max) = 50, and therefore the various dynamical observables are converged up to 0.6 eV. It has been found that it is necessary to include all Coriolis couplings to obtain reliable converged results. Reaction probabilities obtained using the different methods are thoroughly compared as a function of the total energy for a series of J values. Comparisons are also made of total reaction cross sections as function of the collision energy, and rate constants. In addition, opacity functions, integral cross sections (ICS) and differential cross sections (DCS) are presented at 102 meV, 201.3 meV and 524.6 meV collision energy. The agreement between the three sets of results is only qualitative. The QCT calculations fail to describe the overall reactivity and most of the dynamical observables correctly. At low collision energies, the QCT method is plagued by the lack of conservation of zero point energy, whilst at higher collision energies and/or total angular momenta, the appearance of an effective repulsive potential associated with the centrifugal motion "over" the well causes a substantial decrease of the reactivity. In turn, the statistical models overestimate the reactivity over the whole range of collision energies as compared with the WP-EQM method. Specifically, at sufficiently high collision energies the reaction cannot be deemed to be statistical and important dynamical effects seem to be present. In general the WP-EQM results lie in between those obtained using the QCT and SQCT methods. One of the main, unexpected, conclusions of this work is that an accurate description of the reaction and of its various dynamical features requires a computationally expensive, accurate quantum mechanical treatment.

Solution of the time-dependent Schrödinger equation using a linear combination of basis functions, such as Gaussian wavepackets (GWPs), requires costly evaluation of integrals over the entire potential energy surface (PES) of the system. The standard approach, motivated by computational tractability for direct dynamics, is to approximate the PES with a second order Taylor expansion, for example centred at each GWP. In this article, we propose an alternative method for approximating PES matrix elements based on PES interpolation using Gaussian process regression (GPR). Our GPR scheme requires only single-point evaluations of the PES at a limited number of configurations in each time-step; the necessity of performing often-expensive evaluations of the Hessian matrix is completely avoided. In applications to 2-, 5-, and 10-dimensional benchmark models describing a tunnelling coordinate coupled non-linearly to a set of harmonic oscillators, we find that our GPR method results in PES matrix elements for which the average error is, in the best case, two orders-of-magnitude smaller and, in the worst case, directly comparable to that determined by any other Taylor expansion method, without requiring additional PES evaluations or Hessian matrices. Given the computational simplicity of GPR, as well as the opportunities for further refinement of the procedure highlighted herein, we argue that our GPR methodology should replace methods for evaluating PES matrix elements using Taylor expansions in quantum dynamics simulations.

The first calculations of state-to-state reaction probabilities and product state-resolved integral cross sections at selected collision energies (0.05, 0.1, 0.5, and 1.0 eV) for the title reaction on the ab initio potential energy surface of [Zanchet et al. J. Phys. Chem. A 110, 12017 (2006)] with the OH reagent in selected rovibrational states (v = 0-2, j = 0-5) have been carried out by means of the real wave packet (RWP) and quasiclassical trajectory (QCT) methods. State-selected total reaction probabilities have been calculated for total angular momentum J = 0 in a broad range of collision energies. Integral cross sections and state-specific rate coefficients have been obtained from the corresponding J = 0 RWP reaction probabilities for initially selected rovibrational states by means of a capture model. The calculated RWP and QCT state-selected rate coefficients are practically temperature independent. Both RWP and QCT reaction probabilities, integral cross sections, and rate coefficients are almost independent of the initial rotational excitation. The RWP results are found to be in an overall good agreement with the corresponding QCT results. The present results have been compared with earlier wave packet calculations carried out on the same potential energy surface.

The quantum scattering dynamics and quasi-classical trajectory (QCT) calculations have been carried out for the title reaction on an accurate potential energy surface (PES) computed using the full configuration interaction (FCI). On the basis of the PES, the integral cross-sections of He + H₂⁺ (v = 0-3, j = 1) → HeH⁺ + H reaction have been calculated, and the results are generally agreed with the experimental cross-sections obtained by Tang et al. [J. Chem. Phys. 2005, 122, 164301] after taking into account the experimental uncertainties, which proves the reliability of implementing dynamics calculations on the FCI PES. The reaction probability of He + D₂⁺ (v = 0-2, j = 0) → HeD⁺ + D reactions for total angular momentum J = 0 and the integral cross-section (ICS) have been calculated. The significant quantum effect has been explored by the comparison between the QCT reaction probabilities (or ICS) and the quantum mechanical (QM) reaction probabilities (or ICS), which may be attributed to the deep well in the PES of this light atoms system. Furthermore, the role of Coriolis coupling (CC) effects has also been found not important by the comparison between the CC calculation and the centrifugal sudden (CS) approximation calculation, except that the CC total cross-sections for the v = 1 and 2 states show the collision energy-dependent behaviors in the low-energy area, which are different from those based on the CS calculation.

The research presented by the author investigates a polyatomic reaction occurring in the gas phase. This study employs the Quasi-Classical Trajectory (QCT) approach using the Wu–Schatz–Lendvay–Fang–Harding (WSLFH) potential energy surface (PES), recognized as one of the most reliable PES models for this type of analysis. The substantial sample size enables the derivation of detailed results that corroborate previous findings while also identifying potential objectives for future experimental work. The Gaussian Binning (GB) technique is utilized to more effectively highlight the variation in the total angular momentum (J′) of the excited product molecule, HOD*. A key aim of the study is to explore the reaction dynamics due to their importance in excitation and emission processes, which may contribute to the development of a chemical laser based on this reaction. Increasing the vibrational level, v, of one reactant, D2, significantly enhances the excitation of HOD* and shifts the P(J′) distributions towards higher J′ values, while also broadening the distribution. Although the current research focuses on a few initial conditions, the author plans to extend the study to encompass a wider range of initial conditions within the reaction chamber of this type of chemical laser.

The state-to-state (STS) inelastic energy transfer and O-atom exchange reaction between O and CO(v), as two fundamental processes in non-equilibrium air flow around spacecraft entering Mars' atmosphere, yield the same products and both make significant contributions to the O + CO(v) → O + CO(v') collisions. The inelastic energy transfer competes with the O-atom exchange reaction. The detailed reaction mechanisms of these two elementary processes and their specific contributions to the CO relaxation process are still unclear. To address these concerns, we performed systematic investigations on the 3A' and 3A″ potential energy surfaces (PESs) of CO2 using quasi-classical trajectory (QCT) calculations. Analysis of the collision mechanisms reveals that inelastic collisions have an apparent PES preference (i.e., they tend to occur on the 3A' PES), while reactive collisions do not. Reactive rates decrease significantly when the total collision energy approaches dissociation energy, which differs from the inelastic process. Inelastic rates are generally lower than the reactive rates below ∼10 000K, except for single quantum jumps, whereas the reverse is observed above ∼10 000K. In addition, by combining QCT with convolutional neural networks, we have established neural network (NN)-STS1 (inelastic) and NN-STS2 (reactive) models to generate all possible STS cross sections. The NN-based models accurately reproduce the results calculated from QCT calculations. In this study, all calculations have been focused on analyzing collisions at the ground rotational level.

In this study, we explore the initial state selected dynamics of the S + SH ( X 2 Π ) → S 2 ( X 3 ∑ ) + H reaction through the lens of time-dependent quantum dynamics (QD), quasi-classical trajectory (QCT), and statistical quantum mechanical (SQM) approaches, utilising the electronic ground state HS 2 (X 2 A ′′ ) potential energy surface (PES). We present total reaction probabilities and integral cross sections (ICSs) as part of our findings. Our results indicate that at low and moderate collision energies, the reaction predominantly follows an indirect pathway, forming meta-stable quasi-bound complexes. Additionally, we observe that the rotational excitation of the SH reagent initially leads to a decrease and then an increase in reactivity. We conduct a comprehensive analysis and comparison of the outcomes from QD, QCT, and SQM methodologies.

Laboratory angular distributions (LAB ADs) have been measured for the Li+HF (v=1, j=1) reaction in a crossed molecular beam experiment at the collision energies 0.231 eV and 0.416 eV and compared with the results of extensive quasi-classical trajectory (QCT) calculations performed on the most recent ab initio potential energy surface (PES) for this system. The calculations also include the collision energy dependence of the integral and differential cross sections in the range 0.025–0.5 eV (2.4–48.2 kJ mol−1). In particular, the total QCT integral reactive cross sections have been found to be in very good agreement with recent quantum mechanical (QM) calculations carried out on the same PES by Lara et al. (J. Chem. Phys., 1998, 109, 9391). In addition, the triple scattering angle–recoil velocity differential cross section has been calculated in order to simulate the experimental LAB AD. An excellent concordance between both sets of data has been found, indicating that the reaction of Li with HF in v=1 can be very well described by QCT calculations on the mentioned PES.

Integral and differential cross sections for the O(1D)+HD reaction have been obtained from adiabatic and nonadiabatic quasiclassical trajectory calculations performed on new ab initio versions of the 1A′, 1A″ and 2A′ potential energy surfaces at the collision energies of 0.089 and 0.196 eV (2.05 and 4.53 kcal/mol, respectively). Results are reported for both the OH+D and OD+H exit channels of reaction. The new data are compared with those from previous theoretical studies employing other potential energy surfaces, and are also used to simulate experimental differential cross sections obtained from recent molecular beam measurements, which are partially resolved in the internal states of the products. The comparison provides evidence that excited electronic states do participate in the title reaction at 0.196 eV, but that their contribution, particularly that of the A″ state, is overestimated by the quasiclassical trajectory (QCT) calculations employing the latest, and most accurate, potential energy surfaces.

State-to-state dynamics of S+(2D) + H2(X1Σg+)(v, j) collision reaction based on the H2S+ (X2A′′)potential energy surface

The quantum time dependent wave packet (TDWP) and quasiclassical trajectory (QCT) calculations were carried out to study the exchange reaction H(2S) + H′S(2Π) → HS(2Π) + H′(2S) on the1A′potential energy surface (PES). The integral cross sections of the H + H′S (v = j = 0) → HS + H′reaction calculated by the two methods were presented. The results reveal that the integral cross sections (ICS) decrease with the collision energy increasing. The result of the QCT calculations is reasonably consistent with the time-dependent wave packet. Moreover, the differential cross sections (DCS) were calculated by the QCT method at the four different collision energies, which display a forward–backward symmetry. A long-lifetime H2S intermediate complex of the exchange reaction was found according to the trajectories. In the stereodynamics investigation, the polar and dihedral angle distribution functions were calculated, which have the distinct oscillations. The oscillations could be attributed to the deep well on the1A′PES. However, based on the polar-angle and dihedral angle distribution functions, it could be predicted that the main product rotational angular momentum preferentially point to the positive or negative direction of y-axes.

Accurate quantum reactive scattering time-dependent wave packet close-coupling calculations have been carried out to determine total reaction probabilities and integral cross sections for the O(+) + H2 → OH(+) + H reaction in a range of collision energies from 10(-3) eV up to 1.0 eV for the H2 rovibrational states (v = 0; j = 0, 1, 2) and (v = 1; j = 0) using the potential energy surface (PES) by Martı́nez et al. As expected for a barrierless reaction, the reaction cross section decays rapidly with collision energy, Ec, following a behavior that nearly corresponds to that predicted by the Langevin model. Rotational excitation of H2 into j = 1, 2 has a very moderate effect on reactivity, similarly to what happens with vibrational excitation below Ec ≈ 0.3 eV. However, at higher collision energies the cross section increases notably when H2 is promoted to v = 1. This effect is explained by resorting to the effective potentials in the entrance channel. The integral cross sections have been used to calculate rate constants in the temperature range 200-1000 K. A good overall agreement has been found with the available experimental data on integral cross sections and rate constants. In addition, time-independent quantum mechanical and quasi-classical trajectory (QCT) calculations have been performed on the same PES aimed to compare the various methodologies and to discern the detailed mechanism of the title reaction. In particular, the analysis of individual trajectories has made it possible to explain, in terms of the coupling between reagent relative velocity and the topography of the PES, the presence of a series of alternating maxima and minima in the collision energy dependence of the QCT reaction probabilities for the reactions with H2(v=0,1,j=0), which are absent in the quantum mechanical calculations.

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.

Quasiclassical trajectory (QCT) and quantum mechanical (QM) close-coupling calculations have been used to study the state-resolved rotationally inelastic scattering of NO(X(2)Pi(1/2),v = 0,j = 1/2,e/f) by He on the most recent ab initio potential energy surface of J. Kłos et al. [J. Chem. Phys. 2000, 112, 2195.]. Opacity functions, and integral and differential cross sections are reported at collision energies of 63 and 147 meV and compared with previous theoretical calculations and experimental measurements on this and other systems. The existence of double peaks in the QCT and QM differential cross sections is examined in detail. While at a collision energy of 147 meV two rotational peaks appear in both the QCT and open-shell QM results, only a single peak is found in the QM calculations at the lower collision energy. The double peaks in the quantum-state-resolved differential cross sections (DCS) are found to be closely related to structure found in the corresponding state-resolved opacity functions. The structure in the QCT and QM DCSs is attributed to a flattening of the potential energy surface for sideways approach of He to the near-symmetric NO(X) molecule, and in both sets of calculations, it is shown to arise from a specific odd term in the expansion of the intermolecular potential. Although significant differences are found between the QCT and QM data in the forward scattered direction, and for higher final rotational levels, reflecting differences in the nature of the rotational rainbows observed in these two methods, in general, the QCT calculations are shown to give similar results to quantum theory. Furthermore, they provide valuable clues as to the mechanism of rotational energy transfer in this system.