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.

Quantum and quasi-classical dynamics of the C(3P) + O2(3Σ-g) → CO(1Σ+) + O(1D) reaction on its electronic ground state.

The dynamics of the C(3P) + O2(3Σ-g) → CO(1Σ+) + O(1D) reaction on its electronic ground state is investigated by using time-dependent wave packet propagation (TDWP) and quasi-classical trajectory (QCT) simulations. For the moderate collision energies considered (Ec = 0.001 to 0.4 eV, corresponding to a range from 10 K to 4600 K) the total reaction probabilities from the two different treatments of the nuclear dynamics agree very favourably. The undulations present in P(E) from the quantum mechanical treatment can be related to stabilization of the intermediate CO2 complex with lifetimes on the 0.05 ps time scale. This is also confirmed from direct analysis of the TDWP simulations and QCT trajectories. Product diatom vibrational and rotational level resolved state-to-state reaction probabilities from TDWP and QCT simulations agree well except for the highest product vibrational states (v' ≥ 15) and for the lowest product rotational states (j' ≤ 10). Opening of the product vibrational level CO(v' = 17) requires ∼0.2 eV from QCT and TDWP simulations with O2(j = 0) and decreases to 0.04 eV if all initial rotational states are included in the QCT analysis, compared with Ec > 0.04 eV obtained from experiments. It is thus concluded that QCT simulations are suitable for investigating and realistically describe the C(3P) + O2(3Σ-g) → CO(1Σ+) + O(1D) reaction down to low collision energies when compared with results from a quantum mechanical treatment using TDWPs.

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

A machine-learned model for predicting product state distributions from specific initial states (state-to-distribution or STD) for reactive atom-diatom collisions is presented and quantitatively tested for the N(4S) + O2(X3Σg -) → NO(X2Π) + O(3P) reaction. The reference dataset for training the neural network consists of final state distributions determined from quasi-classical trajectory (QCT) simulations for ∼2000 initial conditions. Overall, the prediction accuracy as quantified by the root-mean-squared difference (∼0.003) and the R2 (∼0.99) between the reference QCT and predictions of the STD model is high for the test set, for off-grid state-specific initial conditions, and for initial conditions drawn from reactant state distributions characterized by translational, rotational, and vibrational temperatures. Compared with a more coarse grained distribution-to-distribution (DTD) model evaluated on the same initial state distributions, the STD model shows comparable performance with the additional benefit of the state resolution in the reactant preparation. Starting from specific initial states also leads to a more diverse range of final state distributions, which requires a more expressive neural network compared with DTD. A direct comparison between QCT simulations, the STD model, and the widely used Larsen-Borgnakke (LB) model shows that the STD model is quantitative, whereas the LB model is qualitative at best for rotational distributions P(j') and fails for vibrational distributions P(v'). As such, the STD model can be well-suited for simulating nonequilibrium high-speed flows, e.g., using the direct simulation Monte Carlo method.

The C(3P) + O2(3Σg-) → CO2 ↔ CO(1Σ+) + O(1D)/O(3P) reaction: thermal and vibrational relaxation rates from 15 K to 20 000 K.

Thermal rates for the C(3P) + O2(3Σg-) ↔ CO(1Σ+)+ O(1D)/O(3P) reaction are investigated over a wide temperature range based on quasi classical trajectory (QCT) simulations on 3-dimensional, reactive potential energy surfaces (PESs) for the 1A', (2)1A', 1A'', 3A' and 3A'' states. These five states are the energetically low-lying states of CO2 and their PESs are computed at the MRCISD+Q/aug-cc-pVTZ level of theory using a state-average CASSCF reference wave function. Analysis of the different electronic states for the CO2 → CO + O dissociation channel rationalizes the topography of this region of the PESs. The forward rates from QCT simulations match measurements between 15 K and 295 K whereas the equilibrium constant determined from the forward and reverse rates is consistent with that derived from statistical mechanics at high temperature. Vibrational relaxation, O + CO(ν = 1,2) → O + CO(ν = 0), is found to involve both, non-reactive and reactive processes. The contact time required for vibrational relaxation to take place is τ ≥ 150 fs for non-reacting and τ ≥ 330 fs for reacting (oxygen atom exchange) trajectories and the two processes are shown to probe different parts of the global potential energy surface. In agreement with experiments, low collision energy reactions for the C(3P) + O2(3Σg-, ν = 0) → CO(1Σ+) + O(1D) lead to CO(1Σ+, ν' = 17) with an onset at Ec ∼ 0.15 eV, dominated by the 1A' surface with contributions from the 3A' surface. Finally, the barrier for the COA(1Σ+) + OB(3P) → COB(1Σ+) + OA(3P) atom exchange reaction on the 3A' PES yields a barrier of ∼7 kcal mol-1 (0.300 eV), consistent with an experimentally reported value of 6.9 kcal mol-1 (0.299 eV).

Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N2O and dynamics for the N + NO ↔ O + N2 and N2 + O → 2N + O reactions.

Accurate potential energy surfaces (PESs) have been determined for the 3A' and 3A'' states of N2O using electronic structure calculations at the multireference configuration interaction level with Davidson correction (MRCI+Q) and the augmented Dunning-type correlation consistent polarized triple zeta (aug-cc-pVTZ) basis set. More than 20 000 MRCI+Q/aug-cc-pVTZ energies are represented using a reproducing kernel Hilbert space (RKHS) scheme. The RKHS PESs successfully describe all reactant channels with high accuracy and all minima and transition states connecting them are determined. Quasiclassical trajectory (QCT) simulations are then used to determine reaction rates for N + NO and O + N2 collisions. Vibrational relaxation N2(ν = 1) → N2(ν = 0) and dissociation of N2→ 2N for O + N2 collisions are also investigated using QCT. The agreement between results obtained from the QCT simulations and from available experiments is favourable for reaction and vibrational relaxation rates, which provides a test for the accuracy of the PESs. The PESs can be used to calculate more detailed state-to-state observables relevant for applications to hypersonic reentry.

Machine Learning for Observables: Reactant to Product State Distributions for Atom-Diatom Collisions.

Machine learning based models to predict product state distributions from a distribution of reactant conditions for atom-diatom collisions are presented and quantitatively tested. The models are based on function-, kernel-, and grid-based representations of the reactant and product state distributions. All three methods predict final state distributions from explicit quasi-classical trajectory simulations with R2 > 0.998. Although a function-based approach is found to be more than two times better in computational performance, the grid-based approach is preferred in terms of prediction accuracy, practicability, and generality. For the function-based approach, the choice of parametrized functions is crucial and this aspect is explicitly probed for final vibrational state distributions. Applications of the grid-based approach to nonequilibrium, multitemperature initial state distributions are presented, a situation common to energy and state distributions in hypersonic flows. The role of such models in direct simulation Monte Carlo and computational fluid dynamics simulations is also discussed.

Dynamics on Multiple Potential Energy Surfaces: Quantitative Studies of Elementary Processes Relevant to Hypersonics.

The determination of thermal and vibrational relaxation rates of triatomic systems suitable for application in hypersonic model calculations is discussed. For this, potential energy surfaces for ground and electronically excited state species need to be computed and represented with high accuracy, and quasiclassical or quantum nuclear dynamics simulations provide the basis for determining the relevant rates. These include thermal reaction rates, state-to-state cross sections, and vibrational relaxation rates. For exemplary systems (i.e., [NNO], [NOO], and [CNO]), all individual steps are described, and a literature overview for them is provided. Finally, as some of these quantities involve considerable computational expense, for the example of state-to-state cross sections, the construction of an efficient model based on neural networks is discussed. All such data is required and being used in more coarse-grained computational fluid dynamics simulations.

Luminescence measurements of hyperthermal Xe2+ + O2 and O+ + Xe collision systems.

Emission excitation cross sections are recorded for collisions between Xe2+ + O2 and O+ + Xe over a collision energy range of approximately 2 to 900 eV in the center-of-mass (Ecm) frame. Emissive products of the O+ + Xe reaction are examined in the 700-1000 nm optical range and include neutral atomic oxygen emissions and neutral xenon emissions. Atomic emission products of the O+ + Xe collision appear to have measureable cross sections near Ecm = 14 eV and increase in intensity until about Ecm = 60 eV where they remain approximately constant for the remainder of the measured collision energies. For the Xe2+ + O2 collision system, O2+ charge transfer products are measured through fluorescence of the O2+(A-X) and (b-a) manifolds over the 200-850 nm window. Total cross sections for both manifolds do not vary beyond the experimental precision at all measured energies. Vibrational populations are derived from a fitting of the experimental data. The populations are found to deviate from a Franck-Condon distribution at all collision energies and appear to be well-modeled within a multi-channel Landau-Zener framework over the collision energy range measured.

The N(4S) + O2(X3Σ) ↔ O(3P) + NO(X2Π) reaction: thermal and vibrational relaxation rates for the 2A', 4A' and 2A'' states.

The kinetics and vibrational relaxation of the N(4S) + O2(X3Σ-g) ↔ O(3P) + NO(X2Π) reaction is investigated over a wide temperature range based on quasiclassical trajectory simulations on 3-dimensional potential energy surfaces (PESs) for the lowest three electronic states. Reference energies at the multi reference configuration interaction level are represented as a reproducing kernel and the topology of the PESs is rationalized by analyzing the CASSCF wavefunction of the relevant states. The forward rate matches one measurement at 1575 K and is somewhat lower than the high-temperature measurement at 2880 K whereas for the reverse rate the computations are in good agreement for temperatures between 3000 and 4100 K. The temperature-dependent equilibrium rates are consistent with results from JANAF and CEA results. Vibrational relaxation rates for O + NO(ν = 1) → O + NO(ν = 0) are consistent with a wide range of experiments. This process is dominated by the dynamics on the 2A' and 4A' surfaces which both contribute similarly up to temperatures T ∼ 3000 K, and it is found that vibrationally relaxing and non-relaxing trajectories probe different parts of the potential energy surface. The total cross section depending on the final vibrational state monotonically decreases which is consistent with early experiments and previous simulations but at variance with other recent experiments which reported an oscillatory cross section.

Exhaustive state-to-state cross sections for reactive molecular collisions from importance sampling simulation and a neural network representation.

High-temperature, reactive gas flow is inherently nonequilibrium in terms of energy and state population distributions. Modeling such conditions is challenging even for the smallest molecular systems due to the extremely large number of accessible states and transitions between them. Here, neural networks (NNs) trained on explicitly simulated data are constructed and shown to provide quantitatively realistic descriptions which can be used in mesoscale simulation approaches such as Direct Simulation Monte Carlo to model gas flow at the hypersonic regime. As an example, the state-to-state cross sections for N(4S) + NO(2Π) → O(3P) + N2(X1Σg +) are computed from quasiclassical trajectory (QCT) simulations. By training NNs on a sparsely sampled noisy set of state-to-state cross sections, it is demonstrated that independently generated reference data are predicted with high accuracy. State-specific and total reaction rates as a function of temperature from the NN are in quantitative agreement with explicit QCT simulations and confirm earlier simulations, and the final state distributions of the vibrational and rotational energies agree as well. Thus, NNs trained on physical reference data can provide a viable alternative to computationally demanding explicit evaluation of the microscopic information at run time. This will considerably advance the ability to realistically model nonequilibrium ensembles for network-based simulations.

The C(3P) + NO(X2Π) → O(3P) + CN(X2Σ+), N(2D)/N(4S) + CO(X1Σ+) reaction: Rates, branching ratios, and final states from 15 K to 20 000 K.

The C + NO collision system is of interest in the area of high-temperature combustion and atmospheric chemistry. In this work, full dimensional potential energy surfaces for the 2A', 2A″, and 4A″ electronic states of the [CNO] system have been constructed following a reproducing kernel Hilbert space approach. For this purpose, more than 50 000 ab initio energies are calculated at the MRCI+Q/aug-cc-pVTZ level of theory. The dynamical simulations for the C(3P) + NO(X2Π) → O(3P) + CN(X2Σ+), N(2D)/N(4S) + CO(X1Σ+) reactive collisions are carried out on the newly generated surfaces using the quasiclassical trajectory (QCT) calculation method to obtain reaction probabilities, rate coefficients, and the distribution of product states. Preliminary quantum calculations are also carried out on the surfaces to obtain the reaction probabilities and compared with QCT results. The effect of nonadiabatic transitions on the dynamics for this title reaction is explored within the Landau-Zener framework. QCT simulations have been performed to simulate molecular beam experiment for the title reaction at 0.06 and 0.23 eV of relative collision energies. Results obtained from theoretical calculations are in good agreement with the available experimental as well as theoretical data reported in the literature. Finally, the reaction is studied at temperatures that are not practically achievable in the laboratory environment to provide insight into the reaction dynamics at temperatures relevant to hypersonic flight.

From in silica to in silico: retention thermodynamics at solid-liquid interfaces.

The dynamics of solvated molecules at the solid/liquid interface is essential for a molecular-level understanding for the solution thermodynamics in reversed phase liquid chromatography (RPLC). The heterogeneous nature of the systems and the competing intermolecular interactions makes solute retention in RPLC a surprisingly challenging problem which benefits greatly from modelling at atomistic resolution. However, the quality of the underlying computational model needs to be sufficiently accurate to provide a realistic description of the energetics and dynamics of systems, especially for solution-phase simulations. Here, the retention thermodynamics and the retention mechanism of a range of benzene-derivatives in C18 stationary-phase chains in contact with water/methanol mixtures is studied using point charge (PC) and multipole (MTP) electrostatic models. The results demonstrate that free energy simulations with a faithful MTP representation of the computational model provide quantitative and molecular level insight into the thermodynamics of adsorption/desorption in chromatographic systems while a conventional PC representation fails in doing so. This provides a rational basis to develop more quantitative and validated models for the optimization of separation systems.

Quantum and quasiclassical trajectory studies of rotational relaxation in Ar-N2+ collisions.

The collision of N2+ with Ar is studied using quantum and classical methods. The dynamics was followed on a new potential energy surface based on ab initio energies computed at the UCCSD(T)-F12a/aug-cc-pVTZ level, using the correct analytical long range behaviour and a reproducing kernel representation. Comparison with multi-reference MRCI+Q calculations establish that UCCSD(T)-F12a is a sufficiently high level of theory for this problem. Results from quantum close coupling and quasiclassical trajectory calculations agree favourably with each other and the rates for inelastic collisions are lower than those from Langevin theory. This differs from previous calculations on a zero point-corrected potential energy surface (PES) and indicates that such corrections, although potentially useful, should not be applied in the present case. Despite the rather large differences between the potential energy surfaces, the computed rates are within one order of magnitude of one another which suggests that the quality of the PES is not the main reason for the remaining disagreement between computation and experiment. Also, the fraction of inelastic rotational collisions exceeds 20% in all cases irrespective of whether quantum or classical dynamics is used. Previous experimental rate coefficients for N2+(ν = 0, j = 6) colliding with Ar suggest that the rotational quantum number is largely conserved. This can not be confirmed from any of the simulations and calls for new single molecule experiments.

Communication: Vibrational relaxation of CO(1Σ) in collision with Ar(1S) at temperatures relevant to the hypersonic flight regime.

Vibrational energy relaxation (VER) of diatomics following collisions with the surrounding medium is an important elementary process for modeling high-temperature gas flow. VER is characterized by two parameters: the vibrational relaxation time τvib and the state relaxation rates. Here the vibrational relaxation of CO(ν=0←ν=1) in Ar is considered for validating a computational approach to determine the vibrational relaxation time parameter (pτvib) using an accurate, fully dimensional potential energy surface. For lower temperatures, comparison with experimental data shows very good agreement whereas at higher temperatures (up to 25 000 K), comparisons with an empirically modified model due to Park confirm its validity for CO in Ar. Additionally, the calculations provide insight into the importance of Δν>1 transitions that are ignored in typical applications of the Landau-Teller framework.

Reactive collisions for NO(2Π) + N(4S) at temperatures relevant to the hypersonic flight regime.

The NO(X2Π) + N(4S) reaction which occurs entirely in the triplet manifold of N2O is investigated using quasiclassical trajectories and quantum simulations. Fully-dimensional potential energy surfaces for the 3A' and 3A'' states are computed at the MRCI+Q level of theory and are represented using a reproducing kernel Hilbert space. The N-exchange and N2-formation channels are followed by using the multi-state adiabatic reactive molecular dynamics method. Up to 5000 K these reactions occur predominantly on the N2O 3A'' surface. However, for higher temperatures the contributions of the 3A' and 3A'' states are comparable and the final state distributions are far from thermal equilibrium. From the trajectory simulations a new set of thermal rate coefficients of up to 20 000 K is determined. Comparison of the quasiclassical trajectory and quantum simulations shows that a classical description is a good approximation as determined from the final state analysis.

Integral cross section measurements and product recoil velocity distributions of Xe(2+) + N2 hyperthermal charge-transfer collisions.

Charge exchange from doubly charged rare gas cations to simple diatomics proceeds with a large cross section and results in populations of many vibrational and electronic product states. The charge exchange between Xe(2+) and N2, in particular, is known to create N2 (+) in both the A and B electronic states. In this work, we present integral charge exchange cross section measurements of the Xe(2+) + N2 reaction as well as axial recoil velocity distributions of the Xe(+) and N2 (+) product ions for collision energies between 0.3 and 100 eV in the center-of-mass (COM) frame. Total charge-exchange cross sections decrease from 70 Å(2) to about 40 Å(2) with increasing collision energy through this range. Analysis of the axial velocity distributions indicates that a Xe(2+) - N2 complex exists at low collision energies but is absent by 17.6 eV COM. Analysis of the axial velocity distributions reveals evidence for complexes with lifetimes comparable to the rotational period at low collision energies. The velocity distributions are consistent with quasi-resonant single charge transfer at high collision energies.

Collision-induced rotational excitation in N2 (+)((2)Σg (+),v=0)-Ar: Comparison of computations and experiment.

The collisional dynamics of N2 (+)((2)Σg (+)) cations with Ar atoms is studied using quasi-classical simulations. N2 (+)-Ar is a proxy to study cooling of molecular ions and interesting in its own right for molecule-to-atom charge transfer reactions. An accurate potential energy surface (PES) is constructed from a reproducing kernel Hilbert space (RKHS) interpolation based on high-level ab initio data. The global PES including the asymptotics is fully treated within the realm of RKHS. From several ten thousand trajectories, the final state distribution of the rotational quantum number of N2 (+) after collision with Ar is determined. Contrary to the interpretation of previous experiments which indicate that up to 98% of collisions are elastic and conserve the quantum state, the present simulations find a considerably larger number of inelastic collisions which supports more recent findings.

Communication: Equilibrium rate coefficients from atomistic simulations: The O((3)P) + NO((2)Π) → O2(X(3)Σg(-)) + N((4)S) reaction at temperatures relevant to the hypersonic flight regime.

The O((3)P) + NO((2)Π) → O2(X(3)Σg(-)) + N((4)S) reaction is among the N- and O- involving reactions that dominate the energetics of the reactive air flow around spacecraft during hypersonic atmospheric re-entry. In this regime, the temperature in the bow shock typically ranges from 1000 to 20,000 K. The forward and reverse rate coefficients for this reaction derived directly from trajectory calculations over this range of temperature are reported in this letter. Results compare well with the established equilibrium constants for the same reaction from thermodynamic quantities derived from spectroscopy in the gas phase which paves the way for large-scale in silico investigations of equilibrium rates under extreme conditions.