Rovibrational energy transfer and dissociation in O2-O collisions

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.

State-to-state study of non-equilibrium recombination of oxygen and nitrogen molecules

Rapidly cooled mixtures are of interest for several applications, including hypersonic flows due to the presence of strong cooling temperature gradients in regions such as hypersonic boundary layers and expanding nozzles. There have been very few studies of rapidly cooled mixtures using the high-fidelity rovibrational databases afforded by ab initio potential energy surfaces. This work makes use of existing rovibrational state-specific databases to study rapidly cooled mixtures. In particular, we seek to understand the importance of thermal non-equilibrium in recombining mixtures using both rovibrational and vibrational state-to-state methods for oxygen and nitrogen molecules. We find that although there is significant non-equilibrium during recombination, it is well captured by the vibrational state-specific approach. Finally, we compare the global recombination rate computed based on the state-specific recombination rate coefficients and the global recombination rate computed based on the time local dissociation rate coefficient, which is reversed using the principle of detailed balance. The local dissociation rate coefficient is computed by weighting the state-specific dissociation rate coefficients with the state-specific distribution of energy states. We find a large difference between these rates, highlighting a potential source of errors in hypersonic flow predictions.

Molecular Dynamics Simulation of Thermal Nonequilibrium and Chemical Reaction Processes in Hydrogen Combustion

Using reactive force field (ReaxFF) and molecular dynamics simulation, we investigate the combustion process of hydrogen-oxygen systems in initial thermal nonequilibrium states with different translational and rovibrational temperatures for oxygen. The system studied in this work contains 300 oxygen molecules and 700 hydrogen molecules with a density of 7 times the air density. For this system, the characteristic relaxation times of oxygen and hydrogen vibrational energies are 0.173 and 0.249 ns, respectively. 0.6% of hydrogen undergoes a chemical reaction with oxygen during the thermal nonequilibrium relaxation stage. For the distribution of translational energy and vibrational energy of oxygen in the thermal nonequilibrium state, the maximum mean error of the statistical distribution in the simulation and the Boltzmann distribution at temperature calculated from the average kinetic energy of molecules is about 2.25 × 10-5. At the same time, it was observed in the simulation that many-body interactions play a certain role in the combustion process. Furthermore, we compare the ignition time and temperature rise behavior of different combustion mechanisms and molecular dynamics simulations starting from the thermal equilibrium state. These results will provide meaningful references for the construction of thermal nonequilibrium combustion chemical reaction mechanisms.

Quasi-classical trajectory analysis of three-body collision induced recombination in neutral nitrogen and oxygen

We present theory and a simulation framework to model three-body collisions and gas phase recombination in dilute atom/diatom mixtures of pure oxygen (O/O2) and nitrogen (N/N2) using the Quasi-Classical Trajectory method. We formulate a three-body collision rate constant based on the lifetimes of binary collisions and initialize three-body collisions by sampling the arrival time of a third body within the lifetimes of pre-simulated binary collisions. We use this method to calculate distributions of recombined product energies, probabilities of recombination, and recombination rate constants through different collision pathways. Long-lived binary atom-diatom collisions are observed, but are too rare to play a dominant role in the recombination process for shock-heated air near the equilibrium conditions studied. The resulting recombination rate constants are within an order of magnitude of the predictions of detailed balance. Notably, the recombination simulation framework does not appeal to the principle of detailed balance and could be useful for studying conditions far from equilibrium.

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.

State-to-State Transition Study of the Exchange Reaction for N(4S) and O2(X3Σg-) Collision by Quasi-Classical Trajectory

Based on the new ²A' and ⁴A' potential energy surfaces of NO₂ fitted by Varga et al., we conducted a quasi-classical trajectory study on the N(⁴S) +O₂(X³Σ_g^- ) → NO(²Π) + O(³P) reaction, focusing on the high vibrational state up to ν = 25. For different rovibrational states of O₂, within the relative translational energy (E_c) range of 0.1-30 eV, the total exchange cross section (ECS) is calculated, and it is found that the initial relative translational energy and vibration excitation have a significant effect on ECSs, while rotational excitation has little influence; the rate coefficient of the high rovibrational state of O₂ molecules at high temperatures is studied, and it is found that when the vibrational level ν of O₂ is in the range of 0-15, the value of log₁₀ k(T, ν, j) with the vibrational level ν is almost linear, while when ν is greater than 15, it becomes gentle with the increase in ν. Finally, the state-to-state rate coefficients are calculated; our results supply the advantageous state-to-state process data in the NO₂ system, and they are useful for further studying the related hypersonic gas flow at very high temperature.

Reactive, Inelastic, and Dissociation Processes in Collisions of Atomic Nitrogen with Molecular Oxygen

Collisions of atomic nitrogen with molecular oxygen have been treated with the quasiclassical trajectory method (QCT) in order to obtain a complete database of vibrationally detailed cross sections and rate coefficients for reactive, inelastic, and dissociation processes. For reaction rate coefficients, the agreement with experimental and theoretical data in the literature is excellent on the whole available interval 300-5000 K, with reliable extension to 20,000 K. For the inelastic case and for dissociation, no comparisons are available; therefore, a study of QCT reliability is proposed. In the inelastic case, it is found that "purely inelastic" and "quasireactive" collisions show not only different mechanisms but also different QCT levels of reliability at low energy. For dissociation, similar considerations bring to the conclusion that for the present collisional system, the QCT method is appropriate on the whole energy range studied. Rate coefficients for all the processes studied are provided in the electronic form.

Rovibrationally state-specific collision model for the O2(Σg-3) + O(P3) system in DSMC

A rovibrationally state-specific collision model for the O₂(Σg-3)+O(P3) system is presented for direct simulation Monte Carlo, including rotation-vibration-translation energy transfer, exchange, dissociation, and recombination processes. The two-step binary collision approach is employed to model recombination reactions. Two available cross section databases by Andrienko/Boyd and Esposito/Capitelli are employed for the rovibrationally resolved model (rv-STS) and vibrationally resolved model (v-STS), respectively. The difference between rv-STS and v-STS comes from two contributions: the multisurface factor of dissociation (f_MS) and the rotational averaging process. The dissociation cross section with the constant f_MS is typically larger than with the variable f_MS, especially for the low vibrational energy states. On the other hand, the cross sections resulting from the rotationally averaged database are found to underpredict the dissociation rate coefficient at low temperatures. In the rovibrational heating case, the rv-STS predicts faster relaxation than the v-STS, which also shows a lower quasi-steady-state temperature than v-STS. In the rovibrational cooling case, the rv-STS shows a faster relaxation than v-STS, which also presents a thermal non-equilibrium between rovibrational and translational mode during the cooling process.

Shock wave propagation through air: a reactive molecular dynamics study

Shock compression of air is observed in numerous situations ranging from explosions to hypersonic vehicle entry into atmosphere. In an effort to develop continuum-based equation of state for air subjected to shock compression, it is necessary to understand the dynamics of the shock compression process with regards to formation of new chemical species in air at the molecular level. With this in perspective, three different models of air (consisting a mixture of O 2 , N 2 and CO 2 gas, with or without H 2 O based on presence of humidity) are subjected to shock compression ranging from 0.5 km s −1 to 5.0 km s −1 particle velocities. Thermodynamic quantities are evaluated to plot Rankine Hugoniot planes for the three different air models: dry air at mean sea level (MSL), humid air at MSL and dry air at high altitude level of 36 000 ft above MSL. It is observed that high shock velocities eventually results in dissociation of gaseous molecules and formation of new gaseous species which has been quantified in the manuscript.

Data-Inspired and Physics-Driven Model Reduction for Dissociation: Application to the O2 + O System

This work presents an in-depth discussion on the nonequilibrium dissociation of O₂ molecules colliding with O atoms, combining quasi-classical trajectory calculations, master equation, and dimensionality reduction. A rovibrationally resolved database for all of the elementary collisional processes is constructed by including all nine adiabatic electronic states of O₃ in the QCT calculations. A detailed analysis of the ab initio data set reveals that for a rovibrational level, the probability of dissociating is mostly dictated by its deficit in internal energy compared to the centrifugal barrier. Because of the assumption of rotational equilibrium, the conventional vibrational-specific calculations fail to characterize such a dependence. Based on this observation, a new physics-based grouping strategy for application to coarse-grained models is proposed. By relying on a hybrid technique made of rovibrationally resolved excitation coupled to coarse-grained dissociation, the new approach is compared to the vibrational-specific model and the direct solution of the rovibrational state-to-state master equation. Simulations are performed in a zero-dimensional isothermal and isochoric chemical reactor for a wide range of temperatures (1500-20,000 K). The study shows that the main contribution to the model inadequacy of vibrational-specific approaches originates from the incapability of characterizing dissociation, rather than the energy transfers. Even when constructed with only twenty groups, the new reduced-order model outperforms the vibrational-specific one in predicting all of the QoIs related to dissociation kinetics. At the highest temperature, the accuracy in the mole fraction is improved by 2000%.

State-to-State Master Equation and Direct Molecular Simulation Study of Energy Transfer and Dissociation for the N2-N System

We present a detailed comparison of two high-fidelity approaches for simulating non-equilibrium chemical processes in gases: the state-to-state master equation (StS-ME) and the direct molecular simulation (DMS) methods. The former is a deterministic method, which relies on the pre-computed kinetic database for the N₂-N system based on the NASA Ames ab initio potential energy surface (PES) to describe the evolution of the molecules' internal energy states through a system of master equations. The latter is a stochastic interpretation of molecular dynamics relying exclusively on the same ab initio PES. It directly tracks the microscopic gas state through a particle ensemble undergoing a sequence of collisions. We study a mixture of nitrogen molecules and atoms forced into strong thermochemical non-equilibrium by sudden exposure of rovibrationally cold gas to a high-temperature heat bath. We observe excellent agreement between the DMS and StS-ME predictions for the transfer rates of translational into rotational and vibrational energy, as well as of dissociation rates across a wide range of temperatures. Both methods agree down to the microscopic scale, where they predict the same non-Boltzmann population distributions during quasi-steady-state dissociation. Beyond establishing the equivalence of both methods, this cross-validation helped in reinterpreting the NASA Ames kinetic database and resolve discrepancies observed in prior studies. The close agreement found between the StS-ME and DMS methods, whose sole model inputs are the PESs, lends confidence to their use as benchmark tools for studying high-temperature air chemistry.

The importance of O3 excited potential energy surfaces in O2-O high-temperature kinetics

The mechanism of vibrational relaxation and dissociation in the O₂-O system at elevated temperatures is investigated by means of molecular dynamics. The most recent O₃ potential energy surfaces (PESs), obtained from the first principles quantum mechanical calculations [Varga et al., J. Chem. Phys. 147, 154312 (2017)], are used to derive a complete set of state-specific rate coefficients of vibrational energy transfer and dissociation. Unlike most of the previous efforts that utilize only the lowest and supposedly most reactive 1¹A' O₃ PES [A. Varandas and A. Pais, Mol. Phys. 65, 843 (1988)], this paper demonstrates the necessity to account for a complete ensemble of all excited O₃ PESs that correlate with O₂(X) and O(³P) when high-temperature kinetics is of interest. At the same time, it is found that the Varandas 1¹A' O₃ PES adequately describes vibrational energy transfer and dissociating dynamics when compared to the most recent 1¹A' O₃ PES by Varga et al. [J. Chem Phys. 147, 154312 (2017)]. The differences between this new dataset and previous rate coefficients are quantified by the master equation model.

Principal component analysis acceleration of rovibrational coarse-grain models for internal energy excitation and dissociation

The present work introduces a novel approach for obtaining reduced chemistry representations of large kinetic mechanisms in strong non-equilibrium conditions. The need for accurate reduced-order models arises from compression of large ab initio quantum chemistry databases for their use in fluid codes. The method presented in this paper builds on existing physics-based strategies and proposes a new approach based on the combination of a simple coarse grain model with Principal Component Analysis (PCA). The internal energy levels of the chemical species are regrouped in distinct energy groups with a uniform lumping technique. Following the philosophy of machine learning, PCA is applied on the training data provided by the coarse grain model to find an optimally reduced representation of the full kinetic mechanism. Compared to recently published complex lumping strategies, no expert judgment is required before the application of PCA. In this work, we will demonstrate the benefits of the combined approach, stressing its simplicity, reliability, and accuracy. The technique is demonstrated by reducing the complex quantum N₂(Σg+1)-N(Su4) database for studying molecular dissociation and excitation in strong non-equilibrium. Starting from detailed kinetics, an accurate reduced model is developed and used to study non-equilibrium properties of the N₂(Σg+1)-N(Su4) system in shock relaxation simulations.

Dissociation cross section for high energy O2-O2 collisions

Collision-induced dissociation cross section database for high energy O₂-O₂ collisions (up to 30 eV) is generated and published using the quasiclassical trajectory method on the singlet, triplet, and quintet spin ground state O₄ potential energy surfaces. At equilibrium conditions, these cross sections predict reaction rate coefficients that match those obtained experimentally. The main advantage of the cross section database based on ab initio computations is in the study of complex flows with high degree of non-equilibrium. Direct simulation Monte Carlo simulations using the reactive cross section databases are carried out for high enthalpy hypersonic oxygen flow over a cylinder at rarefied ambient conditions. A comparative study with the phenomenological total collision energy chemical model is also undertaken to point out the difference and advantage of the reported ab initio reaction model.

Vibrational energy transfer and dissociation in O2-N2 collisions at hyperthermal temperatures

Simulation of vibrational energy transfer and dissociation in O₂-N₂ collisions is conducted using the quasi-classical trajectory method on an ab initio potential energy surface. Vibrationally resolved rate coefficients are obtained in a high-temperature region between 8000 and 20 000 K by means of the cost-efficient classical trajectory propagation method. A system of master equations is constructed using the new dataset in order to simulate thermal and chemical nonequilibrium observed in shock flows. The O₂ relaxation time derived from a solution of the master equations is in good agreement with the Millikan and White correlation at lower temperatures with an increasing discrepancy toward the translational temperature of 20 000 K. At the same time, the N₂ master equation relaxation time is similar to that derived under the assumption of a two-state system. The effect of vibrational-vibrational energy transfer appears to be crucial for N₂ relaxation and dissociation. Thermal equilibrium and quasi-steady state dissociation rate coefficients in O₂-N₂ heat bath are reported.

Construction of a coarse-grain quasi-classical trajectory method. I. Theory and application to N2-N2 system

This work aims to construct a reduced order model for energy transfer and dissociation in non-equilibrium nitrogen mixtures. The objective is twofold: to present the Coarse-Grain Quasi-Classical Trajectory (CG-QCT) method, a novel framework for constructing a reduced order model for diatom-diatom systems; and to analyze the physics of non-equilibrium relaxation of the nitrogen molecules undergoing dissociation in an ideal chemical reactor. The CG-QCT method couples the construction of the reduced order model under the coarse-grain model framework with the quasi-classical trajectory calculations to directly construct the reduced model without the need for computing the individual rovibrational specific kinetic data. In the coarse-grain model, the energy states are lumped together into groups containing states with similar properties, and the distribution of states within each of these groups is prescribed by a Boltzmann distribution at the local translational temperature. The required grouped kinetic properties are obtained directly by the QCT calculations. Two grouping strategies are considered: energy-based grouping, in which states of similar internal energy are lumped together, and vibrational grouping, in which states with the same vibrational quantum number are grouped together. A zero-dimensional chemical reactor simulation, in which the molecules are instantaneously heated, forcing the system into strong non-equilibrium, is used to study the differences between the two grouping strategies. The comparison of the numerical results against available experimental data demonstrates that the energy-based grouping is more suitable to capture dissociation, while the energy transfer process is better described with a vibrational grouping scheme. The dissociation process is found to be strongly dependent on the behavior of the high energy states, which contribute up to 50% of the dissociating molecules. Furthermore, up to 40% of the energy required to dissociate the molecules comes from the rotational mode, underscoring the importance of accounting for this mode when constructing non-equilibrium kinetic models. In contrast, the relaxation process is governed primarily by low energy states, which exhibit significantly slower transitions in the vibrational binning model due to the prevalence of mode separation in these states.

Nonequilibrium internal energy distributions during dissociation

In this work, we propose a model for nonequilibrium vibrational and rotational energy distributions in nitrogen using surprisal analysis. The model is constructed by using data from direct molecular simulations (DMSs) of rapidly heated nitrogen gas using an ab initio potential energy surface (PES). The surprisal-based model is able to capture the overpopulation of high internal energy levels during the excitation phase and also the depletion of high internal energy levels during the quasi-steady-state (QSS) dissociation phase. Due to strong coupling between internal energy and dissociation chemistry, such non-Boltzmann effects can influence the overall dissociation rate in the gas. Conditions representative of the flow behind strong shockwaves, relevant to hypersonic flight, are analyzed. The surprisal-based model captures important molecular-level nonequilibrium physics, yet the simple functional form leads to a continuum-level expression that now accounts for the underlying energy distributions and their coupling to dissociation.

Adaptive coarse graining method for energy transfer and dissociation kinetics of polyatomic species

A novel reduced-order method is presented for modeling reacting flows characterized by strong non-equilibrium of the internal energy level distribution of chemical species in the gas. The approach seeks for a reduced-order representation of the distribution function by grouping individual energy states into macroscopic bins, and then reconstructing state population using the maximum entropy principle. This work introduces an adaptive grouping methodology to identify and lump together groups of states that are likely to equilibrate faster with respect to each other. To this aim, two algorithms have been considered: the modified island algorithm and the spectral clustering method. Both methods require a measure of dissimilarity between internal energy states. This is achieved by defining "metrics" based on the strength of the elementary rate coefficients included in the state-specific kinetic mechanism. Penalty terms are used to avoid grouping together states characterized by distinctively different energies. The two methods are used to investigate excitation and dissociation of N₂ (Σg+1) molecules due to interaction with N(Su4) atoms in an ideal chemical reactor. The results are compared with a direct numerical simulation of the state-specific kinetics obtained by solving the master equations for the complete set of energy levels. It is found that adaptive grouping techniques outperform the more conventional uniform energy grouping algorithm by providing a more accurate description of the distribution function, mole fraction and energy profiles during non-equilibrium relaxation.

Dissociation cross sections for N2 + N → 3N and O2 + O → 3O using the QCT method

Cross sections for the homo-nuclear atom-diatom collision induced dissociations (CIDs): N₂ + N and O₂ + O are calculated using Quasi-Classical Trajectory (QCT) method on ab initio Potential Energy Surfaces (PESs). A number of studies for these reactions carried out in the past focused on the CID cross section values generated using London-Eyring-Polanyi-Sato PES and seldom listed the CID cross section data. A highly accurate CASSCF-CASPT2 N₃ and a new O₃ global PES are used for the present QCT analysis and the CID cross section data up to 30 eV relative energy are also published. In addition, an interpolating scheme based on spectroscopic data is introduced that fits the CID cross section for the entire ro-vibrational spectrum using QCT data generated at chosen ro-vibrational levels. The rate coefficients calculated using the generated CID cross section compare satisfactorily with the existing experimental and theoretical results. The CID cross section data generated will find an application in the development of a more precise chemical reaction model for Direct Simulation Monte Carlo code simulating hypersonic re-entry flows.