Quasiclassical molecular dynamic calculations of vibrationally and rotationally state selected dissociation cross-sections: N+N2(v,j)→3N

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.

Formation Mechanisms of Electronically Excited Nitrogen Molecules from N + N2 and N + N + N Collisions Revealed by Full-Dimensional Potential Energy Surfaces

This work reports six new full-dimensional adiabatic potential energy surfaces (PESs) of the N3 system (four 4A″ states and two 2A″ states) at the MRCI + Q/AVQZ level of theory that correlated to N2(X1Σg+) + N(4S), N2(X1Σg+) + N(2D), N2(A3Σu+) + N(4S), N2(B3Πg) + N(4S), N2(W3Δu) + N(4S), and N(4S) + N(4S) + N(4S) channels. The neural networks with a proper account of the nuclear permutation invariant symmetry of N3 were employed to fit the PESs based on about 4000 ab initio points. The accuracy of the PESs was validated by excellent agreement on the equilibrium bond length, vertical excitation energy, and dissociation energy with experimental values. Two possible mechanisms of the formation of N2(A) were found. One is that the collision occurs between N2(X) and N(4S) in the 14A″ state, followed by a nonadiabatic transition through the conical intersection with the 24A″ PES, resulting in the formation of the N2(A) + N(4S) product. The other takes place in the collision among three N(4S) atoms in the adiabatic 24A″ state, and then, N2(A) + N(4S) is formed. This is the first systematical research of the N3 system focusing on the formation of the excited states of N2 via both adiabatic and nonadiabatic pathways.

Potential energy surface for high-energy N + N2 collisions

Potential energy surface calculations yield physical insight into the structure of intermediates and the dynamics of molecular collisions, and they are the first step toward molecular simulations that provide physical insight into energy transfer, reaction, and dissociation probabilities. The potential energy surface for high-energy collisions of N₂ with N can be used for modeling chemical dynamics and energy transfer in atmospheric shock waves. Here we present an analytic ground-state. (⁴A'') potential energy surface for N₃ that governs electronically adiabatic collisions of N₂(¹Σ+g) with N(⁴S). The fitted surface consists of a pairwise potential based on an accurate diatomic potential energy curve plus a connected permutationally invariant polynomial (PIP) in mixed-exponential-Gaussian bond order variables (MEGs) for the three-body part. The three-body fit is based on multireference complete active space second order perturbation theory (CASPT2) calculations. The quality of the quartet N₃ fit is comparable to that for a previous fit of the NO₂ potential. We characterize two local minima of N₃, two tight transition structures, two van der Waals geometries, and the noncollinear reaction path for the symmetric exchange reaction. The nonreactive approach of an N atom to N₂ along the perpendicular bisector is more repulsive than the collinear reproach, but plots of the force on the bond versus the potential energy at the distance of closest approach allow us to infer that vibrational energy transfer should occur much more readily in high-energy collinear collisions than in high-energy perpendicular-bisector collisions.

Coarse-grained modeling of thermochemical nonequilibrium using the multigroup maximum entropy quadratic formulation

This work addresses the construction of a reduced-order model based on a multigroup maximum entropy formulation for application to high-enthalpy nonequilibrium flows. The method seeks a piecewise quadratic representation of the internal energy-state populations by lumping internal energy levels into groups and by applying the maximum entropy principle in conjunction with the method of moments. The use of higher-order polynomials allows for an accurate representation of the logarithm of the distribution of the low-lying energy states, while preserving an accurate description of the linear portions of the logarithm of the distribution function that characterize the intermediate- and high-energy states. A comparison of the quadratic and the linear reconstructions clearly demonstrates how the higher-order reconstruction provides a more accurate representation of the internal population distribution function at a modest increase in the computational cost. Numerical simulations carried out under conditions relevant to hypersonic flight reveal that the proposed model is able to capture the dynamics of the nonequilibrium distribution function using as few as three groups, thereby reducing the computational costs for simulations of nonequilibrium flows.

Coupling of state-resolved rovibrational coarse-grain model for nitrogen to stochastic particle method for simulating internal energy excitation and dissociation

We propose to couple a state-resolved rovibrational coarse-grain model to a stochastic particle method for simulating internal energy excitation and dissociation of a molecular gas. A coarse-grained model for a rovibrational reaction mechanism of an ab initio database developed at the NASA Ames Research Center for the N₂-N system is modified based on variably spaced energy bins. The thermodynamic properties of the modified coarse-grained model allow us to closely match those obtained with the full set of rovibrational levels over a wide temperature range, while using a number of bins significantly smaller than the complete mechanism. The chemical-kinetic behavior of equally and variably spaced bin formulations is compared by simulating internal energy excitation and dissociation of nitrogen in an adiabatic, isochoric reactor. We find that the variably spaced formulation is better suited for reproducing the dynamics of the full database at conditions of interest in the Earth atmospheric entry. Also in this paper, we discuss the details of our particle method implementation for the uniform rovibrational collisional bin model and describe changes to the Direct Simulation Monte Carlo (DSMC) collision algorithm, which become necessary to accommodate our state-resolved reaction mechanism for excitation and dissociation reactions. The DSMC code is then verified against equivalent master equation calculations. In these simulations, state-resolved cross sections are used in analytical form. These cross sections verify micro-reversibility relations for the rovibrational bins and allow for fast execution of the DSMC code. In our verification calculations, we obtain very close agreement for the concentrations profiles of N and N₂, as well as the translational and rovibrational mode temperatures obtained independently through both methods. In addition to macroscopic moments, we compare discrete internal energy populations predicted at selected time steps via DSMC and the master equations. We observe good agreement between the two sets of results within the limits imposed by statistical scatter, which is inherent to particle-based DSMC solutions. As future work, the rovibrational coarse-grain model coupled to the particle method will allow us to study 3D reentry flow configurations.

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.

An ab initio chemical reaction model for the direct simulation Monte Carlo study of non-equilibrium nitrogen flows

A new ab initio based chemical model for a Direct Simulation Monte Carlo (DSMC) study suitable for simulating rarefied flows with a high degree of non-equilibrium is presented. To this end, Collision Induced Dissociation (CID) cross sections for N₂+N₂→N₂+2N are calculated and published using a global complete active space self-consistent field-complete active space second order perturbation theory N₄ potential energy surface and quasi-classical trajectory algorithm for high energy collisions (up to 30 eV). CID cross sections are calculated for only a selected set of ro-vibrational combinations of the two nitrogen molecules, and a fitting scheme based on spectroscopic weights is presented to interpolate the CID cross section for all possible ro-vibrational combinations. The new chemical model is validated by calculating equilibrium reaction rate coefficients that can be compared well with existing shock tube and computational results. High-enthalpy hypersonic nitrogen flows around a cylinder in the transition flow regime are simulated using DSMC to compare the predictions of the current ab initio based chemical model with the prevailing phenomenological model (the total collision energy model). The differences in the predictions are discussed.

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.

Boltzmann rovibrational collisional coarse-grained model for internal energy excitation and dissociation in hypersonic flows

A Boltzmann rovibrational collisional coarse-grained model is proposed to reduce a detailed kinetic mechanism database developed at NASA Ames Research Center for internal energy transfer and dissociation in N(2)-N interactions. The coarse-grained model is constructed by lumping the rovibrational energy levels of the N(2) molecule into energy bins. The population of the levels within each bin is assumed to follow a Boltzmann distribution at the local translational temperature. Excitation and dissociation rate coefficients for the energy bins are obtained by averaging the elementary rate coefficients. The energy bins are treated as separate species, thus allowing for non-Boltzmann distributions of their populations. The proposed coarse-grained model is applied to the study of nonequilibrium flows behind normal shock waves and within converging-diverging nozzles. In both cases, the flow is assumed inviscid and steady. Computational results are compared with those obtained by direct solution of the master equation for the rovibrational collisional model and a more conventional multitemperature model. It is found that the proposed coarse-grained model is able to accurately resolve the nonequilibrium dynamics of internal energy excitation and dissociation-recombination processes with only 20 energy bins. Furthermore, the proposed coarse-grained model provides a superior description of the nonequilibrium phenomena occurring in shock heated and nozzle flows when compared with the conventional multitemperature models.

Simple model for vibration-translation exchange at high temperatures: effects of multiquantum transitions on the relaxation of a N2 gas flow behind a shock

In this paper a simple model is proposed for computation of rate coefficients related to vibration-translation transitions based on the forced harmonic oscillator theory. This model, which is developed by considering a quadrature method, provides rate coefficients that are in very good agreement with those found in the literature for the high temperature regime (≳10,000 K). This model is implemented to study a one-dimensional nonequilibrium inviscid N(2) flow behind a plane shock by considering a state-to-state approach. While the effects of ionization and chemical reactions are neglected in our study, our results show that multiquantum transitions have a great influence on the relaxation of the macroscopic parameters of the gas flow behind the shock, especially on vibrational distributions of high levels. All vibrational states are influenced by multiquantum processes, but the effective number of transitions decreases inversely according to the vibrational quantum number. For the initial conditions considered in this study, excited electronic states are found to be weakly populated and can be neglected in modeling. Moreover, the computing time is considerably reduced with the model described in this paper compared to others found in the literature.

The shape of the potential energy surface and the thermal rate coefficients of the N + N2 reaction

Full-dimensional quantum time-dependent calculations of the detailed probabilities of the N + N2 reaction have been performed on different potential energy surfaces, initial quantum states, and total angular momentum quantum numbers. The calculations allowed a rationalization of the effect of both moving the saddle to reaction out of collinearity and lowering its height. On some of these surfaces, more extended studies of the reactive dynamics of the system were performed. On one of them also, thermal rate coefficients were computed using J = 0 quantum probabilities and the J-shift model after testing the applicability of such a model against centrifugal sudden results. A comparison of the calculated thermal rate coefficients with theoretical and experimental data available from the literature is also made, and possible effects of inserting an intermediate well at the top of the saddle are argued.

On the semiclassical initial value calculation of thermal rate coefficients for the N+N2 reaction

In this paper we compare semiclassical initial value representation, conventional transition state theory with Wigner and Eckart tunneling correction, quantum reduced dimensionality, and quasiclassical thermal rate coefficients for N+N(2) exchange reaction.

Quantum study of the N+N2 exchange reaction: State-to-state reaction probabilities, initial state selected probabilities, Feshbach resonances, and product distributions

We report a detailed three-dimensional time-dependent quantum dynamics study of the state-to-state N+N(2) exchange scattering in the 2.1-3.2 eV range using a recently developed ab initio potential energy surface (PES). The reactive flux arrives at the dividing surface in the asymptotic product region in a series of six packets, instead of a single packet. Further study shows that these features arise from the "Lake Eyring" region of the PES, a region with a shallow well between two transition states. Trappings due to Feshbach resonances are found to be the major cause of the time delay. A detailed analysis of the Feshbach resonance features is carried out using an L(2) calculation of the metastable states in the "Lake Eyring" region. Strong resonance features are found in the state-to-state and initial state selected reaction probabilities. The metastable states with bending motions and/or bending coupled with stretching motions are found to be the predominant source of the resonance structure. Initial state selected reaction probabilities further indicate that the lifetimes of the metastable states with bending motions in the "Lake Eyring" region are longer than those of states with stretching motions and thus dominate the reactive resonances. Resonance structures are also visible in some of the integral cross sections and should provide a means for future experimental observation of the resonance behavior. A study of the final rotational distributions shows that, for the energy range studied here, the final products are distributed toward high-rotational states. Final vibrational distributions at the temperatures 2000 and 10,000 K are also reported.

Nonequilibrium kinetics of a radiative CO flow behind a shock wave

An investigation is presented of a highly nonequilibrium CO flow with consistently coupled vibrational energy exchanges, chemical reactions, and radiation. A detailed state-to-state model taking into account vibration-vibration, vibration-translation, and vibration-electronic transitions, dissociation-recombination reactions, and radiative transitions between vibrational and electronic states is developed on the basis of kinetic theory methods. A closed set of master equations for vibration-electronic level populations, number densities of atomic species, radiation intensity, temperature, and velocity is derived, and a one-dimensional inviscid carbon monoxide flow behind a plane shock wave is studied numerically. Several models of vibrational transition and dissociation rates in high temperature carbon monoxide are tested, and a model satisfying both accuracy and feasibility requirements is recommended. The role of various energy transfers and chemical reactions in the formation of nonequilibrium vibrational distributions in a shock heated CO flow is studied, and the influence of state-to-state distributions on macroscopic flow parameters and radiation intensity is discussed.