In this article we present a comparative atomic level study analyzing the vibrational ex-citation and dissociation of molecular nitrogen due to N2(1Eg+) + N(4Su) and N2(1Eg+) + N2(1 sigma g+) interactions governed by independently developed potential energy surfaces at the University of Minnesota and NASA Ames Research Center. Vibrational excitation was studied for N2 + N2 interactions from T = 10 000 to 25 000 K and for N2 + N from T = 5000 to 30 000 K. Nonequilibrium dissociation is studied from T = 10 000 to 30 000 K under the quasi-steady-state condition for N2 + N2 and N2 + N interactions. Finally, an inviscid Mach 20 dissociating nitrogen flow over a cylinder with a Knudsen number of 0.015 is carried out to study the impact of molecular interactions predicted by independently developed potential energy surfaces on a canonical hypersonic flow.

HCN is an important molecule in interstellar chemistry, atmospheric reentry as well as combustion. This paper presents the construction of the ground state singlet HCN potential energy surface (PES), $^1A'$ and state-to-state (StS) kinetics of the molecule-atom systems associated with HCN. The ground state HCN surface is associated to the ground state of CN ($^2\Sigma^+$) and NH ($^3\Sigma^-$) and the first excited state of CH ($^4\Sigma^-$). Multi-reference configuration interaction calculations are used to compute the ab-initio points on a grid of geometries for the diatomic potentials and the full PES. A total of 11688 ab-initio points are used to construct the potential energy surface.The diatomic potentials are fit to the Modified Morse functional form and the potential energy surface fit is obtained using a permutationally invariant polynomial neural network (PIP-NN). The RMS error in the potential energy surface fit are is upto 0.2 eV in the 0-25 eV energy range. The PES constructed highlights some important topological features. Firstly, the exchange of CH and NH to CN is barrier-less and second, the potential energy surface is characterized by two deep wells corresponding to HCN and HNC molecules in their ground singlet states. The considerably larger depth of the CN molecule diatomic potential and the barrier-less exchange pathway make exchange reactions and exchange assisted dissociation important kinetic features of the system. The potential energy surface constructed is used to carry out quasi-classical trajectory calculations followed by state-to-state isothermal heat bath simulations to study macroscopic quantities of interest to atmospheric entry. Furthermore, the exchange associated dissociation in CH and NH causes the dissociation to happen an order of magnitude faster in time when compared to only direct dissociation with the contribution due to exchange being $84.7\%$ and $82.5\%$ in the dissociation source terms, respectively.

Understanding the kinetics of the HCN system is critical to several disciplines in science and engineering, including interstellar chemistry, atmospheric reentry, and combustion, to name a few. This paper constructs a rovibrational state-specific kinetic mechanism for the HCN system, leveraging electronic structure calculations, classical scattering dynamics, and state-to-state kinetics. To this aim, three accurate potential energy surfaces (PESs), 1A', 3A', and 3A″, are constructed using multireference configuration interaction (MRCI) calculations for a comprehensive arrangement of the nuclei. Quasi-classical scattering calculations provide elementary reaction rate constants resulting from the interaction between the CN, CH, and NH molecules with H, N, and C atoms, respectively. The rovibrational collisional model developed comprises 50 million bound-bound and free-bound collisional processes. This model is used to study the dynamics of energy transfer and dissociation in an isochoric and isothermal chemical reactor via the solution of the master equation for a wide temperature range from 1000 to 10,000 K. This study unravels the dynamics of dissociation of the molecules in the HCN system, which the PESs primarily control via the formation of short-lived intermediates that shortcut the dissociation pathway. The exchange processes in CH and NH enhance the dissociation by over 80%. The importance of exchange processes is also highlighted in comparing the quasi-steady state and thermal dissociation rates with state-of-the-art rate models and experimental fits.

This paper studies the thermochemistry and electronic structure of small carbon clusters and hydrocarbons which are major constituents of pyrolysis gases released into the boundary layer of ablating heat shields. Our focus lies on clusters of up to four carbon atoms including C3H and C4H. A study of electronically excited states of these molecules computed using the EOM-CCSD method has revealed C4 and C4H to be potential sources of radiation absorption in the boundary layer. We also study the effect of low-lying excited electronic states on the thermodynamics in the high temperature regime and show that neglecting these states records a difference of upto 12% in the computed Cp values. Finally, comparisons of the equilibrium mole fractions obtained using the thermodynamics computed in this paper with the existing state-of-the-art tables used for hypersonic applications (for example JANAF and Gurvich Tables) show an order of magnitude difference in the mixture compositions.

We present a method to generate analytical coarse-grain cross sections for internal energy excitation and dissociation of nitrogen and apply it to the NASA Ames N-2 - N ab initio database. State-resolved cross sections from this database are reduced using the Uniform RoVibrational-Collisional bin model. With a 10-bin system as example we compare two sets of coarse-grain cross sections: one obtained by analytical inversion and another by direct binning. With analytical inversion we manage to compress the entire set of state-resolved data into a small set of parameters, sufficient to reconstruct the main features of the full database. This has the potential of massively reducing the computational cost in large-scale direct simulation Monte Carlo (DSMC) calculations, both concerning memory requirements and execution time. Combining this coarse-grain model with the N-2 - N ab initio database will enable much higher-fidelity DSMC simulation of nonequilibrium dissociation in shock-heated flows than is currently possible with conventional models.

A technique to compute vibrationally resolved transport collision integrals for atom-diatom systems directly from ab inito potential energy surfaces (PES) is presented. These calculations are performed for the oxygen systems employing the Varga et al. set of PES, and Guyta-Yos style fits to the data are provided. It is found that simple empirical models are often unable to capture the dependence of these collision integrals on the vibrational state of the molecule. Differences of up to 80% are observed between the model predictions and the values computed directly from the PES.

This work introduces a novel methodology for the quantification of uncertainties associated with potential energy surfaces (PESs) computed from first-principles quantum mechanical calculations. The methodology relies on Bayesian inference and machine learning techniques to construct a stochastic PES and to express the inadequacies associated with the ab initio data points and their fit. By combining high fidelity calculations and reduced-order modeling, the resulting stochastic surface is efficiently forward propagated via quasi-classical trajectory and master equation calculations. In this way, the PES contribution to the uncertainty on predefined quantities of interest (QoIs) is explicitly determined. This study is done at both microscopic (e.g., rovibrational-specific rate coefficients) and macroscopic (e.g., thermal and chemical relaxation properties) levels. A correlation analysis is finally applied to identify the PES regions that require further refinement, based on their effects on the QoI reliability. The methodology is applied to the study of singlet (11A') and quintet (25A') PESs describing the interaction between O2 molecules and O atoms in their ground electronic state. The investigation of the singlet surface reveals a negligible uncertainty on the kinetic properties and relaxation times, which are found to be in excellent agreement with the ones previously published in the literature. On the other hand, the methodology demonstrated significant uncertainty on the quintet surface, due to inaccuracies in the description of the exchange barrier and the repulsive wall. When forward propagated, this uncertainty is responsible for the variability of 1 order of magnitude in the vibrational relaxation time and of factor four in the exchange reaction rate coefficient, both at 2500 K.

The development of a new generation of ablative thermal protection systems based on carbon-phenolic composite materials demands the accurate determination of transport properties of pyrolysis gases mixed in various atmospheres. The present work provides recommended collision data for the calculation of the transport properties for Mars and Earth re-entries. A review of available potential data is given for species in the atmospheres of Earth and Mars. Additional data are provided for species formed during the degradation of the theoretical ablative composite for open testing material. Dipole polarizabilities are calculated from ab initio methods and used for the calculation of transport properties of reduced pyrolysis mixtures over a temperature range representative of the boundary layer for atmospheric entry flows.

The focus of this work is on carbon clusters, hydrocarbons and other carbonaceous species which are constituents of pyrolysis gases injected into the boundary layer. Some of these molecules are observed to have absorption spectra in the VUV and UV region that match the emission spectra of atomic nitrogen and oxygen. Hence, they can potentially absorb the radiation impinging on the heat shield. Accurate thermodynamic data is not available for many of these species over the relevant temperature range for reentry. The objective of this work is to determine the thermochemical properties of potential radiation absorbing molecules using accurate ab initio quantum chemistry calculations. We have compiled a database of formation enthalpies, anharmonic vibrational frequencies and rotational constants for the ground and lowlying excited electronic states of these carbonaceous species. Using these thermochemical properties, we compute equilibrium mole fractions and observe that the mole fractions of some species of interest are significant, thus they could affect the radiative heat flux. Furthermore, comparisons of the formation enthalpies and mole fractions are made with data from literature.

Recent work in the aerothermodynamics community has focused on the development of reduced-order models for thermo-chemical non-equilibrium which avoid the restrictive assumptions of multi-temperature models and the prohibitive cost associated with State-to-State (StS) models. In the present work, this is accomplished by lumping energy states together and assuming groups of states are roughly in equilibrium. As a result, the non-equilibrium behavior of a gas can be captured at a reduced computational cost from a full StS simulation. In this work, we present a hybrid grouping model for studying energy transfer and dissociation in a mixture of nitrogen molecules due to N 2 -N 2 reactions. This is accomplished by making use of a grouping strategy informed by data from the N 2 N StS kinetic data. [1] However, due to the massive computational cost associated with constructing StS data for the N 2 -N 2 system, the kinetic data for the hybrid grouping model are calculated using the quasi-classical trajectory (QCT) method by sampling states for trajectory within the groups. [2,3] This general framework is called the Maximum-Entropy Quasi-Classical Trajectory (ME-QCT) method. The primary challenge associated with this method is that rates for reverse grouped reactions cannot be obtained through detailed balance at a group level, due to the variation of group internal temperatures. To construct the full model for N 2 -N 2 grouped kinetics using the ME-QCT method, detailed balance is invoked at the microscopic level, allowing for the calculation of the full kinetic data from QCT. Results will be presented using the full ME-QCT model for the N 2 -N 2 system in an isothermal and isochoric reactor simulation. In addition, simple CFD test cases for a one-dimensional standing shock and for a quasi-one-dimensional nozzle will be used for demonstration of the ME-QCT method. This method allows for the calculation of

Carbon clusters and hydrocarbons are constituents of the pyrolysis gases injected into the boundary layer of a space vehicle with a carbonaceous heat shield. These molecules have absorption spectra in the VUV and UV region that match the emission spectra of atomic nitrogen and oxygen. Hence, they can potentially absorb the radiation impinging on the heat shield of the space vehicle. This paper studies the ground state thermochemical properties and low-lying excited electronic states of potential radiation absorbing molecules present in the boundary layer using ab initio quantum chemistry methods. These results provide a more accurate prediction of the radiative heat flux on the surface which can lead to improvement in the design of the thermal protection 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.

Comparisons are made between potential energy surfaces (PES) for N2 + N and N2 + N2 collisions and between rate coefficients for N2 dissociation that were computed using the quasiclassical trajectory method (QCT) on these PESs. For N2 + N we compare the Laganà's empirical LEPS surface with one from NASA Ames Research Center based on ab initio quantum chemistry calculations. For N2 + N2 we compare two ab initio PESs (from NASA Ames and from the University of Minnesota). These use different methods for computing the ground state electronic energy for N4, but give similar results. Thermal N2 dissociation rate coefficients, for the 10,000K-30,000K temperature range, have been computed using each PES and the results are in excellent agreement. Quasi-stationary state (QSS) rate coefficients using both PESs have been computed at these temperatures using the Direct Molecular Simulation of Schwartzentruber and coworkers. The QSS rate coefficients are up to a factor of 5 lower than the thermal ones and the thermal and QSS values bracket the results of shock-tube experiments. We conclude that the combination of ab initio quantum chemistry PESs and QCT calculations provides an attractive approach for the determination of accurate high-temperature rate coefficients for use in aerothermodynamics modeling.

In this work we present a molecular level study of N2+N collisions, focusing on excitation of internal energy modes and non-equilibrium dissociation. The computation technique used here is the direct molecular simulation (DMS) method and the molecular interactions have been modeled using an ab−initio potential energy surface (PES) developed at NASA's Ames Research Center. We carried out vibrational excitation calculations between 5000K and 30000K and found that the characteristic vibrational excitation time for the N + N2 process was an order of magnitude lower than that predicted by the Millikan and White correlation. It is observed that during vibrational excitation the high energy tail of the vibrational energy distribution gets over populated first and the lower energy levels get populated as the system evolves. It is found that the non-equilibrium dissociation rate coefficients for the N + N2 process are larger than those for the N2 + N2 process. This is attributed to the non-equilibrium vibrational energy distributions for the N + N2 process being less depleted than that for the N2 +N2 process. For an isothermal simulation we find that the probability of dissociation goes as 1/T(sub tr) for molecules with internal energy (epsilon(sub int)) less than approximately 9.9eV, while for molecules with epsilon (sub int) greater than 9.9eV the dissociation probability was weakly dependent on translational temperature of the system. We compared non-equilibrium dissociation rate coefficients and characteristic vibrational excitation times obtained by using the ab-initio PES developed at NASA's Ames Research Center to those obtained by using an ab-initio PES developed at the University of Minnesota. Good agreement was found between the macroscopic properties and molecular level description of the system obtained by using the two PESs.

This paper represents a summary of results to date of an on-going effort at NASA Ames Research Center to develop a physics-based non-equilibrium model for hypersonic entry into the Martian atmosphere. Our approach is to first compute potential energy surfaces based on accurate solutions of the electronic Schroedinger equation and then use quasiclassical trajectory calculations to obtain reaction cross sections and rate coefficients based on these potentials. We have presented new rate coefficients for N2 dissociation and CO dissociation and exchange reactions. These results illustrate shortcomings with some of the rate coefficients in Parks original T-Tv model for Mars entries and with some of the 30-45 year old shock tube data. We observe that the shock tube experiments of CO + O dissociation did not adequately account for the exchange reaction that leads to formation of C + O2. This reaction is actually the primary channel for CO removal in the shock layer at temperatures below 10,000 K, because the reaction enthalpy for exchange is considerably lower than the comparable value for dissociation.

Vibrationally excited CO 2 , formed by two-body recombination from CO( 1 Σ + ) and O( 3 P) in the wake behind spacecraft entering the Martian atmosphere, is believed to be responsible for the higher than anticipated radiative heating of the backshell, compared to pre-flight predictions. This process involves a spin-forbidden transition of the transient triplet CO 2 molecule to the longer-lived singlet. To accurately predict the singlet-triplet transition probability and estimate the thermal rate coefficient of the recombination reaction, ab initio methods were used to compute the first singlet and three lowest-energy triplet CO 2 potential energy surfaces and the spin-orbit coupling matrix elements between these states. Analytical fits to these four potential energy surfaces were generated for surface hopping trajectory calculations, using Tully’s fewest switches surface hopping algorithm. Preliminary results for the trajectory calculations are presented. The calculated probability of a CO( 1 Σ + ) + O( 3 P) collision leading to singlet CO 2 formation is on the order of 10 -4 . The predicted flowfield conditions for various Mars entry scenarios predict temperatures in the range of 1000K-4000K and pressures in the range of 300-2500 Pa at the shoulder and in the wake, which is consistent with a heavy-particle collision frequency of 10 6 to 10 7 s -1 . Owing to this low collision frequency, it is likely that CO 2 ( 1 Σ g+ ) molecules formed by this mechanism will mostly be frozen in a highly nonequilibrium rovibrational energy state until they relax by photoemission.

Accurate thermodynamic properties for species found in carbon–phenolic gas mixtures are essential in predicting material response and heating of carbon–phenolic heat shields of planetary entry vehicles. A review of available thermodynamic data for species found in mixtures of carbon–phenolic pyrolysis and ablation gases and atmospheres rich with C, H, O, and N such as those of Earth, Mars, Titan, and Venus, is performed. Over 1200 unique chemical species are identified from four widely used thermodynamic databases and a systematic procedure is described for combining these data into a comprehensive model. The detailed dataset is then compared with the Chemical Equilibrium with Applications thermodynamic database developed by NASA in order to quantify the differences in equilibrium thermodynamic properties obtained with the two databases. In addition, a consistent reduction methodology using the mixture thermodynamic properties as an objective function is developed to generate reduced species sets for a variety of temperature, pressure, and elemental composition spaces. It is found that 32 and 23 species are required to model carbon–phenolic pyrolysis gases mixed with air and CO2, respectively, to maintain a maximum error in thermodynamic quantities below 10%.