Jason D. Bender

An improved potential energy surface and multi-temperature quasiclassical trajectory calculations of N2 + N2 dissociation reactions

Accurate modeling of high-temperature hypersonic flows in the atmosphere requires consideration of collision-induced dissociation of molecular species and energy transfer between the translational and internal modes of the gas molecules. Here, we describe a study of the N2 + N2⟶N2 + 2N and N2 + N2⟶4N nitrogen dissociation reactions using the quasiclassical trajectory (QCT) method. The simulations used a new potential energy surface for the N4 system; the surface is an improved version of one that was presented previously. In the QCT calculations, initial conditions were determined based on a two-temperature model that approximately separates the translational-rotational temperature from the vibrational temperature of the N2 diatoms. Five values from 8000 K to 30,000 K were considered for each of the two temperatures. Over 2.4 × 10(9) trajectories were calculated. We present results for ensemble-averaged dissociation rate constants as functions of the translational-rotational temperature T and the vibrational temperature T(v). The rate constant depends more strongly on T when T(v) is low, and it depends more strongly on T(v) when T is low. Quasibound reactant states contribute significantly to the rate constants, as do exchange processes at higher temperatures. We discuss two sets of runs in detail: an equilibrium test set in which T = T(v) and a nonequilibrium test set in which T(v) < T. In the equilibrium test set, high-v and moderately-low-j molecules contribute most significantly to the overall dissociation rate, and this state specificity becomes stronger as the temperature decreases. Dissociating trajectories tend to result in a major loss of vibrational energy and a minor loss of rotational energy. In the nonequilibrium test set, as T(v) decreases while T is fixed, higher-j molecules contribute more significantly to the dissociation rate, dissociating trajectories tend to result in a greater rotational energy loss, and the dissociation probabilitys dependence on v weakens. In this way, as T(v) decreases, rotational energy appears to compensate for the decline in average vibrational energy in promoting dissociation. In both the equilibrium and nonequilibrium test sets, in every case, the average total internal energy loss in the dissociating trajectories is between 10.2 and 11.0 eV, slightly larger than the equilibrium potential energy change of N2 dissociation.

Direct molecular simulation of nitrogen dissociation based on an ab initio potential energy surface

The direct molecular simulation (DMS) approach is used to predict the internal energy relaxation and dissociation dynamics of high-temperature nitrogen. An ab initio potential energy surface (PES) is used to calculate the dynamics of two interacting nitrogen molecules by providing forces between the four atoms. In the near-equilibrium limit, it is shown that DMS reproduces the results obtained from well-established quasiclassical trajectory (QCT) analysis, verifying the validity of the approach. DMS is used to predict the vibrational relaxation time constant for N2–N2 collisions and its temperature dependence, which are in close agreement with existing experiments and theory. Using both QCT and DMS with the same PES, we find that dissociation significantly depletes the upper vibrational energy levels. As a result, across a wide temperature range, the dissociation rate is found to be approximately 4–5 times lower compared to the rates computed using QCT with Boltzmann energy distributions. DMS calculations predict a quasi-steady-state distribution of rotational and vibrational energies in which the rate of depletion of high-energy states due to dissociation is balanced by their rate of repopulation due to collisional processes. The DMS approach simulates the evolution of internal energy distributions and their coupling to dissociation without the need to precompute rates or cross sections for all possible energy transitions. These benchmark results could be used to develop new computational fluid dynamics models for high-enthalpy flow applications.

Potential energy surface fitting by a statistically localized, permutationally invariant, local interpolating moving least squares method for the many-body potential: Method and application to N4

Fitting potential energy surfaces to analytic forms is an important first step for efficient molecular dynamics simulations. Here, we present an improved version of the local interpolating moving least squares method (L-IMLS) for such fitting. Our method has three key improvements. First, pairwise interactions are modeled separately from many-body interactions. Second, permutational invariance is incorporated in the basis functions, using permutationally invariant polynomials in Morse variables, and in the weight functions. Third, computational cost is reduced by statistical localization, in which we statistically correlate the cutoff radius with data point density. We motivate our discussion in this paper with a review of global and local least-squares-based fitting methods in one dimension. Then, we develop our method in six dimensions, and we note that it allows the analytic evaluation of gradients, a feature that is important for molecular dynamics. The approach, which we call statistically localized, permutationally invariant, local interpolating moving least squares fitting of the many-body potential (SL-PI-L-IMLS-MP, or, more simply, L-IMLS-G2), is used to fit a potential energy surface to an electronic structure dataset for N4. We discuss its performance on the dataset and give directions for further research, including applications to trajectory calculations.

Potential energy surfaces of quintet and singlet O4

We present global ground-state potential energy surfaces for the quintet and singlet spin states of the O4 system that are suitable for treating high-energy vibrational-rotational energy transfer and collision-induced dissociation in electronically adiabatic, spin-conserving O2-O2 collisions. The surfaces are based on MS-CASPT2/maug-cc-pVTZ electronic structure calculations with scaled external correlation. The active space has 16 electrons in 12 orbitals. The calculations cover nine kinds of geometrical arrangements corresponding to dissociative diatom-diatom collisions of O2, geometries corresponding to O3-O, geometries identified by running trajectories, and geometries along linear synchronous transit paths. The global ground-state potential energy surfaces were obtained by a many-body approach with an accurate O-O pairwise interaction and a fit of the many-body interaction to 12 684 electronic structure data points for the singlet and 10 543 electronic structure data points for the quintet. The many-body fit is based on permutationally invariant polynomials in terms of bond-order functions of the six interatomic distances; the bond-order functions are mixed exponential-Gaussian functions.

Direct simulation of rovibrational excitation and dissociation in molecular nitrogen using an ab initio potential energy surface

We present an atomic-level study of vibrational excitation and chemical dissociation in molecular nitrogen at high temperature. The computational techniques, quasiclassical trajectory calculations (QCT) and classical trajectory calculation direct simulation Monte Carlo (CTC DSMC), solely rely on the specification of a highly accurate ab initio surface for N2-N2 interactions. We show that the simulations accurately reproduce the vibrational relaxation times obtained from the Millikan-White correlation and further support existing high-temperature corrections. Using both QCT and CTC DSMC methods with the same PES, we show that dissociation proceeds 4 to 5 times faster under equilibrium conditions compared to quasi-steady-state nonequilibrium conditions. At high translational energies (20,000 K and 30,000 K), the overall vibrational energy ladder is depleted, and dissociation proceeds at a rate approximately corresponding to a lower vibrational temperature. Conversely, at lower energies (10,000 K), almost no dissociation occurs from low-lying vibrational energy states. In this case, even a slight depletion of the upper-level vibrational energy states, which preferentially dissociate and are not rapidly re-populated due to slow bound-bound energy transfer mechanisms, causes a remarkable reduction of the dissociation rate. The ab initio CTC DSMC method is able to directly simulate rovibrational excitation and dissociation processes without computing the large number of cross-sections required by a state-resolved approach, and can be used directly to form new CFD models.

Implementation and Comparisons of Parallel Implicit Solvers for Hypersonic Flow Computations on Unstructured Meshes

A study of parallel implicit solvers for accelerating convergence to steady state solutions of the compressible Navier-Stokes equations with finite-rate chemistry is presented. The solvers in question are pertinent to applications of hypersonic flows that can be modeled as laminar, or to turbulent flows that can be simulated using the Reynolds averaged (RANS) equations. The current state-of-the-art method, the Data-Parallel Line Relaxation (DPLR), is examined. Its convergence properties are evaluated for a class of challenging external aerodynamics problems. A more sophisticated method based on the GMRES linear system solver is built around the DPLR method, where the DPLR is used as a preconditioner. The convergence characteristics of the augmented method are studied for model problems of practical interest. Results show that the more sophisticated method has better convergence properties, but exhibits higher cost and should be used selectively.

Calculating high-temperature thermodynamic properties of diatomics in air: Evaluation and accuracy assessment

Construction of a set of thermodynamic properties for air at high temperature is required for accurate modeling of hypersonic flow phenomena. Here we concentrate on the main diatomic species in air: N2, O2 and NO, and we use both state-sum and virial coefficient methods to calculate thermodynamic properties from 200K to 14,000K. We examine the results of these calculations and compare and contrast both methods, and also compare our results with those of other workers. Finally, we assess the accuracy one can realistically expect to obtain for these diatomic properties as the temperature increases to 14,000K and beyond, and the practical implications of these accuracy limitations.