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

Abstract

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.

Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N2O and dynamics for the N + NO ↔ O + N2and N2+ O → 2N + O reactions

“…This level of theory has been found to describe the electronic structures for the C-, N-, O-containing species quite well for the global PES. 27,37,39 State-averaged complete active space self-consistent field [47][48][49][50] calculations were carried out prior to the MRCI calculations in order to obtain a smooth topology of the MRCI PESs. In the State-averaged CASSCF calculations a total of eight states were included (the two lowest states from each spin (singlet and triplet) and spatial (A 0 and A 00 ) symmetry).…”

“…36 and 52 and has also been used to construct PESs for other triatomic systems. [37][38][39] Fig. 1 Schematic energy diagram for the N 2 O system showing different reactant channels, minima (MIN i) and transition states (TS i).…”

“…where b max is the maximum impact parameter for which the event can occur. The impact parameters are sampled using stratified sampling 37,54,59 by subdividing the interval between 0 and b max into six equidistant strata. The rate for an event x on surface i at a particular temperature T is then obtained as…”

“…where, k f (T) and k r (T) are the forward and reverse reaction rate at temperature T. In the rate calculations, for each trajectory the initial relative translational energies of the reactants are sampled from a Maxwell-Boltzmann distribution and ro-vibrational states of the reactant diatom is sampled from a Boltzmann distribution at temperature T. 37,54 For the vibrational relaxation simulations, all trajectories were initialized in the n = 1 state while the rotational states were sampled from a Boltzmann distribution at the corresponding temperature.…”

“…On the other hand the reproducing kernel Hilbert space (RKHS) interpolation procedure can capture the correct long range behavior for different types of interactions. [36][37][38][39] Another relevant quantity that balances the energy content of hot gas flow is the exchange and relaxation of vibrational energy which can also be determined from QCT simulations. 40,41 This property has been found to be sensitive to different regions of the PES than reaction rates 39 and provides an additional possibility to validate the quality of the PESs.…”