Exhaustive state-to-state cross sections for reactive molecular collisions from importance sampling simulation and a neural network representation
Reactive and nonreactive scattering at high impact velocities involves sub-picosecond dynamics of the atomic and molecular species participating in the process. During atmospheric reentry, a space vehicle is exposed to a collisionally dense environment which generates an immensely diverse population of ro-vibrational states of the collision partners. For reaction network modeling of this complex chemistry an exhaustive enumeration of all possible state-to-state collision cross sections is mandatory. However, due to the large number of states (≈ 10⁴) for each collision partner), there are of the order of 10⁸ such cross sections. Determining those from converged quasiclassical trajectory or even quantum wavepacket calculations is not possible. Here we show that training a neural network on a small subset of converged state-to-state cross sections from QCT simulations for the N + NO(v, j) → O + N₂(v' j') reaction provides such a quantitatively realistic description and a computationally extremely efficient model.

FIG. 1. (A) 3D surface (upper panel) and contour color map (lower panel) of QCT calculated and NN predicted state-to-state cross sections for N + NO(v, j) → O + N₂(v' j') at Et = 2.5 eV. (B) Distributions of product vibrational and rotational states and ro-vibrational energies calculated from QCT (blue) and predicted by the NN (red), respectively, for the N + NO → O + N₂ reaction at different temperatures.

Explicitly computing and converging all state-to-state cross section even for elementary atom + diatom reactions is computationally prohibitive because thousands to millions of trajectories are required to statistically converge each of them. In the present work, a total of ≈ 8 x 10⁶ state-to-state cross sections have been explicitly determined from QCT simulations for selectively chosen 1232 reactant ro-vibrational states and relative translational energies.
Local averaging over the product ro-vibrational states (v' j') was performed to reduce the noise of the data set, and importance sampling is used to sample impact parameters for the trajectories which accelerates the convergence of the QCT cross sections. An NN has been trained on ≈ 3 x 10⁶ QCT data and the best model parameter are chosen by validating on another set of ≈ 3 x 10⁵ QCT data.
Although typical training time takes a few days, the evaluation time of the NN for 10⁶ state-to-state cross sections is only a few seconds. It is demonstrated that independently generated reference QCT data are predicted by the NN model with high accuracy, see Figure 1. State-specific and total reaction rates as a function of temperature from the NN are in quantitative agreement with explicit QCT simulations and the final state distributions of the vibrational and rotational states agree as well. Thus, NNs trained on large physical reference data can provide a viable alternative to computationally demanding explicit evaluation of the microscopic information at run time.

See also: AIP - The Journal of Chemical Physics, Editor's Pick

Reference: Koner, D., Unke, O.T., Boe, K., Bemish, R.J., and Meuwly, M. (2019). Exhaustive state-to-state cross sections for reactive molecular collisions from importance sampling simulation and a neural network representation. J Chem Phys 150, 211101.(10.1063/1.5097385)