Machine Learning for Observables: Reactant to Product State Distributions for Atom-Diatom Collisions

Machine learning-based models to predict product state distributions from a distribution of reactant conditions for atom-diatom collisions are presented and quantitatively tested. The models are based on function-, kernel- and grid-based representations of the reactant and product state distributions. While all three methods predict final state distributions from explicit quasi-classical trajectory simulations with R$^2$ > 0.998, the grid-based approach performs best. Although a function-based approach is found to be more than two times better in computational performance, the kernel- and grid-based approaches are preferred in terms of prediction accuracy, practicability and generality. The function-based approach also suffers from lacking a general set of model functions. Applications of the grid-based approach to nonequilibrium, multi-temperature initial state distributions are presented, a situation common to energy distributions in hypersonic flows. The role of such models in Direct Simulation Monte Carlo and computational fluid dynamics simulations is also discussed

The C(3P) + NO(X2Π) → O(3P) + CN(X2Σ+), N(2D)/N(4S) + CO(X1Σ+) reaction: Rates, branching ratios, and final states from 15 K to 20 000 K

The C + NO collision system is of interest in the area of high-temperature combustion and atmospheric chemistry. In this work, full dimensional potential energy surfaces for the 2 A′, 2 A″, and 4 A″ electronic states of the [CNO] system have been constructed following a reproducing kernel Hilbert space approach. For this purpose, more than 50 000 ab initio energies are calculated at the MRCI+Q/aug-cc-pVTZ level of theory. The dynamical simulations for the C( 3 P) + NO(X 2 Π) → O( 3 P) + CN(X 2 Σ + ), N( 2 D)/N( 4 S) + CO(X 1 Σ + ) reactive collisions are carried out on the newly generated surfaces using the quasiclassical trajectory (QCT) calculation method to obtain reaction probabilities, rate coefficients, and the distribution of product states. Preliminary quantum calculations are also carried out on the surfaces to obtain the reaction probabilities and compared with QCT results. The effect of nonadiabatic transitions on the dynamics for this title reaction is explored within the Landau-Zener framework. QCT simulations have been performed to simulate molecular beam experiment for the title reaction at 0.06 and 0.23 eV of relative collision energies. Results obtained from theoretical calculations are in good agreement with the available experimental as well as theoretical data reported in the literature. Finally, the reaction is studied at temperatures that are not practically achievable in the laboratory environment to provide insight into the reaction dynamics at temperatures relevant to hypersonic flight

On the Effect of Aleatoric and Epistemic Errors on the Learnability and Quality of NN-based Potential Energy Surfaces

The effect of noise in the input data for learning potential energy surfaces (PESs) based on neural networks for chemical applications is assessed. Noise in energies and forces can result from aleatoric and epistemic errors in the quantum chemical reference calculations. Statistical (aleatoric) noise arises for example due to the need to set convergence thresholds in the self consistent field (SCF) iterations whereas systematic (epistemic) noise is due to, {\it inter alia}, particular choices of basis sets in the calculations. The two molecules considered here as proxies are H$_{2}$CO and HONO which are examples for single- and multi-reference problems, respectively, for geometries around the minimum energy structure. For H$_2$CO it is found that adding noise to energies with magnitudes representative of single-point calculations does not deteriorate the quality of the final PESs whereas increasing the noise level commensurate with electronic structure calculations for more complicated, e.g. metal-containing, systems is expected to have a more notable effect. However, the effect of noise on the forces is more noticeable. On the other hand, for HONO which requires a multi-reference treatment, a clear correlation between model quality and the degree of multi-reference character as measured by the $T_1$ amplitude is found. It is concluded that for chemically "simple" cases the effect of aleatoric and epistemic noise is manageable without evident deterioration of the trained model - although the quality of the forces is important. However, considerably more care needs to be exercised for situations in which multi-reference effects are present

Communication: Vibrational relaxation of CO(1Σ) in collision with Ar(1S) at temperatures relevant to the hypersonic flight regime

Vibrational energy relaxation (VER) of diatomics following collisions with the surrounding medium is an important elementary process for modeling high-temperature gas flow. VER is characterized by two parameters: the vibrational relaxation time τ vib and the state relaxation rates. Here the vibrational relaxation of CO( ν = 0 ← ν = 1) in Ar is considered for validating a computational approach to deter- mine the vibrational relaxation time parameter ( p τ vib ) using an accurate, fully dimensional potential energy surface. For lower temperatures, comparison with experimental data shows very good agree- ment whereas at higher temperatures (up to 25 000 K), comparisons with an empirically modified model due to Park confirm its validity for CO in Ar. Additionally, the calculations provide insight into the importance of ∆ ν > 1 transitions that are ignored in typical applications of the Landau-Teller framework

Collision-induced rotational excitation in N2 (+)((2)Σg (+),v=0)-Ar: Comparison of computations and experiment

The collisional dynamics of N2 (+)((2)Σg (+)) cations with Ar atoms is studied using quasi-classical simulations. N2 (+)-Ar is a proxy to study cooling of molecular ions and interesting in its own right for molecule-to-atom charge transfer reactions. An accurate potential energy surface (PES) is constructed from a reproducing kernel Hilbert space (RKHS) interpolation based on high-level ab initio data. The global PES including the asymptotics is fully treated within the realm of RKHS. From several ten thousand trajectories, the final state distribution of the rotational quantum number of N2 (+) after collision with Ar is determined. Contrary to the interpretation of previous experiments which indicate that up to 98% of collisions are elastic and conserve the quantum state, the present simulations find a considerably larger number of inelastic collisions which supports more recent findings

Accurate Reproducing Kernel-Based Potential Energy Surfaces for the Triplet Ground States of N2_2O and Dynamics for the N+NO↔\leftrightarrowO+N2_2 and N2_2+O→\rightarrow2N+O Reactions

Accurate potential energy surfaces (PESs) have been determined for the $^3$A$'$ and $^3$A$''$ states of N$_2$O using electronic structure calculations at the multireference configuration interaction level with Davidson correction (MRCI+Q) and the augmented Dunning-type correlation consistent polarize triple zeta (aug-cc-pVTZ) basis set. More than 20000 MRCI+Q/aug-cc-pVTZ energies are represented using a reproducing kernel Hilbert space (RKHS) interpolation scheme. The RKHS PESs successfully describe all reactant channels with high accuracy. The analytical PESs are characterized by computing the minima and transition states on it. Quasiclassical dynamics simulations are then used to determine thermal and vibrational relaxation rates for the N+NO and O+N$_2$ collisions. The agreement between results obtained from the simulations and from available experiments is favourable for both types of observables, which provides a test for the accuracy of the PESs. The PESs can be used to calculate more detailed state-to-state observables relevant for applications to hypersonic reentry.Comment: 32 pages, 11 figure

Exhaustive state-to-state cross sections for reactive molecular collisions from importance sampling simulation and a neural network representation

High-temperature, reactive gas flow is inherently nonequilibrium in terms of energy and state population distributions. Modeling such con- ditions is challenging even for the smallest molecular systems due to the extremely large number of accessible states and transitions between them. Here, neural networks (NNs) trained on explicitly simulated data are constructed and shown to provide quantitatively realistic descrip- tions which can be used in mesoscale simulation approaches such as Direct Simulation Monte Carlo to model gas flow at the hypersonic regime. As an example, the state-to-state cross sections for N( 4 S) + NO( 2 Π ) → O( 3 P) + N 2 (X 1 Σ + g ) are computed from quasiclassical trajectory (QCT) simulations. By training NNs on a sparsely sampled noisy set of state-to-state cross sections, it is demonstrated that independently generated reference data are predicted with high accuracy. State-specific and total reaction rates as a function of temperature from the NN are in quantitative agreement with explicit QCT simulations and confirm earlier simulations, and the final state distributions of the vibra- tional and rotational energies agree as well. Thus, NNs trained on physical reference data can provide a viable alternative to computationally demanding explicit evaluation of the microscopic information at run time. This will considerably advance the ability to realistically model nonequilibrium ensembles for network-based simulations

The N(4S) + O2(X3Sigma) O(3P) + NO(X2Pi) reaction: thermal and vibrational relaxation rates for the 2A', 4A' and 2A'' states

The kinetics and vibrational relaxation of the N(4S) + O2(X3Sigma-g) O(3P) + NO(X2Pi) reaction is investigated over a wide temperature range based on quasiclassical trajectory simulations on 3-dimensional potential energy surfaces (PESs) for the lowest three electronic states. Reference energies at the multi reference configuration interaction level are represented as a reproducing kernel and the topology of the PESs is rationalized by analyzing the CASSCF wavefunction of the relevant states. The forward rate matches one measurement at 1575 K and is somewhat lower than the high-temperature measurement at 2880 K whereas for the reverse rate the computations are in good agreement for temperatures between 3000 and 4100 K. The temperature-dependent equilibrium rates are consistent with results from JANAF and CEA results. Vibrational relaxation rates for O + NO(nu = 1) O + NO(nu = 0) are consistent with a wide range of experiments. This process is dominated by the dynamics on the 2A' and 4A' surfaces which both contribute similarly up to temperatures T 3000 K, and it is found that vibrationally relaxing and non-relaxing trajectories probe different parts of the potential energy surface. The total cross section depending on the final vibrational state monotonically decreases which is consistent with early experiments and previous simulations but at variance with other recent experiments which reported an oscillatory cross section