Inelastic N$$_2$$+H$$_2$$ collisions and quantum-classical rate coefficients: large datasets and machine learning predictions

Abstract

Rate coefficients for vibrational energy transfer are calculated for collisions between molecular nitrogen and hydrogen in a wide range of temperature and of initial vibrational states ($$v\le 40$$ v ≤ 40 for N$$_2$$ 2 and $$w\le 10$$ w ≤ 10 for H$$_2$$ 2 ). These data are needed for the modelling of discharges in N$$_2$$ 2 /H$$_2$$ 2 plasma or of atmospheric and interstellar medium chemistry in different temperature ranges. The calculations were performed by a mixed quantum-classical method, to recover quantum effects associated with the vibrational motion, on a refined potential energy surface. The obtained rates present striking discrepancies with those evaluated by first-order perturbation theories, like the SSH (Schwartz, Slavsky, Herzfeld) theory, which are often adopted in kinetic modelling. In addition, we present a detailed, though preliminary, analysis on the performance of different Machine Learning models based on the Gaussian Process or Neural Network techniques to produce complete datasets of inelastic scattering rate coefficients. Eventually, by using the selected models, we give the complete dataset (i.e., covering the whole vibrational ladder) of rate coefficients for the $$\textrm{N}_2(v)+\textrm{H}_2(0) \longrightarrow \textrm{N}_2(v-\Delta v)+\textrm{H}_2(0)$$ N 2 ( v ) + H 2 ( 0 ) ⟶ N 2 ( v - Δ v ) + H 2 ( 0 ) , $$\Delta v=1,2,3$$ Δ v = 1 , 2 , 3 processes. Graphical abstract

Improved Quantum–Classical Treatment of N2–N2 Inelastic Collisions: Effect of the Potentials and Complete Rate Coefficient Data Sets

“…The discrepancies in the whole temperature range are however more reliable than those obtained by the first-order theory or by widely employed extrapolation techniques, which might present orders of magnitude differences with the calculated data (see, e.g. , ref ). For the highest v = 54, the rate coefficients are very different both at low (up to 2 orders of magnitude) and high (a factor of 3) temperatures.…”

“…The same settings employed in ref 21 are adopted: a Matern kernel where an extra parameter (i.e., ν, taken here equal to 5/2) in the covariance function is used to specify the smoothness of the resulting function. We employed the GPR approach as implemented in scikit-learn 52 (the code is freely available at ref 53), as recently done in ref 13, where we compared the performance of two different machine learning techniques (i.e., GPR and artificial neural network) to predict rate coefficients for the inelastic scattering collisions between N 2 and H 2 . It is found that, as far as interpolation is concerned, i.e., the v values for which rates are predicted fall within the interval of calculated v, GPR is able to perform very well in terms of test set mean squared error (MSE) values.…”

“…It is found that, as far as interpolation is concerned, i.e., the v values for which rates are predicted fall within the interval of calculated v, GPR is able to perform very well in terms of test set mean squared error (MSE) values. 13 Similar to what has been done in ref 13, the level of confidence of the predicted values is estimated by computing the test set average MSEs, which are reported in Figure S1 in the Supporting Information for different GPR models. For each model, we computed the average MSE value among all possible test sets obtained by removing the MQC rate coefficients of one particular initial vibrational state at a time (apart from the first and last vibrational state).…”

“…It is found that, as far as interpolation is concerned, i.e. , the v values for which rates are predicted fall within the interval of calculated v , GPR is able to perform very well in terms of test set mean squared error (MSE) values …”

“…In the last years, we tackled this problem by using a combined strategy consisting of the application of a mixed quantum–classical (MQC) dynamics method, allowing the quantum description of molecular vibrations and rotational–vibrational coupling, and a classical representation of the remaining degrees of freedom, and an analytical nonreactive PES, built according to the improved Lennard-Jones (ILJ) model . We were able to produce large tables and data sets of vibration-to-vibration (V–V) and vibration-to-translation/rotation (V–T/R) rate coefficients in a wide temperature range for a variety of systems, − covering many initial vibrational states of the colliding dimers, not too close to the dissociation limit. The latter choice is because the MQC method is based on an internally consistent use of a Morse-like intramolecular potential and a corresponding Morse-like vibrational wave function, which are known to be deficient for the representation of highly excited states.…”