Inelastic N$$_2$$+H$$_2$$ collisions and quantum-classical rate coefficients: large datasets and machine learning predictions
Qizhen Hong, Loriano Storchi, Massimiliano Bartolomei, Fernando Pirani, Quanhua Sun, Cecilia Coletti
Abstract
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 ( $$v\le 40$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>v</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>40</mml:mn> </mml:mrow> </mml:math> for N $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> and $$w\le 10$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>w</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:math> for H $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> ). These data are needed for the modelling of discharges in N $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> /H $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msub> </mml:math> 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 $$\textrm{N}_2(v)+\textrm{H}_2(0) \longrightarrow \textrm{N}_2(v-\Delta v)+\textrm{H}_2(0)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mtext>N</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>v</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:msub> <mml:mtext>H</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>⟶</mml:mo> <mml:msub> <mml:mtext>N</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>v</mml:mi> <mml:mo>-</mml:mo> <mml:mi>Δ</mml:mi> <mml:mi>v</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>+</mml:mo> <mml:msub> <mml:mtext>H</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , $$\Delta v=1,2,3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>v</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> processes. Graphical abstract