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

Abstract

In this study, complete ( i.e. , including all vibrational quantum numbers in an N 2 vibrational ladder) data sets of vibration-to-vibration and vibration-to-translation rate coefficients for N 2 –N 2 collisions are explicitly computed along with transport properties (shear and bulk viscosity, thermal conductivity, and self-diffusion) in the temperature range 100–9000 K. To reach this goal, we improved a mixed quantum–classical (MQC) dynamics approach by lifting the constraint of a Morse treatment of the vibrational wave function and intramolecular potential and permitting the use of more realistic and flexible representations. The new formulation has also allowed us to separately analyze the role of intra- and intermolecular potentials on the calculated rates and properties. Ab initio intramolecular potentials are indispensable for highly excited vibrational states, though the Morse potential still gives reasonable values up to v = 20. An accurate description of the long-range interaction and the van der Waals well is a requisite for the correct reproduction of qualitative and quantitative rate coefficients, particularly at low temperatures, making physically meaningful analytical representations still the best choice compared to currently available ab initio potential energy surfaces. These settings were used to directly compute the MQC rates corresponding to a large number of initial vibrational quantum numbers, and the missing intermediate values were predicted using a machine learning technique ( i.e. , the Gaussian process regression approach). The obtained values are reliable in the wide temperature range employed and are therefore valuable data for many communities dealing with nonlocal thermal equilibrium conditions in different environments.

Exhaustive State-to-State Cross Sections and Rate Coefficients for Inelastic N2–N2 Collisions using QCT Combined with Neural Network Models

“…In addition to the symmetric VV exchange and VT processes, the contribution of asymmetric multiquantum processes cannot be ignored, especially in collisions with different initial vibrational states, as previously discussed in Hong’s research . For example, as shown in Figure S3­(see the Supporting Information), in the N 2 (0) + N 2 (45) collision at T = 10,000 K, the rate coefficient of the asymmetric VV transition (6.17 × 10 –14 cm 3 /s) is larger than that of the symmetric VV (2.06 × 10 –14 cm 3 /s) and VT1 (4.11 × 10 –14 cm 3 /s) processes but considerably smaller than that of the VT2 process (1.80 × 10 –10 cm 3 /s).…”

“…In Figure a,d, the near-resonance energy exchange processes are more likely to occur between two close vibrational energy levels. When the collision partner is near the dissociation limit (around v 2 = 40), a slight increase of the VV cross sections is found, particularly in low-energy collisions, which can be attributed to the energy mismatch value (Δ E , the energy difference between the initial and final ro-vibrational state) . From a physical perspective, low-energy mismatches are believed to favor the VV process.…”

“…have used DMS techniques to show that the surface of PESMN2 is fine and accurate enough for the description of the high-temperature collisional excitation processes, dissociation, and exchange reactions. To verify the accuracy and reliability of the potential energy surface and calculation method, the calculated rate coefficients by QCT-PESMN1 and QCT-PESMN2 are compared with previous studies, , as shown in Figure . It can be found that the QCT-PESMN1 and QCT-PESMN2 results are in good agreement with Garcia’s QCT results and Hong’s MQC results, respectively, despite the different settings of the initial rotational states ( j 1 , j 2 ).…”

“…It can be found that the QCT-PESMN1 and QCT-PESMN2 results are in good agreement with Garcia’s QCT results and Hong’s MQC results, respectively, despite the different settings of the initial rotational states ( j 1 , j 2 ). Specifically, j 1 and j 2 are randomly selected within the upper limit in Hong’s work and are chosen based on the Boltzmann thermal distribution of the rotation temperature in Garcia’s study, whereas they are fixed at the ground state ( j 1 = j 2 = 0) in our calculations. According to the research on the rotational state-to-state transitions in N 2 + N 2 collisions, the magnitude of rates has the largest value between the j 1 = 0 and j 2 = 0 collision pair in a wide temperature range (2000–32,000 K), which also proves that our results are of certain reference significance for the ro-vibrational specified-state dynamic process.…”

“…In a recent study on N 2 + N 2 collisions, Hong et al calculated the VV and VT rate coefficients for N 2 ( v 1 ) + N 2 ( v 2 = 0,1, v 1 ) collisions using an improved mixed quantum-classical (MQC) dynamics method based on a Morse + ILJ PES, which accurately describes the low-temperature long-range interactions. By employing the Gaussian process regression approach to fill in the missing intermediate values, they obtained a complete data set in the temperature range of 100–9000 K. Differing from Hong’s research, the present work focuses on (1) investigating the vibrational energy transfer behavior at high temperatures (5000–30,000 K), which is crucial for hypersonic flows, based on a potential energy surface (PESN2) that accurately describes short-range interactions and (2) utilizing the initial energy level spacing | v 1 – v 2 | as one of the input features for the first time, the trained neural network model can effectively predict the VV and VT cross sections and rate coefficients for the general N 2 ( v 1 ) + N 2 ( v 2 ) process (allowing two arbitrary energy levels). This successful attempt represents a breakthrough in constructing a dynamic database for molecule–molecule collisions.…”