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

Abstract

Using the quasi-classical trajectory method, we systematically studied the state-to-state vibrational relaxation process of N 2 (v 1 ) + N 2 (v 2 ) collisions over a wide temperature range (5000− 30,000 K). Different temperature dependencies of the single-and multiquantum VV and VT events in various (v 1 ,v 2 ) collisions are captured, with the dominant channel being related to the initial vibrational energy levels (v max = 50). At a specified relative translational energy, there is a monotonic relationship of the VT cross sections with the vibrational energy level, particularly in highenergy collisions. Additionally, we constructed well-trained neural network models (R-values reaching 0.99) using limited quasiclassical trajectory (QCT) data sets, which can be used to predict the state-to-state cross sections and rate coefficients of the VV processes N 2 (v 1 ) + N 2 (v 2 ) → N 2 (v 1 − Δv) + N 2 (v 2 + Δv) and VT processes N 2 (v 1 ) + N 2 (v 2 ) → N 2 (v 1 − Δv) + N 2 (v 2 ) (Δv = ±1, ±2, ±3) for collisions with arbitrary initial vibrational states. This work not only significantly reduces computational resources but also serves as a reference for the study of the state-to-state dynamics of all four-atom collision systems in hypersonic flows.