Exhaustive State-to-State Cross Sections and Rate Coefficients for Inelastic N 2 -N 2 Collisions using QCT Combined with Neural Network Models.

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 high-energy collisions. Additionally, we constructed well-trained neural network models ( R -values reaching 0.99) using limited quasi-classical 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 - Δ v ) + N ₂ ( v ₂ + Δ v ) and VT processes N ₂ ( v ₁ ) + N ₂ ( v ₂ ) → N ₂ ( v ₁ - Δ v ) + N ₂ ( v ₂ ) (Δ v = ±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.