A Full-Dimensional Potential Energy Surface for the Quartet State of N ₂ O ⁺ from Permutationally Invariant Polynomials and Neural Networks

The reaction O⁺(⁴S_u) + N₂(X¹Σ_g⁺) → NO⁺(X¹Σ⁺) + N(⁴S_u) is a critical process both in Earth's ionosphere and in high-temperature nonequilibrium flows surrounding hypersonic vehicles. However, state-resolved dynamical investigations of this process have been hindered by the lack of a full-dimensional potential energy surface (PES) for the N₂O⁺ system. In this work, we construct a full-dimensional analytical PES for the ⁴A″ electronic state of N₂O⁺ using the permutationally invariant polynomial-neural network (PIP-NN) approach, based on 3720 ab initio points computed at the icMRCI + Q level. Scanning the newly developed PES reveals two intermediate minima (IM1 and IM2) and one saddle point (TS). The global minimum energy path is characterized as O⁺ + N₂ (0.0 eV) → IM1 (-1.32 eV) → TS (0.35 eV) → IM2 (-1.80 eV) → NO⁺ + N (-1.13 eV), corresponding to a reaction barrier of 0.35 eV, in excellent agreement with the experimental value of ∼0.33 eV. Using this full-dimensional PES, we further evaluated the integral cross sections over the relative translational energy range of 0.3-20 eV using the quasi-classical trajectory (QCT) method. The computed results show good agreement with available experimental and theoretical results across the entire energy range. Overall, the present PES offers a robust and accurate foundation for probing the microscopic state-to-state dynamics in future studies.