An accurate full-dimensional interaction potential energy surface of CO2+N2 incorporating ∆-machine learning approach via permutation invariant polynomial-neural network

The interaction between CO₂ and N₂, both as essential components of the Earth’s atmosphere, plays a crucial role in investigating the greenhouse effect. In this work, we sampled 40,930 data points within the full-dimensional configuration space of CO₂ and N₂ and performed calculations at the level of explicitly correlated coupled cluster single, double, and perturbative triple level with the augmented correlation corrected valence triple-ζ basis set (CCSD(T)-F12a/AVTZ). To ensure computational accuracy while reducing computational costs, we employed the recently proposed Δ-machine learning (Δ-ML) method based on Permutation Invariant Polynomial-Neural Network (PIP-NN) for basis set superposition error (BSSE) correction. By leveraging the limited extrapolation capability of NN, efficient sampling was performed within the existing dataset, enabling the construction of the potential energy surface (PES) incorporating BSSE correction with only a small number of data points for BSSE calculations. A total of approximately 1100 data points were selected from the initial dataset to construct a BSSE correction PES. Utilizing this correction PES, BSSE predictions were carried out for all remaining data points, resulting in the successful development of a high-precision full-dimensional PES with BSSE correction for the CO₂ + N₂ system. The PIP-NN based Δ-ML method significantly reduced the required BSSE calculations by approximately 97.2%, resulting in a final PES with a fitting error of merely 0.026 kcal/mol.