A Physics-Constrained Synergetic Active- and Transfer-Learning Framework for Constructing a Spectroscopically Accurate Full-Dimensional Potential Energy Surface of H₂O–N₂ Complex

Achieving this level of accuracy places stringent demands on the underlying full-dimensional potential energy surfaces (PESs). However, constructing such PESs remains challenging because flexible configuration space requires dense sampling and the <i>ab initio</i> energies used for fitting must meet spectroscopic accuracy requirements.

Here, we develop a physics-constrained synergetic active- and transfer-learning framework (SynATL) that combines uncertainty-driven active learning, high-level refinement via transfer learning, and an explicit long-range representation to construct spectroscopically accurate full-dimensional PESs. SynATL was used to construct a full-dimensional PES of the H₂O–N₂ complex at the post-CCSD(T) level, achieving a weighted root-mean-square error (RMSE) of 0.815 cm^–1 on the test set and sub-cm^–1 RMSEs in the spectroscopically relevant low-energy and attractive regions.