Machine Learning Meets Spin–Orbit Coupling: Reconstruction of Spin–Orbit-Mixed Potential Energy Curves in MgCa

Abstract Spin–orbit coupling (SOC) induces state mixing and distortions in potential energy curves (PECs), complicating their construction and interpretation for diatomic molecules. We introduce a fully automated machine-learning framework for reconstructing physically consistent SOC-resolved PECs across independent electronic-structure calculations with different basis-set representations. The approach combines generative data augmentation using a conditional Wasserstein Generative Adversarial Network with gradient penalty (cWGAN-GP) with supervised regression models (Ridge Regression, Gradient Boosting, and Extremely Randomized Trees) to learn the relationship between raw SOC-affected PECs, spin–orbit composition tables, and their physically corrected counterparts. Using MgCa as a demonstration system, SOC-resolved PECs and spectroscopic constants were computed at the MRCI level for the ground and 26 low-lying excited states. Models trained on a single manually corrected reference basis accurately predict physically corrected PEC energies for independent basis sets, achieving sub-percent deviations in dissociation energies while preserving asymptotic limits, equilibrium geometries, and fine-structure splittings without explicit constraints. This framework eliminates manual postprocessing of SOC-mixed PECs and provides a scalable strategy for consistent spin–orbit treatment in high-level electronic-structure workflows.