Application of SAP-X2C to Spectroscopy and Comparison to Screened Nuclear Spin--Orbit Approximations

Recently, Surjuse and Valeev [\textit{J. Chem. Theory Comput.} \textbf{22}, 3443--3452 (2026).] suggested to use a simple superposition of atomic potentials to account for two-electron picture-change error in one-electron exact two-component (SAP-X2C) theory. Herein, we generalize this ansatz to analytical derivative theory and apply SAP-X2C to molecular spectroscopy. The accuracy is assessed for NMR, EPR, M\"ossbauer, UV/vis, as well as X-ray absorption spectroscopy. A thorough comparison with four-component results and the even simpler screened nuclear spin--orbit (SNSO) approximation reveals that both SNSO-X2C and SAP-X2C perform excellently for spectroscopic properties. The major advantage of SAP-X2C over SNSO-X2C is consequently its well defined thermochemical limit and its less empirical nature. Therefore, SAP-X2C may be expected to become the default choice to mitigate the two-electron picture-change error in density functional theory approaches for spectroscopy thanks to its accuracy, simplicity, and efficiency. More complicated approaches to account for this error based on atomic mean-field ans\"atze may still be relevant for high-level correlated methods and highly accurate thermochemistry.