Revealing the structural origin of spin-orbit coupling with SOPEL.

Abstract

Spin-orbit coupling is a key ingredient for many photochemical processes, yet it is commonly reported as an opaque scalar quantity with limited chemical interpretability. Here, we introduce the concept of SOPEL (Spin-Orbit Population ELement), an atom-resolved decomposition of spin-orbit coupling matrix elements (SOCMEs) that reveals their structural origin in molecules. We further present practical selection rules for nonzero couplings in the language of real atomic orbitals, providing an intuitive link between local orbital character and the spin-orbit coupling. Together, the concept converts the SOCMEs from a black-box electronic-structure output into a chemically interpretable quantity. By localizing the structural origin of spin-orbit coupling, SOPEL provides a practical framework not only for interpreting spin-forbidden processes in terms of structure and motion, but also for chemically guided molecular design. Applications to iodine-substituted BODIPY, formaldehyde, benzophenone, and triarylamine-terephthalonitrile show that the approach (i) identifies the atoms and fragments that generate spin-orbit coupling, (ii) characterizes spin-vibronic mechanisms, (iii) captures redistribution of the coupling origin across molecular frameworks, and (iv) explains why heavy-atom participation alone does not guarantee strong coupling.