Spin‐Orbit Couplings vis‐á‐vis Complex Beyond Born‐Oppenheimer Theory for Non‐Abelian Systems: F+H 2 as a Test Case

ABSTRACT In order to demonstrate static and dynamic properties of molecular species/processes/phenomena involving complex electron‐nuclear couplings (namely, spin‐orbit (SO) interactions), Complex Beyond Born‐Oppenheimer (CBBO) theory has already been introduced for Abelian systems (two coupled electronic manifold) [ J. Chem. Theory Comput. , 2025, 21 , 10166‐10176], but the newly developed formulation needs to be generalized for non‐Abelian cases involving three or more than three coupled electronic states. In this context, the triatomic reactive scattering system, F+H can be considered as an excellent prototype system exhibiting profound non‐adiabatic as well as SO couplings within the low‐lying three electronic states (1A, 2A and 1A). The present work mainly focuses on the development of CBBO theory for three‐state sub‐Hilbert space (with and without SO couplings) and its applications for the titled system, F+H. The complex nature of SO coupling terms for F+H is reflected in the diabatic Hamiltonian, which is expected to produce more accurate dynamical properties (like spectral bands, reaction cross‐sections, rate constants, etc.) during nuclear dynamics calculations.