Spin-Orbit Couplings vis-á-vis Complex Beyond Born-Oppenheimer Theory for Non-Abelian Systems: F+H2 as a Test Case

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