Spin-Orbit Couplings vis-á-vis Complex Beyond Born-Oppenheimer Theory for Non-Abelian Systems: F+H 2 $$ {}_2 $$ 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${\hspace{0.17em}}_2$ can be considered as an excellent prototype system exhibiting profound non-adiabatic as well as SO couplings within the low-lying three electronic states (1${\hspace{0.17em}}^2$A${\hspace{0.17em}}^{\prime }$, 2${\hspace{0.17em}}^2$A${\hspace{0.17em}}^{\prime }$ and 1${\hspace{0.17em}}^2$A${\hspace{0.17em}}^{″}$). 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${\hspace{0.17em}}_2$. The complex nature of SO coupling terms for F+H${\hspace{0.17em}}_2$ 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.