Accurate incorporation of hyperfine coupling in diabatic potential models using the Effective Relativistic Coupling by Asymptotic Representation approach

The accurate treatment of relativistic couplings like spin-orbit (SO) coupling into diabatic potential models is highly desirable. We have been developing the Effective Relativistic Coupling by Asymptotic Representation (ERCAR) approach to this end. The central idea of ERCAR is the representation of the system using an asymptotic diabatic direct product basis of atom and fragment states. This allows to treat relativistic coupling operators like SO coupling analytically. This idea is extended here to the incorporation of hyperfine (HF) coupling into the diabatic potential model. Hyperfine coupling is due to the magnetic dipole-dipole and the Fermi contact interaction as well as the electric quadrupole interaction. The corresponding operators can be expressed in terms of the angular momentum operators for nuclear spin $\hat I$ and for total angular momentum $\hat J$ of the atomic fine structure states. The diabatic basis of an existing ERCAR model is complemented by nuclear spinors and the HF coupling operators are easily evaluated in that basis. Diagonalization of the resulting full diabatic ERCAR model yields the HF energies and states for any molecular geometry of interest. The new method is demonstrated using an existing accurate diabatic potential model for hydrogen iodide (HI)[J. Chem. Phys. 159 244119 (2023)] to see the effects of hyperfine coupling. The HF coupling effect of the ²P_3/2 ground state and spin-orbit excited ²P_1/2 state of iodine combined with the ²S_1/2 ground state of hydrogen are added to the ERCAR Hamiltonian. It is shown that each fine structure state is split by the hyperfine interactions into sets of seven hyperfine states. The fine structure ground state at the global minimum is split into three degenerate groups of hyperfine states with splittings of 152 and 76 MHz.