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Relativistic magnetic hyperfine interaction Hamiltonian based on theDouglas-Kroll-Hess (DKH) theory up to the second order is implemented withinthe ab initio multireference methods including spin-orbit coupling in theMolcas/OpenMolcas package. This implementation is applied to calculaterelativistic hyperfine coupling (HFC) parameters for atomic systems anddiatomic radicals with valence s or d orbitals by systematically varying activespace size in the restricted active space self-consistent field (RASSCF)formalism with restricted active space state interaction (RASSI) for spin-orbitcoupling. The DKH relativistic treatment of the hyperfine interaction reducesthe Fermi contact contribution to the HFC due to the presence of kineticfactors that regularize the singularity of the Dirac delta function in thenonrelativitic Fermi contact operator. This effect is more prominent forheavier nuclei. As the active space size increases, the relativistic correctionof the Fermi contact contribution converges well to the experimental data forlight and moderately heavy nuclei. The relativistic correction, however, doesnot significantly affect the spin-dipole contribution to the hyperfineinteraction. In addition to the atomic and molecular systems, theimplementation is applied to calculate the relativistic HFC parameters forlarge trivalent and divalent Tb-based single-molecule magnets (SMMs) such asTb(III)Pc$_2$ and Tb(II)(Cp$^\text{iPr5}$)$_2$ without ligand truncation usingwell-converged basis sets. In particular, for the divalent SMM which has anunpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC iscrucial for a proper description of the Fermi contact contribution. Even withthe relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibitstrong tunability of HFC via an external electric field (i.e., strong hyperfineStark effect).

Relativistic Douglas-Kroll-Hess Calculations of Hyperfine Interactions within First Principles Multireference Methods