  Relativistic magnetic hyperfine interaction Hamiltonian based on the
Douglas-Kroll-Hess (DKH) theory up to the second order is implemented within
the ab initio multireference methods including spin-orbit coupling in the
Molcas/OpenMolcas package. This implementation is applied to calculate
relativistic hyperfine coupling (HFC) parameters for atomic systems and
diatomic radicals with valence s or d orbitals by systematically varying active
space size in the restricted active space self-consistent field (RASSCF)
formalism with restricted active space state interaction (RASSI) for spin-orbit
coupling. The DKH relativistic treatment of the hyperfine interaction reduces
the Fermi contact contribution to the HFC due to the presence of kinetic
factors that regularize the singularity of the Dirac delta function in the
nonrelativitic Fermi contact operator. This effect is more prominent for
heavier nuclei. As the active space size increases, the relativistic correction
of the Fermi contact contribution converges well to the experimental data for
light and moderately heavy nuclei. The relativistic correction, however, does
not significantly affect the spin-dipole contribution to the hyperfine
interaction. In addition to the atomic and molecular systems, the
implementation is applied to calculate the relativistic HFC parameters for
large trivalent and divalent Tb-based single-molecule magnets (SMMs) such as
Tb(III)Pc$_2$ and Tb(II)(Cp$^\text{iPr5}$)$_2$ without ligand truncation using
well-converged basis sets. In particular, for the divalent SMM which has an
unpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC is
crucial for a proper description of the Fermi contact contribution. Even with
the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit
strong tunability of HFC via an external electric field (i.e., strong hyperfine
Stark effect).
