  Molecular spin qubits with long spin coherence time as well as non-invasive
operation methods on such qubits are in high demand. It was shown that both
molecular electronic and nuclear spin levels can be used as qubits. In solid
state systems with dopants, an electric field was shown to effectively change
the spacing between the nuclear spin qubit levels when the electron spin
density is high at the nucleus of the dopant. Inspired by such solid-state
systems, we propose that divalent lanthanide (Ln) complexes with an unusual
electronic configuration of Ln$^{2+}$ have a strong interaction between the Ln
nuclear spin and the electronic degrees of freedom, which renders electrical
tuning of the interaction. As an example, we study electronic structure and
hyperfine interaction of the $^{159}$Tb nucleus in a neutral
Tb(II)(Cp$^{\rm{iPr5}}$)$_2$ single-molecule magnet (SMM) using the complete
active space self-consistent field method with spin-orbit interaction included
within the restricted active space state interaction. Our calculations show
that the low-energy states arise from $4f^8(6s,5d_{z^2})^1$,
4$f^8$(5$d_{x^2-y^2}$)$^1$, and $4f^8(5d_{xy})^1$ configurations. We compute
the hyperfine interaction parameters and the electronic-nuclear spectrum within
our multiconfigurational approach. We find that the hyperfine interaction is
about one order of magnitude greater than that for Tb(III)Pc$_2$ SMMs. This
stems from the strong Fermi contact interaction between the Tb nuclear spin and
the electron spin density at the nucleus that originates from the occupation of
the $(6s,5d)$ orbitals. We also uncover that the response of the Fermi contact
term to electric field results in electrical tuning of the electronic-nuclear
level separations. This hyperfine Stark effect may be useful for applications
of molecular nuclear spins for quantum computing.
