Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element Compounds

We present an efficient implementation of paramagnetic NMR shielding
tensors and shifts in a nonrelativistic and scalar-relativistic density
functional theory framework. For the latter, we make use of the scalar
exact two-component Hamiltonian in its local approximation, and generally
we apply the well established (multipole-accelerated) resolution of
the identity approximation and the seminumerical exchange approximation.
The perturbed density matrix of a paramagnetic NMR shielding calculation
is further used to study the magnetically induced current density
and ring currents of open-shell systems as illustrated for [U@Bi12]3–. [U@Bi12]3– features delocalized highest occupied molecular orbitals and sustains
a net diatropic ring current of ca. 18 nA/T through the Bi12 torus similar to the all-metal aromatic heavy-element cluster
[Th@Bi12]4–.