Relativistic effects on Sternheimer shieldings and the polarizabilities of the electric field gradient at the nucleus.

We investigate the relativistic effects on the electric field gradient (EFG) at the nucleus, the generalized Sternheimer shielding constants, and the EFG polarizabilities using analytic quadratic response theory at the four-component Dirac--Hartree--Fock level of theory. Particular attention is paid to the basis set requirements for calculations at the four-component level of theory of these higher-order properties involving operators that probe both the near-nucleus and the outer regions of the electron density. Our results show that relativistic effects become non-negligible for the hydrogen halides starting with hydrogen bromide and the heavier members of the group 17 halides. Interestingly, the relativistic effects are much more pronounced for the heavy-atom in hydrogen bromide, being about 10\% for most of the generalized EFG polarizabilities, than in the homonuclear diatomic molecule Br$_2$, where relativistic effects in general are much less than 10\%.