Calculation of hyperfine tensors and paramagnetic NMR shifts using the relativistic zeroth-order regular approximation and density functional theory

Density functional theory (DFT) calculations of molecular hyperfine tensors were implemented as a second derivative property within the two-component relativistic zeroth-order regular approximation (ZORA). Hyperfine coupling constants were computed for systems ranging from light atomic radicals to molecules with heavy d and f block elements. For comparison, computations were also performed with a ZORA first-order derivative approach. In each set of computations, Slater-type basis sets have been used. The implementation allows for nonhybrid and hybrid DFT calculations and incorporates a Gaussian finite nucleus model. A comparison of results calculated with the PBE nonhybrid and the PBE0 hybrid functional is provided. Comparisons with differing basis sets and incorporation of finite-nucleus corrections are discussed. The second derivative method is applied to calculations of paramagnetic NMR ligand chemical shifts of three Ru(III) complexes. The results are consistent with those calculated using a first-order derivative method, and the results are consistent for different functionals used. A comparison of two different methods of calculating pseudo-contact shifts, one using the full hyperfine tensor and one assuming a point-charge paramagnetic center, is made for the Ru(III) complexes.