Calculation of DFT-GIAO NMR shifts with the inclusion of spin-orbit coupling

Abstract

A formulation for the calculation of nuclear magnetic resonance (NMR) shielding tensors, based on density functional theory (DFT), is presented. Scalar-relativistic and spin-orbit coupling effects are taken into account, and a Fermi-contact term is included in the NMR shielding tensor expression. Gauge-including atomic orbitals (GIAO) and a frozen-core approximation are used. This formulation has been implemented, and ${}^{\mathrm{1}}\mathrm{H}$ and ${}^{\mathrm{13}}\mathrm{C}$ NMR shifts of hydrogen and methyl halides have been calculated and show good agreement with experiment. ${}^{\mathrm{13}}\mathrm{C}$ NMR shifts of $\text{5d}$ transition metal carbonyls have been calculated and show improved agreement with experiment over previous scalar-relativistic calculations. For the metal carbonyls it is shown explicitly that the combination of spin-orbit coupling and magnetic field mixes spin triplet states into the ground state, inducing a spin density that then interacts with the nuclei of the metal carbonyl via the Fermi-contact term. Results indicate that the Fermi-contact contribution to the ${}^{\mathrm{13}}\mathrm{C}$ NMR of the metal carbonyl ions increases with increasing oxidation state of the ion. It is reasoned that as the oxidation state increases, π back bonding decreases and σ bonding increases, within the metal–carbon bond, thus facilitating a greater transfer of spin density from the metal to the carbon nucleus, and thus increasing the Fermi-contact contribution to the NMR shielding of the carbon.