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

Abstract

The PI 4 + cation has an extremely large negative 31 P nuclear magnetic resonance chemical shift, due to spin-orbit coupling: A quantum-chemical prediction and its confirmation by solid-state nuclear magnetic resonance spectroscopy Density functional analysis of 13 C and 1 H chemical shifts and bonding in mercurimethanes and organomercury hydrides: The role of scalar relativistic, spin-orbit, and substituent effects A formulation for the calculation of nuclear magnetic resonance ͑NMR͒ shielding tensors, based on density functional theory ͑DFT͒, 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 ͑GIAO͒ and a frozen-core approximation are used. This formulation has been implemented, and 1 H and 13 C NMR shifts of hydrogen and methyl halides have been calculated and show good agreement with experiment. 13 C NMR shifts of 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 13 C NMR of the metal carbonyl ions increases with increasing oxidation state of the ion. It is reasoned that as the oxidation state increases, back bonding decreases and 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.

Relativistic effects on the nuclear magnetic shielding tensor

“…22,23 It is interesting to point out that in previous calculations of relativistic corrections to the nuclear magnetic shielding tensor, the Darwin and mass-velocity scalar effects were included within the ''unperturbed'' molecular Hamiltonian. 22,23 An alternative approach based on the zeroth order regular approximation ͑ZORA͒ was presented by Wolff et al 24 On the other hand, in agreement with Ref. 6, further contributions are found when the effect of the small component of the electronic bispinors is included in the corresponding large component in the presence of the magnetic potential.…”

Revisiting HgCl2: A solution- and solid-state 199Hg NMR and ZORA–DFT computational study

“…Relativistic spin-orbit calculations using the zeroth-order regular approximation combined with density functional theory (ZORA-DFT) were performed using the Amsterdam Density Functional (ADF) program package [27] and its associated NMR program module [28][29][30][31]. The module DIRAC was applied to generate the core potentials for all atom types.…”

Perspective: Relativistic effects

“…For HI, the relativistic effects are very pronounced: −2.7 (nrel) versus −14.6 (rel); the experimental proton shift for HI is −15.3. 171 Such calculations have been repeated numerous times with different relativistic methods and different levels of correlation treatment (including DFT). A collection of calculations performed until 2008 for the proton and halide NMR shifts in HX has been compiled in Ref.…”