Chemical shifts present crucial information about an NMR spectrum. They show the influence of the chemical environment on the nuclei being probed. Relativistic effects caused by the presence of an atom of a heavy element in a compound can appreciably, even drastically, alter the NMR shifts of the nearby nuclei. A fundamental understanding of such relativistic effects on NMR shifts is important in many branches of chemical and physical science. This review provides a comprehensive overview of the tools, concepts, and periodic trends pertaining to the shielding effects by a neighboring heavy atom in diamagnetic systems, with particular emphasis on the "spin-orbit heavy-atom effect on the light-atom" NMR shift (SO-HALA effect). The analyses and tools described in this review provide guidelines to help NMR spectroscopists and computational chemists estimate the ranges of the NMR shifts for an unknown compound, identify intermediates in catalytic and other processes, analyze conformational aspects and intermolecular interactions, and predict trends in series of compounds throughout the Periodic Table . The present review provides a current snapshot of this important subfield of NMR spectroscopy and a basis and framework for including future findings in the field.

Relativistic effects significantly affect various spectroscopic properties of compounds containing heavy elements. Particularly in Nuclear Magnetic Resonance (NMR) spectroscopy, the heavy atoms strongly influence the NMR shielding constants of neighboring light atoms. In this account we analyze paramagnetic contributions to NMR shielding constants and their modulation by relativistic spin-orbit effects in a series of transition-metal complexes of Pt(II), Au(I), Au(III), and Hg(II). We show how the paramagnetic NMR shielding and spin-orbit effects relate to the character of the metal-ligand (M-L) bond. A correlation between the (back)-donation character of the M-L bond in d Au(I) complexes and the propagation of the spin-orbit (SO) effects from M to L through the M-L bond influencing the ligand NMR shielding via the Fermi-contact mechanism is found and rationalized by using third-order perturbation theory. The SO effects on the ligand NMR shielding are demonstrated to be driven by both the electronic structure of M and the nature of the trans ligand, sharing the σ-bonding metal orbital with the NMR spectator atom L. The deshielding paramagnetic contribution is linked to the σ-type M-L bonding orbitals, which are notably affected by the trans ligand. The SO deshielding role of σ-type orbitals is enhanced in d Hg(II) complexes with the Hg 6p atomic orbital involved in the M-L bonding. In contrast, in d Pt(II) complexes, occupied π-type orbitals play a dominant role in the SO-altered magnetic couplings due to the accessibility of vacant antibonding σ-type MOs in formally open 5d-shell (d). This results in a significant SO shielding at the light atom. The energy- and composition-modulation of σ- vs π-type orbitals by spin-orbit coupling is rationalized and supported by visualizing the SO-induced changes in the electron density around the metal and light atoms (spin-orbit electron deformation density, SO-EDD).

A methodology for optimizing the geometry and calculating the NMR shielding constants is calibrated for octahedral complexes of Pt(IV) and Ir(III) with modified nucleic acid bases. The performance of seven different functionals (BLYP, B3LYP, BHLYP, BP86, TPSS, PBE, and PBE0) in optimizing the geometry of transition-metal complexes is evaluated using supramolecular clusters derived from X-ray data. The effects of the size of the basis set (ranging from SVP to QZVPP) and the dispersion correction (D3) on the interatomic distances are analyzed. When structural deviations and computational demands are employed as criteria for evaluating the optimizations of these clusters, the PBE0/def2-TZVPP/D3 approach provides excellent results. In the next step, the PBE0/def2-TZVPP approach is used with the continuum-like screening model (COSMO) to optimize the geometry of single molecules for the subsequent calculation of the NMR shielding constants in solution. The two-component zeroth-order regular approximation (SO-ZORA) is used to calculate the NMR shielding constants (PBE0/TZP/COSMO). The amount of exact exchange in the PBE0 functional is validated for the nuclear magnetic shieldings of atoms in the vicinity of heavy transition metals. For the PBE0/TZP/COSMO setup, an exact exchange of 40% is found to accurately reproduce the experimental NMR shielding constants for both types of complexes. Finally, the effect of the amount of exact exchange on the NMR shielding calculations (which is capable of compensating for the structural deficiencies) is analyzed for various molecular geometries (SCS-MP2, BHLYP, and PBE0) and the influence of a trans-substituent on the NMR chemical shift of nitrogen is discussed. The observed dependencies for an iridium complex cannot be rationalized by visualizing the Fermi-contact (FC) induced spin density and probably originate from changes in the d-d transitions that modulate the spin-orbit (SO) part of the SO/FC term.