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).

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.

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The role of various factors (structure, solvent, and relativistic treatment) was evaluated for square-planar 4d and 5d transition-metal complexes. The DFT method for calculating the structures was calibrated using a cluster approach and compared to X-ray geometries, with the PBE0 functional (def2-TZVPP basis set) providing the best results, followed closely by the hybrid TPSSH and the MN12SX functionals. Calculations of the NMR chemical shifts using the two-component (2c, Zeroth-Order Regular Approximation as implemented in the ADF package) and four-component (4c, Dirac-Coulomb as implemented in the ReSpect code) relativistic approaches were performed to analyze and demonstrate the importance of solvent corrections (2c) as well as a proper treatment of relativistic effects (4c). The importance of increased exact-exchange admixture in the functional (here PBE0) for reproducing the experimental data using the current implementation of the 2c approach is partly rationalized as a compensation for the missing exchange-correlation response kernel. The kernel contribution was identified to be about 15-20% of the spin-orbit-induced NMR chemical shift, ΔδSO, which roughly corresponds to an increase in ΔδSO introduced by the artificially increased exact-exchange admixture in the functional. Finally, the role of individual effects (geometry, solvent, relativity) in the NMR chemical shift is discussed in selected complexes. Although a fully relativistic DFT approach is still awaiting the implementation of GIAOs for hybrid functionals and an implicit solvent model, it nevertheless provides reliable NMR chemical shift data at an affordable computational cost. It is expected to outperform the 2c approach, in particular for the calculation of NMR parameters in heavy-element compounds.

The importance of relativistic effects on the NMR parameters in heavy-atom (HA) compounds, particularly the SO-HALA (Spin-Orbit Heavy Atom on the Light Atom) effect on NMR chemical shifts, has been known for about 40 years. Yet, a general correlation between the electronic structure and SO-HALA effect has been missing. By analyzing H NMR chemical shifts of the sixth-period hydrides (Cs-At), we discovered general electronic-structure principles and mechanisms that dictate the size and sign of the SO-HALA NMR chemical shifts. In brief, partially occupied HA valence shells induce relativistic shielding at the light atom (LA) nuclei, while empty HA valence shells induce relativistic deshielding. In particular, the LA nucleus is relativistically shielded in 5d-5d and 6p HA hydrides and deshielded in 4f, 5d, 6s, and 6p HA hydrides. This general and intuitive concept explains periodic trends in the H NMR chemical shifts along the sixth-period hydrides (Cs-At) studied in this work. We present substantial evidence that the introduced principles have a general validity across the periodic table and can be extended to nonhydride LAs. The decades-old question of why compounds with occupied frontier π molecular orbitals (MOs) cause SO-HALA shielding at the LA nuclei, while the frontier σ MOs cause deshielding is answered. We further derive connection between the SO-HALA NMR chemical shifts and Spin-Orbit-induced Electron Deformation Density (SO-EDD), a property that can be obtained easily from differential electron densities and can be represented graphically. SO-EDD provides an intuitive understanding of the SO-HALA effect in terms of the depletion/concentration of the electron density at LA nuclei caused by spin-orbit coupling due to HA in the presence of a magnetic field. Using an analogy between the SO-EDD concept and arguments from classic NMR theory, the complex question of the SO-HALA NMR chemical shifts becomes easily understandable for a wide chemical audience.

The significant role of relativistic effects in altering the NMR chemical shifts of light nuclei in heavy-element compounds has been recognized for a long time; however, full understanding of this phenomenon in relation to the electronic structure has not been achieved. In this study, the recently observed qualitative differences between the platinum and gold compounds in the magnitude and the sign of spin-orbit-induced (SO) nuclear magnetic shielding at the vicinal light atom ((13)C, (15)N), σ(SO)(LA), are explained by the contractions of 6s and 6p atomic orbitals in Au complexes, originating in the larger Au nuclear charge and stronger scalar relativistic effects in gold complexes. This leads to the chemical activation of metal 6s and 6p atomic orbitals in Au complexes and their larger participation in bonding with the ligand, which modulates the propagation of metal-induced SO effects on the NMR signal of the LA via the Spin-Orbit/Fermi Contact (SO/FC) mechanism. The magnitude of the σ(SO)(LA) in these square-planar complexes can be understood on the basis of a balance between various metal-based 5d → 5d* and 6p → 6p* orbital magnetic couplings. The large and positive σ(SO)(LA) in platinum complexes is dominated by the shielding platinum-based 5d → 5d* magnetic couplings, whereas small or negative σ(SO)(LA) in gold complexes is related to the deshielding contribution of the gold-based 6p → 6p* magnetic couplings. Further, it is demonstrated that σ(SO)(LA) correlates quantitatively with the extent of M-LA electron sharing that is the covalence of the M-LA bond (characterized by the QTAIM delocalization index, DI). The present findings will contribute to further understanding of the origin and propagation of the relativistic effects influencing the experimental NMR parameters in heavy-element systems.

Relativistic effects play an essential role in understanding the nuclear magnetic resonance (NMR) chemical shifts in heavy-atom compounds. Particularly interesting from the chemical point of view are the relativistic effects due to heavy atom (HA) on the NMR chemical shifts of the nearby light atoms (LA), referred to as the HALA effects. The effect of Spin-Orbit (SO) interaction originating from HA on the nuclear magnetic shielding at a neighboring LA, σ(SO), is explored here in detail for a series of d(6) complexes of iridium. Unlike the previous findings, the trends in σ(SO) observed in this study can be fully explained neither in terms of the s-character of the HA-LA bonding nor by trends in the energy differences between occupied and virtual molecular orbitals (MOs). Rather, the σ(SO) contribution to the total NMR shielding is found to be modulated by the d-orbital participation of the heavy atom (Ir) in the occupied and virtual spin-orbit active MOs, i.e., those which contribute significantly to the σ(SO). The correlation between the d-character of σ(SO)-active MOs and the size of the corresponding SO contribution to the nuclear magnetic shielding constant at LA is so tight that the magnitude of σ(SO) can be predicted in a given class of compounds on the basis of d-orbital character of relevant MO with relative error smaller than 15%. This correspondence is supported by an analogy between the perturbation theory expressions for the spin-orbit induced NMR σ-tensor and those for the EPR g-tensor as well as the A-tensor of the ligand. This correlation is demonstrated on a series of d(5) complexes of iridium. Thus, known qualitative relationships between electronic structure and EPR parameters can be newly applied to reproduce, predict, and understand the SO-induced contributions to NMR shielding constants of light atoms in heavy-atom compounds.

Endohedral actinide fullerenes are rare and a little is known about their molecular properties. Here we characterize the U2@C80 system, which was recently detected experimentally by means of mass spectrometry (Akiyama et al., JACS, 2001, 123, 181). Theoretical calculations predict a stable endohedral system, (7)U2@C80, derived from the C80:7 IPR fullerene cage, with six unpaired electrons. Bonding analysis reveals a double ferromagnetic (one-electron-two-center) U-U bond at an rU-U distance of 3.9 Å. This bonding is realized mainly via U(5f) orbitals. The U-U interaction inside the cage is estimated to be about -18 kcal mol(-1). U-U bonding is further studied along the U2@Cn (n = 60, 70, 80, 84, 90) series and the U-U bonds are also identified in U2@C70 and U2@C84 systems at rU-U∼ 4 Å. It is found that the character of U-U bonding depends on the U-U distance, which is dictated by the cage type. A concept of unwilling metal-metal bonding is suggested: uranium atoms are strongly bound to the cage and carry a positive charge. Pushing the U(5f) electron density into the U-U bonding region reduces electrostatic repulsion between enclosed atoms, thus forcing U-U bonds.