Relativistic Effects on NMR Chemical Shifts

Institut fur Anorganische Chemie, Universitat Wurzburg, Am Hubland, D-97074 Wurzburg, Germany 

the role relativistic effects play for NMR and EPR parameters has been appreciated to very different extents for different properties and by different communities of experimentalists and theoreticians. For example, it has been known early on in the EPR community that the electronic g-tensors of EPR spectroscopy are basically dominated by spin-orbit coupling and are thus intrinsically relativistic [2]. On the other hand, in spite of much early work on relativistic theories of NMR chemical shifts, and much associated recent cori5)utational developments and applications [3,4,5,6,7], most users of NMR spectroscopy still seem largely unaware of the important role of relativistic effects. This holds in particular for the role of spin-orbit effects, in what is often simply called heavy-atom effects on NMR chemical shifts. This can be seen easily when inspecting most NMR textbooks and much of the research literature. 

In this article, we will concentrate on NMR chemical shifts, for which the inportance of spin-free (scalar) relativistic (SFR) and spin-orbit (SO) contributions needs to be better appreciated. Reviews of relativistic calculations of spin-spin coupling constants are available [6,7]. Articles on conten jorary quantum chemical calculations of electronic g-tensors have been published elsewhere [5,8]. Other EPR parameters like zero-field splittings and hyperfine coupling constants are also strongly affected by relativity and are covered. 

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Relativistic Effects on NMR Chemical Shifts Kaupp, M. (2004) in Relativistic Electronic Structure Theory II Applications, Theoretical and Computational Chemistry, Chapter 9 (ed. P. Schwerdtfeger), Elsevier, Amsterdam, pp. 552-597. 

Kaupp, M. (2004). Relativistic effects on NMR chemical shifts. In P. Schwerdtfeger (Ed.), Relativistic electronic structure theory. Part 2. Applications (p. 552). Amsterdam Elsevier. 

Complexes of Group 12 - A review entitled Improvement in NMR structural studies of lignin through two- and three-dimensional NMR detection and isotropic enrichment has been published and contains Hg NMR data." Relativistic and substituent effects on NMR chemical shifts in... 

Relativistic effects on calculated NMR shieldings and chemical shifts have sometimes been divided into "direct" and "indirect" effects. According to this point of view, indirect effects are those that result from relativistic changes of the molecular geometry (the well-known relativistic bond contraction (55) in particular) whereas direct effects refer to a fixed geometry. 

Spin-Orbit/Fermi Contact Effects. While scalar relativistic effects seem to be sufficient for some systems like the metal carbonyls of Table I (even though it has been speculated (9) that spin-orbit might improve the agreement with experiment even further), there are other cases where this is not the case. We have chosen as an example the proton NMR absolute shielding in hydrogen halides HX, X = F, Cl, Br, I (7,9), Figure 1. This series has also been studied by other authors (34-38), and it may well be the most prominent example for spin-orbit effects on NMR shieldings and chemical shifts. 

Relativistic effects cannot be neglected if heavier systems are studied we have discussed the major relativistic effects on calculated NMR shieldings and chemical shifts in this chapter. Besides relativistic effects, electron correlation has to be included for even a qualitatively correct treatment of transition metal or actinide complexes. So far, DFT based methods are about the only approaches that can handle both relativity and correlation, and DFT is, for the time being, the method of choice for these heavy element compounds. In this chapter, we have presented results from two relativistic DFT methods, the Pauli- (QR-) and ZORA approaches. 

Quantum-chemical calculations of MH4 and MCI4 (M = C, Si, Ge, Sn, Pb) demonstrated that it is necessary to take into account the relativistic effects, which are proportional to the square of the atomic number of M and therefore essential when M = Ge, Sn, Pb . This was considered in calculations of the Me4- SnCl (n = 0-4) series . The mixing of orbitals of the unshared electron pairs of the chlorine atoms with the a(Sn—C) orbitals (a-n conjugation) intensifies with the rise of the number of methyl groups. On the contrary, increase in the number of chlorine atoms is accompanied by an increase in the population of the 5d-orbitals of the tin atom due to the d-n conjugation . The calculated HOMO energies and NMR chemical shifts of Me4- SnCl conform satisfactorily with experimental values. 

A detailed presentation of relativistic effects on magnetic properties is found in Ref. [60], especially for the H-atom in a homogeneous magnetic field in Ref. [61] Application of DPT to first-order magnetic properties were published by Hennum, et al. [62]. An earlier, more intuitive formulation, especially for NMR chemical shifts was given by Nomura et al. [63]. The fully relativistic theory has been studied by Pyykko [64] and Pyper [65]. 

It should be clear from the examples provided in this article, that relativistic effects cannot be ignored when one wants to understand NMR chemical shifts throughout the periodic table. While the local heavy-atom effects on the heavy atoms ( HAHA effects) can be very large for absolute shield ings, they tend to cancel to a large extent in relative shifts and are thus probably less important for the interpretation of the observed shifts for different compounds. HAHA effects are nevertheless of interest, not only for the development of reliable relativistic computational methods but also, for example, when deriving absolute shielding scales for heavy nuclei (section 5). 

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