Spin-orbit/Fermi contact effects shieldings

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. 

Figure 1. JH absolute shielding in HX, X = F, Cl, Br, I. The figure illustrates the importance of spin-orbit/Fermi contact effects in these systems (9) scalar relativistic calculation (7) are unable to reproduce the experimental trend.

It follows from Table V that spin-orbit effects are relevant for the heavy metal shieldings and, since the spin-orbit contribution does not always have the same sign, for the relative chemical shifts. In this connection, it is interesting to note that the ZORA spin-orbit numbers are shifted as compared to their Pauli spin-orbit counterparts. This effect can be attributed, at least partly, to core contributions at the metal while scalar contributions of the core orbitals are approximately accounted for by the frozen core approximation (6,7), spin-orbit contributions of the core orbitals are neglected. Hence, the more positive (diamagnetic) shieldings from the ZORA method are due to spin-orbit/Fermi contact contributions of the s orbitals in the uranium core. 

Let us start with the field-free SO effects. Perturbation by SO coupling mixes some triplet character into the formally closed-shell ground-state wavefunction. Therefore, electronic spin has to be dealt with as a further degree of freedom. This leads to hyperfine interactions between electronic and nuclear spins, in a BP framework expressed as Fermi-contact (FC) and spin-dipolar (SD) terms (in other quasirelativistic frameworks, the hyperfine terms may be contained in a single operator, see e.g. [34,40,39]). Thus, in addition to the first-order and second-order ct at the nonrelativistic level (eqs. 5-7), third-order contributions to nuclear shielding (8) arise, that couple the one- and two-electron SO operators (9) and (10) to the FC and SD Hamiltonians (11) and (12), respectively. Throughout this article, we will follow the notation introduced in [58,61,62], where these spin-orbit shielding contributions were denoted... 

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