The Hyperfine Shift

This chapter recalls the principles of the hyperfine coupling between electrons and nuclei in terms of energy and deals with its consequences on chemical shift. The equations for contact and pseudocontact shifts are derived and illustrated in a pictorial way. Their physical/chemical backgrounds are discussed as well as their limits of validity. The mechanisms of spin delocalization are illustrated. The perspectives when high field magnets are used are highlighted. 

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With these assignments at hand the analysis of the hyperfine shifts became possible. An Fe(III) in tetrahedral structures of iron-sulfur proteins has a high-spin electronic structure, with negligible magnetic anisotropy. The hyperfine shifts of the protons influenced by the Fe(III) are essentially Fermi contact in origin 21, 22). An Fe(II), on the other hand, has four unpaired electrons and there may be some magnetic anisotropy, giving rise to pseudo-contact shifts. In addition, there is a quintet state at a few hundred cm which may complicate the analysis of hyperfine shifts, but the main contribution to hyperfine shifts is still from the contact shifts 21, 22). 

Contact shifts give information on the electronic structure of the iron atoms, particularly on the valence distribution and on the magnetic coupling within polymetallic systems. The magnetic coupling scheme, which is considered later, fully accounts for the variety of observed hyperfine shifts and the temperature dependence. Thus, through the analysis of the hyperfine shifts, NMR provides detailed information on the metal site(s) of iron-sulfur proteins, and, thanks to the progress in NMR spectroscopy, also the solution structure 23, 24 ). 

By assuming that the hyperfine shifts are contact shifts in origin, it is possible to evaluate the hyperfine coupling constant from the following equation (50) ... 

Fig. 4. Top Theoretical temperature dependence of the hyperfine shift of the H/3 protons of reduced spinach [Fe2S2] ferredoxin 151). The solid line corresponds to the situation where only one species exists in solution, whereas the dashed line corresponds to a situation where there is fast equilibrium between two species (in a 20/80 ratio) differing for the location of the extra electron 151). Bottom.-. Experimental temperature dependence of the H NMR shifts. The signals are labeled as in Fig. 2B.

As mentioned in the Introduction, in iron—sulfur proteins, the hyperfine shifts of the nuclei of the coordinating cysteines are essentially contact in origin (21, 22). In the case of [Fe4S4l (17) and [FegS4] (112) cluster, it has been shown that the hyperfine shift of the cysteinyl H/3 and Ca nuclei can be related to the value of the Fe-Sy-C/S-H/S/Ca dihedral angle (6) through a Karplus-type relationship of the form... 

The solution structure of Aspl3Cys, a thermostable mutant of Fd, has been solved by H-NMR and compared to that of the wild-type (WT) protein. The overall folding of the WT protein was maintained in the mutant, except for the immediate vicinity of the new cysteine. The geometry of the new cluster was a typical 4Fe-4S cubane, as monitored by the hyperfine shifts of the co-ordinated cysteines. Conformational heterogeneity, which was partly abolished by heat treatment, was observed and ascribed to a kinetic phenomenon. 

Figure 6. Li MAS NMR spectrum of the layered compound Li2MnOs acquired at a MAS frequency, Vr, of 35 kHz. Spinning sidebands are marked with asterisks. The local environment in the Mn +/Li+ layers that gives rise to the isotropic resonance at 1500 ppm is shown. Spin density may be transferred to the 2s orbital of Li via the interaction with (b) a half-filled t2g orbital and (c) an empty d/ Mn orbital to produce the hyperfine shifts seen in the spectrum of Li2MnOs. The large arrows represent the magnetic moments of the electrons in the t2g and p orbitals, while the smaller arrows indicate the sign of the spin density that is transferred to the Li 2s and transition-metal d orbitals.

Table 1. Comparison of the Hyperfine Shifts (in ppm) Observed for Lithium Coordinated to a Single Mn + Ion via an Intervening Oxygen Ion for a Series of Local Environments ...

The effective distances obtained by Nordenskiold et al. (40) are compared with the internuclear distances in Table I. Clearly, the point dipole approximation is reasonable for the hydrogen nuclei in these complexes, while substantial deviations are observed for the oxygen nuclei. The findings of these early quantum chemical studies were confirmed by Sahoo and Das (41-43). Wilkens et al. have reported DFT calculations using Eq. (16) for a 104 atom model for high-spin Fe(III) rubredoxin (44). Large discrepancies between the effective distances and the input distances for the calculations were found for the hyperfine-shifted nitrogen-15 resonances, as well as for proton and carbon-13 nuclei in cysteines bound to the iron center. 

The hyperfine shifts in the proton NMR spectra of paramagnetic hemes and hemoproteins are closely related to the electronic structures of these molecules. At present the most extensive NMR studies of the electronic spin distribution in the heme groups have been done with low spin ferric compounds, which will be discussed in this section. Procedures similar to those described here would apply to the analysis of the NMR spectra of hemoproteins in the other paramagnetic states (Table 1). 

In paramagnetic molecules with anisotropic g-tensors electron-proton dipole-dipole coupling may contribute to the hyperfine shifts observed in the proton NMR spectra. From the data to be discussed in this section it would seem, however, that in low spin ferric heme compounds many of the qualitative spectral features are mainly determined by Fermitype contact shifts. 

The hyperfine shifts in the NMR spectra of ferricytochrome c and its cyanide complex (Horecker and Kornberg (43)) are markedly different (110), so that the complex formation can be observed in the NMR spectrum (Fig. 28). It is found that a 1 1 complex is formed. 

The basic features of the Mb111 (Ns) spectrum are similar to those of cyanoferrimyoglobin (Fig. 14). Only one set of hyperfine-shifted resonances is observed, but the hyperfine shifts are larger and the lines broader than in MbmCN. Furthermore the temperature dependences of the resonances positions show drastic deviations from Curie s law (Eq. 4). Similar data were also obtained for azidoporphyrin-iron(III) complexes in pyridine solution 116). 

The NMR spectra for the different electronic configurations described for myoglobin were also studied for hemoglobin and for the isolated -and -chains (Shulman et al. (99)). The basic spectral features are similar to those of the corresponding myoglobins, but the size of the hyperfine shifts of the heme resonances is quite different. As an illustration the resonances at low fields of deoxymyoglobin and deoxyhemoglobin are compared in Fig. 31. 

From these measurements the resonance positions in ferrocytochrome c of the protons corresponding to the hyperfine-shifted lines in ferricytochrome c are obtained. Gupta and Redfield (123) found that one of the ring methyl resonances of heme c is shifted upfield by ca. 1.5 ppm, indicating close proximity to the face of an aromatic amino acid residue in the reduced cytochrome c. The resonance positions in ferrocytochrome c are probably a better approximation of the diamagnetic heme resonance positions in ferri cytochrome c than are the porphyrin-zinc (II) complexes (Fig. 9). Hence experiments of this type could conceivably contribute towards a more accurate determination of the spin density distribution in the heme groups. 

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