Hyperfine Contact Interaction Shifts

McConnell (74) has shown that for the case of aromatic radical species where the interaction is between a spin density localized on a ptr orbital of a carbon atom and the proton bonded to that carbon atom a relationship exists between an observed proton contact interaction constant a, and the spin density p, on the adjacent carbon atom. This relationship is 

At this point it would be well to differentiate clearly between spin densities, p s, which arc obtained experimentally from contact interaction constants, and electron densities in molecules. If a simple Iluckel LCAO MO calculation is carried out on the allyl radical, the computed distribution of the single unpaired electron is as shown below 

The valence bond calculation as carried out on the allyl radical, however, gives the spin density distribution (75) 

An experimental determination of the spin density distribution in the allyl radical recently has become available (30) and is in fair agreement with the results of the valence bond calculation and in somewhat better agreement with an extended Hartree-Foek calculation to be described below. It is seen that although the allyl radical possesses only a single unpaired electron, the total calculated ir-electron spin density on the molecule is % to % units depending on the approximation employed. However, the relationship (75) 

The origin of total molecular spin densities greater than one for doublet state radicals is most clearly shown by an extended Hartree-Fock calculation on the allyl radical carried out by MacLachlan (79). The distributions of the three ir-elcctroiis of the allyl radical are by this calculation those shown below. 

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The conditions necessary for observation of proton magnetic resonance spectra in paramagnetic systems are well established (1). Either the electronic spin-lattice relaxation time, T, or a characteristic electronic exchange time, Te, must be short compared with the isotropic hyperfine contact interaction constant, in order for resonances to be observed. Proton resonances in paramagnetic systems are often shifted hundreds of cps from their values in the diamagnetic substances. These isotropic resonance shifts may arise from two causes, the hyperfine contact and pseudocontact interactions. The contact shift arises from the existence of unpaired spin-density at the resonating nucleus and is described by 1 (2) for systems obeying the Curie law. 

The hyperfine shifts of groups bound to the donor atom are largely dominated by the contact interaction, even if pseudocontact shift contributions are sizable and any quantitative use of the shifts should rely on the separated contributions. Longitudinal nuclear relaxation times can be used, and have been used in the case of cobalt substitute stellacyanin, to determine metal-proton distances [101]. The contribution of Curie relaxation, estimated from the field dependence of the linewidths, can be used both for assignment and to determine structural constrains [101]. 

Induced shifts of ligand atoms adjacent to rare earth ions are usually attributed to the contact interaction whereas shifts of more remote ligand atoms are generally considered to arise from a dipolar term. McGarvey (378,379) has described a reformulated covalent model which can account for the observed F hyperfine interactions for Yb and Tm " in cubic and tetragonal sites of alkaline earth... 

Fermi contact shifts may also contribute to the hyperfine shift observed in n.m.r. spectra. These shifts arise from the delocalization of electron spin density from the extended orbital of the metal ion to the orbitals of the ligand. This shift is primarily dependent on the contact interaction constant for a given nucleus. Contact shifts yield no distance information or structural information. 

The coupling of the unpaired electrons with the nucleus being observed generally results in a shift in resonance frequency that is referred to as a hyperfine isotropic or simply isotropic shift. This shift is usually dissected into two principal components. One, the hyperfine contact, Fermi contact or contact shift derives from a transfer of spin density from the unpaired electrons to the nucleus being observed. The other, the dipolar or pseudocontact shift, derives from a classical dipole-dipole interaction between the electron magnetic moment and the nuclear magnetic moment and is geometry dependent. 

The chemical shift arising from interaction with the unpaired spin is a sum of two terms contact and dipolar (sometimes called pseudocontact). The Fermi contact interaction is the interaction between the nuclear spin and a net electron spin density at the nucleus, giving rise to a, the electron hyperfine interaction constant at the nucleus N, as observed in ESR experiments. The net electron spin density at the nucleus may arise directly when the unpaired electron wave function involves an s orbital centered on the nucleus, and indirectly when the closed s shells centered on the nucleus are spin-polarized by the unpaired electron in a cl or p orbital. 

The 113Cd Ti values estimated for the various peaks varied from 10 to 50 ms and obeyed the qualitative dependence upon 1/R6 (R = Mn-Cd distance) of the dipolar relaxation mechanism expected to be operative. The broad line widths were also shown to have significant contributions from the T2 relaxation induced by Mn++, with both dipolar and contact terms contributing. The 113Cd shifts of the peaks assigned to different shells were measured as a function of temperature, and observed to follow a linear 1/T dependence characteristic of the Curie-Weiss law, with slopes proportional to the transferred hyperfine interaction constant A. 

Combines sensitivity of EPR and high resolution of NMR to probe ligand super-hyperfine interactions For paramagnetic proteins enhanced chemical shift resolution, contact and dipolar shifts, spin delocalization, magnetic coupling from temperature dependence of shifts Identification of ligands coordinated to a metal centre... 

In addition to the isomer shift and the quadrupole splitting, it is possible to obtain the hyperfine coupling tensor from a Mossbauer experiment if a magnetic field is applied. This additional parameter describes the interactions between impaired electrons and the nuclear magnetic moment. Three terms contribute to the hyperfine coupling (i) the isotropic Fermi contact, (ii) the spin—dipole... 

The observed hyperfine shifts could come from contact coupling or pseudocontact interactions between the electrons and the protons. Contact shifts arise when a finite amount of unpaired electron density is transferred to the observed protons. The contact shifts of the proton resonances for isotropic systems are given by Bloembergen s (9) expression... 

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