Resonance condition hyperfine interactions

When the hyperfine interaction is much smaller than the Zeeman interaction ( much means approximately two orders of magnitude or more), as is usually the case in X-band, then the resonance condition is... 

The example of nitrogen lines in the spectrum of cobalamin points to the necessity of also writing out resonance conditions for the presence of ligand hyperfine interaction. In general we have ... 

The superhyperfine splittings are sufficiently small to ignore second-order effects at X-band, and for adducts of the nitrone compounds splitting from the nitrone-N and the beta-H are the only resolved hyperfine interactions, thus affording the extremely simple resonance condition (cf. Equation 5.10)... 

One key aspect of ENDOR spectroscopy is the nuclear relaxation time, which is generally governed by the dipolar coupling between nucleus and electron. Another key aspect is the ENDOR enhancement factor, as discussed by Geschwind [294]. The radiofrequency frequency field as experienced by the nucleus is enhanced by the ratio of the nuclear hyperfine field to the nuclear Zeeman interaction. Still another point is the selection of orientation concept introduced by Rist and Hyde [276]. In ENDOR of unordered solids, the ESR resonance condition selects molecules in a particular orientation, leading to single crystal type ENDOR. Triple resonance is also possible, irradiating simultaneously two nuclear transitions, as shown by Mobius et al. [295]. 

For nitroxides in dilute liquid solution, the generally anisotropic spin Hamilton operator is simplified tremendously and, if imresolved proton hyperfine couplings are treated as line broadening, only the electron-Zeeman interaction and the hyperfine coupling to the magnetic nucleus (7 = 1) remain [20]. The g- and hyperfine (4-) tensors are averaged to isotropic values due to fast motion of the spin probe and the resonance condition for the irradiated microwave becomes... 

The ESR g-factor is also known as the Lande 7-factor or spectroscopic splitting factor and depends on the resonance condition for ESR (Eq. 3) and is independent of both applied field and frequency. The 7-factor of a free electron is 2.002322, while the 7-factors of organic free radicals, defect centers, transition metals, etc. depend on their electronic. structure. The 7-factors for free radicals are close to the free electron value but may vary from 0 to 9 for transition metal compounds. The most comprehensive compilations of 7-factors are those published in [75], [76]. The magnetic moments and hence 7-faclors of nuclei in crystalline and molecular environments are anisotropic, that is the 7-factor (and hyperfine interactions) depend on the orientation of the sample. In general, three principal 7-factors are encountered whose orientation dependence is given by ... 

ESR spectra of free radicals trapped in polymer matrices reflect the physical properties of the matrix polymer, usually indicated by g-values, hyperfine coupling constants, and line widths of the components of the whole spectra. Effects of the crystalline field and quadrupole interaction are usually very small in the case of polymer radicals. The g-value is defined by the resonance condition ... 

The hyperfine interaction. A, of an unpaired electron with nearby nuclei can be obtained by the electron-nuclear double resonance (ENDOR) technique. The ENDOR resonance condition is given by... 

Observed linewidths of NMR signals in paramagnetic systems vary enormously and the conditions that govern the observed widths are considerably more complex than in diamagnetic systems. Swift (30) reviewed the problem some years ago. Relaxation times of spin-j nuclei are governed by dipolar and hyperfine exchange (Fermi contact) relaxation processes. The dipolar interaction is normally dominant except in some delocalized systems in which considerable unpaired spin density exists on nuclei far removed from the metal ions (e.g. Ti-radicals). Distinction between the two processes can be made by consideration of the different mathematical expressions involved. For dipolar relaxation when o)fx 1 (t = rate constant for rotation of the species containing the coupled pair and to, = nuclear resonance frequency) ... 

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 correlation patterns are more complex if the nuclear quadrupole, the hyperfine, and the nuclear Zeeman interactions are of the same order of magnitude. This situation is often encountered in X-band HYSCORE spectra of weakly coupled nitrogen nuclei in transition metal complexes. A special case, where the spectrum is considerably simplified, is the so-called exact cancellation condition, where Xs 2 coi. Under this condition, the nuclear frequencies within one of the two ms manifolds correspond to the nuclear quadrupole resonance (NQR) frequencies coq = 2Kt], co = K(3 - t]), and cu+ = K 3 + rj) [43], which are orientation independent. Consequently, correlation peaks involving these frequeneies appear as narrow features in the nuclear frequency spectrum. 

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