Nuclear magnetic resonance hyperfine interaction

Electron spin resonance, nuclear magnetic resonance, and neutron diffraction methods allow a quantitative determination of the degree of covalence. The reasonance methods utilize the hyperfine interaction between the spin of the transferred electrons and the nuclear spin of the ligands (Stevens, 1953), whereas the neutron diffraction methods use the reduction of spin of the metallic ion as well as the expansion of the form factor [Hubbard and Marshall, 1965). The Mossbauer isomer shift which depends on the total electron density of the nucleus (Walker et al., 1961 Danon, 1966) can be used in the case of Fe. It will be particularly influenced by transfer to the empty 4 s orbitals, but transfer to 3 d orbitals will indirectly influence the 1 s, 2 s, and 3 s electron density at the nucleus. 

In a paper that appeared in 1979, R.P.J. Merks and R. DeBeer pointed out that the sinusoidal dependence of the stimulated echo ESEEM experiment on x and T (equation 8), presented the opportunity to collect ESEEM data in both time dimensions and then apply a two-dimensional EFT to derive two important benefits. The first benefit was that suppression-free spectra should be obtained along the zero-frequency axis for each dimension while the second benefit would be the appearance of cross-peaks at (tUo, cofs) and (tw, co ) that would allow one to identify peaks that belonged to the same hyperfine interaction. This ESEEM version of the NMR COSY experiment (see Nuclear Magnetic Resonance (NMR) Spectroscopy of Metallobiomolecules) would prove invaluable for ESEEM analysis of complex spin systems. However, the disparity in spin relaxation times in the x and T time dimensions precluded the general application of this method. 

ENDOR spectroscopy offers enhanced resolution compared with conventional ESR for example, isotropic hyperfine interactions as small as 0.004 mT can be measured. This enhanced resolution is achieved partly because the technique lies between ESR and nuclear magnetic resonance (NMR) and also because redundant lines are eliminated from the spectrum essentially the ESR signal is monitored while sweeping through NMR frequencies. The simplification of the spectrum arises from the fact that each fl-value produces only two lines in the spectrum, irrespective of how many nuclei contribute to that hyperfine coupling constant. Other advantages of the method are ... 

The magnetic character of some nuclei also plays an important role in mass-independent fractionation effects. Nuclides characterized by an odd number of protons or odd number of neutrons are characterized by a non-zero nuclear spin. This is what makes these nuclides amenable to investigation by nuclear magnetic resonance (NMR) spectroscopy. A non-zero nuclear spin, however, also affects the interaction between the nucleus and the surrounding electron cloud via hyperfine nuclear spin-electron spin coupling, and thus also the behavior of these nuclides in chemical reactions [49, 50]. 

The methods of nuclear magnetic resonance (NMR) and of Mossbauer effect or nuclear gamma resonance (NGR) spectroscopy furnish a broad basis for the study of the structural, electronic, and magnetic properties of rare-earth metals, alloys, and compounds. Taken together, there is hardly a rare-earth or non rare-earth nucleus whose hyperfine interactions cannot be measured. In many cases, results can be cross-checked with measurements on several isotopes of the same element. 

A large variety of hyperfine spectroscopy methods exist that allow the detection of hyperfine and nuclear quadrupole interactions electron spin-echo envelope modulation (ESEEM), ENDOR, and ELDOR-detected NMR (electron-electron doubleresonance detected nuclear magnetic resonance) [13]. Although there are cases in which ESEEM and ENDOR perform equally well, ESEEM-like methods tend to be... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

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