Fermi-contact interactions

From the isotropic coupling constant one may calculate C12, the fractional occupancy of the nitrogen s orbital, which is equal to AUo/Ao. The term Ao is the Fermi contact interaction for an unpaired electron in a pure nitrogen 2s orbital. For NO2 the value of ci2 = 56.5/550 = 0.103. The fraction of the unpaired electron associated with the N nucleus is then... 

Fermi contact interaction. The coupling constant of the Fermi contact term for the nucleus N has the form127 ... 

The nuclear spins can interact with the time-averaged magnetic moments via either through-space (dipolar) or through-bond (Fermi-contact) interactions. The Li MAS NMR spectrum of LiMn204 is... 

This is a measure of the unpaired electron spin density that is transferred from the paramagnet to the nucleus of the spin under observation. In the regime defined by eq 2, the NMR shift (d = (Acolcoo)) induced by the Fermi-contact interaction is directly proportional to... 

In these expressions, e and N refer to electron and nucleus, respectively, Lg is the orbital angular moment operator, rg is the distance between the electron and nnclens. In and Sg are the corresponding spins, and reN) is the Dirac delta fnnction (eqnal to 1 at rgN = 0 and 0 otherwise). The other constants are well known in NMR. It is worth mentioning that eqs. 3.8 and 3.9 show the interaction of nnclear spins with orbital and dipole electron moments. It is important that they not reqnire the presence of electron density directly on the nuclei, in contrast to Fermi contact interaction, where it is necessary. 

Although attempts have been made to correlate the hyperfine field of a mixed-valence compound with the weighted mean of the Fermi contact-interaction field H, = 220 < Sz > kOe , the orbital and spin-moment contributions Hl and Hd, which may be comparable to H, at Fe(II) ions, make any such correlations dubious ... 

Nuclear spin-spin interactions between directly bonded nuclei also are considered to proceed primarily via the Fermi contact interaction mechanism. Here, however, there is no need to consider structures representing deviations from perfect pairing and indeed such have been ignored in calculations to date as of being of secondary importance. 

The principal M—F coupling mechanism in inorganic fluorides also is believed to be via the Fermi contact interaction. Here, even semiquantita-tive treatment is much more difficult. M—F coupling is possible through... 

The other mechanism is called the Fermi contact interaction and it produces the isotropic splittings observed in solution-phase EPR spectra. Electrons in spherically symmetric atomic orbitals (s orbitals) have finite probability in the nucleus. (Mossbauer spectroscopy is another technique that depends on this fact.) Of course, the strength of interaction will depend on the particular s orbital involved. Orbitals of lower-than-spherical symmetry, such as p or d orbitals, have zero probability at the nucleus. But an unpaired electron in such an orbital can acquire a fractional quantity of s character through hybridization or by polarization of adjacent orbitals (configuration interaction). Some simple cases are described later. 

In high-spin ferric iron this a-valuc is the result of the Fermi contact interaction alone. Hence, this a-value comprises an experimental determination of the Fermi contact interaction of the ferric iron in this protein. The value of —2gsPPx is, by the above procedure, equal to... 

The hyperfine coupling tensor (A) describes the interaction between the electronic spin density and the nuclear magnetic momentum, and can be split into two terms. The first term, usually referred to as Fermi contact interaction, is an isotropic contribution also known as hyperfine coupling constant (HCC), and is related to the spin density at the corresponding nucleus n by [25]... 

The hyperfine coupling frequency in the hydrogen ground state is given to the leading term by the Fermi contact interaction, yielding... 

The isotropic hyperfine coupling observed in e.s.r. spectra of radicals arises from the Fermi-contact interaction between the electronic spin angular... 

The remaining important interactions which can occur for a 2 or3X molecule involve the presence of nuclear spin. Interactions between the electron spin and nuclear spin magnetic moments are called hyperfine interactions, and there are two important ones. The first is called the Fermi contact interaction, and if both nuclei have non-zero spin, each interaction is represented by the Hamiltonian term... 

This is a very important result. The first term in the last line of (4.13) represents the so-called Fermi contact interaction between the electron and nuclear spin magnetic moments, and the second term is the electron-nuclear dipolar coupling, analogous to the electron-electron dipolar coupling derived previously in (3.151). The Fermi contact interaction occurs only when the electron and nucleus occupy the same position in Euclidean space, as required by the Dirac delta function S(-i Rai). This seemingly... 

Fermi contact interaction between the electron and nuclear spins. 

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