Coupling tensor hyperfine

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

Hyperfine-coupling tensor components in Tesla for the intrinsic spin of iron, Spe = 3/2... 

A t)tpical feature of the Mossbauer spectra of five- or six-coordinate iron(IV) with an axial oxo group (or a OCH3, a nitrido or a imido group) is a low isomer shift (+0.1 0.15 mm s ), a large and positive quadrupole splitting (1-2 mm s ), an anisotropic hyperfine coupling tensor with moderately large values for A x/gNl N and (—16 to —23 T) and a rather small value for A Jg i (0 to —10 T)... 

D-HYSCORE was used to characterize radicals of zeaxanthin and violaxanthin photo-generated on silica-alumina and to deduce the anisotropic a-proton hyperfine coupling tensors. The couplings (MHz) were assigned based on DFT calculations. From such a comparison, the presence of the neutral radicals formed by proton loss from the radical cations was confirmed. 

The hyperfine coupling tensors of carotenoids were determined from the HYSCORE analysis of the contour line-shapes of the cross-peaks (Dikanov and Bowman 1995,1998, Dikanov et al. 2000), which provided the principal components of the tensors that appear to be rhombic. Such tensors are characteristic of planar conjugated radicals with the unpaired spin in a pz orbital of the carbon of the C-H group. 

The hyperfine constant a in Eq. (1) was also taken to be a scalar quantity for the hydrogen atom however, it is in general a tensor because of the various directional interactions in a paramagnetic species. The hyperfine term in the spin Hamiltonian is more correctly written as S-a-I, where a is the hyperfine coupling tensor. 

In addition to g tensor anisotropy, EPR spectra are often strongly affected by hyperfine interactions between the nuclear spin I and the electron spin S. These interactions take the form T A S, where A is the hyperfine coupling tensor. Like the g tensor, the A tensor is a second-order third-rank tensor that expresses orientation dependence, in this case, of the hyperfine coupling. The A and g tensors need not be colinear in other words, A is not necessarily diagonal in the coordinate systems which diagonalize g. 

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 authors also reconsidered radical 20, which, in the current work, was formed by x-irradiation and studied at 77 K. The experimentally determined hyperfine coupling tensors for the two methylene protons have the same principal values and agreed with the tensors found in the earlier work.16 These tensors are presumed to be the average of the two individual proton tensors. By assuming that C5 is sp2 hybridized the authors were able to calculate, from the observed average tensors, that Ami = 1.06 mT and Amai = 3.45 mT for the methylene protons. Using the individual tensors for the methylene protons and a 3.6 mT isotropic coupling for the C4(H) proton, a satisfactory simulation of the... 

Purines. - A study of anhydrous deoxyadenosine (compound iv) single crystals x-irradiated (70 kGy) and investigated at 10 K found four base radicals (21-24) and one deoxyribose radical (25) (see p. 251).20 Radical 21, a de-protonated electron loss product, was stable to 100 K and readily photobleached at 10 K. Its nitrogen hyperfine coupling tensors were estimated by using values that resulted in acceptable EPR spectral simulations these were A(N10) = (1.76, 0, 0) mT, A(N3) = (0.99, 0, 0) mT and A(N1) = (0.34, 0, 0) mT. 

A, B are the hyperfine interactions expected for an electron in pure s and pure p orbitals respectively. The elements of the p-orbital hyperfine coupling tensors have cylindrical symmetry and the principal elements can be expressed aa A + B, A — B, A — B. These are obtained from the experimental tensor by use of the relationships (Ax + Ay + AJIZ = A, and Ax-A = B. 

Parameters Derived from Hyperfine Coupling Tensors of Table 14... 

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]... 

Here /, is the 13C nuclear spin, S is the unpaired electronic spin, and A j- is the Fermi contact hyperfine coupling tensor. This coupling is identical for all 13C nuclei as long as the C60 ion is spherical, but becomes different for different nuclei after the Jahn-Teller distortion leading to an inhomogeneous frequency distribution. The homogeneous width of the 13C NMR lines is, on the other hand, mainly determined by the electron-nuclear dipolar interaction... 

X 7 0) with six independent components are widespread the polarizability and the hyperfine coupling tensors are well-known representatives. 

The spectra of polycrystalline samples are broad and represent the envelope of all the anisotropic couplings together with the g-anisotropy. Although in favourable cases it is possible to extract the principal values of the g- and hyperfine coupling tensors from such... 

Here Ra is another orbital-reduction factor (0.5 < Ra < 1.0), P = 2gjvpe 3N. The anisotropic components of the hyperfine coupling tensor (a and a) are dehned as... 

Where (3 is the Bohr magneton, H0 is the applied magnetic field, g is the g-tensor, S is the electron spin, I is the nuclear spin, gn and (3n.are the nuclear splitting factor and the nuclear magneton. The hyperfine coupling tensor A consists of an isotropic contact interaction... 

Table 18-1. Hyperfine Coupling Tensors for Radicals I and II Observed in Adenosine...

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