Coupling tensor

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)... 

Oxirane is an important Lewis base in the present context. The O atom carries two equivalent n-pairs of electrons, as it does in H20, but oxirane has the advantage over water in that it is possible to determine both angles 0 and 9 for its complexes with HC1 and ClF because the non-zero off-diagonal element Xab(Cl) of the Cl nuclear quadrupole coupling tensor is available. The corresponding Lewis base in which an S atom carries two equivalent n-pairs is thiirane. Each of the pair of complexes (CL S- -HC1 and (CL S- -ClF has Cs symmetry and here it is the off-diagonal element Xac(Cl) that is non-zero... 

Use of CW ENDOR techniques to detect P-proton hyperfine couplings and matrix nuclei Pulsed ENDOR techniques to detect P-proton hyperfine couplings and matrix nuclei HYSCORE techniques to detect a-proton anisotropic coupling tensors... 

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 cross-peak coordinates represent two frequency values, va and vp, where va + vp=2v, and v is the proton frequency. When plotted in the coordinates v2a and v2p, the contour lineshape is transformed into a straight line segment. An extrapolation of this straight line permits the determination of the hyperfine tensors. A curve obtained by choosing some frequencies in the range will intersect the line defined by the squares of the values v2a and v2p in two points. The values where the curve intersects the experimental data are (val, vpi) and (va2, vp2), where va=A/2 + v, and vp= Vj-A/2. This gives two values of the anisotropic coupling tensor, Ar... 

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. 

The dipolar coupling tensor D is defined by Eq. (6D). Again taking the case of an unpaired electron localized in a 2pz atomic... 

The coupling tensor Rlm in the laboratory frame is time dependent due to the motions of spin-bearing molecules. It can be expressed in terms of the rotational transformation of the corresponding irreducible components pln in the principal axis system (PAS) to the laboratory frame by... 

Throughout this paper the principal values of magnetic coupling tensors are denoted by lower indices x, y, z if the corresponding principal axes coincide with the g tensor axes. In all other cases, indices 1, 2, 3 are used... 

Proton ENDOR. For the assignment of the proton hfs tensors to corresponding protons in the Cu(sal)2 molecule (Fig. 30) or in the Ni(sal)2 host, the point-dipole formula (5.6) was applied. By symmetry arguments, one of the principal axes of the coupling tensors of the protons belonging to the planar Cu(sal)2 compound has to lie normal to the complex plane. Indeed, the coupling tensors of H11, H15 and H16 are found to behave in this... 

Composite-pulse decoupling schemes like WALTZ [36, 37], DIPSI [38], or GARP [39], which are used in solution-state NMR, have failed to offer any significant improvements in the solid state compared to CW decoupling. The residual line width in CW-decoupled spectra is dominated by a cross term between the chemical-shielding tensor of the protons and the heteronuclear dipolar-coupling tensor [40, 41]. 

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