Hyperfine coupling tensor anisotropic

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 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... 

Unfortunately, it is generally not possible to distinguish between p and d character from the anisotropic part of the hyperfine coupling tensor, since both give rise to a tensor of the same type. For simplicity, it is assmned, for radicals of the class under consideration, that the anisotropy arises largely from the (n) p level, and only slightly from the (n) d level. This neglect is not necessarily justified, however, except, of comse, for oxy radicals of the first row nonmetals. 

This procedure (neglect of nuclear Zeeman term) is sometimes also adopted to obtain hyperfine coupling tensors from ESR measurements of free radicals. The method is, however, not suitable for the analysis of hyperfine structure due to a-H in jr-electron radicals of the type )Cc-H at X-band, and other cases where the anisotropic hyperfine coupling and the nuclear Zeeman energy are of comparable magnitudes, as discussed for case 3 below. 

Powder ENDOR lines are usually broadened by the anisotropy of the hyperfine couplings. The parameters of well resolved spectra can be extracted by a visual analysis analogous to that applied in ESR. The principle is indicated in Fig. 3.25 for an 5 = V2 species with anisotropic H hyperfine structure, where the hyperfine coupling tensor of axial symmetry is analysed under the assumption that 0 < A < Aj. < 2 vh- The lines for electronic quantum numbers ms = V2 and -Vi, centered at the nuclear frequency vh 14.4 MHz at X-band, are separated by distances equal to the principal values of the hyperfine coupling tensor as indicated in the figure. Absorption-like peaks separated by A in the 1st derivative spectrum occur due to the step-wise increase of the amplitude in the absorption spectrum, like in powder ESR spectra (Section 3.4.1). The difference in amplitude commonly observed between the ms = /2 branches is caused by the hyperfine enhancement effect on the ENDOR intensities first explained by Whiffen [45a]. The effect of hyperfine enhancement is apparent in Figs. 3.25 and 3.26. 

Fig. 4.7 Anisotropic ESR spectra of monovalent copper complex in frozen toluene solution, (a) 2 mm band ESR (140 GHz), (b) 3 cm band ESR (9.6 GHz) experimental spectnim, (b ) simulated spectrum with g = (2.0078, 2.0059, 1.9991), A(P ) = (20, 23, 20) G, A(P) = (8, 11, 8) G, and A(Cu) = (20, 0, 17) G for the principal values of the g-tensor and hyperfine coupling tensors of two inequivalent phosphorous and one Cu atom. The spectra are adapted from [R.R. Rakhimov et al. Chem. Phys. Letters 255, 156 (1996)] with permission from Elsevier...

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... 

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... 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

These workers (Adrian et al., 1962) also studied the spin resonance spectrum of DCO radicals and obtained remarkably narrow lines and shoulders which gave sufficient detail that the anisotropic hyperfine tensor could be deduced. This result then enabled them to extract the data tabulated from the spectrum of HCO. In particular, it is pointed out that as the g- and hyperfine-anisotropies have different principal axes, there has to be an extra term (Ayz) where the hyperfine tensor is expressed in terms of the axes of the gr-tensor. A careful analysis of all the data led these authors to the conclusion, based entirely upon experiment, that the large isotropic hyperfine coupling must be positive. 

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