Anisotropic coupling constants

Carotenoid radical intermediates generated electrochemically, chemically, and photochemically in solutions, on oxide surfaces, and in mesoporous materials have been studied by a variety of advanced EPR techniques such as pulsed EPR, ESEEM, ENDOR, HYSCORE, and a multifrequency high-held EPR combined with EPR spin trapping and DFT calculations. EPR spectroscopy is a powerful tool to characterize carotenoid radicals to resolve -anisotropy (HF-EPR), anisotropic coupling constants due to a-protons (CW, pulsed ENDOR, HYSCORE), to determine distances between carotenoid radical and electron acceptor site (ESEEM, relaxation enhancement). 

With a 13CH3 group we can observe two anisotropic coupling constants —one between the protons (Bun) and one between carbon-13 and the protons (Ben)- For the calculation of Bun and BCn we neglect all anisotropic contributions of the indirect spin-spin interactions as well as the influence of vibrational motions. We use Equations 3, 10,... 

Table 28 Calculated and Experimental Hyperfine Isotropic a) and Anisotropic Coupling Constants and Nuclear Quadrupole (P) Coupling Constant for MgO [Li] ...

ENDOR methods can be especially useful for investigating biological systems because powder-type spectra can yield isotropic and anisotropic coupling constants with a higher resolution and precision than can conventional ESR spectroscopy. Typical examples are the radical ions occurring as primary photoproducts in reaction centers of photosynthetic bacteria. Liquid-state ENDOR measurements have been made on biologically active organic species such as the vitamin quinones. 

The and operators determine the isotropic and anisotropic parts of the hyperfine coupling constant (eq. (10.11)), respectively. The latter contribution averages out for rapidly tumbling molecules (solution or gas phase), and the (isotropic) hyperfine coupling constant is therefore determined by the Fermi-Contact contribution, i.e. the electron density at the nucleus. 

Tile ESR spectra of the radical anions, generated by one-electron reduction of the a-oxothioketone 173 and the dithiete 172, were determined, and spin densities were calculated from the coupling constants and, especially, from the anisotropic values (87CB575). 

Notice that the associated spin model has the following three properties (1) it is, in general, anisotropic (i.e. a-2 / CI3), (2) its set of coupling constants hi, hij, /1123) are interdependent (this should be obvious from equation 7.63, which provides a parameterization of each of these seven constants in terms of our original four independent conditional probabilities, aj (equation 7.58)), and (3) its partition function, Z, can be calculated exactly. 

Finally, it is noteworthy that in addition to the isotropic part of spin coupling as treated above, there may also be an anisotropic contribution due to the presence of anisotropic exchange [114] or dipole interaction [106]. In this case, the exchange coupling constant is replaced by a tensor... 

Because the atoms occupy highly symmetric lattice positions, anisotropic parameters such as chemical shift anisotropy (CSA) or nuclear quadrupole coupling constants (NQCC) are either zero or fairly small. 

The MesSn" radical appears to couple to only two of the methyl groups. Moreover, the isotropic and anisotropic tin hyperfine coupling constants indicate that the Sn 5s and 5p orbital contributions are roughly 0.03 and 0.32, respectively (Table 6). Thus, compared... 

For protons (ADD) = 0, so that the dipolar coupling is determined by the two- and three-center contributions. Recently, Keijzers and Snaathorst1271 have shown that the three-center contributions (ADD)3 should not, in general, be neglected in the computation of anisotropic proton hf coupling constants. In most ENDOR work, however, only the two-center contribution (ADD)2>, ( distant term) has been considered. 

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