Anisotropic /-coupling

Some values for Bq of light elements are given in Table 1.1. Values of ao as well as of Bo for the heavier atoms have been provided by J.A. Weil and J.R. Bolton [1]. It should be pointed out that the values are not measured quantities in many instances, but have been computed as quantum mechanical expectation values. 

According to single crystal ESR measurements the unpaired electron of the hydrazine cation, N2H4 (Fig. 1.10) is equally distributed over the two nitrogen atoms, 5ni = Bm = 23.3 MHz. 

From Table 1.1 we can then calculate the probability for the unpaired electron to be located at each of the nitrogen atoms  

This agrees quite well with simple molecular orbital theory. We assume that the molecule is planar, and that the atoms are joined by a-bonds in sp hybridization. Ten electrons are used up for these bonds, and additionally four are at inner Is shells of the two nitrogen atoms. There are totally seventeen electrons. The remaining three are placed in jr-orbitals. These are constmcted as a linear combination of atomic orbitals according to the LCAO method  

The ir-orbital is binding and contains two electrons with paired spins. The antibonding It -orbital contains the unpaired electron. The probability to find the unpaired electron in each of the atomic 2px-orbitals is obtained as the square of the corresponding amplitude  

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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... 

HYSCORE, is a 2D four-pulse ESEEM technique which provides correlation between nuclear frequencies originating from different electron manifolds. The sequence of four microwave pulses is tx/2—x—tx/2—/tx— t2-nl2-x-echo where the echo amplitude is measured as a function of tx and t2 at fixed x. The a-proton anisotropic couplings can be detected by this technique (Konovalova et al. 2001a, Focsan et al. 2008). 

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... 

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). 

Summary. We discuss the concept of the Berry phase in a dissipative system. We show that one can identify a Berry phase in a weakly-dissipative system and find the respective correction to this quantity, induced by the environment. This correction is expressed in terms of the symmetrized noise power and is therefore insensitive to the nature of the noise representing the environment, namely whether it is classical or quantum mechanical. It is only the spectrum of the noise which counts. We analyze a model of a spin-half (qubit) anisotropically coupled to its environment and explicitly show the coincidence between the effect of a quantum environment and a classical one. 

Results for C02 and N02 are important in that they illustrate one of the major successes of the electron spin resonance method. This is that, provided the ratio of p- to s-character is smaller than about ten, the results from the isotropic coupling (giving the s-character) and the anisotropic coupling (giving the p-character) yield a good estimate of the 8+p hybridization of the molecular orbital on the atom concerned. As shown by the squares of the coefficients of the wave function (a2) given in Table 16, both C02- and N02 have appreciable 2s-character for the orbital of the impaired electron, showing that these radicals are bent. The structure of C02 has been discussed in detail by Ovenall and Whiffen (1961) and that of N02 by Atkins et al. (1962). 

The anisotropic coupling of the halogen nuclei arises essentially from the p-character of the wave-function. The axial symmetry of p-electrons then implies that the maximum value of the anisotropic coupling is observed when the magnetic field is parallel to the direction of the p-orbital. It depends on the average value of the inverse cube of the radial wave-function and can be shown to have the value ... 

For free atoms this value can be calculated from the atomic wave-functions so that, to a first approximation, the p-electron density at the magnetic nucleus under study can be calculated from the ratio of the experimental and the atomic coupling constants. Furthermore, the direction of the largest component of the anisotropic coupling tensor coincides with the direction of the p-orbital. This is thus an important factor in the identification of the radical species. 

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... 

J. C. Bonner and M. E. Fisher, Linear magnetic chains with anisotropic coupling, Phys. Rev. 135 A640-A658 (1964). 

To assess the spin-relaxational contribution /Cr ahf of anisotropic hyperfine coupling we only take the contribution from the nitrogen nuclei into account. This approach is justified on the basis of the theoretical DPT calculations showing that the contribution of anisotropic coupling to the H spins is at least by one order of magnitude smaller. Details of the calculations of for the radical pairs are given in Ref. 23. In Fig. 10.5,... 

These five examples illustrate the agreement between theory and experiment that is considered to be more than sufficient for the calculations to verify the experimental radical assignment. It is important to stress once again that the anisotropic coupling can be calculated to a greater degree of accuracy and that some error is expected in the isotropic component. This trend is nicely... 

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