ESEEM powder spectra

The subject has been treated in recent monographs and reviews for applications like solvation structure of electrons, atoms and radicals [54], coordination of ligand molecules to transition metal complexes, metalloproteins and photosynthetic centers [55, 56]. 

The hyperfine couplings can be obtained by direct analysis of the modulations on the echo decay curve. The analysis must then generally be made by fitting a simulated curve to the experimental. This procedure was usually employed in early work. Analysis of frequency domain spectta obtained by Fourier tfansformation (FT) is more common in recent studies. The resulting FT or frequency domain spectrum has lines with the same frequencies as in ENDOR. Like in ENDOR visual analyses of FT spectra are often followed by simulation to obtain accurate values for the anisotropic hyperfine coupling. 

ENDOR and FT ESEEM spectra differ mainly in the intensities of the lines, which in ESEEM are given by a factor related to the ESR transition probabilities. A necessary prerequisite for modulations in the time domain spectrum is that the allowed Ami = 0 and forbidden Ami = 1 hyperfine lines have appreciable intensities in ESR. The zero ESEEM amplitude thus predicted with the field along the principal axes of the hyperfine coupling tensor is of relevance for the analysis of powder spectra. Analytical expressions describing the modulations have been obtained for nuclear spins I = V2 and / = 1 [54, 57] by quantum mechanical treatments that take into account the mixing of nuclear states under those conditions. Formulae are reproduced in Appendix A3.4. 

Allowed and forbidden ESR transitions can also occur by the nuclear quadrupole interaction for / V2. Analytical formulas are applicable when the quadrupole energy is small compared to the combined effect of hyperfine and nuclear Zeeman interactions [57]. Numerical solutions have been applied when this approximation does not hold [58]. Systems with S Vi require special treatments [59, 60]. 

Methods frequently employed in the analysis of ESEEM and HYSCORE data are summarized in Sections 3.4.3.1-3.4.3.7. Advanced methods briefly mentioned in Section 3.4.3.S are described in dedicated works [54, 61]. Simulation programs are referenced in Section 3.4.3.S, while mathematical treatments have been placed in Appendix A3.4. 

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More advanced experiments, such as ENDOR, electron spin echo envelope modulation (ESEEM), or relaxation measurements by pulsed ESR rely on a selective excitation of spins close to the resonance field. Usually, the powder ESR spectrum is much broader than the excitation bandwidth of the pulses, which is in the range between 2 and 10 G. In cases where one anisotropic interaction dominates the spectrum, the experiments thus select contributions only from certain orientations of the molecule with respect to the external magnetic field. Such orientation selection is more efficient and easier to interpret at a field that is high enough for the g anisotropy to dominate. Finally, the size of mw resonators scales with wavelength and thus scales inversely with frequency. At higher frequency, spectra can thus be measured with much smaller sample volumes, yet the concentration does not need to be significantly increased. 

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