Three-Pulse ELDOR Theory Revisited
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The current theory of three-pulse electron double resonance (PELDOR) has been generalized to the case, when paramagnetic particles (spin labels) in pairs or groups have the electron paramagnetic resonance (EPR) spectra, which overlap essentially or coincide. The PELDOR signal modulation induced by the dipole–dipole interaction between paramagnetic spin ½ particles in pairs embedded in disordered systems has been analyzed comprehensively. It has been shown that the PELDOR signal contains additional terms in contrast to the situation considered in the current theory, when the EPR spectra of the spin labels in the pairs do not overlap. In disordered systems, the pairs of spin labels have the characteristic dipolar interaction frequency. According to the current theory for pairs of spin labels, the PELDOR signal reveals the modulation with this characteristic frequency. The additional terms, which are obtained in this work, do not change the modulation frequency of the PELDOR signal for pairs of spin labels. However, these additional terms should be taken into account when analyzing the amplitude of the PELDOR signal and the amplitude of the modulation of the PELDOR signal. The consistent approach to treating the PELDOR data for the groups containing three or more spin labels has been outlined on the basis of the results for pairs of spin labels. It has been also analyzed how the spin flips and molecular motion or molecular isomerization can affect the manifestation of the interaction between the spin labels in PELDOR experiments. PELDOR experiments for the stable biradicals (biradicals I containing 1-oxyl-2,2,5,5-tetramethylpyrroline-3-yl spin labels and biradicals II containing 3-imidazoline spin labels) have been performed. The results have been interpreted within the theory developed in this work.
We are grateful to Prof. V.F. Tarasov and Dr. V.K. Voronkova for discussions and support. We express our gratitude to Prof. G. Jeschke and Dr. A.G. Maryasov for the fruitful discussion of our results and their comment that the three-pulse ELDOR considered in this work is similar to the “2 + 1” pulse train electron spin echo method. We thank Prof. G. Jeschke and Dr. L. Kulik for the biradicals they provided us with. We are very pleased to thank L.V. Mosina for language editing of our manuscript. This work was supported by the grant for the leading scientific school of the Russian Federation NSh-4653.2014.2.
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