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Unpaired electrons that are localized in weakly overlapping orbitals are best treated as individual spins. As electrons are indistinguishable from each other, they can be exchanged even between weakly overlapping orbitals. This exchange leads to a small coupling of the two electrons. Weak exchange (ex) coupling, which is typical for electrons that are separated by at least 5 Å, is an isotropic interaction that is described by the Hamiltonian in Eq. 4, Hˆex ϭ J(Sˆx Iˆx ϩ Sˆy Iˆy ϩ Sˆz Iˆz ) (4) where J is the exchange coupling.

During time τ before echo formation, the coherence thus acquires a phase Ϫ(∆νϪd)τ. The total phase φecho at the time of echo formation is τ (a) ν1 τ π/2 π t ν2 β τ1 (b) ν1 π/2 τ1 τ2 π τ2 π t ν2 β Fig. 3. Pulsed ELDOR (DEER) sequences. (a) Basic PELDOR experiment. Interpulse delay τ is fixed, interpulse delay t is varied, and echo intensity is recorded. (b) Four-pulse DEER. In the constant-time version, interpulse delays τ1 and τ2 are fixed, interpulse delay t is varied, and the intensity of the second echo (solid line) is recorded.

Eds. Symposium Series Vol. 1; MMI Press: Harwood, Chur, 1980. 22. G. : Chichester, UK, 1996; Chapt. 9, pp. 231–252. 23. ; Huber, W. Electron Spin Resonance Spectroscopy of Organic Radicals, WileyVCH: Weinheim, 2003. 24. I. Spin Exchange, Springer: Berlin, 1980. qxd 24 8/8/2006 1:20 PM Page 24 CONTINUOUS-WAVE AND PULSED ESR METHODS 25. W. J. Polym. Sci. A 2004, 42, 5031. 26. ; Huber, M. J. Phys. Chem. A 2001, 105, 10967. 27. L. Proc. Natl. Acad. Sci. USA 1994, 91, 1667. 28. L. ; Academic Press: New York, 1976; Chapt.

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