The main mechanisms for electron relaxation

Mechanisms analogous to those illustrated in Fig. 3.1 apply also to electron relaxation (see below). However, electrons have other more efficient relaxation mechanisms which overcome the former ones. They are based on the presence of spin orbit coupling. Molecular motions modulate the orbital magnetic moment and then affect the electron spin. Several possible mechanisms for electron relaxation 

Solid-state theories ascribe electron relaxation to the coupling of electronic spin transitions with transitions between lattice vibrational levels, or more generally with phonons. Disappearance (depopulation of a vibrational level) or creation (population of a vibrational level) of phonons modulate the orbital component of the electron magnetic moment. 

Electronic relaxation times of some common paramagnetic metal ions and nuclear relaxation rates for a proton at 5 A from the metal, at 800 MHz H resonance frequency, due to dipolar and Curie relaxation, estimated from Eqs. (3.16), (3.17), (3.29) and (3.30), with rc = rs 

Metal ions more suitable for high resolution NMR are underlined. 

Following the solid-state approach, equations have been derived [8,9] also for the electron spin relaxation of 5 = V2 ions in solution determined by the aforementioned processes. Instead of phonons, collisions with solvent should be taken into consideration, whose correlation time is usually in the range 10 11 to 10 12 s. However, there is no satisfactory theory that unifies relaxation in the solid state and in solution. The reason for this is that the solid state theory was developed for low temperatures, while solution theories were developed for room temperature. The phonon description is a powerful one when phonons are few. By increasing temperature, the treatment becomes cumbersome, and it is more convenient to use stochastic theory (see Section 3.2) instead of analyzing the countless vibrational transitions that become active. 

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The electron relaxation is usually field dependent and the main mechanism for electron relaxation is the modulation of transient ZFS caused by collisions with solvent molecules. Small static ZFS have been estimated for several manganese(II) and gadolinium(III) proteins, and somewhat larger ones for iron(III) compounds. In such low symmetry systems, it is reasonable to expect the magnitude of transient ZFS to be related to that of the static ZFS, as the former can be seen as a perturbation of the latter. As a consequence, systems with increasing static ZFS experience faster electron relaxation rates. Modulation of static ZFS by rotation could be an additional mechanism for relaxation, which may coexist with the collisional mechanism. 

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