Electron-spin relaxation

Schell S A J, Mehran F, Eaton G R, Eaton S S, Viehbeck A, O Toole T R and Brown C A 1992 Electron spin relaxation times of< , in solution Chem. Phys. Lett. 195 225-32... 

Electron Spin Relaxation in Liquids, ed. L.T. Muus and P.W. Atkins, Plenum Press, New York, 1972. 

Figure 3 Effect of the water exchange rate, kex, and the rotational correlation time, rR, on inner-sphere proton relaxivity. The plot was simulated for a particular value of the longitudinal electron spin relaxation rate, 1/Tie — 5.28xlOss 1. The marketed contrast agents all have relaxivities around 4—5mM 1s 1 in contrast to the theoretically attainable values over lOOrnM-1 s 1, and this is mainly due to their fast rotation...

Electronic relaxation is a crucial and difficult issue in the analysis of proton relaxivity data. The difficulty resides, on the one hand, in the lack of a theory valid in all real conditions, and on the other hand in the technical problems of independent and direct determination of electronic relaxation parameters. Proton relaxivity is essentially influenced by the longitudinal electron spin relaxation time, Tle, of Gd111. This decay is too fast to be assessed by commonly available techniques, though very recently Tlc values have been directly measured.74 Nevertheless,... 

Outer sphere relaxation arises from the dipolar intermolecular interaction between the water proton nuclear spins and the gadolinium electron spin whose fluctuations are governed by random translational motion of the molecules (106). The outer sphere relaxation rate depends on several parameters, such as the closest approach of the solvent water protons and the Gdm complex, their relative diffusion coefficient, and the electron spin relaxation rate (107-109). Freed and others (110-112) developed an analytical expression for the outer sphere longitudinal relaxation rate, (l/Ti)os, for the simplest case of a force-free model. The force-free model is only a rough approximation for the interaction of outer sphere water molecules with Gdm complexes. 

Up to now, no direct measurements of diffusion coefficients have been reported for any system that show the low-temperature upturn just described, and it may well be that for most systems involving hydrogen such effects would occur only at ultra-low temperatures and minuscule diffusion rates. Also, the impurities and imperfections always present in real materials might well trap nearly all the diffusant atoms at the low temperatures at which coherent transport might be expected in ideal material. However, a recent measurement by Kiefl et al. (1989) of the (electronic) spin relaxation rate of muonium in potassium chloride over a range of temperatures gives spectacular support to the concept of coherent tunneling at low temperatures. (See Fig. 6 of Chapter 15 and the associated discussion.)... 

Rapid Conformational Changes and Electronic Spin Relaxation... 

V. Electron spin relaxation and the PRE in some limiting cases... 

A. Highly symmetric systems and the Redfield theory for electron spin relaxation... 

Molecular vibrations, electron spin relaxation and the PRE Concluding remarks Acknowledgments References... 

The relaxation rates in Eqs. (12) and (13) depend now on the magnetic field in a more complicated way. Not only are the Larmor frequencies in the denominators of the Lorentzians proportional to the field, the electron spin relaxation rates are, in principle, also field-dependent. 

The symbol xso denotes the electron spin relaxation time at zero magnetic field, where Ti = and is another correlation time, associated with distortions of the paramagnetic complex caused by molecular collisions. 

The Bloembergen-Morgan equations, Eqs. (14) and (15), predict that the electron spin relaxation rates should disperse at around msTy = 1. This will make the correlation times for the dipolar and scalar interaction, %ci and respectively, in Eq. (11) dependent on the magnetic field. A combination of the modified Solomon-Bloembergen equations (12) and (13), for nuclear relaxation rates with the Bloembergen-Morgan equations for the field dependence... 

We now come back to the simplest possible nuclear spin system, containing only one kind of nuclei 7, hyperfine-coupled to electron spin S. In the Solomon-Bloembergen-Morgan theory, both spins constitute the spin system with the unperturbed Hamiltonian containing the two Zeeman interactions. The dipole-dipole interaction and the interactions leading to the electron spin relaxation constitute the perturbation, treated by means of the Redfield theory. In this section, we deal with a situation where the electron spin is allowed to be so strongly coupled to the other degrees of freedom that the Redfield treatment of the combined IS spin system is not possible. In Section V, we will be faced with a situation where the electron spin is in... 

The recent versions of the slow motion approach were applied to direct fitting of experimental data for a series of Ni(II) complexes of varying symmetry (97). An example of an experimental data set and a fitted curve is shown in Fig. 9. Another application of the slow-motion approach is to provide benchmark calculations against which more approximate theoretical tools can be tested. As an example of work of this kind, we wish to mention the paper by Kowalewski et al. (98), studying the electron spin relaxation effects in the vicinity and beyond the Redfield limit. 

V. Electron Spin Relaxation and the PRE in Some Limiting Cases... 

The assumption of a single electron spin and a single T2 holds usually for S = 1/2 and for S > 1 in certain limits. Let us assume that the instantaneous distortions of the solvation sphere of the ion result in a transient ZFS and that the time-dependence of the transient ZFS can be described by the pseudorotation model, with the magnitude of the transient ZFS equal to At and the correlation time t . The simple picture of electron relaxation for S = 1 is valid if the Redfield condition (Att <5c 1) applies. Under the extreme narrowing conditions ((Os v 1), the longitudinal and transverse electron spin relaxation rates are equal to each other and to the low-field limit rate Tgo, occurring in Eqs. (14) and (15). The low field-limit rate is then given by (27,86) ... 

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