Electron spin relaxation and the PRE in some limiting cases

Electron Spin Relaxation and the PRE in Some Limiting Cases 

The slow-motion theory describes the electron relaxation processes implicitly, through a combined effect of static and transient ZFS, and reorienta-tional and pseudorotational dynamics. This is necessary under very general conditions, but simpler descriptions, appropriate in certain physical limits, can also be useful. In this chapter, we review some work of this type. 

Highly Symmetric Systems and the Redfield Theory for Electron Spin Relaxation 

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)  

Using the case of S = 5/2 as an illustrative example, he demonstrated that it was possible to derive closed-form analytical expressions for the PRE of the form of the SBM equations times (1 + correction term). For typical parameter values, the effect of the correction term was to increase the prediction of the SBM theory by 5-7%. A similar approach was also applied to the S = 7/2 system, such as Gd(III) (101), where the correction terms could be larger. For that case, the estimations of the electron spin relaxations rates, obtained in the solution for PRE, were also used for simulations of ESR lineshapes. 

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

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