Electron spin relaxation rates

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...

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.)... 

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 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... 

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. 

I J XgJ, Xg2- In this case, the two metal ions can be considered to have a single set of electron spin relaxation rates. If no additional relaxation mechanisms are established, such common relaxation rates are about equal to the fastest relaxation rates of the uncoupled spins. Actually, calculations indicate the presence of different electron relaxation rates for each level and for each transition. The electron relaxation rates for the pair are the sum of the rates of the two spins, weighted by coefficients depending on the transition 108). 

Fig. 1. A Gd(III) complex with one inner sphere water molecule, surrounded by bulk water. Inner sphere proton relaxivity is due to interactions between the Gd electron spin and the water protons on the inner sphere water. Outer sphere relaxivity arises from interactions between the Gd electron spin and bulk water protons. rR stands for the rotational correlation time of the molecule, kex for the water/proton exchange rate and 1/T, 2c for the electron spin relaxation rates of the Gd(III)...

Fig. 2. Simulated inner sphere H relaxivities as a function of the rotational correlation time, tR) and of the water exchange rate, k, at two different magnetic fields and two different electron spin relaxation rates (Tle = 2.9 x 10 8 s (top) and 2.9 x 10-9 s (bottom) rv has been fixed to 1 x 10 12 s )...

For paramagnetic relaxation-reagents, the electron-spin relaxation-rates are long (r,e 2e > 10 ° s), SO that, for small molecules, = x, and x = x. Because this is the same correlation-time as in all other terms of the nuclear-spin relaxation-time r, where... 

Since the electron spin relaxation rate in Eq. 114 is dominated by the low-frequency modes, an understanding of the origin of the unusual temperature dependence for proteins is of particular interest as a probe of the motional properties. Use of the normal-mode calculation for BPTI136 yields an exponent 7 = 0.35 for the density of states in the frequency range of interest (0 to 50 cm-1).493 This is in accord with the experimental estimates, although BPTI is not one of the proteins studied experimentally. However, the inelastic neutron data,29 as well as normal-mode calculations,36a suggest that the frequency dependence of g( ) is similar for different proteins in the low-frequency range. 

For comparison of the hybridization in TTF-TCNQ and TSeF-TCNQ one should use an experimentally measured quantity sensitive to this parameter like the electron spin relaxation rates. In order to understand how the EPR linewidth has any bearing on the band structure, let us understand what relaxation processes contribute to the measured linewidth. The dominant... 

Colvin, J. T Stapleton, H. J. Fractal and spectral dimensions of biopolymer chains solvent studies of electron spin relaxation rates in myoglobin azide. J. Chem. Phys. 1985, 82(10), 4699 706. 

Figure 2. Electron-spin relaxation rate constants for D" " in Mn-depleted PSII membranes (A), in dark-adapted, -state PSII membranes ( ), in S2-state PSII membranes (O), and for the model tyrosine radical ( ).

In this context slowly-relaxing means that the electron spin relaxation rates are slow relative to the magnitude of the dipolar coupling, expressed in hz. This case includes nitroxyl spin labels at room temperature and below and some transition metals at lower temperatures. 

Gaffiiey BJ, Eaton GR, Eaton SS. 1998. Electron spin relaxation rates for high-spin Fe(ni) in iron transferrin carbonate and iron transferrin oxalate. J Phys Chem B 102(28) 5536-5541. 

Figure 8 Mossbauer spectra of a low-spin ferric haemoglobin HiCN - at (A) 195 K, (B) 77 K and (C) 4.2 K. The broadening at 77 K relative to 195 K is due to the slower electron spin relaxation rate. At 4.2 K the relaxation is so slow that the hyperfine pattern is resolved, but complex.

The spin-lattice relaxation, with a characteristic time Ti, is responsible for maintaining the population difference between levels, N and N+. The spin-spin relaxation time T2 reflects the lifetime of the excited state and its effect on the line width. If the electron-spin relaxation rate is too rapid, the lifetime of the excited state is short and the EPR spectrum becomes broadened. At high temperatures the spectrum may become too broad for detection, hence the use of cryogenic temperatures for some transition ions. However, if the spin-lattice relaxation is too slow, the population difference N - N+ cannot be maintained, and the amplitude of the signal is attenuated, a situation known as microwave power saturation. Electron-spin relaxation times may be estimated by measuring the amplitude of the signal as a function of applied microwave power. 

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