Electronic spin-lattice relaxation time

Gayda, J.-P., Bertrand, P., Deville, A., More, C., Roger, G., Gibson, J.F., and Cammack, R. 1979. Temperature dependence of the electronic spin-lattic relaxation time in a 2-iron-2-sulfur protein. Biochimica et Biophysica Acta 581 15-26. 

Furthermore, the method of orientation selection can only be applied to systems with an electron spin-spin cross relaxation time Tx much larger than the electron spin-lattice relaxation time Tle77. In this case, energy exchange between the spin packets of the polycrystalline EPR spectrum by spin-spin interaction cannot take place. If on the other hand Tx < Tle, the spin packets are coupled by cross relaxation, and a powder-like ENDOR signal will be observed77. Since T 1 is normally the dominant relaxation rate in transition metal complexes, the orientation selection technique could widely be applied in polycrystalline and frozen solution samples of such systems (Sect. 6). 

Fig. 13. Predicted magnetic field dependence of the electron spin lattice relaxation time. Solid line pseudorotation model dashed line spin dynamics calculation. Reproduced with permission from Odelius, M. Ribbing, C. Kowalewski, J. J. Chem. Phys. 1996,104, 3181-3188. Copyright 1996 American Institute of Physics.

In these equations, the symbols have their customary meanings (see Toth et al. in this volume for an excellent review of the topic), and the correlation times given in Eq. (3) have the following typical values at 50 MHz in water Tle (electron spin-lattice relaxation time) =10 ns, T2e (electron spin-spin relaxation time) = 1 ns, rm (inner sphere water exchange correlation time) = 130 ns [3], and rR = 60 ps. These values, in the context of Eq. (1 - 3), show why rotational dynamics control relaxivity for such chelates. 

Fig. 21 Temperature dependence of the electron spin-lattice relaxation time Tle in powdered...

If the metal to proton distance, r, is known it is then possible to determine the correlation time, rc. An alternative method measures the nuclear TJm enhancement at several frequencies then the geometric factor and the correlation time can be calculated through a least squares analysis59. It is usually assumed that rc is determined by the electron spin-lattice relaxation time. 

As we pointed out in Section 4.11, lanthanide shift reagents owe their utility partly to the fact that the electron spin-lattice relaxation time for the lanthanides is very short, so that NMR lines are not exceptionally broad. On the other hand, there are shiftless paramagnetic reagents that shorten both Tx and T2 to a moderate degree without causing contact or pseudocontact shifts. 

Low-spin Fe(iii) porphyrins have been the subject of a number of studies. (638-650) The favourably short electronic spin-lattice relaxation time and appreciable anisotropic magnetic properties of low-spin Fe(iii) make it highly suited for NMR studies. Horrocks and Greenberg (638) have shown that both contact and dipolar shifts vary linearly with inverse temperature and have assessed the importance of second-order Zeeman (SOZ) effects and thermal population of excited states when evaluating the dipolar shifts in such systems. Estimation of dipolar shifts directly from g-tensor anisotropy without allowing for SOZ effects can lead to errors of up to 30% in either direction. Appreciable population of the excited orbital state(s) produces temperature dependent hyperfine splitting parameters. Such an explanation has been used to explain deviations between the measured and calculated shifts in bis-(l-methylimidazole) (641) and pyridine complexes (642) of ferriporphyrins. In the former complexes the contact shifts are considered to involve directly delocalized 7r-spin density... 

In an isotropic conductor, the electronic spin-lattice relaxation time... 

The NMR spectra of these complexes under ambient conditions exhibit sharp, paramagnetically shifted features that can span up to 400 ppm (90, 134). Electron exchange is fast on the NMR time scale, so there is an effective twofold symmetry, which approximately halves the number of distinct features observed. The sharpness of the resonances is due to the short electron spin-lattice relaxation time of the Fe(II) center, which allows even the CH2 protons adjacent to the coordinated nitrogen atoms to be observed. 

Two mechanisms of cw ENDOR are generally observed, denoted as steady-state and packet-shifting. Their relative importance is primarily determined by the electron spin-lattice relaxation time T/ and thus can vary with temperature. Each has advantages and disadvantages and requires a different method of detection. 

The two-pulse echo decay is sometimes too fast to obtain a satisfactory frequency spectrum after Fourier transformation. In this case the three-pulse sequence shown in Fig. 2.21(a) is an alternative. It gives rise to a stimulated echo at time r after the third k/2 pulse. The decay rate is limited by the electron spin-lattice relaxation time Ti, which is usually longer than the phase memory relaxation time Tm for the two-pulse decay. 

The conditions necessary for observation of proton magnetic resonance spectra in paramagnetic systems are well established (1). Either the electronic spin-lattice relaxation time, T, or a characteristic electronic exchange time, Te, must be short compared with the isotropic hyperfine contact interaction constant, in order for resonances to be observed. Proton resonances in paramagnetic systems are often shifted hundreds of cps from their values in the diamagnetic substances. These isotropic resonance shifts may arise from two causes, the hyperfine contact and pseudocontact interactions. The contact shift arises from the existence of unpaired spin-density at the resonating nucleus and is described by 1 (2) for systems obeying the Curie law. 

The line broadening in spectra of paramagnetic compounds is caused by short electronic spin-lattice relaxation times and/or hyperfine electron-nuclear coupling. Consequently, it is usually the case that materials giving useful EPR spectra have nuclear magnetic resonances so broad as to be unobservable. The two methods are therefore to a large extent complementary. 

The moving electronic spins can also be used as probes for their own motion. In a similar way as for fixed nuclei, the fluctuating magnetic fields induced by the moving spins are relaxation processes themselves. An expression similar to Eq. (14) can be derived for an electronic spin-lattice relaxation time Tie. For a powder average, it becomes... 

It should be noted that long electron spin-lattice relaxation times (Ti 10" to 10 s) impede recording of the NMR spectra of radicals. Therefore lines in the NMR spectra of radicals become observable only at high rates of electron spin exchange. Spin exchange correlation time Tex is directly proportional to the viscosity rj and inversely proportional to the temperature and radical concentration [R] rj/T[R ]. Therefore,... 

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