Relaxation time, electronic

Electron relaxation times are important parameters that allow us to predict whether high-resolution NMR is feasible. The two most im-... 

For all known cases of iron-sulfur proteins, J > 0, meaning that the system is antiferromagnetically coupled through the Fe-S-Fe moiety. Equation (4) produces a series of levels, each characterized by a total spin S, with an associated energy, which are populated according to the Boltzmann distribution. Note that for each S level there is in principle an electron relaxation time. For most purposes it is convenient to refer to an effective relaxation time for the whole cluster. 

The [Fe4S4p clusters contain four equivalent irons and give relatively narrow signals (3, 7, 62, 63) (Fig. 2E). The electron relaxation time is evaluated around 5 X 10 s (Table I), which is somewhat smaller than that of the Fe(II) monomer. Also, the signals of [Fe4S4l (15, 64-68) (Fig. 2D) and [Fe4S4fi+ (8, 13, 69-71) (Fig. 2F) systems are sharp. 

It is clear from the above equations that numerous parameters (proton exchange rate, kcx = l/rm rotational correlation time, tr electronic relaxation times, 1 /rlj2e Gd proton distance, rGdH hydration number, q) all influence the inner-sphere proton relaxivity. Simulated proton relaxivity curves, like that in Figure 3, are often used to visualize better the effect of the... 

A fully realistic picture of solvation would recognize that there is a distribution of solvent relaxation times (for several reasons, in particular because a second dispersion is often observable in the macroscopic dielectric loss spectra [353-355], because the friction constant for various types or modes of solute motion may be quite different, and because there is a fast electronic component to the solvent response along with the slower components due to vibration and reorientation of solvent molecules) and a distribution of solute electronic relaxation times (in the orbital picture, we recognize different lowest excitation energies for different orbitals). Nevertheless we can elucidate the essential physical issues by considering the three time scales Xp, xs, and Xelec-... 

In a protein-ligand complex the correlation time rc of the vector connecting the electron and nuclear spins, depends on the rotational correlation time of the protein-ligand complex, Tr, on the electron relaxation time, rs, and on the lifetime of the complex, rm [6, 9] ... 

As stated in Section II.B of Chapter 2, the actual correlation time for electron-nuclear dipole-dipole relaxation, is dominated by the fastest process among proton exchange, rotation, and electron spin relaxation. It follows that if electron relaxation is the fastest process, the proton correlation time Xc is given by electron-spin relaxation times Tie, and the field dependence of proton relaxation rates allows us to obtain the electron relaxation times and their field dependence, thus providing information on electron relaxation mechanisms. If motions faster than electron relaxation dominate Xc, it is only possible to set lower limits for the electron relaxation time, but we learn about some aspects on the dynamics of the system. In the remainder of this section we will deal with systems where electron relaxation determines the correlation time. 

Tie are also expected to be field-dependent. Their field dependence can be described by two parameters the electron relaxation time at low fields Tso, and the correlation time for the electron relaxation mechanism Ty (see Eq. (14) of Chapter 2) (5). However, Tso usually depends on (see Eq. (52) of Chapter 2). Therefore, it is preferable to select two different parameters for describing the field dependence of electron relaxation. For S > 1/2 systems, in case the electron relaxation is due to modulation of a time dependent transient zero-field splitting, A, (pseudorotational model), the Bloembergen-Morgan equations are obtained 5,6) ... 

In case Xy is kept constant and At increases (Fig. 2B), low field relaxivity decreases and the ffls 2e dispersion moves at larger frequency, as a result of the decreased electron relaxation time. 

The Florence NMRD program (8) (available at www.postgenomicnmr.net) has been developed to calculate the paramagnetic enhancement to the NMRD profiles due to contact and dipolar nuclear relaxation rate in the slow rotation limit (see Section V.B of Chapter 2). It includes the hyperfine coupling of any rhombicity between electron-spin and metal nuclear-spin, for any metal-nucleus spin quantum number, any electron-spin quantum number and any g tensor anisotropy. In case measurements are available at several temperatures, it includes the possibility to consider an Arrhenius relationship for the electron relaxation time, if the latter is field independent. 

The same approach has been developed for systems in solutions (15,16), and was found relevant in some cases. The electron relaxation time is described in the cases of Orbach-type mechanism by the equation (17)... 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

The electron relaxes through modulation of the A and g anisotropy. Typical examples are copper(II), oxovanadium(IV) and silver(II) aqua ions. The electronic relaxation times are relatively long (10 -10 ° s at room temperature) and the hyperfine coupling with the metal nuclear spin is usually present. No field dependence of the electron relaxation time is usually evident up to 100 MHz. 

Complexes in which there are low-lying excited states, hence allowing the Orhach mechanism to operate efficiently. This causes the electron relaxation time to he faster. Typical examples are titanium(III), with... 

In order to obtain information on the electron relaxation time in copper aqua ion, measurements should not be performed in water solution, because the correlation time for proton relaxation is in that case the reorientational time, which is much smaller than T g. NMRD profiles should be actually acquired in ethylene glycol solution and at temperatures lower that room temperature, so that the reorientational time increases one two orders of magnitude (see Section II.B). In this way T e of the order of 10 s can be estimated. 

No field dependence in the electron relaxation time was ever found in the investigated region between 0.01 and 100 MHz of proton Larmor frequency, or at 800 MHz when high resolution is achieved (28). It was shown that Tie is essentially independent of the reorientational time of the macromolecule and the viscosity of the solution. Therefore, rotation independent mechanisms have to be operative. We also find that Tie decreases with increasing temperature, as also shown in Fig. 5. 

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