Relaxation Curie

In the case of magnetically coupled systems. Curie relaxation is simply additive as long as the magnetic susceptibility is the sum of the two components. When the magnetic susceptibility is not a simple sum of the components, the magnetic susceptibility contribution of each metal ion should be evaluated. 

Upon rotation the average electron induced magnetic moment causes nuclear relaxation. This is called Curie relaxation (see Section 3.6). However, the full electron magnetic moment causes nuclear relaxation through dipolar and contact mechanisms by jumping over the various Zeeman levels. The electron jumps over the Zeeman levels with rates equal to the electronic R or R2 values and such jumps give also rise to nuclear relaxation. 

The present Chapter deals with the hyperfine shifts which are only due to the average electron induced magnetic moment and therefore are related to (Sz). Chapter 3 will deal with nuclear hyperfine relaxation which, as discussed above, depends on both average electron induced magnetic moment (Curie relaxation) and on the full electron magnetic moment (dipolar and contact relaxation). 

Electronic relaxation times of some common paramagnetic metal ions and nuclear relaxation rates for a proton at 5 A from the metal, at 800 MHz H resonance frequency, due to dipolar and Curie relaxation, estimated from Eqs. (3.16), (3.17), (3.29) and (3.30), with rc = rs... 

In principle, there may also be a Curie relaxation contribution of the contact-type whenever there is chemical exchange or intramolecular rotation to modulate the coupling. The contribution to R2M would then be... 

Some qualitative guidelines can be given to make an a priori estimate of the relative weight of dipolar, contact, and Curie relaxation contributions. Consider first the fast motion limit where Rim = Rim and none of the frequency-dependent terms is dispersed. The equations take the simple form already noted ... 

No explicit temperature dependence is included in the equations for R m and Rim, except for cases where Curie spin relaxation is the dominant term (Section 3.6). In the latter case, Curie paramagnetism has a T x dependence and therefore relaxation depends on T 2. The effect of temperature on linewidths determined by Curie relaxation is dramatic also because of the xr dependence on temperature, as shown in Eq. (3.8). All the correlation times modulating the electron-nucleus coupling, either contact or dipolar, are generally temperature dependent, although in different ways, and their variation will therefore be reflected in the values of Rim and Rim-... 

Fig. 5.10. Predominance of dipolar, contact or Curie relaxation in signal linewidths at 800 MHz for different rotational and electron relaxation times, and for different constants for the contact interaction. Calculations have been performed for protons at 5 A from a S = 5h ion.

The hyperfine shifts of groups bound to the donor atom are largely dominated by the contact interaction, even if pseudocontact shift contributions are sizable and any quantitative use of the shifts should rely on the separated contributions. Longitudinal nuclear relaxation times can be used, and have been used in the case of cobalt substitute stellacyanin, to determine metal-proton distances [101]. The contribution of Curie relaxation, estimated from the field dependence of the linewidths, can be used both for assignment and to determine structural constrains [101]. 

E2S(S + 1) is a generic notation that holds for dipolar, contact or Curie relaxation. In the equation for Curie relaxation there is a S2(S + l)2 term because a further S(S + 1) term is contained in the E2 term. 

The amount of cross correlation between the dipolar coupling of nuclei A and X and Curie relaxation of the A spin is [31] ... 

Fig. 8.21. Simulated COSY cross peaks originating from a pair of signals dipole-coupled in the presence of cross relaxation with Curie relaxation and in the absence of scalar coupling. The two degenerate components are in antiphase, but they do not cancel out due to their different linewidths. Note that absorption mode phasing (A) and dispersion mode phasing (B) show opposite patterns with respect to the case of scalar coupling (Fig. 8.15A,B).

In the case of T measurements we have mentioned that cross relaxation provides multiexponential magnetization recovery (Sections 1.7.4 and 7.2.2). A far less known analogy may occur in the linewidths, as already discussed (Section 8.8) when two protons are dipole-dipole coupled and cross correlation occurs between Curie relaxation and proton-proton dipolar relaxation. In this case, we are in the presence of two overlapping signal components with different linewidths, i.e. of biexponentiality in T2 [35], Pulse sequences are available to remove the effects of cross correlation [36]. Such effects are common in paramagnetic metalloproteins where Curie relaxation is usually relevant (in principle, such cross correlation effects can be operative also in the case of 7i, although only to the extent that Curie relaxation on T is effective). 

A polyethyleneglycol (PEG) derivative, with large molecular weight, was investigated and a sizable Curie relaxation was observed (163). 

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