Relaxation nuclear

Some representative infinite dilution relaxation values are set out in Table 1. Theoretical attempts to explain the variation with ion type were developed for the alkali metals and later extended to group II. It is usual to ascribe the relaxation of a quadrupolar nucleus entirely to quadrupole interactions, though the small Q of Li and Cs, and the small of Li and Be , suggest that this might not be true for these nuclei in the relatively symmetrical environment of aqueous solution. The 

Two theories have been developed to attempt to explain the different quadrupolar relaxation rates of these cations. The electrostatic model due to Valiev and Hertz is currently favored and considers the relaxation to be caused by the electric field gradients due to the dipole moments of the solvent molecules modulated by their rotational and translational motion. The fully random distribution (FRD) version of the model leads in the extreme narrowing limit to 

Viscosity and Relaxation. The rate of relaxation of an ion depends upon the rate of motion of the electric field gradient at its nucleus created by the motion of solvent and other solute molecules near to it. The calculation of the overall nature of such fluctuations on a tensor quantity is not straightforward and so other criteria for rate of motion have to be sought. One obvious indication of internal motion is the solution viscosity, though there is no direct relation between this bulk property and the rate of motion near an ion. However, rates of relaxation commonly vary linearly with viscosity changes, and it is customary when making comparisons of relaxation and chemical shift to support the electronic theory, to normalize the former to constant viscosity, since the shifts are independent of viscosity. 

The viscosity of a real solution (only aqueous solutions are considered here) depends on the concentration of the solute, following the well-known Jones-Dole relationship  

On the other hand the proponents of the electronic theory ignore viscosity and use instead an estimate of in equation (2) made from proton relaxation times in the solvent, though this method still uses a bulk property to estimate a local rate of motion. An acceptable value can be given to r, but an adjustable counterion symmetry parameter is still needed to obtain reasonable predicted relaxation times. 

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We begm tliis section by looking at the Solomon equations, which are the simplest fomuilation of the essential aspects of relaxation as studied by NMR spectroscopy of today. A more general Redfield theory is introduced in the next section, followed by the discussion of the coimections between the relaxation and molecular motions and of physical mechanisms behind the nuclear relaxation. 

Meiboom S and Gill D 1958 Modified spin-echo method for measuring nuclear relaxation times Rev. Sci. Instrum. 29 688-91... 

The addition of paramagnetic species, such as the metal ions Cu ", Mn, or CF", can have dramatic effects on both the observed spectmm and the relaxation behavior of a molecule. The added ion reduces nuclear relaxation times, and permitting more rapid data collection. In addition, faster relaxation rates minimize NOE effects in the spectra, which can be useful in obtaining quantitative intensity data. The most widely used reagent for this purpose is chromium acetylacetonate [13681 -82-8] known as Cr(acac)2. Practically speaking, the use of such reagents requires care, because at... 

N-protonation the absolute magnitude of the Ad values is larger than for Af-methylation <770MR(9)53>. Nuclear relaxation rates of and have been measured as a function of temperature for neat liquid pyridazine, and nuclear Overhauser enhancement has been used to separate the dipolar and spin rotational contributions to relaxation. Dipolar relaxation rates have been combined with quadrupole relaxation rates to determine rotational correlation times for motion about each principal molecular axis (78MI21200). NMR analysis has been used to determine the structure of phenyllithium-pyridazine adducts and of the corresponding dihydropyridazines obtained by hydrolysis of the adducts <78RTC116>. 

The NMR phenomenon can be quantitatively described in classical terms. This was first done by Bloch.The approach is helpful in developing an understanding of nuclear relaxation processes. 

In the presence of a field H, rotating at the precessional frequency the nuclear system can absorb energy, following which nuclear relaxation occurs. Thus, the equation of motion must include both the precessional and the relaxation contributions ... 

There is arbitr iriness in describing phenomena as either physical or chemical, but in some sense the nuclear relaxation mechanisms we have discussed to this point are physical mechanisms, based as they are on rotational motions of molecules, magnetic dipole-dipole interactions, quadrupolar interactions, and so on. Now we discuss a nuclear relaxation mechanism that is chemical in origin. 

Turning from chemical exchange to nuclear relaxation time measurements, the field of NMR offers many good examples of chemical information from T, measurements. Recall from Fig. 4-7 that Ti is reciprocally related to Tc, the correlation time, for high-frequency relaxation modes. For small- to medium-size molecules in the liquid phase, T, lies to the left side of the minimum in Fig. 4-7. A larger value of T, is, therefore, associated with a smaller Tc, hence, with a more rapid rate of molecular motion. It is possible to measure Ti for individual carbon atoms in a molecule, and such results provide detailed information on the local motion of atoms or groups of atoms. Levy and Nelson " have reviewed these observations. A few examples are shown here. T, values (in seconds) are noted for individual carbon atoms. 

Usually, nuclear relaxation data for the study of reorientational motions of molecules and molecular segments are obtained for non-viscous liquids in the extreme narrowing region where the product of the resonance frequency and the reorientational correlation time is much less than unity [1, 3, 5]. The dipolar spin-lattice relaxation rate of nucleus i is then directly proportional to the reorientational correlation time p... 

Overhauser limit (Gloss and Gloss, 1969 Gloss, 1969 Gloss and Trifunac, 1969) (v) polarization was obsei ved in radical systems where the radical lifetimes were longer than the nuclear relaxation times in the individual radicals involved (Ward and Lawler, 1967 Lawler, 1967 Fischer, 1969). 

There is an additional problem that must be considered for radicals that escape an original geminate radical pair. Such radicals are polarized. If they form new (encounter) radical pairs, they could yield combination products after undergoing T-S mixing again. However, because of the rapidity of nuclear relaxation in free radicals, the F-type polarization generally predominates. 

Failure to observe polarization in a particular reaction is significant only to the extent that any negative evidence is significant. If other evidence points to a radical pathway for the reaction, it may well be worth checking that the nuclear relaxation times for nuclei in the product are not unexpectedly short and also that polarization is not observable in a different spectral region from that expected for the final product owing to the formation of a metastable intermediate. 

H n.m.r. signals but, in addition, the starting material itself is polarized (Porter et al., 1972). Moreover, the appearance of polarization shows an induction period after irradiation is commenced and continues when the irradiation is interrupted for a time longer than the nuclear relaxation... 

Table I reports the observed NMR linewidths for the H/3 protons of the coordinating cysteines in a series of iron-sulfur proteins with increasing nuclearity of the cluster, and in different oxidation states. We have attempted to rationalize the linewidths on the basis of the equations describing the Solomon and Curie contributions to the nuclear transverse relaxation rate [Eqs. (1) and (2)]. When dealing with polymetallic systems, the S value of the ground state has been used in the equations. When the ground state had S = 0, reference was made to the S of the first excited state and the results were scaled for the partial population of the state. In addition, in polymetallic systems it is also important to account for the fact that the orbitals of each iron atom contribute differently to the populated levels. For each level, the enhancement of nuclear relaxation induced by each iron is proportional to the square of the contribution of its orbitals (54). In practice, one has to calculate the following coefficient for each iron atom ...

In addition to the standard constraints introduced previously, structural constraints obtainable from the effects of the paramagnetic center(s) on the NMR properties of the nuclei of the protein can be used (24, 103). In iron-sulfur proteins, both nuclear relaxation rates and hyperfine shifts can be employed for this purpose. The paramagnetic enhancement of nuclear relaxation rates [Eqs. (1) and (2)] depends on the sixth power of the nucleus-metal distance (note that this is analogous to the case of NOEs, where there is a dependence on the sixth power of the nucleus-nucleus distance). It is thus possible to estimate such distances from nuclear relaxation rate measurements, which can be converted into upper (and lower) distance limits. When there is more than one metal ion, the individual contributions of all metal ions must be summed up (101, 104-108). If all the metal ions are equivalent (as in reduced HiPIPs), the global paramagnetic contribution to the 7th nuclear relaxation rate is given by... 

ISOMORPHISMS AND INTERFERENCES BETWEEN ELECTRONIC AND NUCLEAR RELAXATIONS... 

While mononuclear octahedral Ni11 complexes often show relatively broad signals, nuclear relaxation enhancement and sharp signals may be observed in related dimer species 350,351 This has been taken advantage of for a detailed NMR investigation of a series of weakly ferromagnetically spin-coupled dinuclear octahedral Ni11 centers.352... 

For the metallic regime described above, when the Al S interaction is also responsible for the nuclear relaxation, Korringa [192] showed that the Knight shift and Ti are related by... 

The general theory of solvent nuclear relaxation in the presence of paramagnetic substances was described by Bloem-bergen, Solomon, Morgan, and others (11-16). During the last 10 years, it has been substantially reviewed in the context of MRI contrast agents (1-7,17,18). 

Introduction General Theory of Nuclear Relaxation Daniel Canet... 

Three parameters affect an NMR spectrum the chemical shift, coupling, and nuclear relaxation. These must be accounted for when obtaining the NMR spectrum from the spectrometer s output. Obtaining the NMR spectral plot from the output (the free induction decay, FID) of a modern NMR spectrometer involves the analysis of the mathematical relationship between the time (0 and frequency (go) domains known as the Fourier relationship ... 

Hence, these indirectly induced electronic and/or nuclear relaxations must exhibit the opposite signs with respect to the corresponding NFF indices. 

The HF results generated for representative polyatomic molecules have used the /V-derivatives estimated by finite differences, while the -derivatives have been calculated analytically, by standard methods of quantum chemistry. We have examined the effects of the electronic and nuclear relaxations on specific charge sensitivities used in the theory of chemical reactivity, e.g., the hardness, softness, and Fukui function descriptors. New concepts of the GFFs and related softnesses, which include the effects of molecular electronic and/or nuclear relaxations, have also been introduced. 

In the photolysis of. -dibromo-diphenyl-diazomethane in toluene the geminate pair effect is observed 87). However, it is accompanied by the enhanced emission by the escape product 7. This means that the carriers of the original polarization were the free radicals, whose lifetime is obviously shorter than the nuclear relaxation time. 

T jo = nuclear relaxation times of solvent molecules outside the first coordination shell. 

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