Dipolar Relaxations

The tenn slow in this case means that the exchange rate is much smaller than the frequency differences in the spectrum, so the lines in the spectrum are not significantly broadened. Flowever, the exchange rate is still comparable with the spin-lattice relaxation times in the system. Exchange, which has many mathematical similarities to dipolar relaxation, can be observed in a NOESY-type experiment (sometimes called EXSY). The rates are measured from a series of EXSY spectra, or by perfonning modified spin-lattice relaxation experiments, such as those pioneered by Floflfman and Eorsen [20]. 

In the absence of exchange (and ignoring dipolar relaxation), each z magnetization will relax back to equilibrium at a rate governed by its own T, as in (B2.4.44). 

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 main contribution to the spin-lattice relaxation of C nuclei which are connected to hydrogen is provided by the dipole-dipole interaction (DD mechanism, dipolar relaxation). For such C nuclei a nuclear Overhauser enhancement of almost 2 will be observed during H broadband decoupling according to ... 

Table 4.5-1 gives values for the fit parameters and the reorientational correlation times calculated from the dipolar relaxation rates. 

Kometani K., Shimizu H. Study of the dipolar relaxation by a continued fraction representation of the time correlation function, J. Phys. Soc. Japan 30, 1036-48 (1971). 

The second reason is related to the misconception that proton dipolar relaxation-rates for the average molecule are far too complicated for practical use in stereochemical problems. This belief has been encouraged, perhaps, by the formidable, density-matrix calculations " commonly used by physicists and physical chemists for a rigorous interpretation of relaxation phenomena in multispin systems. However, proton-relaxation experiments reported by Freeman, Hill, Hall, and their coworkers " have demonstrated that pessimism regarding the interpretation of proton relaxation-rates may be unjustified. Valuable information of considerable importance for the carbohydrate chemist may be derived for the average molecule of interest from a simple treatment of relaxation rates. 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

Ratio of Interproton, Dipolar Relaxation Contributions, pij/pik, for a Molecule Which Is Tumbling Isotropically. (Reproduced, with permission, from Ref. 5.)... 

Cross-relaxation The mutual intermolecular or intramolecular relaxation of magnetically equivalent nuclei, e.g., through dipolar relaxation. This forms the basis of nOe experiments. 

For a reUable extraction of distances, it is important that dipolar relaxation is strongly dominating other relaxation processes. Hence, it is important to avoid paramagnetic ions or molecules such as transition metals or (paramagnetic) oxygen. Especially solution of small molecules therefore have to be carefully degased. 

For the simulation a correlation time 1 =0.1 ns is assumed for two protons at cOo=600MHz. (B) Maximum transfer efficiency for an isolated proton spin pair calculated using only dipolar relaxation processes. Note the sign change for the NOE cross-relaxation at cOo Uc=l -12. 

The 113Cd Ti values estimated for the various peaks varied from 10 to 50 ms and obeyed the qualitative dependence upon 1/R6 (R = Mn-Cd distance) of the dipolar relaxation mechanism expected to be operative. The broad line widths were also shown to have significant contributions from the T2 relaxation induced by Mn++, with both dipolar and contact terms contributing. The 113Cd shifts of the peaks assigned to different shells were measured as a function of temperature, and observed to follow a linear 1/T dependence characteristic of the Curie-Weiss law, with slopes proportional to the transferred hyperfine interaction constant A. 

Dipolar relaxation is usually assumed to be the predominant mechanism in a paramagnetic molecule, although this is a simplification. For instance, if the... 

For heteronuclear dipolar relaxation, the dipole-dipole coupling between two unlike spin- nuclei / and S (e.g., 13C-H pair) separated by an internuclear distance rIS is considered. The Zeeman spin-lattice (7jz) and spin-spin (T2) relaxation times for the / spin are given, respectively, by... 

A new NMR method for the determination of the anomeric configuration in mono- and disaccharides has been described.18 The protocol is based on the different cross-correlated relaxation between proton chemical shift anisotropy (CSA) and dipolar relaxation for the a and (3 anomers of sugars. Only the ot-anomers show the presence of CSA (HI or Hl )-proton dipole (H1-H2 or Hl -H2 ) in the longitudinal relaxation of the anomeric protons. The method is of special interest for cases in which vicinal coupling constants between HI and H2 in both anomers a and (3 are similar and small, such as D-mannose, and the non-ambiguous description of the anomeric configuration needs additional measurements. 

Haidar S, Chattopadhyay A (2007) Dipolar relaxation within the protein matrix of the green fluorescent protein a red-edge excitation shift study. J Phys Chem Bill 14436-9... 

Fig. 14.13 Graphical representation of the effect of MW on T2 (dashed-dotted), on the translational diffusion rate D (solid), on the steady state NOE (dashed) and on the build-up of the NOE (dotted). All values are normalized to a 300 Da molecular weight molecule. For the calculation of the parameters involving dipolar relaxation we used a formula that can be found in the literature...

Cross-correlated dipolar relaxation can be measured between a variety of nuclei. The measurement requires two central nuclear spins, each of which is directly attached to a remote nuclear spin (Fig. 16.4). The central spin and its attached remote spin must be connected via a large scalar coupling, and the remote spin must be the primary source of dipolar relaxation for the central spin. The two central spins do not need to be scalar coupled, although the necessity to create multiple quantum coherence between them requires them to be close together in a scalar or dipolar coupled network. In practice, the central spins will be heteroatoms (e.g. 13C or 15N in isotopically enriched biomolecules), and the remote spins will be their directly attached protons. 

Observation of reorientational dynamics of dipolar groups surrounding the fluorophore in response to changes in the dipole moment of the fluorophore occurring upon electronic excitation. Such dynamics result in the appearance of spectral shifts with time,(1 ) in changes of fluorescence lifetime across the fluorescence spectrum,(7,32) and in a decrease in the observable effects of selective red-edge excitation.(1,24 33 34) The studies of these processes yield a very important parameter which characterizes dynamics in proteins— the reorientational dipolar relaxation time, xR. 

A variety of results obtained in studies of dipolar relaxation in the environment of the fluorescence probe 2,6-TNS are illustrated in Figure 2.10. In the model viscous medium (glycerol at 1 °C), the fluorescence spectra exhibit a marked dependence on the excitation wavelength. When 2 varies from 360 to 400 nm, the shift of the fluorescence spectrum maximum is 10 nm with a certain decrease of the half-width. In media with low viscosity, for instance, in ethanol (Figure 2.10a), this effect is never observed. 

J. R. Lakowicz and H. Cherek, Dipolar relaxation in proteins on the nanosecond time scale observed by wavelength-resolved phase fluorometry of tryptophan residue, J. Biol. Chem. 255, 831-834 (1980). 

---