Coupling dipolar

In a polymer solution, where the rates of segmental motion are generally faster than the strength of the dipolar C- H interactions, i.e. approx. 20 kHz, 

Any two magnetic dipole moments interact directly through the magnetic fields created by each one on the position of the other. The magnetic field created by a classical point dipole at a point located by the vector r with origin on the dipole is (in SI units) [16]  

The interaction of a dipole /itj with such field created by a dipole 112 is given by the classical Zeeman interaction energy —/iti The Hamiltonian describing the dipolar interaction can thus be written in the form 

This expression can be rearranged by grouping the terms involving each combination of the Cartesian components of the operators Ii and I2, associated with the two spins. When this is done, only the dominant terms are retained in the secular approximation. For the heteromclear case (i.e., the interaction between two unlike nuclei with ym Yn2) this leads to the simple expression  

The Hamiltonian describing the /-coupling between two nuclear spins Ii and I2 is generally written in the form  

The tensor J possesses non-vanishing trace, which gives rise to the isotropic contribution mentioned above in the NMR spectra of liquids. In terms of the PAS components of the tensor J the following definition is used  

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The dipolar coupling between two nuclei 7,.S is systems containing pairs of... 

In equation (bl. 15.24), r is the vector coimecting the electron spin with the nuclear spin, r is the length of this vector and g and are the g-factor and the Boln- magneton of the nucleus, respectively. The dipolar coupling is purely anisotropic, arising from the spin density of the impaired electron in an orbital of non-... 

Figure 1 The principal sources of structural data are the NOEs, which give information on the spatial proximity d of protons coupling constants, which give information on dihedral angles < i and residual dipolar couplings, which give information on the relative orientation 0 of a bond vector with respect to the molecule (to the magnetic anisotropy tensor or an alignment tensor). Protons are shown as spheres. The dashed line indicates a coordinate system rigidly attached to the molecule.

A similar problem arises with present cross-validated measures of fit [92], because they also are applied to the final clean list of restraints. Residual dipolar couplings offer an entirely different and, owing to their long-range nature, very powerful way of validating structures against experimental data [93]. Similar to cross-validation, a set of residual dipolar couplings can be excluded from the refinement, and the deviations from this set are evaluated in the refined structures. 

Molecular modeling is an indispensable tool in the determination of macromolecular structures from NMR data and in the interpretation of the data. Thus, state-of-the-art molecular dynamics simulations can reproduce relaxation data well [9,96] and supply a model of the motion in atomic detail. Qualitative aspects of correlated backbone motions can be understood from NMR structure ensembles [63]. Additional data, in particular residual dipolar couplings, improve the precision and accuracy of NMR structures qualitatively [12]. 

In 8CB, continued cooling into the smectic phase reveals the appearance of a broad ultra-low-frequency feature centred at around 10 cm where no other modes are seen. This is shown in Fig. 15. This feature appears to be unique to the smectic phase and has been tentatively attributed to intermolecular dipolar coupling across smectic layers [79]. In principle this should be a generic feature of smectics but it will be necessary to explore this issue through extensive computer simulations using realistic, shape-dependent potentials for... 

Transient nOe represents the rate of nOe buildup. The nOe effect (so-called equilibrium value) itself depends only on the competing balance between various complex relaxation pathways. But the initial rate at which the nOe grows (so-called transient nOe) depends only on the rate of cross-relaxation t, between the relevant dipolarly coupled nuclei, which in turn depends on their internuclear distance (r). 

The ROESY spectrum affords homonuclear transverse nOe interactions as cross-peaks between the various dipolarly coupled hydrogens. This... 

The NOESY spectrum of buxatenone shows four cross-peaks, A-D. Cross-peak B represents the dipolar coupling between the most upfield C-19 cyclopropyl proton (8 0.68) with the most downfield olefinic proton (8 6.72). This could be possible only when the double bond is located either between C-1 and C-2 or between C-11 and C-12. The possibility of placing a double bond between C-11 and C-12 can be excluded on the basis of chemical shift considerations, since conjuga-... 

The ROESY spectrum of podophyllotoxin exhibits a number of crosspeaks (A-D) representing interactions between dipolarly coupled (space coupling) hydrogens, which can be helpful to determine the stereochemistry at different asymmetric centers. For example, based on the assumption that the C-1 proton (8 4.53) is /3-oriented, we can trace out the stereochemistry of other asymmetric centers. Cross-peak B represents dipolar coupling between the C-1 proton (8 4.53) and the C-2 proton (8 2.8), thereby confirming that the C-2 proton is also... 

Dipolar coupling The direct through-space coupling interaction between two nuclei. It is responsible for nOe and relaxation, and represents the... 

In addition to sample rotation, a particular solid state NMR experiment is further characterized by the pulse sequence used. As in solution NMR, a multitude of such sequences exist for solids many exploit through-space dipolar couplings for either signal enhancement, spectral assignment, interauclear distance determination or full correlation of the spectra of different nuclei. The most commonly applied solid state NMR experiments are concerned with the measurement of spectra in which intensities relate to the numbers of spins in different environments and the resonance frequencies are dominated by isotropic chemical shifts, much like NMR spectra of solutions. Even so, there is considerable room for useful elaboration the observed signal may be obtained by direct excitation, cross polarization from other nuclei or other means, and irradiation may be applied during observation or in echo periods prior to... 

Instead of measuring only the time-dependent dipolar interaction via NOE, it is also possible to determine dipolar couplings directly if the solute molecule is partially aligned in so-called alignment media. The most important resulting anisotropic parameters are RDCs, but residual quadrupolar couplings (RQCs), residual chemical shift anisotropy (RCSA) and pseudo-contact shifts (PCSs) can also be used for structure determination if applicable. 

Nuclear spins can be considered as dipoles that interact with each other via dipolar couplings. While this interaction leads to strongly broadened lines in soUd-state NMR spectroscopy, it is averaged out in isotropic solution due to the fast tumbUng of the solute molecules. In Uquid-state NMR spectroscopy, the dipolar interaction can only be observed indirectly by relaxation processes, where they represent the main source of longitudinal and transverse relaxation. 

Simon, B., Sattler, M. De novo structure determination from residual dipolar couplings by NM R spectroscopy. Angew. Chem. Int. Ed. 2002, 41, 437 40. 

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