Rapid isotropic tumbling

Rapid isotropic tumbling of molecules is restrained for the network polymers in the gel state. A proton dipolar broadening of many kilohertz is observed in an NMR spectrum due to the strong dipolar-dipolar interaction and chemical shift anisotropy as a result of the restraint on the molecular motion. One method used for the removal of proton dipolar broadening is to employ a high-power proton decoupling field [5]. The scalar couplings are... 

One should note here that despite providing an important relaxation mechanism, dipolar couplings do not usually produce observable splittings in solution state NMR spectra. This is because, although the couplings have a finite value at any instant in time, they are averaged precisely to zero on the NMR timescale by the rapid isotropic tumbling of a molecule. 

In solution-state NMR spectroscopy, rapid isotropic tumbling leads to a complete averaging of chemical shift anisotropy, homonuclear and heteronuclear dipolar couplings, and also, in the case of nuclei with spin > 1/2, of quadrupolar interactions. In contrast, in solids the resonance frequency and the magnitude of intemuclear couplings depend on the orientation of the molecule within the magnetic field. These anisotropic interactions can either be exploited for information on dynamics and orientation, or overcome. This can be accomplished in different ways ... 

Fig. 6.2. 1H-1BN HSQC spectra of folded apomyoglobin at pH 6 (left) and unfolded apomyoglobin at pH 2 (right). Note the wide dispersion in the XH dimension in the left spectrum, and the narrow dispersion on the right. Also, the cross peaks are broader in the left spectrum, due to isotropic tumbling of the folded, globular protein. The cross peaks are narrower in the right spectrum due to rapid segmental motion of the unfolded polypeptide chain...

In Chapter 7 we consider the observed effects of the shielding tensor in solids. However, as we shall see, rapid, random tumbling of molecules in liquids and gases leads to an averaging of the shielding interactions to an isotropic scalar quantity... 

One can see from Eq. (3) that the van Vleck dipolar Hamiltonian is the product of a spatial part and a spin part. In liquids, the rapid isotropic molecular tumbling motion, which occurs at frequencies well above the dipolar linewidth, averages the spatial part (1—3 cos2 6tj) to zero, thus nulling the dipolar broadening. In solids, the spins are constrained to vibrate and rotate about their mean positions, resulting in an effective dipolar Hamiltonian which is generally non-zero, and consequently in... 

Unlike the situation with the dipolar interaction, which averages to zero in liquids due to the rapid molecular tumbling motion, the isotropic rotation leaves a residual chemical-shift Hamiltonian ... 

Figure 24.5b Relative contributions of the predominant modes of cation rotation within the tetramethylammonium dicyanamide salt across a range of temperatures. The static state decreases rapidly with increasing temperature, as does the methyl group spinning. Isotropic tumbling begins to a very small degree at 240 K and increases dramaticaiiy above 315 K. These rotational transitions are unusual for the tetramethylammonium cation.

Severely restricted mobility of molecules in solids so that little averaging can take place in contrast, in solution molecules tumble rapidly, isotropically and chaotically, at a sufficient rate that the NMR parameters are averaged to their isotropic values. 

NMR of solids differs from solution-state NMR in several important ways. First, the solution-state tumbling of molecules is, of course, restricted in the solid phase. In the absence of rapid isotropic motion, magnetic dipolar interaction between neighboring spins affects the NMR line shape. Second, the chemical shift interaction is not just a simple scalar, but is a tensor quantity. In solution-state NMR, only the scalar average is seen while in solid-state NMR, the tensor elements are observed. In the solid state, the chemical shift tensor yields a variety of possible NMR line shapes. Likewise, the quadrupolar interaction also creates a variety of line shapes. Third, a single molecular motion can dominate the process of thermal equilibration of the NMR spin system with its environment... 

In solution, rapid molecular tumbling results in isotropic averaging of the shielding, reducing d to the scalar which defines the chemical shift observed in HR studies. In the solid, the orientation dependence of the shielding is not-averaged away. 

The and operators determine the isotropic and anisotropic parts of the hyperfine coupling constant (eq. (10.11)), respectively. The latter contribution averages out for rapidly tumbling molecules (solution or gas phase), and the (isotropic) hyperfine coupling constant is therefore determined by the Fermi-Contact contribution, i.e. the electron density at the nucleus. 

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