Isotropic tumbling coupling

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. 

The contribution of the hyperfine interactions to the relaxation rates of the radical depends on whether the dominant contribution comes from the anisotropic (dipolar) or the isotropic (scalar) part of the hyperfine interaction. Usually, the anisotropic contribution predominates because this interaction can be readily modulated by the tumbling motion of the molecule. However, in radicals and radical anions such as the trifluoroaceto-phenone (115,116), the rotation of the CF3 group may modulate the isotropic part of the hyperfine interaction and the scalar relaxation W0 could dominate the dipolar transition W2. In such a case, the authors have pointed out that the sign of the resulting CIDNP will be independent of the sign of the isotropic hyperfine coupling constants. 

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. 

The hyperfine properties can thus be computed once the unpaired ground state spin density matrix Pa-/3 is obtained. In solution, where the anisotropic terms are averaged due to molecular tumbling, only isotropic couplings are detectable, and their values are given by the relation Aiso = (l/3)lr T. In a solid, however, the anisotropic effects are observable. It should be noted that although the calculation of the isotropic hf couplings require the spin-density to be evaluated at the position of the nucleus only, the... 

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 ... 

For a rigidly held, three-spin system, or when existing internal motion is very slow compared to the overall molecular tumbling, all relaxation methods appear to be adequate for structure determination, provided that the following assumptions are valid (a) relaxation occurs mainly through intramolecular, dipolar interactions between protons (b) the motion is isotropic and (c) differences in the relaxation rates between lines of a multiplet are negligibly small, that is, spins are weakly coupled. This simple case is demonstrated in Table V, which gives the calculated interproton distances for the bicycloheptanol derivative (52) of which H-1, -2, and -3 represent a typical example of a weakly coupled, isolated three-spin... 

Dkl, Kkl and second rank tensors. DKL, in contrast to Kkl and aK, is a traceless tensor, and vanishes upon spatial averaging. Hence, the parameters relevant for a rapidly tumbling molecule (as in a liquid or in a gas phase) are the isotropic spin-spin coupling constant and the shielding constant. 

As we noted previously, Jtj is a tensor, not a scalar, but unlike Dv it has a nonvanishing trace, hence it is found in molecules tumbling in liquids. In solids and in liquid crystals it is possible in principle to investigate the off-diagonal elements of the J tensor, but measurements are difficult, and few instances of measurable aniostropy in J have been reported. However, one recent result shows that in benzene the anisotropies for one-, two-, and three-bond C-C couplings are approximately +17, —4, and +9 Hz, respectively, as compared with the isotropic values, %c = 56,2JCC = —2.5, and 3JCC = 10 Hz.82... 

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