Deuterium relaxation and vibrationally averaged quadrupole coupling in an alkane/urea clathrate

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Abstract
Measurements of the temperature dependence of deuterium relaxation rates for the methylene groups of perdeuterated n-nonadecane in a urea clathrate single crystal are reported. Individual spectral densities J1(ω0) and J2(2ω0) were determined using Jeener–Broekaert experiments, and data obtained at two orientations of the main crystal axis were fit to a motional model which combines unrestricted rotational diffusion about the alkane long axis with restricted wobbling of the methylene group planes. Both motions are fast on the NMR time scale and both affect the observed, time averaged quadrupole coupling constant (e2qQ/h)eff=163 kHz. However, quadrupole tensor components appearing in the relaxation Hamiltonian should not be averaged over that part of the motion which is in fact responsible for the relaxation, and by fitting the relaxation data together with the observed quadrupolar splitting to the motional model described above we obtain a value ≥ 185 kHz for the methylene quadrupole coupling constant. This value of e2qQ/h has been averaged only over those vibrational motions which are too fast to contribute to observable relaxation.