Deuteron NMR of Methyl Groups in theTunneling Regime. A Single Crystal Study of Aspirin-CD₃

Abstract

We dedicate this paper to Prof. Dr. Werner Müller-Warmuth on the occasion of his 65th birthday. Z. T. L. and U. H. owe much to his advice.We report the first single crystal deuteron NMR spectra of CD3 groups which display the socalled ±ß, ± (|a| ± ß) and ±(2|a| ± ß) lines characteristic of rotational tunneling in a sufficiently clear manner to allow a quantitative comparison with the respective theory developed in 1988 by the group of W. Müller-Warmuth. The molecular system we study is aspirin-CD3. We recorded spectra for differently oriented single crystals and measured spin-lattice relaxation times T\ in a wide temperature range. At 12.5 K we exploit the dependence of the ±(|a| ± ß) and ±(2|a| ± ß) lines on the orientation of the applied field Bo for determining the equilibrium orientation of the CD3 group in the crystal lattice. The spectra display features which allow, by comparison with simulated spectra, a measurement of the tunnel frequency ut. Its low temperature limit is (2.7 ± 0.1) MHz. It allows to infer the height V3 of the potential V(</?) in which the CD3 group moves, provided that this potential is purely threefold. We get V3 = (47.2 ± 0.5) meV. The transition from the tunneling to the classical, fast reorienting regime occurs in the 15 K ~ T ~ 35 K temperature range. In this range we observe a broadening, merging and eventually narrowing of the ± |a | and ±2|a| lines in very much the way predicted by Heuer. His theory, however, must be extended by taking into account all librational levels. The behaviour of the ± ß lines in the transition temperature range signalizes a reduction of the observable tunnel frequency with increasing temperature. This reduction allows an independent measurement of the potential height and represents a test of the assumption of a purely threefold potential. From the T\ -data we derive the temperature dependence of the correlation time t c of the reorientational jumps. The plot of log rc vs. 1 /T follows a straight line for more than five decades. From its slope we get yet another independent number for the potential height. It agrees well with the other ones, which confirms the assumption of the essentially threefold potential V(<p) in aspirin-CD 3. IntroductionAt room temperature the high field deuteron NMR spectrum of a deuterated methyl group consists of one pair of lines. We assume, naturally, that the CD3 group is part of a molecule in a molecular crystal. The pair splitting Auq reflects the interaction of the deuterons' quadrupole moments with the motionally averaged electric field gradients at the sites of the deuterons. The motions in question are rotational jumps of the -CD3 group about the carbon bond which links the Reprint requests to Prof. Dr. U. Haeberlen. group to the rest of the molecule. In this paper we inquire what happens when the temperature T of the crystal is lowered to, say, 10 K.There are two limiting cases. In the first, the (angu lar) coordinate p which describes the reorientations is adequately conceived as a classical stochastic func tion o...

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