Quantum mechanical behaviour of deuterated methyl groups

Abstract

We discuss the temperature dependence of deuterium NMR spectra and spin-lattice relaxation rates 1/T 1 of deuterated methyl groups. We restrict ourselves to the temperature range where it is sufficient to consider only the two lowest librational levels of the CD3 group. Specifically we derive explicit expressions for 1/T 1 and the widthГ NMR of the so-called tunneling resonances in the high-field NMR spectrum in the limit where the tunneling frequencyΔ 0 is large compared to the quadrupole coupling constant of a methyl group. We demonstrate that the disappearance of the tunneling resonances at elevated temperatures follows the scenario of the NMR of nuclei which exchange classically between two inequivalent sites. We further show that the NMR linewidths and relaxation rates are strongly related to the widths of the quasielastic and inelastic lines in incoherent neutron spectra. It turns out that for NMR spectra the classical limit is usually reached at lower temperatures than for neutron spectra. All calculations are based on the projection operator formalism.