Quantum mechanical behaviour of deuterated methyl groups

Abstract

We discuss the temperature dependence of deuterium NMR spectra and spin-lattice relaxation rates i/7"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 CD 3 group. Specifically we derive explicit expressions for 1/T~ and the width FNM R of the so-called tunneling resonances in the high-field NMR spectrum in the limit where the tunneling frequency A 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. tunneling frequencies larger than 10 .5 ~teV, the NMR spectrum of CD 3 groups allows an access of the tunneling process. This has been shown by Lalowicz et al. who calculated deuterium NMR single crystal and powder spectra of CD 3 groups as a function of the tunneling frequency for T= 0 [13]. Apart from the tunneling frequency A 0 the deuterium spectrum of CD 3 groups is governed by the nuclear quadrupole moment -electric field gradient interactions of the deuterons.

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

“…An instructive quan titative example of |0A) for V3 = 40 meV is shown in Fig. 4 of Heuer [10].We are now in a position to define the "tunneling regime" which appears in the title of this paper. It en compasses the regime of temperatures T where T is low enough so that in thermal equilibrium virtually all methyl groups of the macroscopic sample are in the li brational ground state |0).…”

“…The number we get in this way for the potential height is in excellent agreement with that derived from the tunnel frequency see Section 5. A theory of how the deuteron spectrum of a CD3 group in the tunneling regime evolves when the tem perature is raised to, eventually, room temperature has been developed by Heuer [10]. Of particular inter est is the temperature behaviour of the satellite lines.…”

Tacticity effects on the barriers to rotation of the ester methyl group in poly (methyl methacrylate): A deuteron magnetic resonance study

“…The reason for this is very likely phonon-assisted tunneling through the barriers of the threefold methyl group potential. [23][24][25][26][27][28] As mentioned in the Introduction section, such tunneling has been observed in the neutron scattering data from CH 3 rotations for the ester group in PMMA. As we remarked then, there are two effects on the motion when replacing H by D. The hopping frequency shifts down by a factor of 2.…”

Quadrupolar Echo Spectra of the Tunneling CD3Group

“…All modulations are periodic with T m Å 1/ÉaÉ, where ÉaÉ is given by Eq. [2]. Therefore, we introduce the dimensionless parameter t Å tÉaÉ.…”