The low-temperature 13C and 2H spectra and relaxation rates of methyl groups depend on the azimuth of B0 in the molecular frame. Those of 1H do not. Why?

Theory of damped quantum rotation in nuclear magnetic resonance spectra. III. Nuclear permutation symmetry of the line shape equation

The damped quantum rotation (DQR) theory describes manifestations in nuclear magnetic resonance spectra of the coherent and stochastic dynamics of N-fold molecular rotors composed of indistinguishable particles. The standard jump model is only a limiting case of the DQR approach; outside this limit, the stochastic motions of such rotors have no kinematic description. In this paper, completing the previous two of this series, consequences of nuclear permutation symmetry for the properties of the DQR line shape equation are considered. The systems addressed are planar rotors, such as aromatic hydrocarbons' rings, occurring inside of molecular crystals oriented in the magnetic field. Under such conditions, oddfold rotors can have nontrivial permutation symmetries only for peculiar orientations while evenfold ones always retain their intrinsic symmetry element, which is rotation by 180 degrees about the N-fold axis; in specific orientations the latter can gain two additional symmetry elements. It is shown that the symmetry selection rules applicable to the classical rate processes in fluids, once recognized as having two diverse aspects, macroscopic and microscopic, are also rigorously valid for the DQR processes in the solid state. However, formal justification of these rules is different because the DQR equation is based on the Pauli principle, which is ignored in the jump model. For objects like the benzene ring, exploitation of these rules in simulations of spectra using the DQR equation can be of critical significance for the feasibility of the calculations. Examples of such calculations for the proton system of the benzene ring in a general orientation are provided. It is also shown that, because of the intrinsic symmetries of the evenfold rotors, many of the DQR processes, which such rotors can undergo, are unobservable in NMR spectra.

Fingerprints of Damped Quantum Rotation Observed in Solid-State Proton NMR Spectra

(1)H NMR spectra of the methyl group in an oriented crystal sample of methylmalonic acid with all three non-methyl protons replaced by deuterons are interpreted in terms of the damped quantum rotation (DQR) theory of NMR line shapes. The DQR approach offers a perfect theoretical reproduction of the observed spectra while the conventional Alexander-Binsch line-shape model shows evident defects in the present case. The temperature trends of the quantities characterizing the coherent and incoherent dynamics of the methyl group in the DQR approach (the effective tunnelling frequency and two coherence-damping rates) derived from the spectra are fairly reproduced using a model reported previously. The present findings provide further evidence of limitations to the validity of the common belief that molecular rate processes in condensed phases are necessarily classical.