A quantum mechanical alternative to the Arrhenius equation in the interpretation of proton spin–lattice relaxation data for the methyl groups in solids

Abstract

CitationQuantum mechanical alternative to Arrhenius equation in the interpretation of proton spin-lattice relaxation data for the methyl groups in solids 2015 Phys. Chem. Chem. Phys. Theory of nuclear spin-lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups has recently been given a consistently quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate, i.e., coherence-damping processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin-lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius equation is made. The present observations provide further indications that incoherent motions of molecular moieties in condensed phase can retain quantum character over much broader temperature range than is commonly thought. Eprint version

Nonclassical dynamics of the methyl group in 1,1,1-triphenylethane. Evidence from powder 1H NMR spectra

“…In the whole temperature range, they substantially differ from 1. However, contrary to expectations based on general grounds and theoretical calculations, 7,25,33,34 the decreasing with temperature trend of the values of c shows an unexpected reversal above 110-112 K. In Fig. 7, the increasing part of the trend is displayed with open symbols.…”

“…Unlike for ∆, for k t and k K , simple formulations are nonexistent even in the low temperature limit, but at any temperature they can be calculated numerically using a parametrized model described earlier. 7,24,25 For a given set of model parameters, it consistently delivers temperature-dependent values of ∆, k t , and k K .…”

“…23,24 A concise presentation of its version for threefold rotators was reported recently. 25 The eigenstates of a hindered methyl group, a prototypical threefold rotator, are delocalized over the three wells of the hindering potential. They are classified into three symmetry species, A, E a , and E b , of the rotator's feasible permutation group isomorphic with C 3 .…”

“…12,29 The procedure of theoretical calculations of the DQR quantities from first principles was reported previously. 7,24,25…”

“…To assess the adopted assumption about a linear dependence of ∆ on temperature, the temperature behavior of k t was simulated theoretically using the already cited DQR model. 7,23,25 Formerly it afforded a perfect theoretical reproduction of the DQR effects evaluated from spectra of a single crystal 12 and of the spin-lattice relaxation data reinterpreted in the spirit of the DQR approach. 25,34 Before going into details of these calculations, a brief description of the relevant model parameters will be given.…”