Quantum and classical dynamics of a methyl group with tunneling frequency 3.4 MHz studied by low field NMR

Abstract

Nuclear magnetic resonance ͑NMR͒ investigations of methyl tunneling in 2,5-dimethyl-1,3,4-thiadiazole are reported. The tunneling frequency ( t ϭ 3.39 MHz͒ was obtained using low field NMR spectroscopy. By means of rapid field cycling irradiation and relaxation measurements the probabilities of the absorption transitions, responsible for the spectral lines in the low field NMR spectra, can be quantified. The results obtained agree well with the calculated probabilities of rf induced transitions between the eigenstates of a methyl rotor with t ϭ 3.39 MHz. Measurements of the temperature dependence of t , the spin conversion time con and an analysis of the proton spin lattice relaxation time T 1 , the latter two revealing the correlation time c , enabled the study of the methyl group dynamics over a temperature range encompassing both the quantum mechanical and the classical regimes. The dynamical data can be explained well with a threefold hindering barrier of height V 3 /k B ϭ 1175 K and are compared with existing theoretical models.

The Effect of Low-Temperature Dynamics of the Dimethylammonium Group in [(CH3)2NH2]3Sb2Cl9 on Proton Spin−Lattice Relaxation and Narrowing of the Proton NMR Line

“…Usually literature reports one uniform correlation time characterizing all stochastic processes in the molecule. ,, Such a uniform correlation time does not follow the Arrhenius equation and diverts from it at the low-temperature range. The dependencies presented in Figure differ from the temperature course of one uniform correlation time (Arrhenius diagram) known from the literature.…”

Proton Spin−Lattice Relaxation of Tunneling Methyl Groups: Calculation of the Time Dependent Correlation Functions

“…Usually, [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] the correlation time of methyl group tunneling is assumed to follow the exponential temperature dependence as…”

“…The temperature dependence of the spin−lattice relaxation time ( T 1 ) enables a determination of the correlation time ( τ c ) (or correlation times if there are more independent stochastic motions) over a wide temperature range. The fact that the correlation time follows simple Arrhenius behavior with a single activation energy at the high-temperature limit ( E H ) and E 01 activation energy at low temperatures was anticipated by a number of authors. − The authors 11,12 introduced the following phenomenological expression for the temperature dependence of the correlation time ( τ c ): The apparent activation energy ( E L ) has been identified with E 01 = E v 1 − E v 0 , the energy difference between the ground and first excited torsional states of the CH 3 rotator. The activation energy ( E H ) corresponds to the high-temperature classical limit, namely, the barrier height minus the zero point energy.…”

Organosulfur/Conducting Polymer Composite Cathodes

“…DMT ͑see Scheme I for compound notations͒ is a highly symmetric molecule 50 which has been previously used as a model compound for NMR studies, 51 as a nitrification inhibitor in soil, 52 and as Journal of The Electrochemical Society, 149 ͑7͒ A939-A952 ͑2002͒ A940 an antifoulant additive for high temperature hydrocarbon processing. 53 It reactivity to several transition metal centers has been reported.…”