13C NMR of tunnelling methyl groups

Molecular Zeeman interactions in NMR spectra of methyl groups

Methyl groups in organic solids generally behave as uniaxial quantum rotors. The existing NMR theory appears to be complete, capable of describing even the finest details of the temperature-dependent spectra of such objects. However, the once re-ported temperature effects in the carbon spectra of the 13C-labeled methyl group in a single crystal of acetylsalicylic acid have still not been explained. As the temperature decreases, in the quartet corresponding to the rapid motional averaging regime, the inner lines first begin to broaden but then narrow again, so that at 6 K a pattern similar to that at room temperature was observed. In the present work, these puzzling effects are explained quantitatively by invoking the molecular Zeeman (MZ) interaction. Like the spin-rotation (SR) interaction long known to occur in methyl groups, it engages the magnetic moments generated by their torsional motions. How-ever, it has not been considered in NMR spectroscopy until now. This is a surprising situation because in the magnetic fields currently used in NMR spectroscopy, the MZ interaction is orders of magnitude stronger than the (magnetic field independent) SR effects.

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

According to the damped quantum rotation (DQR) theory, hindered rotation of methyl groups, evidenced in nuclear magnetic resonance (NMR) line shapes, is a nonclassical process. It comprises a number of quantum-rate processes measured by two different quantum-rate constants. The classical jump model employing only one rate constant is reproduced if these quantum constants happen to be equal. The values of their ratio, or the nonclassicallity coefficient, determined hitherto from NMR spectra of single crystals and solutions range from about 1.20 to 1.30 in the latter case to above 5.0 in the former, with the value of 1 corresponding to the jump model. Presently, first systematic investigations of the DQR effects in wide-line NMR spectra of a powder sample are reported. For 1,1,1-triphenylethane deuterated in the aromatic positions, the relevant line-shape effects were monitored in the range 99-121 K. The values of the nonclassicality coefficient dropping from 2.7 to 1.7 were evaluated in line shape fits to the experimental powder spectra from the range 99-108 K. At these temperatures, the fits with the conventional line-shape model are visibly inferior to the DQR fits. Using a theoretical model reported earlier, a semiquantitative interpretation of the DQR parameters evaluated from the spectra is given. It is shown that the DQR effects as such can be detected in wide-line NMR spectra of powdered samples, which are relatively facile to measure. However, a fully quantitative picture of these effects can only be obtained from the much more demanding experiments on single crystals.

Spin-lattice relaxation of the methyl group protons in solids revisited: damped quantum rotation approach

Proton spin-lattice relaxation of the methyl group in solids had been one of the most thoroughly addressed theoretical problems in nuclear magnetic resonance (NMR) spectroscopy, considered at different levels of sophistication. For systems with substantial quantum tunneling effects, several quantum mechanical treatments were reported, although in practical applications the quantum models were always augmented with or replaced by the classical jump model. However, the latter has recently proved invalid in the description of NMR line shape effects in variable-temperature spectra of hindered methyl groups, while the competing theory of damped quantum rotation (DQR) was shown to be adequate. In this work, the spin-lattice relaxation issue for the methyl protons is readdressed using the latter theory. The main outcome is that, while the existing formulas for the relaxation rates remain unchanged, the crucial parameter entering them, the correlation time of the relevant random process, need to be reinterpreted. It proves to be the inverse of one of the two quantum-rate constants entering the DQR model, neither of which, when taken separately, can be related to the jump process. It can be identified with one describing the life-time broadening of the tunnel peaks in inelastic neutron scattering (INS) spectra of the methyl groups. Such a relationship between the relaxation and INS effects was reported from another laboratory long ago, but only for the low-temperature limit where thermal population of the excited torsional levels of the methyl group can be neglected. The whole spectrum of cases encountered in practical relaxation studies on protonated methyl groups is addressed for the first time. Preliminary experimental confirmation of this novel approach is reported, based on already published NMR data for a single crystal of methylmalonic acid. The once extensively debated issues of quenching of the coherent tunneling and of the classical limit in the dynamics of the methyl groups are readdressed and presented in a consistent manner.

Spin-lattice relaxation study of the methyl proton dynamics in solid 9,10-dimethyltriptycene (DMT)

Proton spin-lattice relaxation studies are performed for powder samples of 9,10-dimethyltriptycene (DMT) and its isotopomer DMT-d(12) in which all the non-methyl protons in the molecule are replaced by deuterons. The relaxation data are interpreted in terms of the conventional relaxation theory based on the random jump model in which the Pauli correlations between the relevant spin and torsional states are discarded. The Arrhenius activation energies, obtained from the relaxation data, 25.3 and 24.8 kJ mol(-1) for DMT and DMT-d(12), respectively, are very high as for the methyl groups. The validity of the jump model in the present case is considered from the perspective of Haupt theory in which the Pauli principle is explicitly invoked. To this purpose, the dynamic quantities entering the Haupt model are reinterpreted in the spirit of the damped quantum rotation (DQR) approach introduced recently for the purpose of NMR lineshape studies of hindered molecular rotators. Theoretical modelling of the relevant methyl group dynamics, based on the DQR theory, was performed. From these calculations it is inferred that direct assessments of the torsional barrier heights, based on the Arrhenius activation energies extracted from relaxation data, should be treated with caution.

Spectral spin diffusion and magnetic dipolar energy in the NMR of 13CH3 compounds

Spin diffusion between 13CH3 groups in solids is studied both theoretically and experimentally. It is shown to be dominated by mutual spin flip-flops of protons belonging to neighbouring methyl groups. Also nonmethyl protons may contribute significantly if present in the sample. The spin-rotational ground state of 13CH3 consists of 16 sublevels. When their populations are used to describe spin diffusion, eight population combinations are shown to be important, two of them corresponding to the 13C-proton and proton-proton intra-methyl magnetic dipolar energies, Dc and Dp, respectively. Spin-diffusion transitions modulate these combinations so that a further reduction to two sets of four combinations is possible, with no coupling between the sets. Coupled differential equations are derived to describe the time dependence of the combinations in each set. They are solved numerically and compared with experimental results on a single crystal of aspirin with 13C-labelled methyl groups at the carbon resonance. The 13C NMR induction signal was observed as a function of time after the preparation either at the carbon resonance (a two-pulse sequence) or at the proton resonance (proton saturation). Usually carbon spectra were computed first and then three of the mentioned population combinations were obtained from the individual spectral components. Some results on the time dependence of Dc were also obtained directly from the amplitude of the out-of-phase induction signal. Theoretical predictions are found to describe semiquantitatively the overall time dependence of these three combinations and especially their variation with different initial conditions, which are discussed in detail. Also the partial transfer of the magnetic dipolar energy between Dc and Dp is nicely explained. Reasons for discrepancies are discussed.

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.

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?

It is shown that the answer to the question asked in the title is: Because the axial symmetry axes of the H-H dipolar coupling tensors in a -CH3 group are perpendicular to the (assumed) threefold axis of the group. By contrast, those of the 13C-H dipolar and 2H quadrupolar coupling tensors are not. The use of "symmetry adapted" spin functions and of a symmetry adapted form of the (dipolar) coupling Hamiltonian greatly simplifies the analysis.

The shape and information content of high-field solid-state proton NMR spectra of methyl groups

The possible variation of the lineshape of the high-field 1H spectrum of methyl groups is explored by simulation and experiment. The spectrum of an isolated methyl group depends, apart from the orientation of the applied field B0 relative to the C3-axis of the group, on its rotational tunnel frequency vt and on its stochastic reorientation rate k. For quantitative analyses, the directional mobility of the C3-axis must also be taken into account. A distinct but frequently occurring case arises when the methyl groups come as pairs of magnetically equivalent close neighbours. For the experiments, single crystals of four compounds I-IV were grown that were isotopically substituted such that they contained protons only in the methyl positions. The crystal symmetry of all compounds I-IV allowed us to record spectra with all methyl groups being orientationally and otherwise equivalent. I, acetonitrile in deuterated hydroquinone, represents the case of a well-isolated methyl group with a "high" tunnel frequency vt. Its spectrum is (almost) independent of the temperature T. In II, monomethyl malonic acid, vt is comparable in size with the strength of the intramolecular dipolar H-H interaction. All seven theoretically expected lines in the 1H spectrum are clearly resolved in the spectra of II. vt can be inferred with an uncertainty of only +/- 300 Hz. vt(T) is found to possess a (flat) maximum near 40 K. Compound III, L-alanine, allows the study of the case of a methyl group with an extremely low, although nonzero tunnel frequency (vt approximately 3 kHz) while IV, dimethylglyoxime, represents the case of a close pair of equivalent methyl groups. Its spectrum reflects intriguing structural implications.

Spin-lattice relaxation of 13CH3 groups in 13C-enriched aspirin after proton saturation

We studied the spin-lattice relaxation of the 13C magnetisation, M(C), in 13C-enriched single crystal of aspirin (only methyl carbons enriched to 99%) at the carbon resonance frequency of 54.5 MHz. After the carbon saturation the recovery appears exponential except below 30K, where it is biexponential due to the presence of the level crossing omega(t)=omega(C)+omega(H) (the symbols refer, respectively, to the tunnel frequency and the carbon and proton resonance frequencies in angular units). After the saturation of the proton magnetisation, M(H), the description of the M(C) recovery needs three exponentials. The evaluation of the time constants is easiest from the data in this case, since M(C) varies with time in an initial growth-subsequent decrease (or an initial decrease-subsequent growth depending on temperature) manner, instead of the monotonous growth after the carbon saturation. Experimental data agree semiquantitatively with the predictions of our recent model. According to the model the relaxation of M(C) is coupled to M(H) and the tunnel energy TE at temperatures below the minimum of the 13C relaxation time. Sufficiently above this minimum M(C) is coupled to M(H) and the rotational polarization (but not to TE) in agreement with experiment. Also the effect of torsional oscillations of a methyl group on the magnitude of various 13C-related transition rates was considered in detail. In aspirin the rates are reduced roughly by 10% and the reduction should become larger in samples with a larger tunnel splitting. The reduction also changes somewhat the angular dependence of these rates.

Iterative lineshape analysis of quadrupolar echo spectra of a damped CD(3) quantum rotor: preliminary evidence of a novel mechanism of stochastic spin exchange

It is demonstrated that the wealth of information about damped quantum rotation of CD(3) groups, contained in quadrupolar echo spectra, can be fully explored in a broad temperature range using a method of iterative analysis of the spectral lineshapes. The recently reported lineshape equation which, apart from the quantum tunneling and the dissipative Alexander--Binsch terms, contains an additional dissipative term having no classical analog is shown to be capable of describing even subtle details of the spectra of a crystal of acetylsalicylic acid--CD(3) oriented specifically in the magnetic field. Preliminary evidence of the occurrence of this novel dissipative mechanism in the system studied is reported. The results obtained seem to suggest that there is no "classical limit" in the dissipative behavior of this system.