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

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.

Synthesis and structural characterization of exemplary silyl triptycenes

Synthesis of sterically congested silyl triptycenes and their structural characterization via NMR, X-ray and PXRD are presented.

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.

Frozen Rotation of the Ammonium Group Observed for the First Time in Liquid-Phase NMR Spectra

Hindered rotation of the -NH₃⁺ group in a sterically crowded molecular environment was frozen on the NMR time scale. These effects were observed for solutions of 1,2,3,4-tetrabromotriptycyl-9-ammonium tetrafluoroborate in tetrahydrofuran with and without excess of HBF₄. In the absence of acid, the hindered rotation is accompanied by a number of other effects originating in part from practically nonremovable traces of water in the solvent. Because of these additional effects, an effective rate constant of the hindered rotation could be evaluated at only one temperature for the neutral solution of the salt. For one of the acidified samples, which was prepared with special precautions against moisture, these complications are practically nonexistent at low and intermediate temperatures. For the latter sample, the Arrhenius parameters of the hindered rotation could be determined from the rotation rates evaluated in the range 194-226 K.

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

The 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 have recently been given a consistent 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 the condensed phase can retain quantum character over much broader temperature range than is commonly thought.

The effect of a broad activation energy distribution on deuteron spin-lattice relaxation

Deuteron NMR spectra and spin-lattice relaxation were studied experimentally in zeolite NaY(2.4) samples containing 100% or 200% of CD3OH or CD3OD molecules of the total coverage of Na atoms in the temperature range 20-150K. The activation energies describing the methyl and hydroxyl motions show broad distributions. The relaxation data were interpreted by improving a recent model (Stoch et al., 2013 [16]) in which the nonexponential relaxation curves are at first described by a sum of three exponentials with adjustable relaxation rates and weights. Then a broad distribution of activation energies (the mean activation energy A0 and the width σ) was assumed for each essentially different methyl and hydroxyl position. The correlation times were calculated from the Arrhenius equation (containing the pre-exponential factor τ0), individual relaxation rates computed and classified into three classes, and finally initial relaxation rates and weights for each class formed. These were compared with experimental data, motional parameters changed slightly and new improved rates and weights for each class calculated, etc. This method was improved by deriving for the deuterons of the A and E species methyl groups relaxation rates, which depend explicitly on the tunnel frequency ωt. The temperature dependence of ωt and of the low-temperature correlation time were obtained by using the solutions of the Mathieu equation for a threefold potential. These dependencies were included in the simulations and as the result sets of A0, σ and τ0 obtained, which describe the methyl and hydroxyl motions in different positions in zeolite.

Unusual effects in variable temperature powder NMR spectra of the methyl group protons in 9,10-dimethyltriptycene-d₁₂

Variable temperature (1)H wide line NMR spectra of polycrystalline 9,10-dimethyltriptycene-d12 deuterated in the aromatic positions were studied. The spectra show different patterns in an unrepeatable dependence on the way of preparation of the powdered samples. Simultaneously, no anomalies were seen in the MAS and CPMAS proton-decoupled room-temperature (13)C spectra as well as in powder X-ray diffraction patterns. The effects observed in the (1)H spectra are tentatively explained in terms of a phenomenological model. For one of the examined samples it afforded a consistent interpretation of the entire series of temperature dependent spectra in terms of structural non uniformity of the solid material studied. Quantum character of the stochastic dynamics of the methyl groups in the investigated compound was confirmed, although these dynamics are close to the classical limit where the familiar random jump model applies.

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.

A heuristic model of damped quantum rotation effects in nuclear magnetic resonance spectra

The damped quantum rotation (DQR) theory describes temperature effects in NMR spectra of hindered molecular rotators composed of identical atoms arranged in regular N-gons. In the standard approach, the relevant coherent dynamics are described quantum mechanically and the stochastic, thermally activated motions classically. The DQR theory is consistent. In place of random jumps over one, two, etc., maxima of the hindering potential, here one has damping processes of certain long-lived coherences between spin-space correlated eigenstates of the rotator. The damping-rate constants outnumber the classical jump-rate constants. The jump picture is recovered when the former cluster appropriately around only as many values as the number of the latter. The DQR theory was confirmed experimentally for hindered methyl groups in solids and even in liquids above 170 K. In this paper it is shown that for three-, four-, and sixfold rotators, the Liouville space equations of NMR line shapes, derived previously with the use of the quantum mechanical reduced density matrix approach, can be be given a heuristic justification. It is based on an equation of motion for the effective spin density matrix, where the relevant spin hamiltonian contains randomly fluctuating terms. The occurrence of the latter can be rationalized in terms of fluctuations of the tunneling splittings between the torsional sublevels of the rotator, including momentary liftings of the Kramers degeneracies. The question whether such degeneracy liftings are physical or virtual is discussed. The random terms in the effective hamiltonian can be Monte Carlo modeled as piecewise constant in time, which affords the stochastic equation of motion to be solved numerically in the Hilbert spin space. For sixfold rotators, this way of calculating the spectra can be useful in the instances where the Liouville space formalism of the original DQR theory is numerically unstable.

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.

A field-cycling NMR investigation of resonant spin-lattice relaxation features arising from tunnelling methyl groups

(1)H nuclear spin-lattice relaxation has been investigated in sodium acetate trihydrate and sorbic acid using field-cycling NMR in the solid state. The relaxation is dominated by the reorientation of the methyl groups. Resonant features arising from coherent tunnelling are observed in both the magnetic field dependence of the spin lattice relaxation rate, T(1)(-1)(B(z)) and in the inverse temperature dependence, T(1)(-1)(1/T). The two systems have different barrier heights and tunnelling frequencies, providing different perspectives on the tunnel resonance phenomena. The magnetic field dependence enables different spectral density components to be separately investigated and in the carboxylic acid, sorbic acid, concerted proton transfer in the hydrogen bonds is also identified at low field and low temperature. The methyl hindering barriers and the correlation times characterising the reorientational dynamics has been accurately determined in both materials.

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.

Hindered rotation of the silyl group in liquid-phase NMR spectra of 9-silyltriptycene derivatives: a comparison with the methyl analogues

Three 9-silyltriptycene derivatives, 1,4-dichloro- (DCST), 1,4-dibromo- (DBST), and 1,4-dimethyl-9-silyltriptycene (DMST) were synthesized, and temperature-variable (1)H NMR spectra thereof were measured. Below 220 K for DMST, and below 250 K for DCST and DBST, rotation of the silyl group becomes practically frozen on the NMR time scale. Iterative line shape analysis of the silyl proton spectra reveals that the familiar Alexander-Binsch line shape equation, employing only one rate constant for the observed rate process, is adequate in these cases. This is at a striking variance with the behavior of the methyl group in the analogous compounds, investigated by us recently, where fingerprints of the damped quantum rotation effect, a phenomenon once predicted by us, are clearly visible in the experimental spectra of the methyl protons. In the damped rotation approach, the relevant dynamics are described in terms of two quantum rate processes characterized by two coherence-damping constants, and the Alexander-Binsch model is obtained as a limiting case where these two constants become equal. The possible reasons of the differences between the dynamics of the silyl and methyl groups in the same molecular environment are discussed.