Methyl Groups In Solids Research Articles

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.

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.

NMR relaxation study of methyl groups in solids from low to high temperatures

The calculation of the correlation functions of complex motion consisting of jumps over the barrier (classical motion) and jumps through the barrier (incoherent tunneling) is presented. The Schrodinger equation has been applied in the calculation of the rate constant of tunneling jumps through the barrier. This rate constant determines directly the temperature at which incoherent tunneling ceases. The calculated spectral densities are applied to analyze the temperature dependencies of the spin-lattice relaxation rate in solids containing a methyl group. © 2005 Wiley Periodicals, Inc. Concepts Magn Reson Part A 27A: 38–53, 2005.

Rotational motion of methyl groups in solids.

The symmetry properties of the X${\mathrm{H}}_{3}$-type molecules are investigated. The possible wave functions of the molecule in the ground electronic state are calculated in the Born-Oppenheimer approximation and the question of the symmetry group of the molecular Hamiltonian (${\mathit{C}}_{3}$ or ${\mathit{C}}_{3\mathit{v}}$ or other) is considered. Further, the concept of quantum coherence is examined for the case of tunneling methyl groups. The results are extended to the high temperature region by introducing a suitable ``pointer basis'' which appears to be appropriate for the description of dynamics of the methyl groups interacting with lattice. Finally, the spin-lattice relaxation time is calculated within this model and is found to agree closely with the semiclassical result. \textcopyright{} 1996 The American Physical Society.

Anyons and coherent methyl rotational spectroscopy

Low temperature coherent tunnelling rotation of methyl groups in solids is described. Rotating wavepacket states carry the nuclear spin states round the three proton sites in the lattice. The nuclear spin states behave as quasi-particles which obey a generalised form of quantum statistics. The cyclic boundary condition which constrains delocalised stationary states to integral wavenumbers is relaxed for wavepackets, allowing a continuous range of angular velocities. The theory of coherent methyl rotation is very similar to that of NMR. Experiments aimed at exciting rotating wavepacket states at 4.2K are described.

Thermally driven hindered internal rotation

The study of the coupling between the overall rotation of a molecule and its hindered internal rotation supports the concept of asymmetric driven tunnelling of methyl groups in solids at low temperatures as an explanation of the experimental observations.

Fast hopping of deuterated methyl groups

Methyl groups in solids reorientate at high temperature in a manner that is essentially dependent on the temperature of the host lattice but not on its phonon spectrum. The reorientation rate of CH3 groups can be easily predicted by evaluating a thermal average over all excited torsional states of the expectation values of the angular momentum, thus making it a calculable function of the hindering potential barrier V and temperature T. The aim of the experiments described was to extend the theory for fully deuterated compounds containing methyl groups; and consequently see how the temperature dependent reorientation rates of CD3 could be predicted from measurements of CH3 tunnel splittings of the analogous compound at low temperature. Theory-and the subsequent experiments-show how it is not necessary to carry out the full calculation again; instead, it is sufficient to calculate the energy levels of a CH3 group in a potential of height 2V and then divide these energies by two. The expectation values of the angular velocities are also reduced by a factor of two. The above can be summarised into what the authors call the 'rule of two', which may be stated by saying that a CD3 group hops at half the rate of a CH3 group of twice the barrier height at twice the temperature. The result is that the same set of curves of hopping rate ( tau -1) against inverse temperature (T-1) and potential barrier height VH of CH3, can be used for CD3 of one halves the ( tau -1) and doubles the (T-1) scales and replaces VH by 2VH. Agreement with this theory is shown to be satisfactory; the data were obtained using the time-of-flight (IN5) and back-scattering (IN10) spectrometers of the Institute Laue-Langevin, Grenoble, for four fully deuterated samples (acetone, nitromethane, iodoethane and toluene). The measurements fall in a region of very fast hopping motion.

The transition from free quantum tunnelling to thermally driven motion of methyl groups

Methyl groups in solids are representative of systems which exhibit tunnelling at low temperatures and thermally activated hopping motion at high temperatures. They exhibit very clearly all the features of the transition between free and thermally driven quantum tunnelling, the latter being describable in terms of classical hopping concepts. A satisfactory theoretical description has been lacking because the usual approaches, which treat the dynamic part of the scalar hindering potential by time-dependent perturbation theory are, the author suggest, incomplete. It is shown that a better description is possible if a vector potential arising from the motion of the lattice is introduced in addition to the scalar potential. This leads to a new Hamiltonian and a representation in which the important terms, which lead to the experimentally observed spectroscopic changes with increasing temperature, are diagonal. In this new representation a simple model emerges which exhibits most, if not all, of the observed experimental features. It also resolves an old problem: how to reconcile the quantum mechanical requirement that the rotation angles phi =0 and phi =2 pi are identical, with the classical assumption that they are distinguishable, and thus provides a bridge between the quantum and classical descriptions of rotation.

Quantum rotations of Methyl groups in solids at low temperatures

Abstract Molecular rotation, libration and the associated quantum tunnelling reorientation phenomena are described, in particular for CH 3 -groups. Four ranges of tunnel frequencies and the corresponding methods for direct determination of tunnel frequencies and line widths and of nuclear spin conversion rates are discussed. As examples, experimental results, obtained with new methods developed in the authors' laboratory, about CH 3 -groups in Ge(CH 3 ) 4 , 4-methylpyrid ne and pentamethylbenzene are given and discussed.

Quantum rotations of methyl groups in solids at low temperatures

Molecular rotation, libration and the associated quantum tunnelling reorientation phenomena are described, in particular for CH 3 -groups. Four ranges of tunnel frequencies and the corresponding methods for direct determination of tunnel frequencies and line widths and of nuclear spin conversion rates are discussed. As examples, experimental results, obtained with new methods developed in the authors' laboratory, about CH 3 -groups in Ge(CH 3 ) 4 , 4-methylpyridine and pentamethylbenzene are given and discussed.

Dynamic nuclear polarisation by the cooling of tunnelling methyl groups

The energy associated with the tunnelling motion of methyl groups in solids at low temperatures relaxes extremely slowly to the lattice bath. Paramagnetic centres speed up this relaxation enormously when an external magnetic field is chosen so that the methyl tunnel frequency and the electronic Larmor frequency are nearly equal. The difference between the two energies is made up by nuclear spin flips. The consequent nuclear dynamic polarisation provides a sensitive way of following the cooling of the methyl groups by the paramagnetic centres, with the associated diffusion of tunnelling energy to the vicinity of paramagnetic ions. The characteristic signature of the process is an anomaly in the field dependence of the nuclear magnetism having the approximate form of the derivative of a bell-shaped curve. Three examples of this are reported and a theoretical explanation is given.

Existence of spin symmetry species in reorienting methyl groups at high temperatures

Reonentations of methyl groups in solids are symmetry restricted. Consequently long-lived spin symmetry species and reorientations coexist even at high temperatures. This is a refinement of the usual reorientation model. The possibility of creating an angular momentum imbalance between symmetry species is shown. The possibility of observing exponential relaxation is discussed.

A nuclear relaxation and neutron scattering study of the rotational states of methyl groups in solids with low hindering barriers

The proton spin-lattice relaxation rate of toluene, of toluene diluted in toluene- d 8 and of toluene- d 5 diluted in toluene- d 8 has been measured over the temperature range 10–75 K. The inelastic neutron scattering peak associated with torsional energy splittings of the methyl group has been studied at low temperature. Data of the random jump rotation has been obtained from the width of the quasi-elastic scattering peak between 30 and 80 K. The results confirm the basic ideas of the theoretical relaxation model of Haupt. By removing dipole interactions of methyl protons with protons outside the CH 3 group the field dependent peak in the relaxation disappears. There is excellent agreement between NMR and neutron scattering in explaining the two types of activation process: random jump reorientation (1.3 kJ/mol) over the barrier and torsional excitation (0.55 kJ/mol) connected with tunnelling. Rotational potentials and energy levels have been derived from the experimental quantities using tabulated eigenvalues.

Detection of proton NMR-signals of methyl groups at arbitrary temperatures of the tunnelling system

The lock-in detected proton NMR-signals of methyl groups in solids is considered at arbitrary temperatures of the spin system. In the high temperature approximation the results reduce to those of Goldman and others, extended with coupled spin-lattice relaxation equations. At low temperatures of the tunnelling system some quite unusual features are to be expected, due to spin symmetry conversion causing time- as well as temperature-dependent lineshape and deviation of the magnetization from the Curie law. In particular, the lock-in detected signals in the absorption and dispersion modes are discussed.

The nonexponential character of the Zeeman relaxation of reorienting methyl groups in solids

If the rapid reorientations of methyl groups in solids are the dominant relaxation mechanisms, it is theoretically found that the Zeeman system is dynamically coupled to the so-called rotational polarization system, resulting in a nonexponential Zeeman relaxation. Though this result has been confirmed experimentally, in many samples within measuring error an exponential Zeeman relaxation has been observed. In order to decide whether or not this is contradictory to the theory the degree of nonexponentiality has been further investigated in this paper. It is shown that the nonexponential character depends stronly on the following parameters: (i) the way in which the spin system is prepared for the observation of the Zeeman relaxation, (ii) the number of protons not belonging to the methyl groups, (iii) the relaxation due to the intermethyl dipolar interactions, and (iv) the temperature. It is found that under specific conditions the observed relaxation can become almost exponential. The corresponding time constant, however, can differ considerably from that predicted by the usual spin temperature theory. Therefore, the interpretation of the experiments with this theory can lead to incorrect values of the different parameters characterizing the relaxation process. The various results have been illustrated with experiments on polycrystalline samples of 2,6-dimethylphenol, methylcyanide, 2-methylpiperazine, and 1,4-dimethoxy-2,6-dimethylbenzene.

Flip-flop motion and spin symmetry conversion of methyl groups

It is commonly supposed that hindered methyl groups in solids undergo phonon induced rotations through +or-120. This may be symbolized (1) to (2) or (1) to (3) where (1), (2) and (3) indicate equivalent orientations of the group. The authors show both theoretically and experimentally that a second type of motion may be more important. In this motion a transition to a mixed state occurs: (1) to 2/3((2)+(3)-1/2(1)). The operator which converts (1) to the mixed state converts the latter back to (1) so the motion involves two states only and may be described as flip-flop motion. It may be distinguished experimentally from rotation because it does not modulate matrix elements between pairs of states of E symmetry. Both the rotation and flip-flop rates are measured for the 4-methyl group in 4-methyl-2,6-ditertiarybutylphenol (MDBP) between 10K and 50K. The flip-flop rate is six times greater than the rotation rate. The measurement technique combines proton spin-lattice relaxation measurements with a novel way of determining the rate of conversion between proton spin symmetry species.

Proton spin-lattice relaxation studies of reorienting methyl groups in solids

Spin-lattice relaxation times (T1) have been measured at 30 MHz as a function of temperature for the methyl protons in a series of compounds, each of which contains a single methyl group. In all cases except one, the measurements were carried out above 77°K, where thermally activated motion predominates. The purpose was to determine activation energies for methyl rotation and to detect phase transitions. The following activation energies were found for polycrystalline samples from the slopes of plots of ln T1 vs T−1 on the low-temperature side of the T1 minimum: CH3PCl2 (2.25 kcal/mole), CH3PSCl2 (2.35), CH3SCN (2.4), CH3CD2I (3.2), and CH3CD2Br (3.6). For CH3COCl and CH3NCS, which apparently form glasses, only the high-temperature side of the T1 minimum could be observed. The apparent activation energies were 1.45 and 0.57 kcal/mole, respectively. Significantly nonexponential behavior was observed near and to the high-temperature side of the T1 minima. The relationship of these activation energies to internal rotation barriers obtained from ir, microwave, and cw NMR absorption studies is discussed.

A nuclear resonance and infrared investigation of the motional states of methyl groups in solids

It is demonstrated unambiguously that a single methyl group can be responsible for two well resolved minima in the temperature dependence of its proton spin-lattice relaxation time. The analysis of seven infrared absorption bands verifies that these minima are due to (i) hindered threefold reorientation of the methyl group and (ii) transitions of the methyl group between its ground and first excited torsional state. The investigations were made on the isolated methyl group in p-tert-butyltoluene, which was found to have a threefold potential barrier hindering its reorientation of amplitude (4.13+or-0.07)kJ mole-1.