13C NMR of tunnelling methyl groups

The dipolar interactions between the protons and the central ¹³C nucleus of a ¹³CH₃ group are used to study rotational tunnelling and incoherent dynamics of such groups in molecular solids. Single-crystal ¹³C NMR spectra are derived for arbitrary values of the tunnel frequency ν_t. Similarities to ESR and ²H NMR are pointed out. The method is applied to three different materials. In the hydroquinone/acetonitrile clathrate, the unique features in the ¹³C NMR spectra which arise from tunnelling with a tunnel frequency that is much larger than the dipolar coupling between the methyl protons and the ¹³C nucleus are demonstrated, and the effects of incoherent dynamics are studied. The broadening of the ¹³C resonances is related to the width of the quasi-elastic line in neutron scattering. Selective magnetization transfer experiments for studying slow incoherent dynamics are proposed. For the strongly hindered methyl groups of L-alanine, an upper limit for ν_t is derived from the ¹³C NMR spectrum. In aspirin? (acetylsalicylic acid), incoherent reorientations dominate the spectra down to the lowest temperatures studied; their rate apparently increases with decreasing temperature below 25 K.     

Tunneling of coupled methyl groups

A method is developed which allows the calculation of tunneling frequencies for coupled methyl groups in strong or weak orientational potentials to any desired accuracy. The method is applied to two coupled methyl groups and the results of the calculation are compared with a recent experiment. The comparison allows conclusions on the strength and symmetry of the potential. A further important point is the prediction of coupling effects in rotational tunneling also in the limit of strong potentials.     

Structure factors for neutron scattering on tunnelling methyl groups in nitromethane

The elastic, quasielastic and inelastic structure factors for neutron scattering on CH₃ groups tunnelling in a sinusoidal hindering potential with threefold symmetry are calculated as a function of the momentum transferQ. A comparison is made with data on methyl groups in nitromethane obtained with high resolution inelastic neutron scattering experiments at high momentum transfer.     

Spin-lattice relaxation by tunnelling motions of methyl groups in some organic compounds

The proton spin-lattice relaxation times, T₁, of methyl groups in (CH₃CO)₂O, CH₃COCl, CH₃ COBr and (CH₃)₂S₂ have been measured below melting points at 52 MHz. The observed T₁ minima display the presence of tunnelling rotation. From the fit of the experimental results the ground, the first excited state tunnelling frequencies and the energy difference between the ground and the first excited states of the compounds have been estimated.     

The rotational energy levels of four methyl groups

The energy level spectrum for a system of four interacting methyl groups belonging to an X(CH₃)₄ type molecule is calculated by numerical methods. The rotational potential at the site of each methyl group is assumed to be of a three-fold symmetry. The torsion-torsion interaction is defined as a term in the multipole expansion of the electrostatic interaction of two rigid charge distributions. It is shown, that the tunneling frequency characterizing the ground state manifold in the absence of methyl-methyl interaction, splits into a set of closely spaced frequencies.     

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.     

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.     

Dynamics of a coupled pair of two-level tunnelling systems

An exact solution for the dynamics of a coupled pair of symmetric two-level-systems is given by calculating the resolvent of the Liouvillian and the statistical operator of the problem. At low temperatures interference effects between the two systems turn out to be of major importance. Depending on the value and the sign of the interaction parameter the susceptibility of the pair increases or decreases compared to the situation of isolated systems. For high temperatures the interference contributions disappear.     

Rotational tunnelling: The width of the quasi-elastic line

The tunnelling spectrum of methyl groups or amine molecules in crystals can be measured by high-resolution neutron scattering. With rising temperatures the lines broaden considerably. The broadening mechanism is quite different for the inelastic and quasi-elastic components. The latter mechanism has recently been identified and the quasi-elastic line broadening has been calculated in a perturbative approach. In this paper we examine the same mechanism for the latter, but the perturbation expansion is avoided. This is achieved by a transformation to a surrogate harmonic Hamiltonian for which the relevant correlation function can be calculated for arbitrarily strong coupling to the lattice. The quasi-elastic line is found to be much narrower than the inelastic ones, in agreement with recent experiments.     

Theory of the temperature dependence of rotational tunnelling phenomena of coupled pairs of CH3 groups

A discussion of the need to go beyond the single-isolated-molecular group approximation for the temperature dependence of rotational tunnelling properties is given. As a simple model calculation the case of a coupled-pair of methyl groups is considered in the Hewson [8] approximation. Some recent experimental results on lithum acetate [1] are discussed in the framework of the model.     

Tunneling of coupled methyl groups in lithium acetate: The isotope effect

We studied by high resolution inelastic neutron scattering the isotope effect of tunneling of coupled methyl groups in lithium acetate dihydrate (LIAC). Fully protonated, fully deuterated and mixed LIAC samples were investigated. The results are described by a simple model in which it is assumed that the single particle potential hindering rotation is strongly increased by deuteration, whereas the coupling potential is nearly unchanged. This allows to interpret the very strong isotope effect and also the spectra of the mixed compounds. The strong increase of the single particle potential by deuteration is tentatively explained by phonon mediated coupling.     

Rotational tunnelling and methyl group reorientation in Sn(CH3)4 by inelastic neutron scattering and nuclear magnetic resonance

Tunnelling frequencies, torsional excitations and spin-lattice relaxation times have been measured at various temperatures in tetramethyltin using INS and NMR techniques. All the results can be explained in terms of the molecular and crystal structure which establishes the existence of two types of non-equivalent methyl groups in the ratio 3∶1. The more frequent CH₃(1) groups show a tunnel splitting of 13.3 μeV and a torsional excitation of 13.2 meV in the ground state, and an activation energy of 1.9 kJ/mol. The corresponding values for CH₃(2) are 1.72 μeV, 17.7 meV and 3.4 kJ/mol, respectively. Rotational potentials have been derived using tabulated eigenvalues. The experiment confirms the theory of Hewson on the temperature dependence of tunnelling states.     

Pressure dependence of tunneling and librational modes of coupled methyl groups in lithium acetate

The pressure dependence of the tunneling and librational modes of the coupled methyl groups in lithium acetate dihydrate was studied by inelastic neutron scattering at liquid helium temperatures and the results compared with detailed model calculations. An increase of both the single particle and coupling potential parameters with increasing pressure was observed.     

Rotational frequencies of methyl group tunneling.

Methyl tunnel frequencies, measured at 4 K, are found to be 455 +/- 8 kHz in methyl malonamide and 496 +/- 8 kHz in methyl ethyl ketone. The first is unaffected by deuteration of the amide groups. Measurements of the temperature dependence of the spin lattice relaxation time are also reported for methyl malonamide and a further test is made of a previously reported correlation between tunnel frequency and the temperature of the T1 minimum. The measurements are in good agreement with the universal correlation curve.     

Rotational tunnelling in (CH3)2SnCl2: a neutron scattering study

The temperature dependence of the rotational tunnelling excitations in (CH₃)₂SnCl₂ is investigated between 5 and 232K. The quasi-elasticE ^a –E ^b -transitions are found to be narrower than the inelasticA–E-transitions. At high temperatures the broadening is linear in the temperature. The results are in qualitative agreement with a recent theory.     

Evidence of coupled rotational tunnel states of methyl groups of hexamethylbenzene by nuclear magnetic resonance

Two tunneling frequencies were identified for methyl groups in hexamethylbenzene from 4.2 up to 30.9 K by means of the N.M.R. field cycling method. The frequencies were 9.6 ±- 0.4 MHz (A) and 7.9 ±- 0.4 MHz (B) at 4.2 K. The frequency A was almost independent of the temperature whereas the frequency B decreased as the temperature increased, the decrease being a linear function of T³. These facts indicate that the six methyl groups in hexamethylbenzene molecule are not independent but are coupled to one another rather strongly.     

Proton spin conversion of coupled methyl groups in lithium acetate studied by inelastic neutron scattering

The temperature dependence of the tunneling spectrum of methyl groups in lithium acetate dihydrate has been studied in the temperature range between 1.2 and 8.0 K by inelastic neutron scattering. The results unambiguously prove that it is to a first order approximation correct to describe the tunneling motions by a model of coupled CH₃ pairs which are isolated from each other. However, from the fact that the tunneling frequencies shift to higher values with decreasing spin temperature, we conclude that coupling effects are important not only between nearest neighbour CH₃ groups. Quantitatively we can describe the observations by a model of coupled pairs with a fixed value for the interaction potentialW ₃ and a variable single particle potentialV ₃ which depends linearly on the concentration of the spin symmetry species.     

Spin lattice relaxation rates of tunnelling CD3 groups

The spin lattice relaxation rates of deuterated methyl groups are calculated for threefold and sixfold potentials. It is shown that it should be possible to determine the symmetry of the potential hindering the methyl groups from deuteron spin lattice relaxation experiments. The temperature dependence of the spin lattice relaxation rates is discussed using a simple model. The similarities and the differences between proton NMR and deuteron NMR are pointed out. The main difference is thatEaEb transitions are forbidden by spin selection rules in case of CH₃, but not for CD₃. Therefore, and due to the fact that the quadrupolar interaction is a single particle interaction, deuteron NMR allows the study of the rotational dynamics of single methyl groups.     

Rotational tunneling dynamics of methyl groups inn-alkane host lattices: An optical investigation of the internal and external isotope effect

We exploited the slow relaxation of methyl group rotational tunneling states to perform optical hole burning inn-alkane crystals. The dye probe used was dimethyl-s-tetrazine and its perdeuterated derivative. We investigatedn-octane, perdeuteratedn-octane andn-hexane as host crystals. By comparing the experimentally observed hole-antihole splitting of the protonated and perdeuterated dye probe, all parameters, i.e. the tunneling splitting in the ground-and in the electronically excited state as well as the respective heights of the potential can be determined, assuming a threefold rotational symmetry axis. We found that matrix deuteration has a severe influence on the potential heights, which increase by a factor of two. With these parameters determined, many features of the complex relaxation behavior of the tunneling states can be qualitatively understood: We found Raman-type conversion processes inn-octane-h ₁₈, Orbach-type processes inn-octane-d ₁₈ and inn-hexane we found, in addition, a relaxation regime governed by a Direct process. The experimental activation energies as well as the cross-over temperatures are in satisfying agreement with current theories.