A Heidemann

The rate of thermally activated methyl group rotation in solids

Evidence is presented which suggests that the thermally activated reorientation rate tau -1 of methyl groups in a very wide range of solids closely follows a universal law which relates tau -1 to the hindering barrier height V and the temperature theta . Thus tau -1 simply measures theta with a calibration curve dependent on V. A simple theory of the calibration curves is described, using a thermal average over all methyl group torsion-rotation states of the modulus of the expectation value of angular momentum. No adjustable parameters are involved if a simple cosine hindering potential is assumed. The relationship is tested on a large number of methyl-containing solids for which V has been deduced from measurements of the tunnel splitting at low temperatures. The predicted temperature-dependent reorientation rate turns out to be very similar to that given by a modified version of the theory of Stejskal and Gutowsky (1958). The relationship between the theories is discussed. Comparison is made with experimental data derived from magnetic resonance relaxation time measurements, and from inelastic neutron scattering studies.

Coupled tunnelling motion of a pair of methyl groups in lithium acetate studied by inelastic neutron scattering

The tunnelling and torsional motions of methyl groups in lithium acetate dihydrate (CH3COOLi·2H2O) have been studied in detail by incoherent inelastic neutron scattering. The results are interpreted by a model of pairs of methyl groups performing a coupled tunnelling motion. The strength of the coupling term is estimated to be about twice as strong as the threefold hindering barrier for the single particle motion.

The approach to classical dynamics of reorienting methyl groups

The authors have studied the approach towards classical behaviour of a dynamical system which exhibits strong quantum effects at low temperature. By combining nuclear magnetic relaxation and inelastic neutron scattering data, the rate of thermally activated methyl-group reorientation is measured from 10 to 65K for the 4-methyl group of MDBP (4-methyl-2,6-ditertiarybutylphenol). At low temperatures reorientation occurs by thermally assisted quantum tunnelling processes. The reorientation rate converges towards the predictions of classical theory with increasing temperature, but still deviates significantly at 65K. It appears that the classical theory may be used without important errors only at temperatures for which kT exceeds the methyl torsion splitting. In this high-temperature range a simple classical calculation of the reorientation rate is within a factor of 2 or 3 of the measured value.

The temperature dependence of methyl tunnelling motion in three acetates

High-resolution inelastic neutron scattering is used to study the excitations of the three proton spin symmetry species of the tunnelling CH3 group in sodium, zinc and ammonium acetates at temperatures below 30K. The inelastic and quasi-elastic peaks are found to have similar widths. This shows that the thermal excitations of the three species due to fluctuations of the hindering barrier are statistically independent. The methyl tunnelling splittings are obtained from the positions of the inelastic peaks at low temperature. The tunnel splitting decreases in each case with increasing temperature. The observed splitting is in approximate agreement with a thermally weighted average of the splittings of the ground and first excited torsional states.

Methyl tunnelling and torsion in acetates : the shape of hindering potentials

Methyl tunnel splittings and torsion frequencies have been measured by inelastic neutron scattering for seven acetates. The parameters of the hindering potential V, cos 345 + V, cos 645 where 45 is the methyl rotation angle, were determined from the spectra. The ratio V,/V, is similar (about 015) for six of the samples though sodium acetate appears anomalous. The dependence of this ratio on the form of interatomic potentials is discussed.

Neutron scattering transitions between spin symmetry species of methyl groups

The methyl tunnel splittings have been measured by inelastic neutron scattering at 4K for ammonium and lithium acetates. They are 16.2+or-0.2 and 250+or-10 mu eV respectively. An interesting difference between the two neutron energy transfer spectra is the relative intensities of the inelastic and quasi-elastic peaks. These are measured at a temperature at which the quasi-elastic peak is several times broader than the elastic peak so that the two can be separated. For ammonium acetate the inelastic and quasi-elastic peaks are of similar intensity, while in lithium acetate the quasi-elastic peak is relatively very weak. This is explained by a calculation which shows that a big difference between the intensities of the two types of peak is characteristic of almost freely rotating groups or of groups hindered by a potential of six-fold symmetry as in lithium acetate. A three-fold hindering potential tends to equalise the intensities as observed for ammonium acetate.

A study of the temperature dependence of a methyl tunnelling spectrum by inelastic neutron scattering

High-resolution inelastic neutron scattering is used to study the tunnelling rotation spectrum of the 4-methyl group in MDBP (4-methyl-2, 6-ditertiarybutylphenol) over a temperature range 4-30K. The spectrum shows the approximately Lorentzian inelastic and quasi-elastic peaks and the measured parameters are the two widths and the energy transfer of the inelastic peak. At low temperatures the latter is equal to the tunnelling splitting of the ground torsional state, but at higher temperatures the energy of the inelastic peak also depends on the tunnelling splitting of excited torsional states of the methyl group. The observed temperature dependence is used to test a stochastic model for the dynamic averaging of the splittings of the thermally occupied states. The results show two different rotational processes are dominant above and below 15K. These are assigned to a torsional excitation process and a Raman process involving only a virtual torsional excitation.

Tunneling of methyl groups in toluquinone: Dependence on the electronic state of the molecule

The torsional frequency and the tunneling splitting of the methyl group of crystalline toluquinone are reported for different electronic states of the molecule. Whereas in the ground state both values can be derived from a conventional cos 3φ potential with a barrier height of approximately 8 kJ/mol, the values in the lowest excited triplet state cannot be reconciled with such a simple potential. It is suggested that a chemical interaction between the methyl protons and the adjacent oxygen of the excited carbonyl group is responsible for the modification of the potential. Numerical calculations based on a simple modeling of this chemical interaction support this idea.

Tunneling motions of methyl groups in manganese acetate tetrahydrate

The temperature dependence of the tunneling motions of the methyl groups in Manganese Acetate Tetrahydrate has been studied by high resolution inelastic neutron scattering in a range between 0.06 K and 40 K. The results are in qualitative agreement with models based on rotor-phonon and rotor-rotor coupling valid for temperature regions above and below 5 K respectively. The finite line width of one of the tunneling lines which persists at very low temperatures and the anomalous positive shift of the same line at higher temperatures is not understood.

The pressure dependence of methyl tunnelling motion

The energy level splitting due to tunnelling motion of the methyl groups in sodium acetate trihydrate, Na(CH3COO)3H2O, has been measured by inelastic neutron scattering at 4K for hydrostatic pressures up to 5 kbar. The splitting falls from 5.7 mu eV at atmospheric pressure to 2.2 mu eV at 5 kbar with an exponential pressure dependence indicating a linear dependence of the height of the hindering potential on pressure.