Rotational dynamics of methyl groups in m-xylene

Oliver Kirstein (ANSTO), Michael Prager (J?lich), Rob Dimeo (NIST) and Arnaudt Desmedt (BENSC)

The rotational dynamics of the methyl groups of m-xylene has been investigated by using incoherent inelastic and quasi-elastic neutron scattering. To our knowledge coupling of methyl rotations to low energy lattice phonons and coupling of rotation of neighbouring methyl groups have been observed in one system for the first time.

The high-resolution experiment, using the HFBS spectrometer at NIST, showed two tunneling lines, with mean peak positions at 13.92 MeV and at 25.15 MeV, and their relative integrated intensities agree with the crystallographic results predicting methyl groups of equal occurrence probabilities.

Figure 1. Temperature dependent inelastic neutron spectra of m-xylene. Data were taken using the high-flux backscattering spectrometer HFBS at NIST.

The quasi-elastic experiment using the NEAT spectrometer the HMI yielded two activation energies, 19.7 MeV and 14.9 MeV, which were obtained from the temperature dependent width of the experimental peaks.

Figure 2. Temperature dependent quasi-elastic neutron spectra of m-xylene. Data were taken using the disc-chopper spectrometer NEAT at HMI.

The combination of tunneling, librational and activation energies allow one to estimate three- and sixfold potential terms within the Single-Particle Model which is a mean-field model and energy transition are obtained by diagonalising the following angle dependent Hamiltonian

The temperature dependence of the position of the tunneling peak at 13.92 MeV is somewhat unusual: Typically, the position of the peak shifts towards lower energy transfers if the temperature is increased.

In m-xylene there is a shift to higher energy transfers if the temperature is slightly increased before moving to lower energy transfers higher temperatures, fig. 3. This behaviour can be understood by coupling the rotation of the methyl group to low energy lattice phonons.

Figure 3. Temperature dependent position of the tunneling transition at 13.92 MeV showing the unusual temperature dependence.

However, the Single-Particle Model describes very accurately the experimentally obtained mean values for the tunnel splittings, first librational and activation energies, which were obtained from the T-dependence of the experimental spectra for V3=26.2 MeV and V6=2.3 MeV:

Whereas the Single-Particle Model gives reasonable results for the mean values for the positions of the tunneling transitions it cannot explain the asymmetry of the transition at about 25 meV. The asymmetry can be understood if coupling between two rotating CH3 groups is assumed. The Hamiltonian modeling the coupling becomes.

The coupling results in an extended energy level scheme and increased number of tunneling transitions.
 

Figure 4. The asymmetry of the tunneling transition at 25 MeV cannot be explained by the Single-Particle Model but a model in which the rotation of two methyl groups are coupled to each other resulting in an split of the (Single-Particle Model-) tunneling transition.

For a combination of (V3,W3)=(14.73 meV, -6.07 meV) an average tunneling transition of 25.13 meV is obtained and the calculated value for the activation energy of Ea=15.7 meV, i.e. the distance between the ground state and the saddle point of the 2-dimensional potential energy surface, is in good agreement with the experimentally determined value of Ea=14.9 meV.

In addition, the more extended excitation scheme regarding the librational transition combined with some dispersion could be an explanation for the lack for librational peaks in the experimental spectrum of the vibrational density of states, which was observed in earlier experiments.