The theory of hindered molecular motion and its application to spectroscopic studies

Abstract

A stochastic theory of the classical local hindered motion of small molecules in molecular and ionic crystals is presented in detail. The so-called extended angular jump model, being intermediate between the rotational diffusion model and the model of fixed angular jumps, approximates the motion. In spite of the fact that dynamical quantities of the model do not relate to the hydrodynamic parameters of the continuous medium, the outcomes of the theory are suitable for molecular liquids. Two crystallographic point symmetries, the symmetry of the molecular motion and the site symmetry, including their distortions, are taken into account in the model. Applications of the theory to the description of NMR-relaxation rates and the homogeneous broadening of spectral lines excited by dielectric, infrared, Raman, Rayleigh and neutron spectroscopy techniques are given. The validity of the approach presented is confirmed by the experimental data performed in single crystalline and powder samples.

Keywords:

• angular autocorrelation function
• anisotropy
• correlation time
• crystallographic point symmetry group
• dielectric properties
• extended angular jump model
• hindered molecular motion
• incoherent neutron scattering
• infrared absorption
• line width
• line intensity
• molecular crystals and liquids
• NMR-relaxation
• probability density
• Raman scattering
• representation theory
• residual intensity
• single crystal
• site symmetry
• symmetry distortion
• spectroscopy

Acknowledgements

The authors are grateful to Prof. R.A. Dautov, Kazan State University, Russia, who invited one of us (F. Bashirov) to begin the experimental study of the thermal molecular motion in crystals, to Prof. K.A. Valiev, member of the Russian Academy of Sciences, Russia, for helpful collaboration, and to Prof. B.Z. Malkin, Kazan State University, Russia and Prof. U. Haeberlen, Germany, for useful discussions.

Notes

Note added in the proof: The Editors have drawn our attention to a new computer program VIBRATE! A program to compute irreducible representations for atomic vibrations in crystals, by A.M. Glazer, J. Appl. Cryst. 2009, 42, 1194–1196.