The motional collapse of the methyl C–H stretching vibration bands

The asymmetric CH stretching bands of the methyl groups of a number of alkane systems have been examined as a function of temperature. At low temperatures, two bands are seen for a CH3 group. These bands collapse into one as the temperature is raised. Examination of crystals of alkanes with both odd and even numbers of carbon atoms, alkanes in urea clathrates, and deuterium substituted alkanes allows the separation of intramolecular and intermolecular contributions to the band splittings and widths. Model Hamiltonians that express the stretching energy levels as a function of both the methyl torsional coordinates and the external coordinates of the alkanes are set up. These are used in the Redfield equations to derive expressions for the splittings and widths in terms of parameters which give the coupling of the various types of motion. The splittings are found to be proportional to the average of cos 5ϑ, where ϑ is the torsional angle, and a contribution to the width is found to be due to fluctuations in...

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