Torsional vibrations of long-chain hydrocarbons

Abstract
The torsional vibrations of long-chain hydrocarbons represent rotational oscillations of small amplitude around the carbon-carbon bonds. On the assumption that the forces hindering rotation around the various C— C bonds are equal and independent of each other, the frequencies of isolated long-chain hydrocarbon molecules in the plane configuration are calculated exactly. In the case of L carbon atoms, there are L — 3 m odes of torsional vibration. The frequencies extend from a maximum value ω m in the far infra-red region, down to low values The introduction of a polar group into the molecule makes the torsional vibrations active in the absorption spectrum. In a subsequent paper, the present results will be used to derive the torsional absorption spectrum of dipolar long-chain substances in the solid state .

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