The vibration spectrum and molecular configuration of cyclohexane

The physical evidence for the structure of the cyclohexane molecule (X-ray, electron diffraction, dipole moment, vibration spectra) is all in favour of the ‘chair’ configuration. The twelve vibration frequencies for the carbon skeleton of this model have been calculated, using a simple valency force field. There are eight distinct frequencies, four being doubly degenerate. The two force constants are evaluated from two of the Raman frequencies and used to calculate the remaining six frequencies. Five of these frequencies are found to agree with the observed frequencies to within 4%, while the sixth frequency is too low to be observed conveniently in the infra-red and is forbidden in the Raman spectrum. The value calculated (206 cm.-1) for this sixth frequency is, however, consistent with the specific heat data. The selection rules are shown to be obeyed by the assigned frequencies. The value for the C-C stretching force constant, viz. 3⋅7 x 105 dynes/cm. is considerably lower than that for the same bond in ethane, viz. 4.5 x 105 dynes/cm., indicating a weakening of the C-C bond in cyclohexane relative to ethane.