Raman and Infrared Intensities in the Vibrational Spectra of Hydrocarbons. I. Skeletal Vibrations of Straight Zigzag Chains

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Abstract
The vibrational frequencies and normal coordinates of finite, straight, zigzag chains are calculated from an Urey-Bradley potential, the boundary effects being taken into account by a perturbation method. The dominant perturbation terms fall off with 1/N2 (N = number of C atoms) and are found to be negligible for N>5. The intensities of infrared and Raman bands are calculated without using the simplifications implied in ``bond moment'' and ``bond polarizability'' theories. All the vibrations are found inactive as fundamentals in infrared absorption. The Raman active vibrations produce branches of lines with relative intensities approximately 1, 1/9, 1/25..., 1/N2 and with line spacing rapidly decreasing with increasing N. The strong Raman line observed near 890 cm-1 cannot be assigned to a vibration of the carbon skeleton. One low-frequency vibration (v∼1150/N cm-1) perpendicular to the molecular plane should be Raman active. Its low intensity (it has not been observed so far) indicates cylindrical symmetry of the polarizability about the molecular axis.