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

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.