Optical Activity of Vibrational Origin. I. A Model Helical Polymer

Abstract

Measurements of optical rotatory dispersion (ORD) and circular dichroism (CD) in the visible and ultraviolet region of the electromagnetic spectrum are common. Largely due to technical difficulties, however, few measurements of Cotton effects have yet been made at infrared frequencies. If the usefulness of such measurements could be demonstrated, it might be that the experimental difficulties would be overcome in the near future. It is such a demonstration which is undertaken in this paper. The model system studied is an infinite helical polymer of point masses each with an effective charge. The normal modes of vibration for the polymer are calculated using a valence‐force approximation, and using these normal‐modes expressions for molecular polarizability and optical rotatory dispersion are derived for infrared frequencies. It is seen that under certain conditions there will be normal vibrations which are not easily observed in the absorption spectrum but which should exhibit Cotton effects which are more readily observable. Also, the chirality of the helix is implicitly given by the signs of the Cotton effects. These results are analogous to what is found in ORD spectra at visible frequencies. In addition to these effects, however, a frequency dependence proportional to ${\mathrm{(\omega }}_0^2{\mathrm{–\omega }}^2{)}^{\text{−2}}$ appears in the infrared ORD spectrum at frequencies corresponding to the “perpendicular” band of the absorption spectrum. It is possible that the identification of such a band in the ORD spectrum could be used to identify helical conformations of polymers in solution.