Circular Dichroism of Large Oriented Helices: A Free Electron on a Helix

Abstract

An electron free to move on a helical path is a simple optically active system; the optical properties of which can be calculated exactly. Such a helical system was discussed in the small molecule (or dipole or Rosenfeld) approximation by Tinoco and Woody (1964). The wavefunctions and energies necessary to calculate the optical properties of the helix are identical to those for a particle in a one-dimensional box. Thus, this simple optically active system offers the possibility of furnishing insights into the origins of the optical properties of many chiral systems. For example, it is of interest to understand the origins of the interesting circular dichroism (CD) bands often associated with molecular aggregates such as cholesteric liquid crystals, chromosomes, nucleic acid in various condensed states, viruses, etc. These chiral systems generally have spatial dimensions that are large compared to the wavelength of the incident light giving rise to the CD bands. Thus, the usual Rosenfeld approximation to the optical properties of such systems will, in general, be inadequate.