Optical and magneto-optical rotation due to transverse electronic motion in thick helices of nonintegral turns

Abstract

The induction of time-oscillating (and radiating) dipoles in a helical structure is first discussed from a classical, geometrical viewpoint. It is shown that not only the longitudinal but also the transverse component of the helix can contribute to this dipole moment. The transverse contribution is also chiral in that it can give rise to opposite signs for optical rotation for the left vs right helices. Such transverse effects cannot be accounted for by the existing treatment of a free electron in a one-dimensional helix. We used a nonorthogonal curvilinear arc coordinate system to represent a three-dimensional helix and computed general transverse excitation matrix elements for optical rotation based on a free electron in a three-dimensional potential box. As a rough comparison of transverse vs longitudinal effect, the parameters in the conjugated hexahelicene molecule are used as examples. It is suggested that the transverse effect will be present not only in the optical rotation of inherently asymmetric molecules in random systems, but also in Rayleigh and Raman optical activity and in the optical rotation of oriented helices. It may also some day be useful for the determination of the absolute configuration of optical isomers.