Microscopic Description of Optical Rotation

Abstract

A microscopic theory of optical rotation in terms of the linear response theory is developed. The gauge invariance of optical rotatory strength is discussed. The general theory is applied to the long helical polymer by using the exciton model. It is shown that the result obtained by Moffitt, Fitz and Kirkwood may be derived under the assumption of the periodic boundary condition. When the helical axis of the polymer is parallel to the direction of incident beam, the rotational strength is shown to be independent of the helical radius of the polymer. Effect of the Umklapp process is evaluated. § 1. Introduction· Since the excellent review on the optical rotation was reported by Condon l) about thirty years ago, little theoretical investigation has been performed for a long time. Recently the optical rotatory dispersion (O.R.D.) or the circular dichroism (C.D.) has come to be observed precisely in the biopolymers of various kinds. Since theO.R.D. is closely related to the structures of the biopolymers and the interactions between the chromophors, the theoretical investigations also have come to be performed actively with renewed interest, in order to make the. interpretation of the experimental data clear.2) A standard theory of the O.R.D. of helical polymers was given by.Moffitt. B) He used the exciton. model and the periodic boundary condition, which enable us to neglect the boundary effect, for the helical polymer. He showed that the helical polymer has an anomalous dispersion compared with the simple dispersion in the random coil polymer. Moffitt, Fitz and Kirkwood 4) (M.F.K.), after Moffitt's work, calculated the O.R.D. for a finite chain and found an error in Moffitt's work. Namely, they found that there is the term neglected by Moffitt with the same order of magnitude and with sign opposite to the Moffitt's result. Namely, if the origin of the missing term in Moffitt's result is due to the boundary effect, their result indicates that the boundary and the bulk effects are of the same order. Condon's formula used by them, however, is correct only when the polymer length is· much smaller than the wave length of the incident light. It should be noted that Moffitt's treatment is out of this limitation. On the other hand G6 5) has handled Stephen's formula using the multipole expansion, which does not suffer the restriction about the wave length and the polymer length, and has shown that Condon's formula is correct whenever the