On the polarizability theory of optical rotation

Abstract

An equation is derived expressing optical rotation in terms of a set of ``relaytensors,'' which describe the manner in which the external field acting at one unit of a molecule induces a dipole moment in another unit. These tensors can be calculated from the polarizabilities of the units and the geometry of the molecule using either an exact treatment of point dipole interactions or perturbation approximations of any order. The derivation corrects certain previous errors in the calculation of induced electric and magnetic moments. The equation is transformed into alternative forms expressing the rotation in terms of electric and magnetic moments associated with certain sets of molecular normal modes in a manner analogous to Rosenfeld's quantum mechanical equation. One form gives an analytical expression for rotatory dispersion in terms of the polarizability dispersion parameters for individual units. Calculated rotations are given for a simple hypothetical molecule and for CHFClBr, in both cases showing that the lowest order perturbation terms disagree substantially with exact calculations.