Optical Rotation of Time‐Reversal Degenerate States

Abstract

AbstractIt is shown that time‐reversal (doubly‐) degenerate, many‐electron states in molecules of point‐group symmetry C3, C4, C6, S4, and S6 and T etc., can have non‐vanishing matrix elements over a time‐odd (electric dipole‐electric dipole) polarizability operator contributing to optical rotation. In agreement with well‐known results for Kramers' doublets, the optical rotations of the two separated and oriented states of this doublet have opposite signs in this polarizability mechanism, and they have the same sign in the time‐even pseudoscalar mechanism which is the usual natural optical rotation of chiral molecules. These results are proven, in an alternative formulation using time‐reversal in a second‐order process, to hold regardless of even or odd numbers of spins—in contrast to the first‐order processes such as the Jahn‐Teller effect. The universality of time‐reversal in spin, orbital and rotational angular momentum, in point and continuous groups, is show in a unified treatment with consistent phases. It was shown also how time‐reversal symmetry can resolve the ambiguities in lower point‐groups and determine relationships for which the point‐group symmetry is powerless.