Degenerate states in optical rotation and time-reversal invariance

The consequence of time-reversal symmetry in a general second-order optical process between degenerate initial and final states is elucidated. The principle is applied to the pseudoscalar natural-optical-rotation operator ($R_L$⋅$M_L$), which involves the interference of an electric-multipole ($R_L$) transition and a magnetic-multipole ($M_L$) transition. In addition to deriving point-group selection rules, time-reversal effects on matrix elements between degenerate states of a chiral versus an achiral molecule are compared and contrasted. Other non–time-reversal-degenerate states in chiral versus achiral molecules ($D_3$ versus $C_{3v}$ and $D_4$ versus $D_{2d}$) are also compared.