Optical rotation of achiral compounds

Oriented achiral molecules and crystals with D_2d symmetry or one of its non-enantiomorphous subgroups, S₄, C_2v, or C _s, can rotate the plane of transmitted polarized light incident in a general direction. This well-established fact of crystal optics is contrary to the teaching of optical activity to students of organic chemistry. This Minireview gives an overview of the measurement and calculation of the chiroptical properties of some achiral compounds and crystals. Methane derivatives with four identical ligands related by reflection symmetry are quintessential optically inactive compounds according to the logic of van 't Hoff. Analysis of the optical activity of simple achiral compounds such as H₂O and NH₃ provides general aspects of chiroptics that are not readily broached when considering chiral compounds exclusively. We show here, through the use of group theoretical arguments, the transformation properties of tensors, and diagrams, why some achiral, acentric compounds are optically active while others are not.