Origin of Optical Activity in Cubic NaClO3 and NaBrO3 Crystals at 296K

Abstract

The optical activity is theoretically determined both in the dextro- and levorotatory crystals of NaClO₃ and NaBrO₃. Both compounds have identical structures and they crystallize in the space group P2₁3 as ionic solids from the water solution at room temperature. The net charges of Cl, Br and O atoms in the XO₃^‒ ions are variables, when the ratios of the electric moments of second rank in the two principal axis directions and the ratios of the defined isomorphic and measured refractive indices of the two crystals are iterated to a topological equivalence. The difference of the net charges of Cl- and Br-atoms brings the opposite sense of optical rotation in these compounds. The rotation is computed from the principal axis components of the second electric moments and axial vectors derived from the point charge model. The unit cells have four XO₃^‒ ions of three-fold symmetries lying on the four diagonals. The components of the dominant axial vectors of two ions, standing in the right- and left-handed symmetries, are pointing towards each other in the principal axis directions and contribute to the optical rotation. The left-handed component against the propagation direction of the plane-polarized light changes its handedness and rotation character making the compounds optically active. Optical activity is observed in all three principal axis directions. NaBrO₃ is dextro- and NaClO₃ levorotatory in the right-handed coordinate axis system. The compounds have opposite senses of optical rotation when crystallizing in the left-handed coordinate axis system, but the they are not enantiomorphs, because the space group is not chiral.