Optical Activities of Organic Crystals: Crystal Orbital Formulation of Anisotropic Gyration

To describe the optical activities of crystals, gyration tensors are necessary for all wavelengths of incident light. To date, few studies on direct calculations of gyration tensors from Bloch states have been conducted. Herein, a practical procedure to obtain gyration tensors of organic crystals is presented using the crystal orbital method. The extended Hückel method was adopted to evaluate the gyration tensors, epitomizing the one-electron formulation. To confirm the validity of the formulation, the optical rotatory power of alanine and γ-glycine was examined. The reproduced profiles of the optical rotatory power were consistent with the results of recent experiments. This is a general formulation of the one-electron theory of optical activities for three-dimensional crystals. In principle, the optical rotatory strength tensor is not invariant with translation. For systems with small unit cells, however, the formalism is quasi-invariant with respect to translation. The quasi origin-independent formalism is sufficiently substantial to be applicable to modern crystal optics.