Band-theoretic calculations of the optical-activity tensor of α-quartz and trigonal Se

We present a formalism to compute the optical-activity tensor in the long-wavelength limit neglecting local-field corrections with a nearly first-principles approach. The calculation of optical activity requires perturbation theory in the vector potential in order to describe the rotation of the plane of polarization perpendicular to the direction of propagation. We contrast this approach with perturbation theory in the scalar potential which can be used for the other optical response properties we compute. Band structures are obtained within the Kohn-Sham local-density approximation using standard plane-wave and separable norm-conserving pseudopotential techniques. Self-energy effects necessary to obtain the correct band gap are included by the use of a ‘‘scissors operator.’’ In the long-wavelength limit, two components of the optical-activity tensor are computed for both selenium and α-quartz. For selenium in the low-frequency range, the optical rotatory power along the optic axis is about a factor of 2 too small compared with some of the experimental data. For α-quartz, the ratio ${\mathit{g}}_{11}$/${\mathit{g}}_{33}$ and the frequency dependence of both components obey the phenomenological coupled-oscillator model and are in agreement with experiment. Yet both ${\mathit{g}}_{11}$ and ${\mathit{g}}_{33}$ (or the optical rotatory power) are about a factor of 5 too small compared with the available experimental data. In addition, the dielectric constants and second-harmonic-generation susceptibilities including local-field corrections are calculated for selenium and α-quartz in terms of scalar-potential theory. Excellent agreement (discrepancies of a few percent) is obtained with the experiments for these properties.