Ab Initio Calculation of Chirality in Crystals

The chirality of a free molecule in solution is relatively easy to determine by measuring its optical activity or rotatory power, but this is not the case in the solid state. Indeed, the absolute structure of tartaric acid, for example, as obtained from the magnitude and sign of the chirality, c, did not become available until 150 years after the discovery of Pasteur. This is due to the fact that, in solids, c is a small quantity that contributes weakly to the refractive index n of crystal, and its circular birefringence, according to the expression: n ~ e^1/2 ± ε ω c (for a non-magnetic material), where ϵ is the relative dielectric matrix and ω is the light frequency.