Calculation of the birefringences of nematic liquid crystals at optical and infrared wavelengths

In this paper we critically examine computational methods for predicting the birefringences of nematic liquid crystals, with a view to screening molecules for potential use in infrared applications. Using the liquid-crystal 5CB as a test molecule, we calculate molecular electronic polarizabilities using ab initio quantum-mechanical techniques and a wide range of basis sets. We show that the polarizabilities tend to a limiting value as the quality of the basis set is improved. However, the biggest hurdle remains the determination of the refractive index from the polarizability data. We examine several methods for performing this conversion and conclude that the simplest equation, due to Vuks, is adequate for predicting the birefringence, given the uncertainties involved in other parameters. The agreement between calculation and experiment is best described as "semiquantitative." We perform similar calculations for a wide range of nematic liquid crystals at both 589 and 1550 nm, taking into account the likely impact of molecular vibrations at the longer wavelength. We demonstrate that there is a simple scale factor, for conventional nematics, between the birefringence at visible wavelengths and in the infrared. Thus knowledge of the birefringence at optical wavelengths, as widely available in the literature, is a good guide to the usefulness of conventional nematic liquid crystals as active elements for optical switching in the telecommunications industry