Calculations of the macroscopic linear and nonlinear optical properties of nematic liquid crystals

Many studies have focused on the computation of the structural and electronic properties of liquid crystal molecules in a single static conformation. However, a complete and quantitatively accurate description of the macroscopic optical properties of liquid crystals must also include effects due to the long-range nematic order, the anisotropic local environment surrounding the molecules, and the dynamical fluctuations of the molecules. In this paper, we explore methods to simplify computation of the molecular average second hyperpolarizability of the nematogen 4-n-pentyl-4-cyanobiphenyl (5CB). The model we develop relates changes in the geometrical parameters of the molecule to corresponding changes in the hyperpolarizability. The model is first applied to a simple donor-acceptor substituted polyene, and then to 5CB. Use of a small set of geometrical variables results in a slight increase in the RMS deviation of the predicted hyperpolarizability over the deviation obtained from a complete set. We then discuss the importance of this work for the development of means to calculate macroscopic optical properties.