Infrared optical properties of $\alpha$ quartz by molecular dynamics simulations

This paper is concerned with theoretical estimates of the refractive--index curves for quartz, obtained by the Kubo formul\ae\ in the classical approximation, through MD simulations for the motions of the ions. Two objectives are considered. The first one is to understand the role of nonlinearities in situations where they are very large, as at the $\alpha$--$\beta$ structural phase transition. We show that on the one hand they don't play an essential role in connection with the form of the spectra in the infrared. On the other hand they play an essential role in introducing a chaoticity which involves a definite normal mode. This might explain why that mode is Raman active in the $\alpha$ phase, but not in the $\beta$ phase. The second objective concerns whether it is possible in a microscopic model to obtain normal mode frequencies, or peak frequencies in the optical spectra, that are in good agreement with the experimental data for quartz. Notwithstanding a lot of effort, we were unable to find results agreeing better than about 6%, as apparently also occurs in the whole available literature. We interpret this fact as indicating that some essential qualitative feature is lacking in all models which consider, as the present one, only short--range repulsive potentials and unretarded long--range electric forces.