Infrared optical properties of α quartz by molecular dynamics simulations

This paper is concerned with theoretical estimates of the refractive-index curves for
quartz, obtained by the Kubo formulæ 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 α-β structural phase transition.
We show that, on the one hand, they do not 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 α phase, but not in the β 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.