Within the local-density approximation we have used the linear muffin-
tin orbital method, without geometrical approximations, to calculate t
he electronic structure of red HgI2. Using the self-consistent potenti
al we have calculated the energy bands and from these derived the anis
otropic frequency-dependent dielectric function and the reflectivity s
pectrum. The calculated dielectric function is in good agreement with
the experimental data in contrast to previous theoretical work. The ef
fect bf the spin-orbit coupling on the optical properties has also bee
n studied and found to be significant. In this work we predict a rathe
r large anisotropy in the dielectric function resulting from the low-s
ymmetry crystal structure.