  We report ab initio calculations of the electronic band structure, the
corresponding optical spectra, and the phonon dispersion relations of trigonal
alpha-HgS (cinnabar). The calculated dielectric functions are compared with
unpublished optical measurements by Zallen and coworkers. The phonon dispersion
relations are used to calculate the temperature and isotopic mass dependence of
the specific heat which has been compared with experimental data obtained on
samples with the natural isotope abundances of the elements Hg and S (natural
minerals and vapor phase grown samples) and on samples prepared from isotope
enriched elements by vapor phase transport. Comparison of the calculated
vibrational frequencies with Raman and ir data is also presented. Contrary to
the case of cubic beta-HgS (metacinnabar), the spin-orbit splitting of the top
valence bands at the Gamma-point of the Brillouin zone (Delta_0) is positive,
because of a smaller admixture of 5d core electrons of Hg. Calculations of the
lattice parameters, and the pressure dependence of Delta_0 and the
corresponding direct gap E_0~2eV are also presented. The lowest absorption edge
is confirmed to be indirect.
