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 The calculated dielectric functions are compared with unpublished optical measurements by Zallen and coworkers.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.
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