Electronic, elastic, vibrational, thermodynamical, and optical properties of alpha-Si3N4 are studied by density functional theory. An assignment of the symmetry for each particular zone-center optical phonon mode in the alpha phase of Si3N4 has been performed for the first time. The reflectivity and energy-loss spectra are determined from the calculated dielectric function. The contributions to the static dielectric tensor due to purely electronic screening and infrared-active phonon modes are analyzed. Based on the calculated electronic structure the major contributions to optical transitions are identified on the elemental and orbital basis. Vibrational an optical properties of alpha-Si3N4 are compared to the respective properties of beta-Si3N4 and available experimental data. We extend description of the Si3N4 system by investigating the structural stability of its alpha polymorph as a function of temperature and pressure. The phase diagram, involving the alpha and gamma polymorphic structures of Si3N4 is predicted within the approach of the quasiharmonic theory. Results of our studies are analyzed and discussed with respect to the available experimental and theoretical data. Most of the investigated quantities remains in close correspondence with the data determined experimentally. (C) 2014 Elsevier B.V. All rights reserved.