EN
Using the first-principles projector augmented wave method, the structural and electronic properties of wurtzite crystals, AlN, GaN, InN and ZnO have been calculated. Different exchange-correlation approximations: LDA, LDA+U, GGA, GGA+U and hybrid Heyd-Scuseria-Ernzerhof method were used. We also present the values of band gap calculated within different GW approximations (G_0W_0, GW_0, GW and U+G_0W_0, the last one for materials with shallow d states). In case of structural parameters the best agreement with experiment was obtained for hybrid Heyd-Scuseria-Ernzerhof functional and in case of band gap the best agreement was for GW and U+G_0W_0 approximation.