A detailed study of the M3N4 (M =Si,Ge,Sn) nitrides in their tetragonal,monoclinic and orthorhombic phases has been performed with the plane-wave pseudo-potential method combined with the quasi-harmonic approximation,including the phononic effects.We rationalize the main puzzle,i.e.,the fundamental properties of these phases are unclear,by calculating the crystal structures,density of states,and optical properties.The direct band gaps of t-Ge3N4,m-Si3N4,and o-Ge3N4 benefit the opto-electrical properties.t-,m-,and o-Si3N4 can be used as refractive materials while m-M3N4 (M =Si,Ge,Sn) are optically transparent in the visible light region.Our results improve the understanding of the detailed electronic structures of all compounds,as well as the influences of electronic structure on their stabilities.Furthermore,we find that thermodynamic quantities are sensitive to structures and,therefore,depend on various temperature and pressure conditions.