The elastic constant,structural phase transition,and effect of metallic bonding on the hardness of RhN2 under high pressure are investigated through the first-principles calculation by means of the pseudopotential plane-wave method.Three structures are chosen to investigate for RhN2,namely,simple hexagonal P6/mmm (denoted as SH),orthorhombic Pnnm (marcasite),and simple tetragonal P4/mbm (denoted as ST).Our calculations show that the SH phase is energetically more stable than the other two phases at zero pressure.On the basis of the third-order BirchMaghan equation of states,we find that the phase transition pressures from an SH to a marcasite structure and from a marcasite to an ST structure are 1.09 GPa and 354.57 GPa,respectively.Elastic constants,formation enthalpies,shear modulus,Young’s modulus,and Debye temperature of RhN2 are derived.The calculated values are,generally speaking,in good agreement with the previous theoretical results.Meanwhile,it is found that the pressure has an important influence on physical properties.Moreover,the effect of metallic bonding on the hardness of RhN2 is investigated.This is a quantitative investigation on the structural properties of RhN2,and it still awaits experimental confirmation.