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In order to investigate the effect of rare earth elements on the properties of Mg-Zn magnesium alloys, the structural stability, electronic structure, elastic and optical properties of Mg₂Y, Mg₂La and Mg₃La are calculated and analyzed by using the plane wave pseudo-potential method based on the first principles calculation. The calculated heats of formation and cohesive energies show that Mg₃La has the strongest forming ability and Mg₂La has the most stable structure. The stabilization mechanism of the structure is analyzed based on the calculation of electron densities of states (DOS), electron occupation number and electron density difference. The bulk modulus B, shear modulus G, Young"s modulus E, and Poisson"s ratio ν are further calculated by the elastic constants. The calculated results show that Mg₂Y has the strongest ability of resisting deformation, Mg₃La has the strongest stiffness and resistance to shear deformation, Mg₂La has the strongest plasticity, Mg₂Y and Mg₂La are ductile phases while Mg₃La is brittle phase. Furthermore, the calculated results of hardness and melting temperature shown that Mg₃La has the best abrasive resistance and Mg₂Y has the best heat resistance among the three intermetallic compounds. Finally, the refractive index, reflectivity, absorption coefficient and loss function of the three crystal structures were calculated and analyzed..