In the chalcopyrite (or tetragonal) phase, different physical properties of the ternary LiMX 2 (M = Al, Ga, In and X = S, Se, Te) compounds are studied by the very accurate density functional method. The optimized lattice constants and the bandgaps are close to the existing experimental data. In addition, for most of the LiMX 2 compounds, when the cations change from Al to In and anions from S to Te, the lattice constant and equilibrium volume for the crystal unit cell increase whereas the bulk modulus decreases. Using different generalized gradient approximations, the band structure calculations are performed. Generally, it was observed that there exists a decreasing tendency of the bandgap energies except for the LiAlSe 2 , LiInSe 2 , and LiGaTe 2 compounds due to the change from Al to In as well as the change from S to Te. The bonding analysis shows that ionic bonds are present between the Li-X atoms, while a covalent bond exists between the M cations and X anions. The optical properties of the compounds are studied by calculating the real and imaginary components of the refractive index, reflectivity, optical conductivity, and birefringence. In addition, the optical properties from the calculations show that these materials are appropriate applicants to be utilized as Bragg’s reflector or applied in optoelectronic and solar cell technology.