The solid-state Cd0.75X0.25Te (X= Cu, Ag, and Au) solutions crystallize in the cubic structure and are studied in the framework of density functional theory. The theoretical first-principle calculations of the electronic band structure, density of states, and refractive index of solid-state Cd0.75X0.25Te (X= Cu, Ag, and Au) solutions are estimated by the generalized gradient approximation (GGA). A Perdew–Burke–Ernzerhof functional (PBE) was utilized. Formation energy is calculated based on the results of the total energy of the study samples. The effective mass of the electrons and holes was calculated based on the electronic band structure. The influence of atom substitution on electron conductivity and mobility is discussed. To study the optical properties was use a complex dielectric function ε(ħω). The spectral behaviour of the refractive index was calculated based on the dielectric function.