Abstract: We studied the optical, elastic and thermodynamic properties of brookite-TiO₂ crystal by using firstprinciple calculations based on the density functional theory. The results show that the corresponding energies of the plasma oscillating frequency of brookite-TiO₂ crystal are 224,404 eV, respectively,  and the structure of brookite-TiO₂ crystal is mechanically stable and thermodynamically stable.

Key words: firstprinciple calculation, optical property, elastic coefficient, thermodynamic property