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A recent experimental study found the phase transition from cubic to tetragonal phase at 17.2 GPa in BaZrO_{3}. In this paper, we investigate the structural, electronic, elastic, and optical properties of BaZrO_{3} in the cubic and tetragonal structures under pressure by using first-principle density-functional theory. The main results are summarized as follows: (1) An indirect band structure is displayed for both cubic and tetragonal phases. The band gap increases by ~1 eV as a result of the phase transition. (2) The elastic constants C_{ij}'s indicate that the cubic and tetragonal phases are mechanically stable. The easiest deformation mechanism in both phases is the shear along the (100) plane. (3) The real and imaginary parts of dielectric function for the cubic and tetragonal phases shift towards higher energies with pressure. Our results are in agreement with the available experimental and prior theoretical data.
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