We present a comprehensive theoretical investigation of paraelectric (cubic) and ferroelectric (tetragonal) BaTiO${}_3$. The atomic and electronic structure, piezoelectric tensor, Debye temperature, zone center phonon frequencies, and optical absorption are calculated for both phases from first principles. The structural and vibrational properties predicted from density functional theory are in good agreement with experiment and earlier theoretical work. The electronic structure and optical response are found to be very sensitive to quasiparticle and electron-hole attraction effects, which are accounted for by using the GW approach and by solving the Bethe-Salpeter equation, respectively. Electronic self-energy effects are found to open the band gap substantially, to 3.7 and 3.9 eV for the cubic and tetragonal phases, respectively. In contrast to earlier calculations, good agreement with the measured optical data is achieved. The ab initio thermodynamics predicts that the ferroelectric ordering will disappear at 419 K. It is shown that the phase transition is driven by the vibrational entropy of a variety of modes.

• Received 21 September 2010

DOI:https://doi.org/10.1103/PhysRevB.83.054112