  We report our first-principles investigations on three polytypes of BaTiO3
(BTO): a paraelectric phase with cubic Pm-3m structure and two ferroelectric
(FE) phases with tetragonal P4mm and rhombohedral R3m structures. We compared
the structural and the electrical properties of BTO obtained by using various
approaches: e.g., the Hartree-Fock (HF) theory, the density functional theory
(DFT) with the local density approximation (LDA) or with the two generalized
gradient approximations (two GGAs: PWGGA and PBE), and three hybrid functionals
of the HF and the DFT (B3LYP, B3PW, and PBE0). For the P4mm structure, the two
GGAs and the hybrid functionals reproduced the cell volumes, but slightly
overestimated the c/a ratio. The hybrid functionals provided accurate
predictions for the experimental energy gaps, but slightly underestimated the
experimental dielectric constants. The calculated dielectric constants were
inversely proportional to the c/a ratios for the P4mm structure (or the cH/aH
ratio for the R3m structure), irrespective of the functional choice. Also, the
over-estimated polarization could be ascribed to a super-tetragonality in the
GGA/hybrid functionals. The pressure dependences for the cell parameters,
fractional atomic displacements, energy gaps, dielectric constants, and FE
polarizations were calculated by using the B3PW hybrid functional. As pressure
was increased, the polarization decreased monotonically until it reached zero
at a critical pressure of ~ 20 GPa for both the P4mm and the R3m structures.
Anomalous behaviors were also observed in the atomic movements and the
polarizations for the P4mm structure: (Omitted due to length..) Such behaviors
of the polarizations, together with super-tetragonality/super-trigonality, are
discussed.
