  Using a linear combination of atomic orbitals approach, we report a
systematic comparison of various Density Functional Theory (DFT) and hybrid
exchange-correlation functionals for the prediction of the electronic and
structural properties of prototypical ferroelectric oxides. It is found that
none of the available functionals is able to provide, at the same time,
accurate electronic and structural properties of the cubic and tetragonal
phases of BaTiO$_3$ and PbTiO$_3$. Some, although not all, usual DFT
functionals predict the structure with acceptable accuracy, but always
underestimate the electronic band gaps. Conversely, common hybrid functionals
yield an improved description of the band gaps, but overestimate the volume and
atomic distortions associated to ferroelectricity, giving rise to an
unacceptably large $c/a$ ratio for the tetragonal phases of both compounds.
This super-tetragonality is found to be induced mainly by the exchange energy
corresponding to the Generalized Gradient Approximation (GGA) and, to a lesser
extent, by the exact exchange term of the hybrid functional. We thus propose an
alternative functional that mixes exact exchange with the recently proposed GGA
of Wu and Cohen [Phys. Rev. B 73, 235116 (2006)] which, for solids, improves
over the treatment of exchange of the most usual GGA's. The new functional
renders an accurate description of both the structural and electronic
properties of typical ferroelectric oxides.
