  The nonlinear optical properties and electro-optic effects of some
oxygen-octahedric ferroelectrics are studied by the density functional theory
(DFT) in the local density approximation (LDA) expressions based on first
principle calculations without the scissor approximation. We present
calculations of the frequency- dependent complex dielectric function and the
second harmonic generation response coefficient
\c{hi}(2)(-2{\omega},{\omega},{\omega}) over a large frequency range in
tetragonal and rhombohedral phases. The electronic linear electrooptic
susceptibility \c{hi}(2) (-{\omega},{\omega},0) is also evaluated below the
band gap. These results are based on a series of the LDA calculation using DFT.
Results for \c{hi}(2) (-{\omega},{\omega},0) are in agreement with the
experiment below the band gap and those for
\c{hi}(2)(-2{\omega},{\omega},{\omega}) are compared with the experimental data
where available.
