  Phonon frequencies at {\Gamma},X,M,R-points of Brilloin zone in cubic phase
of Ba(Ti,Zr,Hf)O3 were first time calculated by frozen phonon method using
density functional theory (DFT) with hybrid exchange correlation functional
PBE0. The calculations use linear combination of atomic orbitals (LCAO) basis
functions as implemented in CRYSTAL09 computer code. The Powell algorithm was
applied for basis set optimization. In agreement with the experimental
observations the structural instability via soft modes was found only in
BaTiO3. A good quantitative agreement was found between the theoretical and
experimental phonon frequency predictions in BaTiO3 and BaZrO3. It is concluded
that the hybrid PBE0 functional is able to predict correctly the structural
stability and phonon properties in perovskites.
