  We report first principles density functional perturbation theory
calculations and inelastic neutron scattering measurements of the phonon
density of states, dispersion relations and electromechanical response of
PbTiO3, BaTiO3 and SrTiO3. The phonon density-of-states of the quantum
paraelectric SrTiO3 is found to be fundamentally distinct from that of
ferroelectric PbTiO3 and BaTiO3 with a large 70-90 meV phonon band-gap. The
phonon dispersion and electromechanical response of PbTiO3 reveal giant
anisotropies. The interplay of covalent bonding and ferroelectricity, strongly
modulates the electromechanical response and give rise to spectacular
signatures in the phonon spectra. The computed charge densities have been used
to study the bonding in these perovskites. Distinct bonding characteristics in
the ferroelectric and paraelectric phases give rise to spectacular vibrational
signatures. While a large phonon band-gap in ATiO3 perovskites seems a
characteristic of quantum paraelectrics, anisotropy of the phonon spectra
correlates well with ferroelectric strength. These correlations between the
phonon spectra and ferroelectricity, can guide future efforts at custom
designing still more effective piezoelectrics for applications. These results
suggest that vibrational spectroscopy can help design novel materials.
