  The crystal structures and phonon spectra of orthorhombic cadmium titanate
with the $Pbnm$ structure and of its two possible ferroelectrically distorted
phases with $Pbn2_1$ and $Pb2_1m$ space groups were calculated from first
principles within the density functional theory. The obtained structural
parameters and frequencies of Raman- and infrared-active modes are in good
agreement with available experimental data for the $Pbnm$ phase. Expansion of
the total energy in a Taylor series of two order parameters showed that the
ground state of the system corresponds to the $Pbn2_1$ structure into which the
$Pbnm$ phase transforms through a second-order phase transition without
intermediate phases. A substantial discrepancy between the calculated and
experimentally observed lattice distortions and spontaneous polarization in the
polar phase was explained by quantum fluctuations as well as by existence of
twinning and competing long-period structures.
