  While the tetragonal antiferro-electrically distorted (AFD) phase with space
group $I4/mcm$ is well known for SrTiO$_3$ to occur below 105 K, there are also
some hints in literature of an orthorhombic phase, either at lower temperature
at high pressure. A previously proposed orthorhombic layered structure of
SrTiO$_3$, known as the post-perovskite or CaIrO$_3$ structure with space group
$Cmcm$ is shown to have significantly higher energy than the cubic or
tetragonal phase and to have its minimum volume at larger volume than cubic
perovskite. It thus cannot correspond to a high-pressure phase of SrTiO$_3$. We
also study an alternative $Pnma$ phase obtained by two octahedral rotations
about different axes. This phase is found to have slightly lower energy than
the $I4/mcm$ phase in spite of the fact that its parent, in-phase tilted
$P4/mbm$ phase is not found to occur. Alternative ferro-electric tetragonal and
orthorhombic structures are also considered. These are not found to occur in
our zero temperature calculations but have been suggested in previous
literature to occur at higher temperature.
