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

Instability of the layered orthorhombic post-perovskite phase of SrTiO$_3$ and other candidate orthorhombic phases under pressure