  Density-functional simulations are used to calculate structural properties
and high-symmetry phonons of the hypothetical cubic phase, the stable
orthorhombic phase and an intermediate tetragonal phase of magnesium silicate
perovskite. We show that the structure of the stable phase is well described by
freezing in a small number of unstable phonons into the cubic phase. We use the
frequencies of these unstable modes to estimate transition temperatures for
cubic--tetragonal and tetragonal--orthorhombic phase transitions. These are
investigated further to find that the coupling with the strain suggests that
phonons give a better representation than rigid unit modes. The phonons of an
intermediate tetragonal phase were found to be stable except for two rotational
modes. The eigenvectors of the most unstable mode of each of the cubic and
tetragonal phases account for all the positional parameters of the orthorhombic
phase. The phase boundary for the orthorhombic--tetragonal transition
intersects possible mantle geotherms, suggesting that the tetragonal phase may
be present in the lower mantle.
