  MgGeO$_3$-perovskite is known to be a low-pressure analog of
MgSiO$_3$-perovskite in many respects, but especially in regard to the
post-perovskite transition. As such, investigation of spin state changes in
Fe-bearing MgGeO$_3$ might help to clarify some aspects of this type of state
change in Fe-bearing MgSiO$_3$. Using DFT+U calculations, we have investigated
pressure induced spin state changes in Fe$^{2+}$ and Fe$^{3+}$ in MgGeO$_3$
perovskite and post-perovskite. Owing to the relatively larger atomic size of
germanium compared to silicon, germanate phases have larger unit cell volume
and inter-atomic distances than equivalent silicate phases at same pressures.
As a result, all pressure induced state changes in iron occur at higher
pressures in germanate phases than in the silicate ones, be it a spin state
change or position change of (ferrous) iron in the perovskite cage. We showed
that iron state transitions occur at particular average Fe-O bond-length
irrespective of mineral composition (silicate or germanate) or functionals
(LDA+U$_{sc}$ or GGA+U$_{sc}$). Ferrous iron substitution decreases the
perovskite to post-perovskite (PPv) transition pressure while coupled ferric
iron substitution increases it noticeably.
