  FeO is a crucial phase of the Earth's core, and its thermodynamic properties
are essential to developing more accurate core models. It is also a notorious
correlated insulator in the NaCl-type (B1) phase at ambient conditions. It
undergoes two polymorphic transitions at 300 K before it becomes metallic in
the NiAs-type (B8) structure at $\sim$100 GPa. Although its phase diagram is
not fully mapped, it is well established that the B8 phase transforms to the
CsCl-type (B2) phase at core pressures and temperatures. Here we report a
successful \textit{ab initio} calculation of the B8$\leftrightarrow$B2 phase
boundary in FeO at Earth's core pressures. We show that fully anharmonic free
energies computed with the PBE-GGA + Mermin functional reproduce the
experimental phase boundary within uncertainties at $P > 240$ GPa, including
the largely negative Clapeyron slope of $-52 \pm 5$ MPa/K. This study validates
the applicability of a standard DFT functional to FeO under Earth's core
conditions and demonstrates the theoretical framework that enables complex
predictive studies of this region.
