d-Electrons' Occupancy and Crystal Structure in Transition Metal Sesquioxides*

We present a systematic density functional study of phase relations in transition metal sesquioxides: Y$_2$O$_3$, Rh$_2$O$_3$, and In$_2$O$_3$. Y$_2$O$_3$ and In$_2$O$_3$ undergo pressure-induced transitions accompanied by increase in cation coordination number from 6 to 7. However, in Rh$_2$O$_3$, such transition does not occur up to $\sim$350 GPa. This cannot be explained simply arguments based on ionic radii ratios. Inspection of the electronic structure reveals that, in Rh$_2$O$_3$, the spatial distribution of the partially-occupied 4d states plays a very important role in the extraordinary stability of the Rh$_2$O$_3$(II)-type structure against others with higher coordination numbers. This study suggests that the complexity of phases in 3d/4d-transition-metal sesquioxides is not only due to ratio ionic radii but also by filling of the d states.