Charge-ordering transitions without charge differentiation

The distorted perovskite nickelate system RNiO$_3$ (R=rare earth except La) undergoes a metal-insulator transition (MIT) at a temperature that varies smoothly with the R ionic radius. This MIT is accompanied by structural transition which leads to two inequivalent Ni sites in the cell, and has been explained by charge ordering (CO): charge is transferred between the Ni1 and Ni2 sites in a long-range ordered fashion. Experimental data on core binding energies, ionic radii, and Mossbauer shifts are interpreted in terms of Ni cation charges of 3$\pm \delta$ with, for example, $\delta \approx$ 0.3 for YNiO$_3$. Making use of first principles DFT results and a new approach not invoking integration of the charge density, we find\footnote{Y. Quan, V. Pardo, and W. E. Pickett, Phys. Rev. Lett. (2012, in press)} that the Ni $3d$ occupation is identical (to high accuracy) for the two Ni sites. We also present results for other compounds (La$_2$VCuO$_6$, YNiO$_3$, CaFeO$_3$, AgNiO$_2$, V$_4$O$_7$), all of which have distinct ``charge states'' that have identical $3d$ occupation. This quantitative procedure will be discussed and some implications will be outlined.