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Formal Valence, $d$ Occupation, and Charge-Order Transitions

While the formal valence and charge state concepts have been tremendously important in materials physics and chemistry, their very loose connection to actual charge leads to uncertainties in modeling behavior and interpreting data. We point out, taking several transition metal oxides (La$_2$VCuO$_6$, YNiO$_3$, CaFeO$_3$, AgNiO$_2$, V$_4$O$_7$) as examples, that while dividing the crystal charge into atomic contributions is an ill-posed activity, the 3d occupation of a cation (and more particularly, differences) is readily available in first principles calculations. We discuss these examples, which include distinct charge states and charge-order (or disproportionation) systems, where different "charge states" of cations have identical 3d orbital occupation. Implications for theoretical modeling of such charge states and charge-ordering mechanisms are discussed.