Analysis of charge states in the mixed valent ionic insulator AgO

The doubly ionized $d^9$ copper ion provides, originally in La$_2$CuO$_4$ and later in many more compounds, the platform for high temperature superconductivity when it is forced toward higher levels of oxidation. The nearest chemical equivalent is Ag$^{2+}$, which is almost entirely avoided in nature. AgO is an illustrative example, being an unusual nonmagnetic insulating compound with an open $4d$ shell on one site. This compound has been interpreted in terms of one Ag$^{3+}$ ion at the fourfold site and one Ag$^{+}$ ion that is twofold coordinated. We analyze more aspects of this compound, finding that indeed the Ag$^{3+}$ ion supports only four occupied $4d$-based Wannier functions per spin, while Ag$^+$ supports five, yet their physical charges are nearly equal. The oxygen $2p$ Wannier functions display two distinct types of behavior, one type of which includes conspicuous Ag $4d$ tails. Calculation of the Born effective charge tensor shows that the mean effective charges of the Ag ions differ by about a factor of two, roughly consistent with the assigned formal charges. We analyze the $4d$ charge density and discuss it in terms of recent insights into charge states of insulating (and usually magnetic) transition metal oxides. What might be expected in electron- and hole-doped AgO is discussed briefly.