| Summary: | Knowledge about the formation energies of compounds is essential to derive phase diagrams of multicomponent phases with respect to elemental reservoirs. The determination of formation energies using common (semi-)local exchange-correlation approximations of the density functional theory (DFT) exhibits well-known systematic errors if applied to oxide compounds containing transition metal elements. In this work, we generalize, reevaluate, and discuss a set of approaches proposed and widely applied in the literature to correct for errors arising from the over-binding of the O<sub>2</sub> molecule and from correlation effects of electrons in localized transition-metal orbitals. The DFT+<i>U</i> method is exemplarily applied to iron oxide compounds, and a procedure is presented to obtain the <i>U</i> values, which lead to formation energies and electronic band gaps comparable to the experimental values. Using such corrected formation energies, we derive the phase diagrams for LaFeO<sub>3</sub>, Li<sub>5</sub>FeO<sub>4</sub>, and NaFeO<sub>2</sub>, which are promising materials for energy conversion and storage devices. A scheme is presented to transform the variables of the phase diagrams from the chemical potentials of elemental phases to those of precursor compounds of a solid-state reaction, which represents the experimental synthesis process more appropriately. The discussed workflow of the methods can directly be applied to other transition metal oxides.
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