On the prediction of the crystal and electronic structure of mixed-valence materials by periodic density functional calculations: The case of Prussian Blue

The consistency of periodic density functional approaches to properly describe the crystal and electronic structure of mixed-valence materials is investigated by taking Prussian Blue as prototypical example. Hybrid B3LYP, GGA, and, GGA+U exchange-correlation potentials have been explored. Localized Gaussian-type orbitals or plane waves have been chosen to expand the valence electron density, and the effect of the core electrons on the electronic structure was accounted for either (i) explicitly by including all electrons in the calculations, (ii) by making use of ultrasoft pseudopotentials, or (iii) by the use of the projected augmented wave method. Comparison to available experimental data shows that all-electron calculations within the hybrid exchange-correlation potential can be taken as appropriate benchmarks. It is also concluded that a proper description of the complex magnetic ground state of Prussian Blue can be reached by using a plane-wave basis set and nonhybrid density functional potentials but only if the electronically distinct iron centers in the material are treated in an independent manner. Physical reasons for such rather unexpected results are given and implications for the description of mixed-valence materials by means of density functional approaches are discussed.