Quantifying charge ordering by density functional theory: Fe3O4 and CaFeO3

We demonstrate that charge ordering can be quantitatively predicted by analyzing the Born effective charge (BEC), resolving the long-standing discrepancy between first-principles charge analysis and the nominal concepts of charge disproportionation in Fe3O4 and CaFeO3. In particular, the BEC differences between the disproportionated Fe ions are calculated to be ∼2e, being in excellent agreement with the nominal charge separation in CaFeO3 while suggesting the charge disproportionation in Fe3O4 is understood by the charge separation ∼2e instead of the nominal separation of ∼1e.