Role of covalency in ``Charge Ordering'' perovskite ferrates

Transition-metal oxides (TMO) with the perovskite crystal structure exhibit strong electron--electron correlation effects and complex structural distortions. The balance of those factors determines the stability of charge ordered states in chemistries susceptible to valence instabilities. We use first-principles density functional calculations to investigate the role of symmetry-unique structural distortions on covalent bonding in the ``charge-ordered'' insulator CaFeO$_3$. We evaluate the electronic density distribution along the Fe--O bonds to assess the ground state stability by tracing the evolution in the oxygen environment, which appears as octahedral expansion/contractions and rotations. We show that nearly zero charge transfer occurs; the insulating phase results from a complex interplay of symmetry-lowering structural distortions and enhanced covalent interactions. Finally, we discuss possible routes to control the metal--insulator transition by fine-tuning the covalency.