Many-Body Destabilization of Intermediate Oxygen-Hole States
Oxygen holes in transition-metal oxides can appear as localized polarons, symmetry-delocalized ligand holes, or intermediate states whose stability is controlled by subtle electron-correlation effects. In layered Na$_{2-x}$Mn$_3$O$_7$, hybrid density functional theory (DFT) predicts an unusual bond-centered split oxygen-hole polaron stabilized near ordered Mn vacancies. Here we resolve the nature of this state using diffusion Quantum Monte Carlo (QMC). Although hybrid DFT favors the split configuration, QMC reverses the energetic ordering and identifies the localized oxygen polaron as the lower-energy state. The result is robust to the class of trial wavefunctions used, including hybrid and generalized-gradient DFT wavefunctions. Many-body spin densities further show that the nominal split state partially collapses toward a localized polaron. Because localized and split configurations produce similar O K-edge spectral features, this qualitative failure is not resolved by conventional X-ray absorption signatures alone. These findings identify Na$_{2-x}$Mn$_3$O$_7$ as a stringent benchmark for oxygen-hole polarons and reveal a failure mode of hybrid functionals in correlated oxides.