Disproportionation Transition at Critical Interaction Strength: Na₁/₂CoO₂

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Charge disproportionation (CD) and spin differentiation in Na₁/₂CoO₂ are studied using the correlated band theory approach. The simultaneous CD and gap opening seen previously is followed through a first order charge disproportionation transition 2Co³.⁵⁺ → Co³⁺+Co⁴⁺, whose ionic identities are connected more closely to spin (S=0, S=1/2 respectively) than to real charge. Disproportionation in the Co ag orbital is compensated by opposing charge rearrangement in other 3d orbitals. At the transition large and opposing discontinuities in the (all-electron) kinetic and potential energies are slightly more than balanced by a gain in correlation energy. The CD state is compared to characteristics of the observed charge-ordered insulating phase in Na₁/₂CoO₂, suggesting the Coulomb repulsion value U is concentration-dependent, with U(x=1/2)≃3.5 eV.