Understanding Birnessite MnO$_2$: Effects of Small Polaron and Local Dipole

Birnessite MnO$_2$, usually with cations like K and Na intercalated between layers, is a class of potential cheap oxygen evolution reaction (OER) catalyst. Using hybrid density functional calculations, we investigate the electronic structures of the layered MnO$_2$ with the intercalated cation modelled as a defect. We found that an electron small polaron will form when an extra electron is doped in the pure MnO$_2$, turning a Mn(IV) to a Mn(III) with a singly occupied $e_g$ orbital located within the band gap, and the resulting small-polaron hopping conduction explains the observed low electric conductivity. The inter-layer doped K atom will donate one electron to one Mn ion as expected, and also contributes to a local dipole forming between K and the Mn(III), raising the electrostatic potential of the specific layer. With a certain spatial distribution of such local dipoles, the small-polaron $e_g$ states become comparable in energy with the global conduction band minimum, and charge transfer occurs. This further results in a singly or partially occupied $e_g$ orbital near the Fermi level, which has been regarded as a signal for an excellent OER catalyst. Our calculation helps understanding several experimental observations.