Electronic Structure and Valence-Bond Band Structure of Cuprate Superconducting Materials

From ab initio calculations on various clusters representing the La$_{2-x}$Sr$_{x}$Cu$_{1}$O$_{4}$ and Y$_{1}$Ba$_{2}$Cu$_{3}$O$_{7}$ classes of high-temperature superconductors, it is shown that (i) all copper sites have a Cu$^{\text{II}}$ (d$^{9}$) oxidation state with one unpaired spin that is coupled antiferromagnetically to the spins of adjacent Cu$^{\text{II}}$ sites; (ii) oxidation beyond the cupric (Cu$^{\text{II}}$) state leads not to Cu$^{\text{III}}$ but rather to oxidized oxygen atoms, with an oxygen p$\pi $ hole bridging two Cu$^{\text{II}}$ sites; (iii) the oxygen p$\pi $ hole at these oxidized sites is ferromagnetically coupled to the adjacent Cu$^{\text{II}}$ d electrons despite the fact that this is opposed by the direct dd exchange; and (iv) the hopping of these oxygen p$\pi $ holes (in CuO sheets or chains) from site to site is responsible for the conductivity in these systems (N-electron band structures are reported for the migration of these localized charges).