Electronic structure of Cu-O chains in the high-$T_c$ superconductor Y${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

The electronic structure of Cu-O chains in the high-$T_c$ superconductor Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ is investigated by self-consistent, all-electron, spin-polarized cluster calculations in the local-spin-density approximation for the cluster ${\mathrm{Ba}}_4$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_7$. Four different charge states are considered. No localized moments are present on the Cu atoms in any of the charge states considered. The ground state of the cluster shows strong covalent bonding between the copper and oxygen atoms. Transition-state calculations are made to determine electronic relaxation occurring in photoemission, to calculate the effective Hubbard interaction parameter $U$ for both copper and oxygen sites, and to find the energy required for charge transfer between oxygen and copper atoms. The results are compared with experiment.