Electronic structure of copper-oxygen clusters in the high-$T_c$ superconductor ${\mathrm{La}}_{2\mathrm{-}\mathrm{x}}$${\mathrm{Sr}}_{\mathrm{x}}$${\mathrm{CuO}}_4$

We report a density-functional study of two copper-oxygen clusters (${\mathrm{CuO}}_6^{\mathrm{-}10}$ and ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{16}^{\mathrm{-}26}$) that are present in ${\mathrm{La}}_{2\mathrm{-}\mathrm{x}}$ ${\mathrm{Sr}}_{\mathrm{x}}$ ${\mathrm{CuO}}_4$. All-electron, self-consistent, spin-polarized calculations are performed by using the linear combination of Gaussian orbitals method. Several charge states of these clusters are considered in order to study the effects of doping. Results are presented for the charge and spin densities and total and partial density of states. These clusters have local moments on the Cu atoms. Our results indicate strongly covalent bonding between copper and oxygen. Transition-state calculations are made to study the electron-electron correlations and charge-transfer transitions. The parameters of a model Hamiltonian are determined. We have performed some nonlocal spin-density-functional calculations for the ${\mathrm{CuO}}_6$ cluster to study the effects of self-interaction corrections. Both the size of the local moment and the exchange splitting are increased by the use of the nonlocal corrections.