Cluster-model calculation of the electronic structure of CuO: A model material for the high-$T_c$ superconductors

In this paper we describe the details of several model Hamiltonian cluster calculations, suitable for describing various spectroscopic data of CuO. By treating the d-d Coulomb and exchange interactions within the full atomic multiplet theory and using symmetry-dependent Cu-O hybridizations, we do a detailed comparison to photoelectron spectroscopic data, thereby obtaining reliable values for the parameters of an Anderson-model Hamiltonian. We present a study of the allowable ranges of such parameters and a discussion of the applicability to high-$T_c$ copper compounds. For the latter we investigate the influence of the out-of-plane apex oxygen, which is found to be small for the photoelectron spectrum for known Cu-O distances. From a study of the dependence of the nature of the first ionization state on the apex-O–to–Cu distance as well as on the apex-O 2p state orbital energy, we determine the values for which this state changes from a singlet to a triplet. However, in all cases this state remains $d^9$L in character. From the parameters obtained for CuO, we derive an O 2p–Cu 3d exchange interaction of 3.4 eV for $x^2$-$y^2$ symmetry orbitals. In addition we calculate the energies of the optical d-d transitions and find all three of these to be clustered around 1.4±0.1 eV.