Ab Initio determination of Cu 3d orbital energies in layered copper oxides

It has long been argued that the minimal model to describe the low-energy physics of the high T-c superconducting cuprates must include copper states of other symmetries besides the canonical 3d(x2-y2) one, in particular the 3d(z2) orbital. Experimental and theoretical estimates of the energy splitting of these states vary widely. With a novel ab initio quantum chemical computational scheme we determine these energies for a range of copper-oxides and -oxychlorides, determine trends with the apical Cu-ligand distances and find excellent agreement with recent Resonant Inelastic X-ray Scattering measurements, available for La2CuO4, Sr2CuO2Cl2, and CaCuO2.