  It has long been argued that the minimal model to describe the low-energy
physics of the high-Tc superconducting cuprates must include copper states of
other symmetries besides the canonical x2-y2 one, in particular the 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 -oxyclorides,
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.
