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 one, in particular the 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.

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By ab initio many-body quantum chemistry calculations, we determine the strength of the symmetric anisotropy in the 5d 5 j ≈ 1/2 layered material Ba2IrO4. While the calculated anisotropic couplings come out in the range of a few meV, orders of magnitude stronger than in analogous 3d transition-metal compounds, the Heisenberg superexchange still defines the largest energy scale. The ab initio results reveal that individual layers of Ba2IrO4 provide a close realization of the quantum spin-1/2 Heisenberg-compass model on the square lattice. We show that the experimentally observed basal-plane antiferromagnetism can be accounted for by including additional interlayer interactions and the associated order-by-disorder quantum-mechanical effects, in analogy to undoped layered cuprates.