Natural orbitals and two-particle correlators as tools for the analysis of effective exchange couplings in solids

Using generalizations of spin-averaged natural orbitals and two-particle charge correlators for solids, we investigate the electronic structure of antiferromagnetic transition-metal oxides with a fully self-consistent, imaginary-time GW method. Our findings disagree with the Goodenough-Kanamori (GK) rules that are commonly used for the qualitative interpretation of such solids. First, we found a strong dependence of the natural orbital occupancies on momenta, contradicting GK assumptions. Second, along the momentum path, the character of natural orbitals changes. In particular, the contributions of oxygen 2s orbitals are important, which has not been considered in the GK rules. To analyze the influence of the electronic correlation on the values of effective exchange coupling constants, we use both natural orbitals and two-particle correlators and show that electronic screening modulates the degree of superexchange by stabilizing the charge-transfer contributions, which greatly affects these coupling constants. Finally, we give a set of predictions and recommendations regarding the use of density functional, Green's function, and wave-function methods for evaluating effective magnetic couplings in molecules and solids.