  Using generalizations of natural orbitals, spin-averaged natural orbitals,
and two-particle charge correlators for solids, we investigate electronic
structure of antiferromagnetic transition-metal oxides with a fully
self-consistent, finite-temperature GW method. Our findings disagree with
Goodenough-Kanamori (GK) rules, commonly used for qualitative interpretation of
such solids. First, we found a strong dependence of natural orbital occupancies
on momenta contradicting GK assumptions. Second, along the momentum path, the
character of natural orbitals changes. In particular, contributions of oxygen
2s orbitals are important, which has not been considered in the GK rules. To
analyze the influence of 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, greatly
affecting 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.

Strongly Correlated Electrons;Materials Science;Chemical Physics