Abstract
We propose a new ab initio method designed for the accurate calculation of effective exchange integrals between atoms with numerous open shells. This method applies to ferromagnetic as well as antiferromagnetic exchange, direct or ligand-mediated exchange. Test calculations on high spin transition metal oxides such as KNiF3, Ba2CoS3 or YMnO3 exhibit a very good accuracy compared either to the best ab initio calculations —when those are feasible— and with experimental evaluations.