We want to quantitatively calculate effective exchange integral (Jab) values between two metal centres within a dimer structure having different configurations. The aim is to check ferromagnetism, anti-ferromagnetism in the dimeric structures.
Jab can be calculated by making parallel and antiparallel alignment of the magnetic moments. An easy way would be to run two parallel calculations, antiferromagnetic case with the spin multiplicity of 1, and ferromagnetic case with spin multiplicity of 2S+1, where S is the total spin angular momentum. I don't know what the total spin of your system is but you can calculate the spin contributions to the total magnetic moment of the unpaired electrons in your system. Jab is obtained using:
Jab=(Eaf − Efm)/2
where Jab is the exchange coupling constant between a and b. Eaf and Efm are the DFT total energies calculated for antiferromagnetic and ferromagnetic cases respectively.
PS: I assumed the orbital contribution is negligible to the total magnetic moment.
Have you tried "broken symmetry" ? Is the common way to measure Jab. You also should check the High Spin configuration, if its triplet, the difference between triplet and singlet is the Jab, otherwise, (i.e, 5, 6, 7, .... the HSpin) you should take into account the Landé interval rule to measure the J value