The DFT based ligand field model for magnetic exchange coupling proposed recently, has been extended to systems containing more than one impaired electron per site. The guidelines for this extension are described using a model example - the complex (NH3)(3)Cr-III(OH)(3)Cr-III(NH3)(3)(3+). The exchange Hamiltonian, H-ex = -J(12)S(1)S(2) has been simplified using symmetry principles, i.e. utilizing the D-3h(C-3v) Cr-III - dimer(site) symmetry. Both antiferro-and ferromagnetic exchange coupling constants are found to yield important contributions to the value of the (negative, antiferromagnetic) exchange coupling constant in good agreement with experiment. (C) 2003 Elsevier B.V. All rights reserved.