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The antiferromagnetic phenomena of the chromium(III) dimer in acid erothro chloride [(NH3)(5)CrOHCr(NH3)(4)(H2O)]Cl-5. H2O and LaAlO3:Cr3+ have been explained in terms of the Girerd-Journaux-Kahn (GJK) model and the Heitler-London (HL) model, respectively. For the Cr ... Cr distance R in the range 3.2 < R < 4.4 Angstrom, the values of the exchange interaction parameter J calculated with the GJK model are higher by a factor 2-3 than those with the HL model. This means that the contribution of the excited charge-transfer configuration (CTC) is considerably important and the main physical mechanism of the antiferromagnetic characteristics in acid erothro chloride and in LaAlO3:Cr3+ can be attributed to the combined effect of the direct exchange and the superexchange interactions. (C) 2000 Elsevier Science Ltd. All rights reserved.