The structural dependence of the coupling constant in a series of [L3Cu(mu -C2O4)CuL3](2+)complexes is analyzed by means of ab initio difference-dedicated configuration interaction (DDCI2) calculations on the model (mu -oxalato)bis[triamminecopper(II)] cation, [(NH3)(6)Cu-2(mu -C2O4)](2+), in which the nitrogen-coordinated ligands have been substituted by NH3. Two types of geometrical structures have been considered: three different C-2h geometries and four crystallographic centrosymmetric geometries taken from [(Et(5)dien)(2)Cu2Cu-(muO(4))](BPh4)(2) and [(Et(5)dien)(2)Cu-2(mu -C2O4)] (PF6)(2) (Et(5)dien = 1,1,4,7,7-pentaethyldiethylenetriamine), [(tmen,2-MeIm)(2)Cu-2 (mu -C2O4)](PF6)(2) (tmen = N,N,N',N'-tetramethylethylenediamine and 2-MeIm = 2-methylimidazole), and [(dien)(2)Cu-2(mu -C2O4)](ClO4)(2) (dien = diethylenetriamine). The results show that the antiferromagnetic coupling is strongly underestimated when pure DDCI2 calculations are performed, but when the CI space includes the relaxation of the oxalato-copper charge transfer, quantitative agreement with the experimental results is reached with an error smaller than 5 cm(-1). The role of the external ligands in the model is also discussed by means of broken symmetry DFT calculations. At this level of theory, a very different influence of the ligands is predicted by different exchange-correlation functionals. Therefore, the use of DFT to investigate this effect should be considered with caution.