The mechanism of the magnetic coupling in the [CuMCu(pda)4Cl2] complexes with M = Pd, Pt is analyzed. First principles calculations based on the wave function theory are performed (DDCI + SO-RASSI): it is shown that the interaction without spin-orbit coupling is antiferromagnetic while the contribution due to the spin-orbit is ferromagnetic. The agreement between calculations and experiment is very good for the CuPdCu complex but is lesser for the CuPtCu complex. A Hubbard model is used in order to rationalize these results: this shows that the two d frontier orbitals of the central atom play a key role in these two interactions. Although the model parameters extracted from CASCI calculations do not permit to recover the order of magnitude of the interactions, it allows understanding the main interactions that give physical insight.