The monomer [Ce(COT)(2)](-) and the dimer [Ce-2(COT)(3)], with Ce(III) and COT = 1,3,5,7-cyclooctatetraenide, are studied by quantum chemistry calculations. Due to the large spin-orbit coupling, the ground state of the monomer is a strong mixing of sigma and pi states. The experimental isotropic coupling in the dimer was evaluated by Walter et al. to be J = 7 cm(-1) (with a Heisenberg Hamiltonian (H) over cap (S) = J (S) over cap (A)center dot(S) over cap (B)) with a small anisotropic coupling of 0.02 cm(-1). The coupling between the two Ce(III) in the dimer is calculated using CI methods. The low energy part of the spectra are modeled by spin Hamiltonians. All spin Hamiltonians parameters are deduced from ab initio calculations. g factors are calculated for both the pseudodoublet of the monomer and the pseudotriplet of the dimer and their sign have been determined. The magnetic coupling in the dimer is rationalized by a model based on crystal field theory. The kinetic and exchange contributions arising from the different configurations to the isotropic and anisotropic couplings are evaluated. It is shown that the main contribution to isotropic coupling is kinetic and originates from the f(sigma)-f(sigma) interaction due to the large transfer integral between those orbitals. However, the f(pi)-f(pi) interaction plays a non-negligible role. The anisotropic coupling originates from the difference of exchange energy of states arising from the f(sigma)-f(pi) configuration and is, in no matter, related to the anisotropy of the local magnetic moments as already pointed by van Vleck for a fictitious s-p system. The analysis of the natural orbitals evidences a superexchange mechanism through a sigma(CH)* orbital of the bridging cycle favored by a local 4f(sigma)/5d(sigma) hybridization and that the delta type orbitals, both the HOMOs of the ligands and the virtual f(delta) orbitals of the cerium atoms play an important polarization role, and to a less extend the pi type orbitals, the HOMOs-1 of the ligands, and the metal f(pi) orbitals.