For the ternary thioferrate crystal Na6Fe2S6, ab initio quantum chemical calculations using a cluster model ansatz have been performed to examine the magnetic coupling of the two half-filled Fe 3d shells in the isolated dimeric [Fe2S6](6-) complexes having the structure of edge-linked double tetrahedra. The active-electron approach using complete active space configuration interaction (CASCI) with 10 electrons in 10 orbitals yields the multiplet splitting of a two-center Heisenberg Hamiltonian with an antiferromagnetic coupling constant J = -19 cm(-1), which is by a factor of 5 smaller than the experimental value. Correlation effects are essential for the magnetic coupling, as the application of multireference second-order Moller-Plesset perturbation theory based on the CIPSI algorithm (CAS-2nd) and the recently proposed difference-dedicated CI method lead to values J(4-->5) = -158 and -66 cm(-1), respectively, which clearly agree better with experiment. The different electronic contributions to the chemical bonding in the binuclear transition metal complex have been investigated using the constrained space orbital variation method.