Extended Huckel, DFT, and ab initio MP2 calculations have been carried out to rationalize the unprecedented structural characteristics of the recently synthesized complex (mu-eta (1)-S-2)(3) (Fe-TACN)(2) (TACN = triazacyclononane). The orbital interaction diagram between the metal-macrocycle dimer and the three disulfide ligrands accounts for some of the observed properties of the complex: diamagnetism, existence of an Fe-Fe single bond, nucleophilicity of the terminal sulfur atoms. The unprecedented occurrence of a M2S6 core, as the very unusual mu-eta (1) coordination of the St ligands, however, requires further analysis. It was assumed that the key to the structural singularities of this complex should be sought in the network of intramolecular H . . .S bonds revealed by the crystallographic analysis and involving all six NH groups and all three terminal S atoms. We therefore report the first quantitative theoretical investigation of the energetics of intramolecular II S bonds. Geometry optimizations have been carried out by means of the Density Functional Theory (DFT) on two configurations of (mu-eta (1)-S-2)3(Fe-TACN)2 deduced one from another by inverting the pyramidality at the proximal sulfur atoms. The experimental conformation 1, characterized by six "strong" N-H . . .S bonds (d(H . . .S) = 2.31 Angstrom), is more stable by 10.0 kcal(.)mol(-1) than the hypothetic structure 2 with "weak" hydrogen bonds (d(H . . .S) = 2.65 Angstrom). Replacing persulfide by sulfoxide ligands leads to a similar energy difference (11.4 kcal(.)mol(-1)), despite the well-documented tendency to obtain stronger H bonds with oxygen than with sulfur. Those results are rationalized by means of a systematic investigation, at the DFT and MP2 levels, of the N-H . . .S and N-H . . .O interactions in the model systems C2H4SX . . . HNH2 (X = S, O). The strength of the N-H . . .X interaction is shown to be highly dependent on the directionality of the hydrogen bond characterized by the angle theta = H-X-S. For X = S, the optimal interaction is obtained for theta similar to 80 degrees, which almost exactly reproduces the angular parameter optimized in 1 (76.7 degrees). For X = 0, the interaction is most favorable for higher values of theta (similar to 115 degrees) which cannot be obtained in the hypothetic compound (mu-eta (1)-SO)(3)(Fe-TACN)(2) because of structural constraints. Finally, varying the H X distance in the models shows that those interactions are extremely far-reaching. The energy difference between conformations 1 and 2 then accounts for only a small part of the global stabilization assigned to the hydrogen bond network, which could hence represent the key to the stabilization of the Fe2S6 core.