We relied on the density functional theory (DFT) to study the electronic structure of the [2Fe-2S*](SH)4 model of the active site of 2Fe ferredoxins and other proteins containing reduced [2Fe-2S*] clusters. The two (Fe(3+)-Fe(2+)-S-H) dihedral angles Omega1 and Omega2 defined for the two ligands on the ferrous side were allowed to vary, while the two other (Fe(2+)-Fe(3+)-S-H) angles Omega3 and Omega4 on the ferric side were kept constant. The Landé (g), magnetic hyperfine, and quadrupole tensors for two geometries, C2 (Omega1 = Omega2) and Cs (Omega1 = -Omega2), were calculated. To apply our model to the actual proteins, we listed all of the crystallographic structures available for the [2Fe-2S*] systems. A classification of these proteins, based on the four dihedral angles [Omega(i)](i=1-4), separates them into three main classes. The main structural feature of the first class (Omega1 approximately Omega2), with an average dihedral angle Omega(av) = (Omega1 + Omega2)/2 comprised between 115 degrees and 150 degrees, corresponds to a local ferrous C2 geometry (rather than C2nu, as previously assumed by Bertrand and Gayda: Biochim. Biophys. Acta 1979, 579, 107). We then established a direct correlation between the three principal g values and Omega(av). It is the first time that such a link has been made between the spectroscopic and structural parameters, a link, moreover, fully rationalized by our DFT calculations. We finally point out the basic differences between our C2 results with those of the C2nu phenomenological model proposed in the late 1970s by Bertrand and Gayda.