The concept of quadruple bonding at a dimetal center has been used very successfully to account for the eclipsed conformation of unbridged dimers, contrary to steric demands. The situation is more complicated in the case of bridged dimers with sterically dictated eclipsed structures. Electronic factors operating through bridging, as well as axial, ligands have such a serious influence on observed bond lengths and conformations that, in this case, the effective bond order of the formally quadruply-bonded systems is moot. A strategy is defined whereby different factors contributing to the observed trends can be separately assessed. This is achieved by systematic molecular modeling of a large number of Mo-2 and Cr-2 derivatives to establish a general mathematical relationship among strain-free bond lengths, force constants, and bond orders. The modeling of compounds with Mo-Mo/4 bonds and well-refined crystallographic structures is reported here. All structural details independent of the dimolybdenum bond are simulated in terms of a transferable force field. Simulation of the dimetal-bond properties is then achieved by trial-and-error procedures, in terms of a family of matched pairs of harmonic force constant (k(r)) and characteristic bond length (r(0)), for each bond. These solution curves have different slopes for bridged and unbridged compounds, and they intersect within a sufficiently small region to define a characteristic solution pair of k(r) = 4.07 mdyn Angstrom(-1) and r(0) = 2.02 Angstrom. A torsional twist through the angle chi, away from eclipsing, is calculated to reduce the delta stabilization by a factor of cos 2(chi) from a maximum of 50 kJ mol(-1) at (chi 0).