A theoretical study on the strength of multiple metal-metal bonds in binuclear complexes and transition-metal dimers by a non-local density functional method

The strength of multiple metal-metal bonds in the metal dimers M₂ (M = Cr, Mo or W) and binuclear complexes M₂(OH)₆ (M = Cr, Mo or W), M₂Cl₄(PH₃)₄ M = V, Cr, Mn, Nb, Mo, Tc, Ta, W or Re) has been studied by a non-local density functional theory. The method employed here provides metal-metal bond energies [D(M-M)] in good accord with experiments for Cr₂ and Mo₂, and predicts that W₂ of the three dimers M₂ (M = Cr, Mo or W) has the strongest metal-metal bond with D(W-W) = 426 kJ mol⁻¹ and R(W-W) = 2.03 Å. Among the binuclear complexes studied here we find the 3d elements to form relatively weak metal-metal bonds (40–100 kJ mol⁻¹), compared to the 4d and 5d elements with bonding energies ranging from 250 to 450 kJ mol⁻¹. The metal-metal bond for a homologous series is calculated to be up to 100 kJ mol⁻¹ stronger for the 5d complex, than for the 4d complex. An energy decomposition of D(M-M) revealed that the σ-bond is somewhat stronger than each of the π-bonds, and one order of magnitude stronger than the δ-bond. For the same transition metal we find D(M-M) to be larger for M₂(PH₃)₄Cl₄ (M = Cr, Mo or W) than for M₂(OH)₆ (M = Cr, Mo or W), and attribute this to a stronger π-interaction in the former series. While many of the findings here are in agreement with previous HFS studies, the order of stability D(3d-3d) « D(4d-4d) < D(5d-5d) differs from the order D(3d-3d) « D(5d-5d) < D(4d-4d) obtained by the HFS method, and the present method provides in general more modest values for D(M-M) than the HFS scheme.