Theoretical calculations on aseries of dinuclear vanadium and niobium clusters

Abstract

Electronic structures of chalcogenide-bridged binuclear clusters of vanadium and niobium with the {M2(μ-Q2)2}4+, {M2(μ-Q)2}4+ and {M2(μ-Q)(μ-Q)2}4+ cores (Q = S, Se, Te) have been studied by density functional theory methods. In the vanadium clusters, the V–V distances are calculated to be in the range of 2.766–3.193 Ǻ, whereas in the niobium clusters the calculated Nb–Nb bond lengths fall in the range of 2.881–3.380 Ǻ, in accordance with the experimentally determined values. The calculated M–M bond distances generally decrease in the order {M2(μ-Q2)2}4+ > {M2(μ-Q)2}4+ > {M2(μ-Q)(μ-Q)2}4+ (M = V, Nb, Q = S, Se). The calculated enthalpies of formation for the V clusters are higher than for the corresponding Nb clusters. On the other hand, the M2Q2 clusters have always higher enthalpies of formation than the M2Q3 species, and also (with the exception of M = V, Q = S) higher values of enthalpy of formation than for the M2Q4 species. The hardness η of the niobium clusters are higher than that of the vanadium analogs, except for the [V2S2(SH2)8]4+ case. The enthalpies ΔH298 and the free energies ΔG298 for the reactions of hydrogen addition to the [V2(μ-S2)2(H2O)8]4+ and the [Nb2(μ-S2)2(H2O)8]4+ clusters at constant pressure are −121.75 and −59.73 kJ/mol for the vanadium cluster, and 13.97 and 75.15 kJ/mol for the niobium cluster.