Bond Multiplicity in Transition-Metal Complexes: Applications of Two-Electron Valence Indices

In the present study the applicability of the bond multiplicities from the Nalewajski and Mrozek valence indices was demonstrated for a variety of transition metal-based systems. The Nalewajski−Mrozek valence indices and bond multiplicity indices have been implemented in the Amsterdam Density Functional program. Selected examples comprise the carbonyl complexes (selected tetra- and hexacarbonyls, binary monocarbonyls of the first-row transition metals), phosphines, the ligands’ trans-influence, as well as multiple metal−ligand and metal−metal bonds. The results show that the calculated bond multiplicity indices correspond well to experimental predictions based on bond lengths and vibrational frequencies for all discussed classes of complexes. Almost perfect linear correlation between the bond indices and vibrational frequencies was observed for carbonyls and the oxo complexes; the calculated bond multiplicity reproduces the accepted order for the trans-influence of different ligands, rationalizes unusually low vibrational freqencies in the [OsO3N]−complex compared to other nitrido complexes, explains the geometrical asymmetry in the MoO3 solid, and confirms the multiple character of the metal−metal bond in the [Re2Cl8]2- complex. Thus, the Nalewajski and Mrozek method can be successfully used as a supplementary analysis tool for electronic structure for studies involving transition metal complexes.