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

Abstract

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 [OsO 3N] (-)complex compared to other nitrido complexes, explains the geometrical asymmetry in the MoO 3 solid, and confirms the multiple character of the metal-metal bond in the [Re 2Cl 8] (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.

Synthesis and Platinum Complexes of an Alane‐Appended 1,1′‐Bis(phosphino)ferrocene Ligand

“…The PtÀAl Nalewajski-Mrozek (NM; Set 3) [22] bond orders in 3 calc -6 calc are 0.39, 0.37, 0.37, and 0.34, respectively (cf. 0.40-0.46 for the Pt À P bonds), indicative of significant Pt À Al bonding.…”

Computational Analysis of n→π* Back-Bonding in Metallylene–Isocyanide Complexes R2MCNR′ (M = Si, Ge, Sn; R =tBu, Ph; R′ = Me,tBu, Ph)

“…Michalak and co-workers have found a similar correlation between bond multiplicities calculated using Nalewajski-Mrozek (NM) theory and changes in carbonyl ν(CO) stretching frequency in different transition-metal complexes. 46 It is interesting to note that the NM bond multiplicities, 47 bAB, are closely related to NOCV eigenvalues, νi, through the concept of overall valence V. 23b In fact, V can be written either as a sum over bond multiplicities between all atomic pairs in the molecule (∑ ∑ ) or as a sum over the squares of all NOCV eigenvalues ( …”

On the asymmetry in molybdenum–oxygen bonding in the MoO3 structure: ETS–NOCV analysis

“…The third oxygen type O3 (and O3 0 , O3 00 ) is bound symmetrically to two molybdenum atoms (1.94 Å ) and weakly interacting with the third one of another layer (2.33 Å ). The Mo-O bonding was characterized previously by the electron density-difference maps (deformation density), [10] as well as by the quantumchemical bond-order indices originating from various approaches; [7][8][9][10]25] the electronic properties of the three oxygen sites on the (010) and (100) surfaces were characterized, and the oxygen-vacancy formation energies were determined [7][8][9][10].…”