Assessing the Strength of Metal–Metal Interactions

Abstract

A proper comparison between bond strengths of different atom pairs is relevant only for the same formal bond order (BO) of atomic interactions, e.g., for single bonds, because it is clear that the higher is the BO or the number of the electron pairs responsible of bonding, the stronger is the bond. For the metal−metal interactions, such a comparison of the bond strengths is especially problematic because formal BOs may differ from the effective ones by more than 1 v.u. (valence units). In this paper, we investigated the strength of bonding and its correlation to structural parameters (bond length/BO) for 24 metal-metal pairs. A simple way of the BO and bond-strength analysis was proposed and verified on the transition metal dimers. In contrast to the previous studies, the effective BOs were not calculated from spectroscopic data or related to reference compounds, but determined independently based on the Pauling model and bond valence parameters obtained from recent quantum chemistry data. To characterize the bond strength, we used the force constants based on the available experimental or DFT data of stretching frequencies. A linear correlation between the effective BOs and force constants of the metal−metal bonds, which was confirmed in this work, allows for prediction of the stretching frequencies according to the effective BOs (and/or the bond lengths) and vice versa.

Steric and Electrostatic Effects in Compounds with Centered Clusters Quantified by Bond Order Analysis

“…Our previous bonding analysis based on Pauling’s principles not only allowed for the description of the matrix effect but also revealed the unusual distribution of ionic charges on the ligand atoms around clusters, which explains the different ligand reactivity and structural peculiarities of cluster compounds. ,− In addition, the analysis showed a linear correlation between the calculated BOs and the stretching force constants of the M–M bonds . The previous works were devoted to simple diatomics, M 2 , where the matrix effect is absent, or to M n -clusters (with n from 2 to 6), stabilized by ligands located outside of the clusters.…”

“…16,22−25 In addition, the analysis showed a linear correlation between the calculated BOs and the stretching force constants of the M−M bonds. 26 The previous works were devoted to simple diatomics, M 2 , where the matrix effect is absent, or to M n -clusters (with n from 2 to 6), stabilized by ligands located outside of the clusters. In this study, we will perform a similar analysis for octahedral M 6 -clusters stabilized by additional Z atoms inside the clusters (Figure 2).…”

“…In fact, the higher the BO of the M−Z bond, the lower the BO of the M−M bond. Taking into account the values of the force constants for the single Nb−Nb and Zr−Zr bonds (1.45 and 0.74 mdyn/Å, respectively 26 ), it is clear that the Nb−Nb bonds in Cs 2 EuNb 6 Br 18 are effectively stronger than the Zr−Zr bonds in Cs 3 (CZr 6 )Br 15 , not to mention those in (CoZr 6 )Cl 15 .…”