Bond Order Conservation Principle and Peculiarities of the Metal–Metal Bonding

Abstract

Pauling's principles developed later in the bond valence model (BVM) are fundamental in description of bonding in ionic solids and surface phenomena on metals, but applicability of these principles to the metal−metal bonds in the bulk compounds was demonstrated only recently, with a spotlight on the bond valence−bond length correlations. This work is focused on the bond order conservation in cluster compounds and determination of empiric bond valence parameters for the metal−metal bonds, which ensure very simple and reasonably accurate bonding analysis, with zero cost, in any complex cluster compound. Such peculiarities of cluster compounds as matrix effect and nonuniform distribution of the ionic charges (bond valence sums) on the ligands around metal clusters, as well as other important examples of the BVM application to compounds with metal−metal bonds, are discussed.

Be–Be π‐Bonding and Predicted Superconductivity in MBe2 (M=Zr, Hf)

“…The value for l is smaller than the bond length of the Be dimer (2.45 Å, only bound by 2.5–3 kcal mol −1 ), [18] but larger than that computed for the cation‐stabilized Be 2 4− and Be 2 6− species (2.0 Å). This can be rationalized by the difference of having three Be–Be bonds per Be in MBe 2 versus one in those hypothetical species; this would be in line with the bond order conservation principle [19] …”

Redox Potential and Crystal Chemistry of Hexanuclear Cluster Compounds

“…[ 20 , 34 ]. Nevertheless, due to redistribution of electron density around TMs, the valence (or bond order) deficiency in the metal–metal interactions is commonly compensated for by valence excess in the metal–ligand bonds (bond order conservation principle) [ 23 ]. As a result, the total BVS of TMs is equal or very close to the formal number of their valence electron.…”

“…In general, in compounds without metal–metal bonds, the lattice strains impact the material instability [ 17 ]. In contrast, the bond strains in compounds under study are associated with more symmetric distribution of the electron density around TMs, stabilizing cluster units [ 23 ].…”

“…The effective ionic charge of the TM in a given cluster compound can be calculated as BVS of the metal–ligand bonds based on the lengths of these bonds, R TM-L , and respective empirical constants, R 0 TM-L [ 22 ]. To avoid any problem in the choice of these parameters, we used an alternative way, namely, the method based on the bond order or valence conservation in these type of cluster compounds (See Section 3.3.1 ) [ 23 ]. Hence, the calculations were performed by the following formula: V TM = N TM − Σ s TM-TM where N TM is the number of valence electrons of TM (7 for the Re atoms and 6 for the Mo and W atoms.…”

“…R 0 TM-TM and b TM-TM are the bond valence parameters, transferable for the TM-TM pair in different compounds. These parameters were established in our previous works based on quantum chemistry and crystal chemistry data: R 0 Re-Re = 2.495 Å, b Re-Re = 0.26 Å; R 0 Mo-Mo = 2.51 Å, b Mo-Mo = 0.34 Å; R 0 W-W = 2.535 Å, b W-W = 0.29 Å [ 23 ].…”