Chemical structures from the analysis of domain‐averaged Fermi holes: Multiple metalmetal bonding in transition metal compounds

Abstract

The recently proposed approach based on the analysis of domain-averaged Fermi holes was applied to the study of the nature of metal-metal bonding in transition metal complexes and clusters. The main emphasis was put on the scrutiny of the systems assumed to contain direct multiple metal-metal bonds. The studied systems involve: (1) systems of the type M(2)X(6) (M = Mo, W, X = CH(3)) anticipated to contain metal-metal triple bonds; (2) the molecule of W(2)Cl(8) ((4-)) as the representative of the systems with quadruple metal-metal bonding; (3) diatomic molecules Mo(2) and V(2) considered as the potential candidates for higher than quadruple metal-metal bonding. Although the resulting picture of bonding has been usually shown to agree with the original expectations based on early simple MO models, some examples were also found in which the conclusions of the reported analysis display dramatic sensitivity to the quality of the wave function used for the generation of the Fermi holes. In addition to this we also report some examples where the original theoretical predictions of multiplicity of metal-metal bonds have to be corrected.

Structure and bonding in binuclear metal carbonyls from the analysis of domain averaged Fermi holes. I. Fe2(CO)9and Co2(CO)8

“…Here it is, of course, fair to say that the DFT extension, in which the pair density is formally constructed from KohnSham orbitals using the Hartree-Fock-like formula, lacks strict theoretical justification and its success apparently relies only on the similarity of Hartree-Fock and Kohn-Sham orbitals. Nevertheless, as the results of such a formal generalization proved to provide reasonable and realistic description of other metal-metal bonds, [40][41][42] we believe that the above approach can be accepted as a feasible alternative especially for applications in inorganic chemistry where DFT theory represents the contemporary computational standard.…”

“…In addition to the above simplification, yet another approximation, used also in previous studies of the bonding in transition metal complexes, [40][41][42] was adopted in this study. This approximation concerns the determination of the integrals over the domain X and consists in replacing the integrals over real AIM domains by the Mulliken-like approximation according to which the electron is in the domain of a given atom, if it is in the orbital localized on that atom.…”

“…This analysis was repeatedly shown to provide a simple and chemically appealing picture of the bonding in various molecules with complicated bonding pattern including metal-metal bonds [40][41][42] and it was thus of interest to see whether or to what extent it can help in revealing and clarifying the final picture of bonding in the most stable binuclear iron and cobalt carbonyls. In the remainder of the article we first briefly summarize the theory and the technical details of DAFH analysis, then present the results of the analysis of the electronic structure of Fe 2 (CO) 9 and of Co 2 (CO) 8 , respectively.…”

Electron pairing and chemical bonds: Pair localization in ELF domains from the analysis of domain averaged Fermi holes

“…[29][30][31][32][33][34] The domain-averaged Fermi holes can most straightforwardly be introduced by eq. (1) in which (r 1 ,r 2 ) and (r 1 ) are the pair and first order density, respectively, and the averaging (integration) is performed over the finite domain O.…”

Chemical structures from the analysis of domain‐averaged fermi holes. Nature of the MnMn bond in bis(pentacarbonylmanganese)

“…[7][8][9][10][11][12][13][14] Nontrivial and controversial bonding patterns have also been dealt with in our recent studies based on the analysis of the so-called domain-averaged Fermi holes. [15][16][17][18][19] In view of the success of this new theoretical methodology in the description and visualization of the complicated bonding patterns, we decided to also apply it to the scrutiny of another widely discussed metalmetal bond whose nature is still not completely understood, namely the Mn-Mn bond in the bis(pentacarbonylmanganese). 20 -26 Most of the studies of the bonding in this carbonyl cluster are based on the topological analysis 27 of either experimental 22,23,26 or calculated 23 electron density, but despite considerable effort the nature of this bond is still far from being clear.…”