Comparative Analysis of Electron-Density and Electron-Localization Function for Dinuclear Manganese Complexes with Bridging Boron- and Carbon-Centered Ligands

Abstract

Bonding in borylene-, carbene-, and vinylidene-bridged dinuclear manganese complexes [MnCp(CO)₂]₂X (X=B-tBu, B=NMe₂, CH₂, CCH₂) has been compared by analyses based on quantum theory of atoms in molecules (QTAIM), on the electron-localization function (ELF), and by natural-population analyses. All of the density functional theory based analyses agree on the absence of a significant direct MnMn bond in these complexes and confirm a dominance of delocalized bonding via the bridging ligand. Interestingly, however, the topology of both charge density and ELF related to the Mn-bridge-Mn bonding depend qualitatively on the chosen density functional (except for the methylene-bridged complex, which exhibits only one three-center-bonding attractor both in −∇²ρ and in ELF). While gradient-corrected functionals provide a picture with localized two-center XMn bonding, increasing exact-exchange admixture in hybrid functionals concentrates charge below the bridging atom and suggests a three-center bonding situation. For example, the bridging boron ligands may be described either as substituted boranes (e.g., at BLYP or BP86 levels) or as true bridging borylenes (e.g., at BHLYP level). This dependence on the theoretical level appears to derive from a bifurcation between two different bonding situations and is discussed in terms of charge transfer between X and Mn, and in the context of self-interaction errors exhibited by popular functionals.