Theoretical study of Cr–Cr bonding in [Cp*2Cr2(CO)2(µ-PMe2)2], [Cp*2Cr2(CO)4(µ-H) (µ-PMe2)], and [Cp*3Cr3(CO)3(μ-S) (μ-PMe2)] complexes by QTAIM theory

Chromium–chromium and chromium–ligand bonding interactions existing in the [Cp*₂Cr₂(CO)₂(μ-PMe₂)₂], [Cp*₂Cr₂(CO)₄(μ-H) (μ-PMe₂)], and [Cp*₃Cr₃(CO)₃(μ-S) (μ-PMe₂)] complexes are studied at DFT level of theory. Several local and integral topological parameters of the electron density such as electron density ρ_(b), Laplacian ∇²ρ_(b), local energy density H_(b), local kinetic energy density G_(b), potential energy density V_(b), ε_(b), and bond localization index (A, B) were evaluated according to QTAIM (quantum theory of atoms in a molecule). The calculated topological parameters are consistent with the relevant transition metal complexes in the literature. The computed data allow comparisons between the topological properties of related but different atom–atom interactions, such as other ligand-bridged Cr–Cr interactions and H-bridged ligand interactions versus S and P ligands. The QTAIM results confirm that the metal atoms bridged by two phosphorus atoms in binuclear complex1 are connected through a localized Cr–Cr bond that implicates little electron density (0.040). In contrast, such bonding was not found in binuclear complexes 2 (bridged by H and P) and trinuclear complex 3 (bridged by S and P). A multicenter 4c–5e, 4c–3e, and 4c–4e interactions are proposed to exist in the bridged parts, Cr(1)–P(1)–Cr(2)–P(2) in complex 1, Cr(1)–H–Cr(2)–P in complex 2, and Cr3–S in complex 3, respectively. Finally, the delocalization indices δ(Cr····O) calculated for the Cr–CO bonds in the three compounds confirm the presence of significant CO to Cr π-back-donation except for Cr(2)–O(2) and Cr(3)–O(1) bonds in complex 3, indicating that there is no π-back-donation.