QTAIM view of Ru–Ru bonding in a series of tri-ruthenium hydride clusters: [{CpRu(μ-H)}3(μ3-BH)], [{CpRu(μ-H)}3(μ3-H)2], [{CpRu(CO)}3(μ-BO)(μ-H)2], and [{CpRu(μ-H)}3(μ3-AlEt)]

Context

The ruthenium–ruthenium and ruthenium-ligand bonding interactions in the [{CpRu(μ-H)} ₃(μ³-BH)](1), [{CpRu(μ-H)}₃(μ³-H)₂](2), [{CpRu(CO)}₃(μ-BO)(μ-H)₂](3), and [{CpRu(μ-H)}₃(μ³-AlEt)](4) clusters were examined using density functional theory (DFT). Various parameters related to electron density, including the electron density ρ(b), Laplacian ∇²ρ(b), local energy density H(b), local kinetic energy density G(b), potential energy density V(b), and bond delocalization index (A, B), were calculated using the quantum theory of atoms in a molecule (QTAIM). Other QTAIM indicators, such as the electron localization function (ELF) and source function (SF) were computed. According to the transition metal complexes referenced in the academic literature, the computed topological parameters are consistent. The calculated data have made it possible to compare the topological characteristics of related but distinct atom-to-atom interactions, including Ru–H interactions against Ru-BH, Ru-BO, and Ru-Al interactions, as well as H-bridged Ru–Ru interactions versus BH-, BO-, and Al-bridged interactions. The electron density distribution of the Ru–Ru interactions is influenced by different bridging ligands. Despite the presence of bridged hydride and boron in clusters 1 and 3, H in cluster 2, and H and Al in the Ru–Ru interactions of 4, no localized bond, bond critical, or bond path was observed. However, the large delocalization indices δ(Ru, Ru) indicate that significant indirect Ru–Ru interactions are mediated through bridging ligands. For clusters 1, 2, 3, and 4, we propose the following interactions for their core components: H₃-Ru–B (7c–14e), H₅-Ru (8c–12e), H₂-Ru₃-B (6c–8e), and H₃-Ru₃-Al (7c–14e). The AdNDP analysis confirms the presence of 4c–2e multicenter bonds in several Ru₃-based clusters, emphasizing the critical role of electron delocalization in stabilizing their core structures. The BO ligand has a higher delocalization index of 1.023, indicating that it shares a pair of electrons. Moreover, the delocalization index for cluster 3, δ(Ru…O_CO), is very large at 0.576. This suggests that CO ligands play a significant role in M π-back-donation.

Methods

Using the PBE1PBE hybrid functional and an effective core potential LanL2DZ basis set for the atoms of Ru as well as the all-electron 6-31G(d) basis set for the other atoms (Al, B, H, C and O), the optimizations were performed using the Gaussian 09 program. The geometries were verified as a local minimum by examining if imaginary vibrational frequencies were present after unrestricted optimization was carried out. Utilizing AIM2000 and Multiwfn software, we conducted QTAIM analysis, incorporating PBE1PBE/WTBS for the Ru atoms. 6-31G(d,p) and 6–311 +  + G(3df,3pd) were the basis set for the atoms of Al, B, H, C and O. Moreover, we employed the SF and ELF.