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Various local and integral topological parameters of the electron density of relevant bonding interactions in the tri-osmium cluster [( μ -Cl)Os 3 ( μ 2 -σ, π -CH = CH 2 )(CO) 10 ], which is di-bridged, were analyzed by means the quantum theory of atoms in molecules (QTAIM) methodology. Seven criteria based on QTAIM properties, including the values of electron density ρ (b) and its Laplacian ∇ 2 ρ (b) at the BCP, kinetic energy density ratio G (b) / ρ (b) , potential energy density ratio V (b) / ρ (b) , total energy density ratio H (b) / ρ (b) , ellipticity ε (b) , and indices related to delocalization δ (A–B), have been considered and compared with the corresponding ones in other transition metal clusters. A comparison of topological properties was performed for related atom–atom interactions, including different bond orders, bridging, and ligand-unbridged interactions. A multicenter 6c − 9e interaction is proposed to exist in the core part Os 3 [( μ -Cl)( μ 2 -C = C)]. As expected, the calculated local topological parameters for the unbridged Os − Os bonds differ significantly from those of the bridged Os…Os interaction. There is no direct bond path found for the interaction between the bridged Os atoms. However, a non-negligible delocalization index has been obtained for this non-bonding interaction. The electron density shared between the bridged Os atoms is smaller but it is compensated by a greater electron density shared between the atoms in Os − C and Os − Cl bonds. This study also shows that the electron density distribution and the topological parameters of metal–metal interactions are significantly affected by the presence of bridging Cl and C ligands. Furthermore, other methodologies, such as source function (SF) and electron localization function (ELF) methods, have been employed to investigate the Os − Os, Os − C (2) , and Os–Cl interactions. Finally, the computed delocalization index, δ (Os…O CO ), in the tri-osmium cluster supports the existence of some π -back donation from CO to Os.

The bonding in the hydride triruthenium carbonyl cluster [Ru3 (μ-H)(μ3-κ2-Haminox-N,N)(CO)9 is investigated by using the Quantum Theory of Atoms-in-Molecules (QTAIM). Calculated metal-metal and metal-ligand bond critical points (bcp) properties, electron density ρ(b), Laplacian ∇2ρ(b), local energy density H(b), local kinetic (Lagrangian) energy density G(b), local potential energy density V(b) ellipticity ε(b), and bond delocalization indices δ(A, B) are consistent with the relevant transition metal clusters in the literature. The topological data recognizes bond paths (bp) and bond critical points for metal-metal interactions in the core of the hydride triruthenium cluster [Ru(1)-Ru(3) and Ru(2)-Ru(3)]. However, no direct bond path is found for the interaction between the hydride bridged Ru atoms, while a non-negligible delocalization index δ(Ru(1)...Ru(2)) is obtained for this non-bonding interaction. An interaction of 5-center 6-electron type is proposed for the core. The topological parameters of Ru-N oxazoline ring bond suggest a pure σ-bond.

Initially, 4,4'-(1,4-phenylene)di(sulfonic)pyridinium tetrachloroferrate (PDSPTCF) as a novel organic–inorganic hybrid salt was synthesized and identified by elemental mapping, energy-dispersive X-ray spectroscopy, inductively coupled plasma atomic emission spectrometer, Raman spectroscopy, Fourier-transform infrared spectroscopy, X-ray diffraction, field emission scanning electron microscopy, vibrating-sample magnetometry, and thermal gravimetric (TG) techniques. Then, the catalytic performance of this hybrid salt was assessed for the producing benzo[ a ]benzo[6,7]chromeno[2,3- c ]phenazine derivatives via one-pot multicomponent domino reaction (MDR) of benzene-1,2-diamine, 2-hydroxynaphthalene-1,4-dione and aldehydes under optimal conditions (70 °C, solvent-free, 5 mol% PDSPTCF) in short reaction times and high yields. Highly efficacy of the PDSPTCF for the production of benzo[ a ]pyrano[2,3- c ]phenazines can be assigned to the synergistic effect of Lewis and Brønsted acids, and having two positions of each acid (i.e., FeCl 4 ˉ and –SO 3 H). In addition, this catalyst showed good reproducibility with six cycles of recycling.

The tri-nuclear heterometallic tetrahedral cluster [Mo–Ru–Co( µ 3 –S)(CO) 8 (Cp)COOCH 3 ] (Cp =  η 5 -C 5 H 4 ) was studied employing quantum theory of atoms in molecules (QTAIM) to examine bonding interactions, including metal–metal (M–M), metal–sulfur (M–S), metal–carbonyl (M–CO), and metal–cyclopentadienyl (M–Cp) interactions. The electron density of bonding interactions within the cluster has its topological properties calculated based on this theory. Interestingly, the computed local topological characteristics for the Mo–Ru bond show notable distinctions in comparison to the parameters for interactions involving Mo–Co and Ru–Co, since for the latter, critical points and paths were not observed. The distribution of electron density was notably affected by the presence of bridging sulfide ligands in Mo…Co, Ru…Co interactions, much more than in the Mo–Ru bond. The characteristics of the latter bond exhibited attributes typical of interactions between open-shell metals. These features included slightly positive values for ρ ( b) and ∇ 2 ρ (b) , along with small negative values of H (b) / ρ (b) approaching zero. Additionally, using the source function (SF) and electron localization function (ELF) methods, more focus has been given to the Mo–Ru bond. The core part, [Mo–Ru–Co( µ 3 –S)], was found to have a multicenter 4 c –6 e interaction. In this core, the three M–S bonds between the metal atoms and the sulfide ligand showed similar topological parameters that were typical of open-shell (covalent) interactions. Substantial π –back donation from CO to M was identified through the execution of δ (M…O CO ) delocalization index calculations.

Chromium–chromium and chromium–ligand bonding interactions existing in the [Cp* 2 Cr 2 (CO) 2 (μ-PMe 2 ) 2 ], [Cp* 2 Cr 2 (CO) 4 (μ-H) (μ-PMe 2 )], and [Cp* 3 Cr 3 (CO) 3 (μ-S) (μ-PMe 2 )] 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 ∇ 2 ρ (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.

The electron density of the [(μ 3 -S) Fe 3 (CO) 9 (μ 3 -CO)] cluster was analyzed using the quantum theory of atoms in molecules (QTAIM) to explore its topological properties. This analysis provides valuable insight into the interactions between Fe–Fe, Fe–C, and Fe–S as well as other important topological properties of the compounds. Analysis of the core part, especially the S–Fe 3 –CO region, does not show the presence of bcp (bonding critical points) and bp (bonding pathways) for any pair of M–M (metal–metal) bonds, indicating significant delocalization. There may be multicentric (5c–4e) interactions in the central region of the junction. Examining topological data for Fe–Fe, Fe–S, and Fe–CO bonds, we find that all of these bonds exhibit typical properties of closed-shell metal–metal interactions. However, there is evidence that there is an actual chemical bond between the Fe metal and the carbon atoms of the CO ligand, rather than just an “interaction.” The presence of sulfide-bridging ligands plays an important role in effectively reducing the delocalization of electron density between sulfide-bridged iron pairs as opposed to iron pairs that are not bridging and are coordinated by carbonyl ligands.

The nature of the chemical bonding interactions in the trigonal–bipyramidal chromium–manganese chalcogenide clusters, [E 2 CrMn 2 (CO) 9 ] −2 (E = S, Se, and Te), has been studied using two methods of the quantum chemical topology analysis: electron density q(r) and electron localization function (ELF). The evaluation of these properties reveals important details about chemical bond interactions within the clusters. According to the results, it has been confirmed that the bonding between Mn–Mn and Mn–Cr is absent in all three trinuclear clusters 1–3 . The presence of bridging chalcogenide atoms (S, Se, and Te) concerning M–M is a key factor in determining the distribution of electron densities. This factor has a significant impact on the formation of bonds between these transition metal atoms. Calculations of the non-negligible delocalization index for clusters 1–3 confirm a 5c–12e bonding interaction that is delocalized over the five-membered CrMn 2 (μ−E) 2 ring. In clusters 1–3 , the M–E bonds between Mn and Cr metal atoms and E ligands (S, Se, and Te) exhibit similar topological parameters that are comparable to that of pure covalent single bonds between nonmetal atoms. Furthermore, the source function calculations reveal that the bonded E atoms contribute the most at each Mn–E and Cr–E bcps, with a small contribution from the bonded metal atom and OCO atoms. Interestingly, non-bonded transition metal atoms act as sinks rather than sources of electron density. The M…OCO delocalization indexes and SF calculations indicate significant CO to M π -back-donation. This work aims to provide insights into the interactions between Mn–Mn and Mn–Cr, and the changes in bonding interactions across the di-bridging chalcogen elements series. It also aims to examine the role of carbonyl groups in M–M interaction within the clusters.

Context This research aims to offer a deeper understanding of the bonding interactions between M-Se and M-CO and how these interactions change across the group 6 transition metal series: [Se 2 M 3 (CO) 10 ] 2- (M = Cr, Mo, W). It also seeks to explore the impact of carbonyl groups on M-M interactions within the clusters. Seven criteria, which are based on QTAIM properties, have been considered and compared with the corresponding criteria in other transition metal clusters. The results confirm that no such bond critical points or bond baths occur between transition metals, which instead have 5c–7e bonding interactions delocalized over their five-membered M 3 (μ-Se) 2 ring, as evidenced by the non-negligible nonbonding delocalization indices. The topological properties of three bond clusters, Cr-Se, Mo-Se, and W-Se, resemble those of “intermediate closed shell characters,” which combine covalent and electrostatic properties. Source function calculations indicated that the bonded Se atom contributed the most to each Cr-Se and Mo-Se bcp. The O CO atoms and nonbonded Se atoms also contributed to some extent. However, metal atoms act as sinks rather than as sources of electron density. In contrast, the majority of the metal atoms, both bonded and nonbonded, contribute to Cr-W bcps. Analysis of the delocalization indices δ (M…O) in the three clusters indicates that CO significantly contributes to Cr π-back donation in cluster 1 . In contrast, no π-back donation occurs from CO to Mo or W in clusters 2 or 3 , respectively. Methods The B3P86 hybrid functional was used for computations in the Gaussian 09 software. The LanL2DZ basis set was employed for Cr, Mo, and W, while the 6-31G (d, p) basis set was used for C, O, and Se atoms. We performed QTAIM analysis using the AIM2000 and Multiwfn packages, incorporating B3P86/WTBS for Cr, Mo, and W atoms. The 6-311++G(3df,3pd) basis set was used for C, O, and Se atoms. Additionally, we utilized the ELF and SF.

This research aims to offer a deeper understanding of the bonding interactions between M-Se and M-CO and how these interactions change across the group 6 transition metal series: [Se2M3(CO)10]2- (M = Cr, Mo, W). It also seeks to explore the impact of carbonyl groups on M-M interactions within the clusters. Seven criteria, which are based on QTAIM properties, have been considered and compared with the corresponding criteria in other transition metal clusters. The results confirm that no such bond critical points or bond baths occur between transition metals, which instead have 5c-7e bonding interactions delocalized over their five-membered M3(μ-Se)2 ring, as evidenced by the non-negligible nonbonding delocalization indices. The topological properties of three bond clusters, Cr-Se, Mo-Se, and W-Se, resemble those of \"intermediate closed shell characters,\" which combine covalent and electrostatic properties. Source function calculations indicated that the bonded Se atom contributed the most to each Cr-Se and Mo-Se bcp. The OCO atoms and nonbonded Se atoms also contributed to some extent. However, metal atoms act as sinks rather than as sources of electron density. In contrast, the majority of the metal atoms, both bonded and nonbonded, contribute to Cr-W bcps. Analysis of the delocalization indices δ(M…O) in the three clusters indicates that CO significantly contributes to Cr π-back donation in cluster 1. In contrast, no π-back donation occurs from CO to Mo or W in clusters 2 or 3, respectively.CONTEXTThis research aims to offer a deeper understanding of the bonding interactions between M-Se and M-CO and how these interactions change across the group 6 transition metal series: [Se2M3(CO)10]2- (M = Cr, Mo, W). It also seeks to explore the impact of carbonyl groups on M-M interactions within the clusters. Seven criteria, which are based on QTAIM properties, have been considered and compared with the corresponding criteria in other transition metal clusters. The results confirm that no such bond critical points or bond baths occur between transition metals, which instead have 5c-7e bonding interactions delocalized over their five-membered M3(μ-Se)2 ring, as evidenced by the non-negligible nonbonding delocalization indices. The topological properties of three bond clusters, Cr-Se, Mo-Se, and W-Se, resemble those of \"intermediate closed shell characters,\" which combine covalent and electrostatic properties. Source function calculations indicated that the bonded Se atom contributed the most to each Cr-Se and Mo-Se bcp. The OCO atoms and nonbonded Se atoms also contributed to some extent. However, metal atoms act as sinks rather than as sources of electron density. In contrast, the majority of the metal atoms, both bonded and nonbonded, contribute to Cr-W bcps. Analysis of the delocalization indices δ(M…O) in the three clusters indicates that CO significantly contributes to Cr π-back donation in cluster 1. In contrast, no π-back donation occurs from CO to Mo or W in clusters 2 or 3, respectively.The B3P86 hybrid functional was used for computations in the Gaussian 09 software. The LanL2DZ basis set was employed for Cr, Mo, and W, while the 6-31G (d, p) basis set was used for C, O, and Se atoms. We performed QTAIM analysis using the AIM2000 and Multiwfn packages, incorporating B3P86/WTBS for Cr, Mo, and W atoms. The 6-311++G(3df,3pd) basis set was used for C, O, and Se atoms. Additionally, we utilized the ELF and SF.METHODSThe B3P86 hybrid functional was used for computations in the Gaussian 09 software. The LanL2DZ basis set was employed for Cr, Mo, and W, while the 6-31G (d, p) basis set was used for C, O, and Se atoms. We performed QTAIM analysis using the AIM2000 and Multiwfn packages, incorporating B3P86/WTBS for Cr, Mo, and W atoms. The 6-311++G(3df,3pd) basis set was used for C, O, and Se atoms. Additionally, we utilized the ELF and SF.

Context The ruthenium–ruthenium and ruthenium-ligand bonding interactions in the [{CpRu(μ-H)} 3 (μ 3 -BH)]( 1 ), [{CpRu(μ-H)} 3 (μ 3 -H) 2 ]( 2 ), [{CpRu(CO)} 3 (μ-BO)(μ-H) 2 ]( 3 ), and [{CpRu(μ-H)} 3 (μ 3 -AlEt)]( 4 ) clusters were examined using density functional theory (DFT). Various parameters related to electron density, including the electron density ρ (b), Laplacian ∇ 2 ρ (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: H 3 -Ru–B (7c–14e), H 5 -Ru (8c–12e), H 2 -Ru 3 -B (6c–8e), and H 3 -Ru 3 -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.