A Theoretical Investigation on Chemical Bonding of the Bridged Hydride Triruthenium Cluster: [Ru3

Ruthenium-Ruthenium and Ruthenium–ligand interactions in the triruthenium "[Ru3(μ-H)(μ3-κ 2 Hamphox-N,N)(CO)9]" cluster are studied at DFT level of theory. The topological indices are evaluated in term of QTAIM (quantum theory of atoms in molecule). The computed topological parameters are in agreement with related transition metal complexes documented in the research papers. The QTAIM analysis of the bridged core part, i.e., Ru3H, analysis shows that there is no bond path and bond critical point (chemical bonding) between Ru(2) and Ru(3). Nevertheless, a non-negligible delocalization index for this non-bonding interaction is calculated. The interaction in the core Ru3H can be described as a (4centre– 4electron) type. For Ru-N (oxazoline ring) bond, the calculated topological data propose a pure σ-bond. The computed topological parameters of oxazoline ligand reveal the presence of slightly some double bond characters within ligand ring.


Introduction:
The properties of metal-metal interaction in clusters have been developed and widely studied as some important research dealt with the synthesis and characterization of the anionic complexes (1)(2)(3)(4)(5). Some were studies of cluster with low valent metal such as Fe 2 (CO) 9 , showed that the Fe-Fe separation was short enough to imply a M-M bond (6)(7)(8)(9)(10)(11). The important development in the topological analysis, specifically, the atoms in molecules (AIM) theory which developed by Bader and his group, is to study both experimental and theoretical electron density distributions. Additionally, this approach provides a useful tool for studying various interactions in a molecular system (12)(13)(14)(15)(16)(17).
In this paper, we aim to study the nature of the interactions between the various Ru-Ru metal atoms and Ru-ligand in mono hydride triruthenium clusters "[Ru 3 (μ-H)(μ 3 -κ 2 -Hamphox-N,N)(CO)9] (H 2 ox = H 2 aminox)" (18), (Fig. 1), by applying QTAIM method. The Ru-Ru vectors are bridged by hydride ligands, rather than by the N-H group. In addition, one of the ruthenium atoms is attached to the N atom of the oxazoline ring. This would then offer a good opportunity to examine the topological features of different bonding interactions inside the cluster. Computational Methods: The optimization of the cluster, where the X-ray diffraction structure was used as a starting point (18), was carried out using PBE1PBE functional as implemented in the GAUSSIAN09 (19). The LANL2DZ basis set (20) was applied for Ru and 6-31G(d,p) basis set for other atoms (21). The geometry optimization with no restrictions was carried out and stationary points were confirmed to be real minima by computation of its vibrational frequencies. The topological parameters of the optimized structure were computed with the PBE1PBE functional and WTBS basis set for Ru (22) and 6-31G (d, P)for other atoms using the AIM2000 programs (23).

Results and Discussion:
The topological analysis of the electron density offers a deep investigation of the nature of interactions in the clusters. A chemical bond, according to this analysis, is characterized by a line called bond path (bp) which binds the nuclei of two bonded atoms through a bond critical point (bcp). Fig. 2 shows the molecular graph of the cluster which was obtained by using the QTAIM method. In this Figure (2) and Ru(3) the bps and bcps cannot be observed. In the same plane, the bps and bcps existed within both bridged ligand atoms (H(1) and N(2)) and Ru (2) and Ru(3) metals are also observed in the plot.  Based on QTAIM, as presented in Table 1, the topological parameters for the cluster under study were studied.  In the Ru 3 H core, as mentioned above, no bond path or bond critical point was found between the hydride-bridged Ru(2)…Ru (3) interaction. For Ru(1)-Ru (2) and Ru (1)  A lack of a bcp and bond path between Ru(2) and Ru(3) limit an interpretation of any interaction properties between them. Therefore, to give more insight to this interaction, and also to Ru(1)-Ru (2,3) bonds, we calculated the delocalisation index δ (A,B) (27) which is a measure of the number of shared electrons. This index is an appropriate indicator of the interaction that does not depend on the presence of bond critical point.
The numerical results in Table 2, show that the calculated delocalization indices of the Ru(1)-Ru(2,3) bonds are 0.487 and 0.500, respectively. The results obtained are in agreement with the calculated delocalization indices for the M-M bonds (25,28,29). In contrast, the value of delocalization indices for nonbonding Ru(2)...Ru (3) is 0.202, which is in excellent agreement with As seen in Table 2, the average value of the calculated Ru-H delocalization index is 0.455, and is close to that computed by Cabeza et al (26) for the Ru-H bonds in the "[Ru 3 (μ-H) 2 (μ 3 -MeImCH) (CO) 9 ]" cluster (0.474). Furthermore, the results obtained are in agreement with the few cases calculated for the M-H interactions (30). As it is expected, these data pointed out that the number of shared electron in the Ru-H bond is a half electron pair. Interestingly, comparing the data in Table (1) and Table (2) shows that the delocalisation index for Ru(1)-Ru(2,3) bonds is quite similar, whereas the topological parameters for these bonds show remarkable differences. The most significant observation is that the number of electron pairs in the Ru(1)-Ru(2)-H(1)-Ru(3) core is 2.1 electron pairs (summation of bonding and non-bonding delocalization indices). Our results indicate that a multicentre 4c-4e interaction exists in the bridged core parts.
The calculated values of topological properties of the Ru-CO bonds are depicted in Table  1 and are in line with the literature (30). Our results indicate that the average value of ρ BCP for Ru-CO bonds (1.465 Åe -3 ) are significantly higher than Ru-Ru bonds and are lower than the calculated value for covalent bonds between non-metal atoms. By reasons of πback donation, that contains the M...O CO interaction, the computed delocalization indices have been taken as a proof for the existing of π-back bonding in Metal-CO bonds (31,32). For the same reason, the M...O CO delocalization indices were calculated, see Table 2.
The six topological parameters in Table (1), i.e. ρ BCP , ∇ 2 ρ BCP , G BCP , H BCP , V BCP and ε BCP , show high similarities for both (1)-N(1) and Ru(2,3)-N(2) bonds. Importantly, the calculated ellipticity (ε BCP ) of Ru(1)-N(1) (0.070) is higher than the ellipticity of Ru(2,3)-N(2) (0.018) indicating that the former bond has a marginally greater double bond features. From Table 2, the calculated delocalization indexes for both Ru(2,3)-N(2) and Ru(1)-N(1) bonds are around 0.51. This indicates that the number of electron pair shared is 0.5. Fig. 6 shows the distortion in VSCCs for both nitrogen atoms in which linked to ruthenium metal atoms. In a similar manner for Ru-CO calculations, the Ru(1,2,3)…C(1,3) delocalization indices were computed in order to confirm the existence or absence of π bonding in the Ru(1,2,3)-N(1,2) as presented in Table 2. Depending on small and nearly equal values in Table 2, one can conclude that there is no π-bonding features between Ru and oxazoline but only pure σ-donor.
The trajectory map of the oxazoline ring ligand (the bcps, bps and atomic basins), which is presented in Fig.4, shows an interesting point. The bcps is shifted toward the less electronegative atoms, i.e. C (1,2,3). The topological values of O(1)-C(1,2) and N(1,2)-C(1) pointed out that, those bonds have a slightly double bond characters.

Conclusion:
The interactions in the triruthenium "[Ru 3 (μ-H)(μ 3 -κ 2 -Hamphox-N,N)(CO) 9 ]" cluster are explored by means of using topological indices derived from the QTAIM analysis. The AIM analyses of the bridged core part Ru 3 H reveal the absence of a bond critical point and bond path in the Ru(2)…Ru (3) interaction. According to our calculations, the bridged core part a 4c-4e type is suggested to exist. The topological analysis of the Ru-N bond confirms the presence of σ-bond. The AIM analyses of the calculated topological indices of the oxazoline ligand suggest a substantial degree of π-electron delocalization within the ligand rings. The topological results for Ru-Ru and Ru-ligand bonds are comparable with those previously found for other compounds such as Fe, Co, Ni, Ru and Os, carbonyl complexes.