QTAIM study of the bonding in triosmium trihydride cluster [Os3(μ-H)3(μ-ɳ-CC7H3(2-CH3)NS)(CO)8]

The Atoms in Molecules (AIM) analysis for triosmium cluster, which contains trihydridede, carbon, carbonyl and 2-methylbenzothiazolide ligands, [Os3(μ-H)3(μ -ɳ-CC7H3(2-CH3)NS)(CO)8] is reported. Bonding features in this cluster has been analyzed based on QTAIM ("Quantum Theory of Atoms in Molecules") in this work. The topological indices derived from electron density of relevant interactions in triosmium compound have been studied. The major interesting point of the AIM analyses is that the core of part (Os3H3) reveals the absence of any critical points and bond paths connecting any pairs of Os metal atoms. However, bond critical points with their bond paths occurring between all Os-H interactions were observed. For the bridged core part (Os3H3), a 6c–6e multicenter interaction is proposed. The topological parameters computed for the bridging 2-methylbenzothiazolide ligand interactions indicate that all of these interactions are typical related to the covalent bonds with a contribution of some double-bond character.


Introduction:
The reactivity of benzoheterocyclic ligands with osmium carbonyl clusters giving the electrondeficient triosmium compounds, plays a central role in organometallic chemistry. In recent years, the electron-deficient triosmium clusters have extensively been studied to model the heterogeneously catalyzed hydrodinitrification of these heterocycles (1,2). Also, these clusters have been widely used to functionalize heterocyclic substrates resulting in the synthesis of new useful compounds which are not easy to gain by using classical organic methods (3,4). The analysis of the electron density distribution, using QTAIM theory (5)(6)(7)(8)(9), has been considered as a good tool to analyze chemical bonds and to compare the properties of atoms and molecules (10,11) . This model is very important to distinguish the existence of chemical bond interactions between any two neighbored atoms within the expression of bond critical points (BCP) along the nuclear attractors in the neighborhood atoms (bond path, Bp), (12). Based on the QTAIM analysis, the electronic energy density H(b), electron density ρ(b) and Laplacian ∇ 2 ρ(b) calculated at critical points of the bond, offer important information about the properties of the bond. This methodology is able to a deep study of the characteristics of a metal-metal and metalligand interactions in cluster compounds (13). In this work, we present AIM study of triosmium cluster [Os3(µ-H)3(µ 3 -ɳ 2 -CC7H3(2-CH3)NS)(CO)8] (14), shown in Fig. 1, focusing on the bonding behaviour between various atomic interactions, such as Os-Os, Os-Hbridged, Os-Cbridged and Os-Ccarbonyl interactions. The complex under this study has been chosen due to the lack of any previous AIM study on triosmium compound contains tribridging hydride ligands and bridging C spans the Os-Os edges. In addition, this work also discusses and compares between different topological properties of a variety interactions in M-M and M-L.

Theoretical Methods:
The optimized geometry of the triosmium cluster was obtained from the PBE1PBE level (15) using Gaussian 09 (16) program. The SDD (17) basis set augmented with a set of f-polarization functions (18), was used for Os atoms. whereas 6-31G (d,p) (19) basis set was used for other atoms of (H, C, N, O and S). The cluster was also characterized by analytical calculation of frequencies and has positive eigenvalues thus confirming that the optimised geometry is minima on the potential energy surface. The QTAIM analysis was calculated using the AIM2000 package (20) at the PBE1PBE/WTBS for Os atoms (21) in conjunction with the 6-31G(d,P) basis set for other atoms.

Results and Discussion:
According to QTAIM method, the structure of a compound is totally specified by the set of critical points at which the gradient of electron density ∇ 2 ρ(b) is zero. The existence of a bcp and bp connecting between two neighbored atoms is taken as an indicator for the chemical bonding (22). The molecular graph for triosmium compound is presented in Fig. 2. The bcps and their bps correspond to the Os-H, Os-C, Os-N, C-C, C-H, C-N, and C-S bonds were clearly found. Remarkably, the results showed the lack of any bond critical point or bond path between any two of the osmium atoms. Six rcp (ring critical point) were found for the "N(  A gradient trajectory map of (Os(1)-H(1)-Os(2)-H(3)-Os(3)-H(2)-Os(1)-C(1)) core is shown in Fig. 3. This figure shows the absence of bond critical points as well as bond paths link any pair of osmium atoms. Whereas, in the same plane, the bond paths as well as bond critical points can be observed between osmium metal atoms and bridged hydride atoms.  A gradient trajectory map for 2methylbenzothiazolide ligand, presented in Fig. 4, clearly shows the bond and ring critical points linked by bond paths associated with this ligand. For the interactions of Os(1) and C(1) with the 2methyl benzo thiazolide, the bps and bcps can also be observed.  Table 1. Table 1. The topological indexes calculated at bcps of the studied cluster. "Where (ρb) electron density(eÅ -3 ), (∇ 2 ρb) Laplacian of the electron density(eÅ -5 ) (Gb) kinetic energy density ratio (he -1 ), (Vb) potential energy density ratio (he -1 ), (Hb) total energy density ratio and (εb) ellipticity." Os (1) The main point of interest, as mentioned above, is the full absence of any bond critical point between Os atoms of the core which are bridged by both H and C atoms. This finding is significant since it is attributed to the absence of any trace of localized electron density between Os atoms. Therefore, it can be concluded that there are no features of chemical bonding between any pair of Os atoms in the core (22). The strong ligand bridging interaction (H and C groups) destroys the topological Os-Os. Bond critical points with their bond paths, have been observed between supported and unsupported metal-metal atoms interaction (25)(26). For Os-H bonds, the topological properties were calculated as presented in Table 1 (i) (ii) Figure 5

. Laplacian distribution ∇ 2 ρ(b) plot of the triosmium cluster though (i) Os (1)-H (3)-Os (2)-C (1) plane. (ii) Os (3) with H(2) and H(3) and CO ligands plane.
As mentioned above, the absence of a bcps between any pair of the Os metal atoms limits the interpretation of the Os-Os interaction. Instead, the delocalization index, δ(A, B) (29), is a measure of the electrons shared between two atoms. This index can be considered as an appropriate AIM indicator to characterize the chemical bonding between atoms which do not depend on the existence of a bond critical point. The values of delocalization index δ(A-B) computed for Os cluster are presented in Table 2. The magnitude of δ(Os, Os) is within range 0.158-0.172 and this, in fact, is very similar to that computed by Cabeza group (28)  , it can be concluded that the total δ(A-B) for the core is 3.06 electron pairs in the core part (Os3H3). Therefore, the interaction in this core can be described as a 6c-6e interaction. The computed topological values for Os-C(1) and Os-C(CO) bonds are listed in Table 1

C-N, C-S and C-C Interactions in the 2-Methylbenzothiazolide Ligand.
The topological properties of the atom-atom interactions in bridging 2-methylbenzothiazolide ligand are presented in Tables 1. In this ligand, the nature of the bonding may also be appreciated in the graphically representations of the gradient map (shown in Fig. 4) and the Laplacian map (depicted in Fig. 6). Those two maps clearly show all the bond critical point, bond paths and atomic basins which existed in the bridging 2methylbenzothiazolide ligand. Also, the polarization of the VSCCs of the bridging ligand C(1) is shifted toward the interatomic surface of Osmium atoms (Fig. 6), whereas the N(1) polarised to the Os(1). The topological parameters computed for the bonds within bridging 2-methylbenzothiazolide, presented in Table 1, are typical for covalent interactions, with values for ρ(b) higher than zero and a significantly negative ∇ 2 ρ(b) and H(b) values, with some degree of delocalization (22,(33)(34)(35).

Figure 6. Laplacian distribution ∇ 2 ρ(b) plot of the triosmium cluster though the Os(1)-Os(2)-C(1)-N(1) plane
Regarding the N(1)-C(7) and N(1)-C(8) interactions, it is very important to compare their topological parameters with the C(6)-S(1) and C(8)-S(1) bonds. The computed electron density ρ(b) and H(b) for N-C bonds slightly higher than S-C bonds and this finding indicates that the former has a slightly double bond character.

Conclusion:
Topological properties of electron density for triosmium cluster "[Os3(µ-H)3(µ 3 -ɳ 2 -CC7H3(2-CH3)NS)(CO)8]" have been calculated and interpreted based on AIM theory. Also, the bonding features in this cluster have been analyzed. The AIM analyses of the core part, Os3H3, reveals the existence of a bond critical point and its bond path within Os−H bond. Conversely, no bond critical points linked by bond paths between any pair of Os metal atoms are observed. However, a delocalization index has been computed. The interaction in the Os3H3 core can be described as a multiple 6c-6e interaction. The numerical values of the topological indices of the bridging 2methylbenzothiazolide ligand interactions indicate that all the bonds are typical for covalent bonding mode with a slight degree of double-bond character.