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Ru(3)−Ru(3′) = 2.9932(5) Å. The Ru−Ru bonds within the
Ru3 triangles are shorter, Ru(1)−Ru(3) = 2.8544(4) Å, Ru(1)−
Ru(2) = 2.8650(3) Å, and Ru(2)−Ru(3) = 2.8840(3) Å, and
are similar to those found in 2, 2.841(6) and 2.844(6) Å.11 As
in 2, each Ru−Ru bond within the Ru3 triangles contains a
bridging hydrido ligand (located and refined in the structural
analysis), but two of these, H(3) and H(3′), serve as triply
bridging ligands by extending to the ruthenium atom, Ru(3), in
the neighboring Ru3 triangle. The Ru(2)···Ru(3′) distance
between the two Ru3 clusters, 3.627(1) Å, is too long for a
direct bonding interaction.
Compound 1 contains a total of 92 valence electrons. A six-
metal cluster with seven metal−metal bonds should have 94
electrons, (6 × 18) − (7 × 2), if all of the metal atoms formally
have an 18-electron configuration.12 In order to obtain a clearer
picture of bonding in 1, several DFT calculations have been
performed: first, a geometry optimization starting with the
structure as found in the solid state, followed by a vibrational
frequency calculation to confirm the stationary point as a
minimum, and then a fragment analysis to help explain the
bonding (details are given in the Supporting Information). To
better understand the stability of the dimer, 1, DFT calculations
were also performed on the two Ru3(CO)8(μ3-CMe)(μ-H)3
monomer units of 1, and the proposed intermediate that
contains the direct Ru(3)−Ru(3′) bond, but without triply
bridging H(3) or H(3′) ligands. The details of the optimized
structures for these three species are shown in Figure 2. Our
the geometry that they display in the optimized dimer struc-
ture, rather than at their independently optimized geometry
as described above. These calculations show that the total
(intrinsic) electronic bond energy of −33.40 kcal/mol is
comprised mostly of orbital interactions (−31.58 kcal/mol) and
a small contribution (−1.82 kcal/mol) from the sum of the
electrostatic (attraction in this case) and Pauli repulsions. The
source of this orbital stabilization is mixing of the LUMO of
each monomer fragment with several occupied fragment
orbitals, specifically the HOMO-2, HOMO-8, and HOMO-
11, of the other fragment. The key features of this mixing are
described below, and related orbital contour drawings are
shown in Figure 3. The most significant pair of interactions
Figure 3. Orbital contour diagrams at the isosurface value of 0.03 for
the fragment orbitals and 0.02 for the dimer orbitals showing (a)
HOMO-11 of fragment A (the electron-donor orbital) in relation to
the LUMO of fragment B (the electron-acceptor orbital), (b) HOMO-
27, the major MO making a net contribution to the bonding between
the two fragments in the dimer 1, (c) HOMO-8 of fragment A (the
electron-donor orbital) in relation to the LUMO of fragment B (the
electron-acceptor orbital), (d) HOMO-18, a MO making a net
contribution to the bonding between the two fragments in the dimer
1, (e) the HOMO-2 of fragment A (the electron-donor orbital) in
relation to the LUMO of fragment B (the electron-acceptor orbital),
and (f) HOMO-5, the second most important MO making a net con-
tribution to the bonding between the two fragments in the dimer 1.
Note that the orientation has the bridging Ru atoms upper right and
lower left.
Figure 2. Schematic representations of the monomer, the intermediate
with the Ru(3)−Ru(3′) bond, and the dimer, showing bond distances
of the optimized structures and the relative Gibbs free energies of the
systems.
occurs when the LUMO of one of the monomer fragments
accepts electron density from the HOMO-11 of the other
fragment, as shown in Figure 3a for one of the pairs. This
mixing leads to significant bonding in the HOMO-27 of the
dimer 1, as shown in Figure 3b. The HOMO-8 of each
fragment has a similar, but somewhat weaker, interaction with
the LUMO of the other fragment, as shown in Figure 3c. This
second interaction enhances the bonding in the HOMO-18 of
the dimer 1, shown in Figure 3d. Finally, the LUMO of each
fragment also mixes with the HOMO-2 of the other fragment
(Figure 3e), in a way that enhances the bonding from the
HOMO-5 of 1, shown in Figure 3f.
The unsaturation of the monomer fragment is concentrated
in the LUMO, which is the orbital that a two-electron-donor
ligand such as a carbonyl or a phosphine would use to make an
additional bond. In the dimer 1, the unsaturation is resolved by
electron donation from the HOMO-11, HOMO-8, and
analysis shows that the combination of the two Ru3(CO)8-
(μ3-CMe)(μ-H)3 units to form the intermediate with only the
Ru(3)−Ru(3′) bond lowers the Gibbs free energy (ΔG°) of the
system by 2.73 kcal/mol and creates a metal−metal bond at
2.91 Å. The rearrangement of this structure into the observed
dimer with contributions from the triply bridging H(3) and
H(3′) lowers the ΔG° of the system to 8.96 kcal/mol below
that of the two monomers and lengthens the Ru(3)−Ru(3′)
bond to 3.06 Å. These results indicate that the Ru(3)−Ru(3′),
H(3)−Ru(3′), and H(3′)−Ru(3) interactions all contribute to
the bonding in 1.
The fragment analysis describes the nature of the bonding
between two monomers (labeled A and B) that are frozen in
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dx.doi.org/10.1021/om2012375 | Organometallics 2012, 31, 50−53