Communications
orbitals. The two dg MOs are always the HOMO and
chromium–chromium bond corresponds to the delocalization
index d(WCr1,WCr2) between the touching density basins
(QTAIM method)[23] WCr1 and WCr2 of the chromium atoms.
The density basin of one chromium atom is depicted in
Figure 3b. It includes the complete third shell and cuts the
two ELI-D bonding basins in the middle between the two
HOMOÀ1, and the two pu MOs HOMOÀ5 and HOMOÀ6.
Energetically, the sg MO and two ligand-centered MOs with a
strong Namido contribution can be found between these two
groups. The HOMO–LUMO gap lies between 1.5 eV and
1.7 eV, depending on the corresponding model.
For further analysis, the electron density and ELI-D were
calculated in position space.[20a] As recently shown, ELI-D can
be split in a physically transparent way into additive positive
orbital contributions (pELI-D contributions),[17e] where the
corresponding orbital density is simply multiplied by a
position-dependent weighting function (the so-called pair–
volume function). An illustration of the pELI-D contribu-
tions for the five chromium-centered MOs is given in
Figure 3a. The isosurfaces encompass the regions where the
corresponding MOs have the highest localizability contribu-
tions (pELI-D contributions) to the total ELI-D distribution.
From Figure 3a, it can be seen that the sg MO, the two pu
MOs, and the one dg MO have pELI-D maxima in the region
between the two chromium atoms. The remaining dg MO
(HOMO; 2d in Figure 3a) has a pELI-D topology with four
maxima at each atom (according to the shape of the dd
orbital), and not in the interatomic region, which closely
resembles a situation with two separated chromium atoms.
Interestingly, this behavior is observed for only one of the two
dg MOs. The other MO shows a strong mixing of Cr(4s)
contributions, which largely eliminates the dd contributions in
the direction of the ligand and reinforces those in the
perpendicular direction. This results in the formation of a
pELI-D maximum perpendicular to the molecular plane and
relatively far from the bond axis. The sum of these five pELI-
D contributions yields the pELI-D distribution shown in
Figure 3a. It shows the topological points for the chromium–
chromium bonding situation displayed by total (all-electron)
ELI-D (Figure 3b). These are the two ELI-D maxima which
are perpendicular to the molecular plane, resulting from the
sum of a pu and dg pELI-D orbital contribution (so-called
banana bonds), and two axially situated maxima, which are
not found for the less-simplified model 4a, on the bond-
opposed side of the chromium atoms. Furthermore, a
significant structuring of the chromium third atomic shell
signals the participation of the d orbitals in the bond
formation. The electronic population of the two bonding
chromium atoms. In the present case, a value for d(WCr1,WCr2)
of 4.2 is found (2.4 of which results solely from the
delocalization between the two chromium third atomic
shells, see above), which significantly differs from the
formal bond order of 5.0. However, this finding is consistent
with the weakly bonding dd MO discussed above. Interest-
ingly, a very similar bond order of 4.3was obtained for a
similar compound using natural resonance theory analysis in
Hilbert space.[6] As the d bonds in the Cr2 model have only a
small contribution to the bond formation, and the 4s–4s bond
is energetically repulsive at the equilibrium distance,[4b] the
most important effect of these electrons for the short bond
distance in Cr2 (1.68 )[15] could be the avoidance of a positive
charge at the metal centers. This would then be the decisive
factor which has to be overcome to realize similar short
distances with formally fivefold-bonded metal atoms.
In future investigations, we are interested in minimizing
the metal–metal bond through variation of the ligand
environment and to explore the reactivity of the such
metal–metal bonds, and to describe in detail the bonding
situation for 4 in position space at an explicitly correlated
level of theory.
Received: March 10, 2008
Revised: May 13, 2008
Published online: August 13, 2008
Keywords: chemical bonds · chromium · electronic structure ·
.
multiple bonds · N ligands
[1] a) L. Pauling, Die Natur der chemischen Bindung, 3rd ed., VCH,
762 – 785; c) “90 Years of Chemical Bonding”: G. Frenking, S.
[2] F. A. Cotton, L. A. Murillo, R. A. Walton, Multiple Bonds
Between Metal Atoms, 3rd ed., Springer, Berlin, 2005.
[3] a) T. Nguyen, A. D. Sutton, M. Brynda, J. C. Fettinger, G. J.
Gagliardi, P.-O. Widmark, P. P. Power, B. O. Roos, Angew. Chem.
basins in the valence region amounts to 1.8 eÀ (banana bond)
[20b]
in total, and for the two bond-opposed basins only 0.3e À
.
The electronic population of the chromium third atomic shell,
having a total of 11.8 eÀ, exceeds the value corresponding to a
3s2p6 configuration by 3.8 eÀ. Therefore, the electrons for the
chromium–chromium bonding interaction are not only local-
ized in the valence region, but can also largely be found in the
spatial region of the third shell of the chromium atoms, where
they contribute to the above-mentioned structuring of ELI-D.
The former statement can be verified by calculation of the
delocalization index[18] d(A,B) between the third shells of
both chromium atoms. A relatively high value of 2.4 for the
corresponding delocalization index is found,[21] which repre-
sents an indirect contribution in the calculation of the bond
order in position space according to ngyµn, Loos, and
Mayer.[22] Thus, the bond order in the case of a symmetrical
[6] K. A. Kreisel, G. P. A. Yap, O. Dmitrenko, C. R. Landis, K. H.
[7] R. Wolf, Ch. Ni, T. Nguyen, M. Brynda, G. J. Long, A. D. Sutton,
R. C. Fischer, J. C. Fettinger, M. Hellman, L. Pu, P. P. Power,
ꢀ 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2008, 47, 7246 –7249