Chemistry Reference
In-Depth Information
In the case of unsaturated systems, the local property values listed in Table
9
exhibit quite
unexpected
trends versus the formal bond order. To include the case of
a formal bond order of one, the Co.8.1.0 saturated system with a Co-Co bcp and
formal bond order of one is added to the unsaturated series [Co
2
(CO)
x
,
x
¼
7-5] in
2
this part of the discussion. The
r
value is always positive and regularly increases
with increasing formal bond order. Despite being at odds with the dichotomous
classification based on
r
2
r
, this trend is clearly anticipated. For all systems, the bcp
or mp falls within the
M
-shell charge depletion region of the isolated atom, and the
Laplacian past the maximum of depletion in this region has to decay monotonically
down to zero with increasing distance from the nucleus. The shorter the Co-Co
distance is, the more positive will thus be the Laplacian at the Co-Co mp or bcp.
The bond classification index based on the |V| /G ratio decreases monotonically
along the unsaturated series reaching a value of 1.31 in the system with formal bond
order of four. The largest value of 1.95 is instead observed for the saturated bonded
Co.8.1.0 isomer with formal bond order of one. This is clearly the opposite trend
one would have expected from this descriptor, which appears to depict as very close
to a shared interaction the system with a formal bond order of one and as close to the
closed-shell regime that with a formal bond order of four. On top of this, all systems
in the [Co
2
(CO)
x
,
x
r
8-5] series are described as lying in the transit region for
incipient covalent bond formation, despite the noticeable decrease in the Co-Co
bond distance through the series. The bond degree, H
b
/
r
b
, is almost constant
through this series, with almost equal values for the first (
¼
0.33) and the last
(
0.34) term of the series. The kinetic energy per electron, G
b
/
r
b
, monotonically
rises along the series, as found also for standard covalent bonds (0.23, 0.39, and
0.68 in ethane, ethene, and ethyne). However, the last term of the series has a G
b
/
r
b
value greater than one, which is normally regarded [
6
] as a sign of a closed-shell
interaction or of an interaction with large polarization and/or charge transfer (which
is obviously not the case here). Taken as a whole, use of standard local descriptors
for the M-M bonding in the unsaturated [Co
2
(CO)
x
,
x
8-5] series appears
problematic and leading to apparent contradictions with respect to the known
behavior of such indices for bonds between atoms of the first three rows of the
periodic table. Conversely, the S%(M) and the
d
(M,M
0
) values lead to a qualita-
tively similar and meaningful description, which features a notable departure from
the formal bond order classification based on the 18-electron rule model.
The M
2
(formamidinate)
4
(M
¼
Nb, Mo, Tc, Ru, Rh, and Pd) binuclear 4
d
metal
complexes form a series of isostructural compounds which differ only for the nature
of their metal atom and exhibit formal bond orders varying from zero (M
¼
¼
Pd) up to
four (M
Mo) as a function of the number of electrons available for the M-M bond.
The notation we adopt for these tetra-bridged systems, which have a paddlewheel
structure, is analogous to that used for the 3
d
binuclear metal carbonyls. For
instance, Ru.4.2.4 will denote the M
2
(formamidinate)
4
complex with M
¼
Ru
and formal bond order of 2. The number of ligands, four, and their bridging nature
are clearly fixed through the series.
The study of these complexes enables us to examine M-M bonding between 4
d
metal atoms and to observe whether this bonding has distinct features from that
¼
