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values for Mn
2
(CO)
10
with respect to those of the model system where the bond
between the two Mn atom is hindered (Fig.
8
, bottom left) simply reveal that the
decrease in the charge depletion around the bcp is not large enough to compensate
for the effects of the accompanying charge concentration decrease in the
M
shell of
the metal. Analysis of the LS profiles enables one to dissect the diverse modifica-
tions occurring in the various atomic shell regions of the metal when the metal
atoms get bonded to one another and to disclose how these local changes affect the
overall metal source contribution to the density at the bcp.
Figure
8d
displays delocalization index values
d
showing how electrons are
shared among vicinal and 1,3 atomic pairs in Mn
2
(CO)
10
. These indices were
already introduced in Sect.
3.2.1
, where the description provided by the SF and
by the
d
in a number of prototypical systems was compared, and where the
necessary caveats related to this kind of comparison were pointed out. Keeping in
mind that delocalization indices and source function contributions are not physi-
cally related in a direct way, it is yet worth noting a number of evident correspon-
dences. The small magnitude of the S%(bcp,Mn) value complies with the very low
d
(Mn,Mn
0
) value of 0.28 (Table
9
), which is clearly quite far from that expected for
a formal single bond.
18
It is rather comparable to that found between Mn and either
the axial or the equatorial oxygen atoms (
d¼
0.22 and 0.17 respectively), which are
both only 1,3 indirectly bonded to Mn through their corresponding C atoms. The
relatively large number of electrons shared between the Mn atom and the carbonyl
O atoms goes with the important S% contributions from the O atoms to the Mn-Mn
0
bcp density. As discussed earlier, Mn-C and C-O bonds are characterized by much
higher S% contributions from the bonded atoms than is for the bond between metal
atoms and so, not surprisingly, the
d
(
O
0
) values are close to 1 and to about 1.6 for
the Mn-C and the C-O bonds, respectively. Moreover, the
d
for the equatorial or
axial bonds is found to be ordered in value as are the sums of the percentage SF
contributions from the two bonded atoms [
14
].
Table
9
summarizes M-M
0
bond properties for the binuclear 3
d
and 4
d
metal
complexes mentioned at the beginning of this section. Metal complexes in this table
and from now on in this section are identified as M.
x
.FBO.nb, where M is the metal,
x
the total number of ligand in the complex, FBO the formal bond order based on
the 18-electron rule, and nb the number of bridged ligands (nb
O
,
¼
0 for an unbridged
system). For instance, Mn
2
(CO)
10
and Fe
2
(CO)
9
are thus denoted as Mn.10.1.0 and
Fe.9.1.3, since both have a formal bond order of one but 0 and 3 bridging ligands,
respectively.
Among the saturated binuclear 3
d
metal carbonyls, only the two unbridged
compounds Mn.10.1.0 and Co.8.1.0 exhibit an M-M bcp, despite all systems
share the same formal bond order of one. Features of metal-metal bonding in the
two unbridged compounds are qualitatively alike, with the M atoms in both
18
2
r
distribution into the Mn basin induced by Mn-Mn bonding and to a minor extent to bonding to
ligands, as shown earlier in this chapter. No special relationship may be sought instead between a
negative S% value and
d
, which is necessarily
The fact that S(bcp,Mn) is not only small but also negative is due to the polarization of the
r
0 by definition.
