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vanishing density gradient [
83
]. The SF contributions patterns nicely reflect such a
delocalized nature of the Mn-ring interaction. All basins of the
-hydrocarbyl
ligand determine in a significant way the electron density in the annulus, and
relative contributions from all basins are almost unchanged regardless the rp is at
a bcp (Fig.
12d
) or at an rcp (Fig.
12e
). As a consequence, the SF pattern for the
Mn-C7 interaction, which lacks a bcp, was found to be almost indistinguishable
from that of the remaining four bonded Mn-C
ring
interactions, provided the
corresponding rp is also taken to lie in the annulus. The SF contribution from
the Mn(CO)
3
group is significant too and independent of the rp position within the
annulus. It amounts to about 30%, one third of it coming from the Mn atom. Taken
as a whole, the SF patterns for the metal-ring bonding suggest not only that such
interaction is delocalized through the whole ring, but that it involves, besides the
metal atom, also the carbonyl ligands bonded to the metal. Finally, Fig.
12f
shows
the S% pattern when the rp is taken at the (C-C)
ring
bcp. The two bonded C atoms
determine about 84% of the density at their bcp, which is consistent with that found
for benzene (84.7%, Table
4
). Even contributions from the other C atoms in the ring
and from the H atoms are very much alike to those obtained for benzene. According
to Farrugia et al. [
83
], the dominant S% contribution of the two bonded C
ring
atoms
to their bcp density may be seen as surprising, given the delocalization of the
p
p
density in these conjugated rings. However, we did already show in Sect.
3.2.2
that
the effect of
-conjugation is visible through the SF approach, though it is clearly
dampened when analyzed by placing the rp in the nodal plane. In that case, only the
indirect effect of
p
-distribution becomes manifest, which is to
a good approximation the situation being analyzed in Fig.
12f
(the ring plane may
be roughly considered as a “nodal” plane since the metal-ring interaction is a small
perturbation with respect to the strong covalent interactions within the ring, as the
likeness with the SF pattern found for benzene would confirm). In order to get
further insight on the perturbing effect of the metal-ring interaction on the electron
distribution of the hydrocarbyl ring (and in particular that of “
p
-conjugation on the
s
-electrons”), we
suggest to compare the SF patterns when the rp is displaced above and below the
(C-C)
ring
bcp as we did for benzene. Differences in S% patterns when the rp is
closer or farther to the metal atom would allow to estimate the perturbation of the
p
p
-electron conjugation and distribution which is caused by the onset of the metal-
ring interaction.
Discussion in [
83
] is supplemented with the SF analysis of the theoretical
densities of a homologous series of 18-electron model compounds having the
formula (
n
C
n
H
n
)M(CO)
3
and varying ring sizes which range from
n
¼
3to
n
8)
along the first TM series. Also for these model compounds, an unpredictable
number of metal-C
ring
bond paths are observed, and fewer M-C bond paths than
expected from the formal hapticity are found, for ring sizes greater than four.
However, both delocalization indices and S% patterns agree in describing a similar
level of bonding for all M-C
ring
interactions, regardless of the presence or lack of a
corresponding bond path and in full compliance with the expected chemical picture.
The reader is addressed to the original paper for more details.
¼
8, according to the change of the metal from Co(
n
¼
3) down to Ti (
n
¼
