Chemistry Reference
In-Depth Information
path criterion [
60
], but they are not necessarily so when continuous descriptors of
bonding, like the delocalization indices or other tools discussed below, are used.
13
Within interacting quantum atoms (IQA) theory [
90
], for instance, this dichot-
omy may be interpreted [
8
] as a delicate case of exchange energy competition,
where a bond path is found to link which of the two alternative atom pairs, M-M or
M-L, has a dominant interatomic exchange energy; the existence of a possibly
notable electron sharing and covalent interaction also between the “nonbonded”
pair of atoms is not denied within this approach, but, rather precisely defined and
quantitatively evaluated [
8
].
The domain-averaged Fermi hole (DAFH) analysis [
91
-
93
] is another very
useful interpretive tool adopted in this area. When applied to the highly debated
case of the triply bridged Fe
2
(CO)
9
coordination complex, where the 18-electron
rule would predict a direct Fe-Fe bond, the DAFH approach rather than this direct
M-M interaction suggests the existence of a multicenter 3c-2e character of the
bonding of the bridging ligands [
60
,
65
]. This view nicely fits with the nonnegli-
gible electron sharing found between the two metal atoms, despite the absence of a
direct Fe-Fe bond, since the existence of nonvanishing delocalization indices
between all pair of atoms has been proved to be a necessary requirement for the
presence of 3c-2e bonding in any A-B-C fragment [
94
].
The ELF approach [
54
,
55
], instead, distinguishes among different bonding
schemes by assigning a synaptic order to each of the recovered ELF valence basins
and by finding the number and type of core basins with which they have a boundary
[
95
,
96
]. For instance, disynaptic valence basins are associated with conventional
two-center bonds and trisynaptic basins with 3c-2e bonds. Electron populations of
such ELF valence basins then denote their hierarchical importance.
Another tool, able to overcome the problems inherent to the possibly discontin-
uous description of bonding provided by the electron density topology and the bond
path criterion, is clearly the SF. Although lacking the very important physical
meanings associated with either the delocalization indices or the IQA, DAFH,
and ELF analyses, the SF has the great advantage of not requiring the pair density
(or at least the first density matrix if single determinant theoretical approaches are
used) for its application and for being so, as repeatedly mentioned in this review,
immediately applicable to both experimental and theoretical electron densities.
This is an important mark since until recently the most decisive features of the
experimental studies of bonding in organometallics were often derived from com-
plementary theoretical calculations - a situation that clearly raises the question of
whether it is indeed worth performing the more time-consuming experimental
determinations for such systems [
14
].
13
It is worth noting that there is nothing wrong nor contradictory in the QTAIM description of
these bonds; simply, different though complementary views emerge when, using such theory,
information from the position space, where bond paths are made manifest, is combined with that
derived from the six-dimensional pair density space, where electron sharing among atomic basins
and electron localization within atomic basins take place and compete between themselves.
