Chemistry Reference
In-Depth Information
As a first example, F&M examined, at the theoretical level, the case of the C
3v
borane carbonyl BH
3
CO, a simple model for carbonyl coordination to a strong
Lewis acid and, by extension, to transition metals. A comparison was made first
between the MO's decomposition of the B-C, C-O, and B-H bcp densities, and that
of the delocalization indices for these same pairs of atoms. By definition, the
electron density at a point r,
r
(r), equals S(r, all space), the SF contribution from
the whole space, with the rp taken at r. While it was noted that the two descriptors
d
(B,H) and S(bcp
B-H
, all space) have very similar overall MO contributions, this
was obviously not the case for the two bonds (C-O and B-C) whose bcp lies on the
symmetry axis and which have
p
-components. For instance, the major contributions
to
d
(C,O) come from an E pair of
p
-bonding MOs essentially localized around the
C-O bond, whereas these same orbitals, because of their symmetry, cannot clearly
contribute to
r
b
(C-O), and hence to S(bcp
C-O
, all space). When the MO's decom-
position is applied to the SF contributions from the atomic basins, a very similar
picture is obtained, since the E pair of
-bonding MOs localized around the C-O
bond yields again a negligible, though nonzero contribution, to
r
b
(C-O).
33
F&M
thus argue that, at variance with
d
(C,O), essentially “no information about the
extent of
p
-back donation is contained in the SF at r
b
(C-O)” [
12
].
This observation on C-O was then generalized by observing that “when the rp is
close to the nodal plane of an orbital, this orbital makes a low to negligible
contribution to the SF which has clear implications for the interpretation of
p
-bonding or
p
-
interactions” [
12
]. Of course, we agree with the indirect suggestion by F&M that
moving the rp out from the nodal plane enables such an orbital to enhance its
contribution to the SF, so providing insights on the
p
-bonding mechanisms, as we
demonstrated for benzene in Sect.
3.2.2
. However, while the F&M observation is
correct in a, let to say, “zero-order” approach (direct effect), it is no longer so if
higher-order, indirect effects are considered. Indeed, “essential to the orbital theory
of electronic structure is the property of self-consistency - that each orbital be
determined by its interaction with the average Coulomb and exchange potential
generated by electrons in the other occupied orbitals. Thus the density distributions
derived from
p
s
p
orbitals are not independent of one another” ([
6
]; p. 76) at any
point of the molecular space. The interdependence of
and
s
p
electron distributions
is a well-known, documented fact in the literature [
20
,
127
] and was already
exploited earlier in this chapter (Sect.
3.2.2
) when analyzing whether the SF
contributions may be affected in some way by
and
p
-electron conjugation when the rp
lies in the
-
orbital, this latter will be unable to provide a
direct
contribution to the density at
that point, but it will supply an
indirect
one through its interaction with the other
orbitals, including those of
p
-nodal plane. As said earlier, if a bcp lies in the nodal surface of a
p
-symmetry, able to contribute to the electron density at
bcp. A very simple
gedanken
example on the C
2
H
4
+
n
s
(
n
¼
0-4) series illustrates
33
It is the integration over the whole space that results in a null contribution to the
r
b
(C-O) density
from the
-bonding MOs. Separate integration over the atomic basins may yield non-zero values
(typically less than 1% of the |
p
r
b
| value) which are constrained to sum up to zero.
