Chemistry Reference
In-Depth Information
this behavior. Although the
-orbitals do not contribute to the electron density at the
C-C bcp, removing electrons from them while keeping the geometry fixed and
allowing for self-consistency has a great effect on the contributions from the
p
-
orbitals. To compensate for the increasing positive charge and the concomitant lack
of occupied bonding
s
-ones are found to increase
their overall contribution at the bcp, hence to
r
b
, despite the total number of
electron in the system is being drastically decreased through the series. The increase
is relevant,
r
b
being 0.344 au for
n
p
-orbitals along the series, the
s
¼
0, rising to 0.361 and 0.381 au for
n
¼
1 and
2 and reaching 0.395 au for
n
¼
4 (DFT/B3LYP 6-311++G** level). All in all, the
p
p
contribution of
-bonding at points lying on the nodal surface may be
revealed to some extent by the SF through the effect the
-orbitals and
p
-orbitals have on the
values of the
s
-orbitals contributions at these points. The SF description for rps
lying on the nodal surface will be clearly unchanged whether an electron density
given in terms of MOs or an equivalent one, like for instance a numerical electron
density obtained from maximum entropy method for which
separation is
unavailable, is used. Both densities will contain those physical effects that are
translated into the
s
/
p
model using a MO formulation, and the SF will simply
reflect such effects, regardless a
s
-
p
decomposition may be actually realized or not.
The merit of the MO model and of the SF decomposition in terms of MOs is that
these approaches solicit and drive to explore rps other than the bcps and out from
the nodal plane(s), and then they offer a rationale for interpreting the resulting,
often significantly varied, atomic SF patterns (see, e.g., Sect.
3.2.2
). Hence,
although it is in principle false that “the SF taken at the C-O bcp cannot provide
any information about the extent of C-O
s
/
p
-bonding” [
12
], one may anticipate a
large enhancement of the effect of such bonding scheme on the atomic SF values
when the rp is moved out from the
p
-orbital nodal plane.
F&M also noted that, at variance from the localization indices, a substantial
contribution to the SF at the C-O bcp comes from the core electrons. Percentage
orbital contributions to
d
(C, O) from the three MO core orbitals is less than 1%,
whereas the MO core orbital 2, which is essentially the unhybrized 1
s
orbital of C,
yields the dominant source from C (19.0% out of a total of 39.8%) and a non-
negligible negative sink from O (
p
12.5% out of a total of 58.4%). According to
F&M, this “reinforces the idea that the
d
(
O
0
) is more closely reproducing the
concepts of electron sharing” [
12
]. While we clearly have no doubt that
d
(
O
,
O
0
) are
more intimately connected to electron sharing, we also believe that one should
never ask to a descriptor under exam, i.e., the SF in this case, to comply with what
one would expect to deduct from it, but rather focus on what it is actually observed.
As we will discuss below, the large source and sink arising from the core orbital
2 when this orbital is respectively integrated over the C and O atoms is a natural,
physical consequence of the large electronegativity difference of these two atoms
and of the consequent large shift of the C-O bcp position toward the more
electropositive C. The net charges of C and O in BH
3
CO amount to
O
,
þ
0.88 and
1.09 e
, respectively. The bcp lies so close to the
atomic
core-shell depletion
region of C that the C 1
s
core MO contribution to the bcp density from C will be
totally different from that found for standard, nonpolar C-C bonds in hydrocarbons.
