Chemistry Reference
In-Depth Information
delocalization. One argues that such an increased S% contribution should become
even more evident when analyzed using reference points for which the effect of
p
-
electron conjugation takes place directly through
p
-electron distribution, rather than
indirectly through
electron interdependency. Table
4
indeed shows that the S%
contributions to the C-C bond bcp density from the neighboring C atoms increase
dramatically in benzene when the rp is moved along a line perpendicular to the
bond path and directed above (or below) the molecular plane. The S% contribution
from the nearest neighbor C atoms increases from 5.3% to 8.9% at 1 au above the
molecular plane and becomes as large as 24.3% at 2 au above such plane. Contri-
bution from the next-nearest neighbor C atoms is smaller, but also largely increases
with increasing distance from the molecular plane, reaching a value of about 10% at
2 au above the plane.
Note that this ability of the SF to reflect
p
-electron conjugation is totally
independent from a
s
-
p
separation of the electron density since the SF tool
has been applied to the total density. Were this separation not realizable, the same
results shown in the Table
4
could have been obtained by analyzing an equivalent
density distribution, albeit expressed in a completely different form, e.g., numeri-
cally or in terms of multipole model pseudoatom contributions. This observation is
of great importance in view of the possibility to recover and quantify electron
conjugation effects both when using electron densities derived experimentally
(hence without
s
and
p
separation being allowed) and when a departure from
perfect symmetry would inhibit anyhow a proper separation of
s
and
p
electron
contributions. Such a use of the SF has not yet been explored in detail despite it
appears to be very promising. Clearly the same would hold true for more complicate
situations, like in organometallics, where a mixing of
s
and
p
s
,
p
, and
d
contributions can
be envisaged for some bonds.
Since we deal here with densities derived from a molecular orbital approach, the
separate, though interrelated,
contributions to the source function values
can also be precisely quantified. These are listed in Table
4
, in the second-row entry
for each of the considered distances from the molecular plane. The
s
and
p
%
contributions from two bonded C atoms to the density at their bcp in benzene are
shown to significantly decrease and, respectively, increase with distance from the
molecular plane, as anticipated from the different relative weight of the associated
electron distributions with such a distance. The corresponding SF contributions
from the nearest neighbor C atoms show that the observed five times increase of
their percentage total contribution to the density, on passing from the C-C bcp on
the molecular plane (5.3%) to a point 2.0 au above this plane (24.3%) is the result of
a less than a two times increase (from 3.4 to 5.8%) in the
s
% and
p
s
% contribution and of a
dominant ten times increase in the
% contribution (from 1.9 to 18.5%). It is thus
this latter contribution which leads to an increasingly importance of the nearest
neighbor C atoms in determining the electron density of the benzene C-C bond
when the rp for this bond is moved above or below the molecular plane. Note that
the contributions from the nearest neighbor H atoms follow an opposite trend.
Although their total S% contribution also increases with increasing distance from
the molecular plane, the observed enhancement is the result of a seven time increase
p
