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is that this population analysis would be definitely much faster and easy to calculate,
but it also has significant drawbacks respect to that based on the source function.
First, the atomic boundaries and the apportioning among atoms of the density within
them would be biased by the independent atom model (IAM) [
10
] approach, which
is arbitrary and also not unique. Second, the so-defined atoms would not be quantum
objects. Third the HS space partitioning is not necessarily exhaustive, which would
imply the existence of basins - the voids of usual HS studies [
18
] - not associated
with any nucleus. In any case, the analogy between these two populations would be
only formal since the one making use of HS surfaces and the stockolder recipe is
defined, as usual, in terms of direct contributions to the density, while that based on
the double integration of the local source, in terms of contributions
determining
the
density. Preliminary results and numerical difficulties and problems using (11)-(13)
are reported in Sect.
5.1
.
2.3 Which Other Reference Points, Beyond the Bond
Critical Points?
Before concluding this general introduction to the LS and the SF, it is worth
spending few words on the choice of the more relevant reference points when
using these functions. Needless to say this problem does not come up when the LS
is used in its double integrated form.
As discussed above, both the LS and the SF often use bcps as reference points,
but clearly any reasonable choice may be exploited and proved to be useful. The
case of the SF profile along a bond path has already been introduced earlier. Among
the many other possible and convenient choices, we mention (a) the positions of
maximum local charge concentrations or depletions [
6
], so as to explore in an
atomic-wise detail how their Laplacian values are affected by chemical substitu-
tion, and (b) the points along a line perpendicular to the bond path and directed
above and below the molecular
s
-plane in a
p
-conjugated system. This latter option
p
is expected to provide information on how
-conjugation is mirrored by the SF.
s
p
In fact, even though
- and
-distributions are well known to be self-consistently
interrelated [
6
,
20
],
orbitals do not yield
direct
contributions to the electron
density in the molecular
p
-plane for those systems where symmetry allows for a
complete
s
and
p
separation. Hence, one anticipates an increase in the S%
contribution from atoms other than the two linked by a bond path when the relative
contribution from
s
-orbitals to the total density rises on moving out from the
molecular plane. An example of such behavior is shown in Sect.
3.2.2
.
As we discussed in [
21
], in reply to a question by Professor Bultinck, use of the
ring critical points (rcp) [
6
] in aromatic systems as rp's could reveal different S%
(rcp,
p
) contributions from the various atoms in the ring and so provide a measure of
departure, if any, from the perfect atomic symmetry necessarily present in benzene.
Such a departure, although not yet extensively analyzed, might be used to define an
alternative (local) index of benzenoid character [
22
].
O
