Chemistry Reference
In-Depth Information
The points associated with the attractors of nonnuclear basins [
23
,
24
], that is the
maxima of
r
(r) at positions other than nuclei, have also been used [
9
] as rp's so as
to explore whether the SF is able to distinguish between these peculiar maxima,
with anticipated highly delocalized character for their density sources, and those
associated with the nuclei, presumably characterized by very localized sources.
Gatti et al. [
9
] surveys the results obtained by applying such an analysis to a number
of alkali metal clusters exhibiting nonnuclear basins in their electron distribution.
Other rp's choices are clearly possible besides those listed, but a discriminating
point needs to be mentioned [
14
]. The relative accuracy by which
r
(r) is obtained
as a sum of atomic sources, (2), is given [
14
] by the quantity ER%(r)
rð
r
Þ
P
O
S
ð
r
; OÞ
ER
%ð
r
Þ¼
100
;
(14)
rð
r
Þ
which turns out to be usually less than 1% when
r
(r) is greater than 10
2
au, but
which may increase up to about 5% when
r
(r) is one order of magnitude lower. For
regions of very low density,
r
(r)
10
4
au, reconstruction of
r
(r) through (2) often
becomes problematic. The modulus of the sum of atomic sources
P
O
<
S
ð
r
; OÞ
hardly
becomes lower than 10
5
au, or, in some case, even than 10
4
au, which easily
explains why
ER
%(r) is rapidly increasing up to and above 100% for rp's with very
low density values. This accuracy problem clearly sets a minimum density value
constraint (
10
3
au) on the choice of possible rps. It has also been shown [
14
] that
the ability of reconstructing the density through (2) is strictly related to the
departure of the integrated atomic Laplacian magnitudes,
R
;
2
rð
O
r
r
Þ
dr
from
their required value of zero. For instance, in the isolated H atom, with an integrated
Laplacian magnitude less than 10
11
au,
r
(r) values as small as 10
10
au are found
to be reconstructed with ER% less than 10%, while for the H
2
molecule, with an
integrated Laplacian of about 10
5
au, ER% values become already noticeable for
r
(r) values as large as 10
4
au. More details on the problem of reconstructing the
electron density from atomic sources and on the numerical techniques which have
been devised to increase the overall reconstruction accuracy are discussed in [
14
].
3 The Source Function: Only a Mathematical Identity
or Also an Interesting Chemistry Descriptor?
This section enters into the realm of the source function applications to chemistry.
The main concern we had [
1
,
9
] since the first proposal of such a function in 1998
was to explore whether (2) was indeed able to provide chemical insight or whether
it represented just a mathematical identity for a
trivial
“tautological reconstruction
