Chemistry Reference
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and its integration over a basin
O
Z
r
0
Þ
dr
0
;
S
ð
r
; OÞ¼
LS
ð
r
;
(9)
O
were introduced and termed, respectively,
Local Source
(LS) function and
(integrated)
Source Function
(SF) for the electron density at r. They express the
contribution in determining
r
(r) of a local source at r
0
or of the sum of this source at
all points within
, respectively.
A standard use of the SF approach [
1
,
9
,
14
] involves the evaluation of the SF
contribution of an atomic basin or of a convenient union of atomic basins (e.g., a
chemical group) in determining the density at r, chosen as a reference point (rp).
Typically, the bcp is used as the least biased choice for the point representative of a
bonding interaction. Analogously to the calculation of the atomic population N(
O
),
integration of the LS is usually performed using nucleus-centered spherical coordi-
nates. Therefore, the SF contribution from a given group of atoms is conveniently
performed [
1
,
9
,
14
] by summing up the individual S(r,
O
) contributions of the
various atoms composing the group, rather than by a direct integration over the
basin of the whole group.
The SF values, S(r,
O
), are often reported [
9
,
14
] in terms of their percentage
contribution to the electron density at r,
O
S
ð
; OÞ
rð
r
Þ
r
%ð
; OÞ¼
:
S
r
100
(10)
) quantities have a quite distinct
meaning. For instance, in the case the rp corresponds to a bcp, S(r,
It is worth noting that the S(r,
O
) and S% (r,
O
) is strictly
related both to the nature and strength of the associated interaction, as conveyed
by the electron density at bcp,
r
b
, and by the relative “contribution” from
O
O
to
r
b
.
On the other hand, S%(r,
to
r
b
, and it
is therefore in principle independent on how strong or weak the interaction is.
S(r,
O
) just expresses the percentage share from
O
) being, respectively, very close
to and even larger than 100%
5
or definitely much less than so. As we will show
S%(r,
O
) may be very small or large, despite S%(r,
O
) reflects the localized vs. delocalized character of a given chemical inter-
action, with the two bonded atoms having large S%(r,
O
) values when the interaction
is localized and quite small when highly delocalized. Both quantities, S(r,
O
O
)and
S%(r,
), will be used and analyzed in the examples discussed in the next sections.
With respect to its integral forms, the local SF brings further detail. The LS
is currently analyzed [
13
] by evaluating its profile along a line and using a con-
venient point as rp. When the line is a bond path, the bcp is usually taken as the rp.
O
5
Negative S(r,
) may thus be negative, which implies that
the percentage contributions from other atoms may occasionally become greater than 100.
O
) values are not uncommon and S%(r,
O
