Chemistry Reference
In-Depth Information
In this way, atomic regions yielding positive and negative contributions to
r
b
become clearly visible along the bond [
13
,
14
] and may be associated with the
corresponding regions of charge concentration and charge depletion as obtained
from the radial profile of
2
r
in the isolated atom [
6
]. Comparison of LS profiles
for the same system and for the same rp, but using electron densities coming from
different models, allows one to get a deeper understanding of the changes brought
in by the various adopted models into the description of bonding at the bcp [
13
-
15
].
Comparison of LS profiles may also disclose interesting differences in how the
electron density is determined at a bcp or at this same location when two atoms are
linked or not linked by a bond path. Examples of such an use of the LS profiles are
detailed in Sects.
3.4.2
and
4
, where the application of the SF tool to the study of
metal-metal bond and of the multipole bias in charge density investigations from
X-ray structure refinements is, respectively, discussed.
Analogously to the LS profile along a line, one may also investigate S(r,
r
O
)or
S%(r,
) along this same line [
13
,
14
](seeSects.
3.1
and
3.4.2
). The resulting
profile clearly bears a quite different interpretation, since in this case, at variance
with the LS profile, it is the rp that is changing along the line and not the LS
contributing point. The S(r,
O
) profiles thus give information on how
the total or percentage “contribution” from
O
)orS%(r,
O
to
r
(r) varies as a function of the
position of r along the line. If the line is a bond path linking
O
O
0
,the
O
and
O
0
. Participa-
tion from other atoms will also vary, with a generally larger importance in regions
around the bcp and far from either of the two linked nuclei. The relative small or
large weight of contributions from atoms other than
O
0
will generally increase on going from
“contribution” from
O
to
O
0
, in the region around
the bcp, may be respectively related to the high or low covalent character of the
interaction
O
or
O
0
.
Although only partly explored thus far [
3
,
16
], the SF tool may also be used to
define the extent to which a basin contributes to determine both its own electron
population N(
O
-
O
) and that of the remaining basins in the system. By integrating (2)
over
O
Z
Z
Z
X
; O
0
Þ
N
ðOÞ¼
rð
r
Þ
dr
¼
S
ð
r
; OÞ
dr
þ
S
ð
r
dr
¼
N
i
ðOÞþ
N
o
ðOÞ;
(11)
O
0
6¼O
O
O
O
or, analogously, (6)
Z
N
ðOÞ¼
rð
r
Þ
dr
O
8
<
9
=
Z
Z
I
2
rð
r
0
Þ
1
4
p
r
j
1
rð
d
r
0
þ
¼
dS
ð
r
S
Þr
j
r
r
S
r
S
Þ
d
r
:
r
j j
r
;
O
O
S
O
¼
N
i
ðOÞþ
N
o
ðOÞ;
(12)
