Chemistry Reference
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overlap population between atoms A and B [
124
]. Due to their definition, it is
natural to make a formal association between these quantities and the
corresponding elements of the matrix
M
defined through the SF approach.
Figure
14a
shows that the interchanged population (ICP)
M
(
X
,H) +
M
(H,
X
)
increases with increasing covalency along the series. It so reaches a maximum of
about 1.7 e
at
X
¼
C and then monotonically decreases to about 0.8 e
at
X
¼
¼
F.
Note that the curve is not symmetric with respect to
X
C, the central member of
the series, because, at variance with Li-H, the H-F molecule retains a significant
covalent character (compare the Laplacian distributions in Fig.
3
).
The
M
matrix defined through the SF approach is not symmetric and therefore
the two curves
M
(
X
,H) and
M
(H,
X
) differ between each other with the contribution
from
X
to the population of H exceeding that of H to
X
, except for LiH. It is pleasing
that the external contributions to the population follow a similar trend, both
increasing/decreasing with covalency increase/decrease through the series. Inspec-
tion of Fig.
3
easily explains why the two external contributions need to be
generally different. Using their expression given by the surface term in (12), one
observes that both contributions are evaluated on the same X
¼
H interatomic surface
and using the same electron density on this surface. However, the two contributions
do not simply and necessarily differ in sign as would naively suggest the opposite
direction of their normals to the surface, but differ in value because the electron
density on the surface is weighted by a term involving the gradient of the scalar
1/
j
. This term reflects both the size and shape of the basin being integrated
which are in turn related also to the convex or concave nature of the interatomic
surface (IAS). Concave shapes are typical of anionic-like atomic basins, whereas
convex ones characterize those of cations. The contribution of one atom to the
population of an atom bonded to it and the magnitude of such contribution relative
to the corresponding one from the linked atom is therefore deeply related to the
nature of the associated bonding interaction. Contrary to what observed for other
members of the series, the H-basin in LiH is largely anionic, exhibits a clearly
concave IAS, and thus found to contribute more to the Li population than Li does to
that of the H atom.
Figure
14b
compares the trend of the ICP values with those of the formally
associated overlap Mulliken's populations [
M
(
X
,H)
j
r - r
s
j
M
(H,
X
)]
M
. It is gratifying
that the former values appear quite more realistic. They exhibit much larger and
chemically reasonable values in general, and with comparatively larger values for
the shared interactions than for the ionic ones. The Mulliken's overlap populations,
instead, show not only a quite erratic behavior but also an unrealistic larger overlap
for ionic than for shared interactions. Figure
14c, d
compares the self-population
contributions in the two population schemes. The
M
(H,H) values decrease with
increasing
X
electronegativity and show a clearly sharper decrease in the central
part of the graph where the nature of the H changes from anionic to cationic,
whereas the
M
(H,H)
M
values exhibit an unexpected peak for
X
þ
B before decreas-
ing with increasing electronegativity of
X
. The
M
(
X
,
X
)
M
values, instead, show the
expected monotonic increase with increasing
Z
, analogously to the
M
(
X
,
X
) values.
¼
