Chemistry Reference
In-Depth Information
As the local source contributions (positive or negative, as a function of the local
Laplacian value) have a
j jÞ
1
dependence [
84
], the largest positive and
negative contributions to a selected point in the ED should arise from the atoms
in the near vicinity and should decrease with larger distances. However, taken
separately they possess well-known slow convergence. If they are considered
together, a more rapid convergence of atomic SF values with distance from the rp
is obtained because of the vanishing of the integrated Laplacian within an atomic
basin. Indeed, for very large distances of a basin from the reference point r, the
importance of the different local weighting of Laplacian values with
r
0
ð
r
jÞ
1
r
0
ð
j
r
j jÞ
1
with 1/r which results, in this
limiting case, in a null SF contribution (since 1/r may be taken out from the integral
and, by definition, the integral of the Laplacian over a QTAIM basin is zero). To test
the actual decay, we analyzed the topological parameters of the terminal C-H and
C-C bond for the series of hydrocarbons ranging from methane to decane. All
structures were chosen in an almost linear zigzag conformation and fully optimized
at the B3LYP/TZVP level of theory. The resulting EDs were analyzed for critical
points according to the QTAIM theory, and selected BCPs were chosen for the
source function analysis. These BCPs were those of a terminal C-H bond and the
C-C bond between a terminal methyl group and the adjacent CH
2
unit (see Fig.
18
).
The results are summarized in Tables
18a
and
19a
. The computations showed
that the value of the ED at the BCP of the terminal C-H bond BCP
A
are almost
constant at 1.86 e/
˚
3
throughout the complete series. A similar behavior can be found
for BCP
B
at the terminal C-C bond for which the EDs are found to be 1.64 e/
˚
3
.
The source function analysis shows that for both critical points, the major contribu-
tions to the ED arise from the two atoms forming the corresponding bond. Never-
theless, about 12% of the contributions to BCP
A
and 23% of those to BCP
B
come
from the remaining atoms. As expected and especially so for covalently bonded
atoms, the contribution of an atom to the ED decreases rapidly with its distance to
the considered BCP. Already the contributions of atoms further than two bonds
away from the BCP are almost negligible.
ð
r
0
decreases and at the limit one may replace
r
Fig. 18 Structure of the decane molecule and the two bond critical points, one along the terminal
C-H bond BCP
A
, the other along the bond between the terminal methyl group and the next atom
BCP
B
