Chemistry Reference
In-Depth Information
reported in Table
1
is much more than a simple falloff in the source contributions
with chain length increase. The value of the source function for each succeeding
increment is predetermined as it must equal the contribution of the hydrogen atom it
replaces.
In our second example [
9
], we examine the Li-
X
(
X
F, O, N, Cl, H) diatomics
where the Li atom is known to exhibit almost constant and transferable integral
properties, including its net charge and atomic energy, through the series [
6
,
28
].
Before introducing the SF view of transferability along this series, it is worth
remembering that the charge distributions of Li-H, Li-O, and Li-F were used
back in 1972 by Bader as the examples to “illustrate the all important observation
that the transferability of atom's density is accompanied by a paralleling transfer-
ability in its kinetic energy density” [
28
]. Indeed, the paralleling behavior of
r
(r)
and G(r) was the “crucial observation” that eventually led to the QTAIM [
6
], next
the demonstration [
29
] that the virial theorem not only holds for a system in its
entirety, but also applies to each of its regions of space bounded by a zero-flux
surface in
¼
rr
. Constancy of Li integral properties also serves as a simple example
of the most important observation at the basis of the concept of a functional group:
“that atoms or linked groupings can exhibit characteristics forms and properties in
spite of gross changes in their immediate neighbors” [
25
].
In the limit of perfect transferability of the Li basin electron distribution, the
source contribution from Li to the density at the bcp, S(r
b
,Li), should remain
constant, regardless of the nature of
X
and of the corresponding value of
r
b
[
9
].
Within the limit above, changes in the
r
b
value should only be determined by
corresponding changes in the source contribution from the
X
atom, S(r
b
,
X
). Table
1
shows, instead, that the S(r
b
,Li) value provides a more sensitive measure of
departure from perfect transferability of the Li basin than its integral properties.
S(r
b
,Li) is found to decrease with decreasing electronegativity through the series
and to become in LiH about half the value in LiF, the first member of the series. The
decrease in S(r
b
,Li) parallels the corresponding decrease in the
r
b
values, whereas
both the atomic electron population N(Li) and the energy E(Li) remain almost
unvaried through the series. Interestingly, an almost constant source percentage
contribution from Li at the bcp density, S%(r
b
,Li)
40%, is also observed
(Table
1
). The constancy in Li energy and net population through the series is
translated in the SF language in a constancy of the percentage share of the electron
density at the bcp, rather than in an unaffected SF contribution. The chemical
cationic nature of Li in the series thus implies a constant share of the bcp density
and not a constant
r
b
value, which also confirms how the information provided by
S(r
b
,
) may substantially differ in many cases, as anticipated earlier.
The source function is also able to reveal that a mechanism of compensatory
transferability operates within the Li basin to ensure constant integral properties.
These latter are preserved in the series (Table
1
) through a noticeable basin
expansion toward
X
with decreasing
X
's electronegativity. Figure
1
shows that
the S(r,Li) profiles along the Li-
X
axis for the various members of the series
coincide up to a distance from the Li nucleus almost equal to that of the closest
bcp to Li (LiF, R
Li
¼
O
) and S%(r
b
,
O
1.128 au) and then start to only slightly differ after this
