Chemistry Reference
In-Depth Information
Indeed, F&M found that in acetamide the C-C bcp density is clearly dominated by
the valence density, with core contributions lower than 1%. The bcp in C-O lies at
0.39
˚
from the C nucleus and, as mentioned above, within the
atomic K
shell
(core) depletion region of C which ends at about 0.43
˚
from the C nucleus,
whereas for a less polarized bond the bcp is normally located at a much larger
distance from the C nucleus (0.6-0.75
˚
in hydrocarbons) and well inside the
region of the
atomic
VSCC of carbon. The SF from C and the large magnitude of
the core “contribution” to the SF from C takes precisely into account this differ-
ence. When integrated over the O basin, the core orbital 2 yields instead a negative
source at bcp because this basin may only include that outer part of the C 1
s
MO
where the associated Laplacian is positive.
34
The “odd” contributions from the C 1s
MO should therefore not be taken as a “problem” of the SF, but rather as a very
interesting property of this approach. The SF demonstrates to be capable of
discriminating the way a given atom determines the density at its various bcps as
a function of the relative electronegativity of the atoms to which it is bonded.
In particular, one should never forget that the SF yields two, usually different,
values for the density contribution of two bonded atoms
O
0
at their intervening
bcp, while the number of shared pair of electrons between these atoms is repre-
sented by just a single
d
(
O
-
O
0
) value. On top of not being physically related among
them in a direct way, delocalization indices and SF values need to differ in given
circumstances. For instance, the latter are by nature able to distinguish whether two
bonded atoms are playing similar or quite distinct roles in their bonding interaction.
F&M properly recognize that, while useful for relating the SF to chemical
concepts expressed in a MO framework model, the decomposition of an observable
like
r
in terms of molecular orbitals is arbitrary and subject to the particular choice
of MO settings (canonical, localized, etc). As an obvious consequence, the SF
decomposition in terms of MOs is arbitrary as well. Because of this, F&M propose
to examine the decomposition of the atomic SF into core and valence contributions,
as another, potentially more useful, approach. In the case of BH
3
CO, which is
characterized by largely polar bonds, the core densities provide important contribu-
tions from individual basins toward the total SF, but for other two investigated
systems (acetamide and thiocumarin), including second and third period atoms and
generally much less polar interactions, the valence density was found to provide the
determining contributions, as for the delocalization indices. The only notable
exception was for the polarized C-O and C-S bonds, which further confirms the
interpretation given earlier for the core contributions in borane carbonyl. For
heavier elements such as the iron atom in Fe(CO)
5
, the core density plays a
significant role, if a large [Ar] core description is used for such a density. Indeed
the [Ar] core density provides a source from iron which amounts to about 40/49%
of the Fe-C bcp density, whereas the valence part acts as a moderate sink,
O
,
34
The large negative source obtained at the bcp density when the C 1
s
MO is integrated over the O
basin demonstrates that such orbital cannot be longer safely identified as a C 1
s
MO in a molecular
context. This is just an example of the limits of the MO model interpretation.
