Chemistry Reference
In-Depth Information
On the whole, the population analysis based on the SF appears promising, but it
is to be considered in its infancy as for a general application. At present, we are
unable to say whether it is just conceptually relevant or also practically feasible. As
discussed in Sect.
2.2
, it would represent a unique, unambiguous tool for comparing
populations derived from experimental and theoretical densities.
6 Orbital and Core-Valence Decompositions of the Atomic
SF Contributions
In a very recent paper [
12
], entitled
On the Interpretation of the Source Function
,
Farrugia and Macchi critically analyzed the “chemical” information present in the
SF in several case studies. In the following, we concisely illustrate their adopted
approach and review some of the results obtained along with the main conclusions
which were drawn from such study. We also discuss a number of issues that in our
opinion would deserve a different interpretation and propose alternative, possibly
more apt ways for partitioning the atomic SF.
Farrugia and Macchi (F&M) were essentially aimed at verifying “whether the SF
in fact carries information comparable with other well-established decomposition
schemes that relate, more or less straightforwardly, to commonly accepted chemical
concepts,” in particular the electron delocalization. A quantitative and physically
sound measure of the latter is provided by the delocalization indices, which yields
the average fractional number of electron pairs shared between two atomic basins,
as discussed repeatedly in this review. As no formal relationship exists between the
SF and the delocalization indices [
14
], F&M proposed to test it inductively by
comparing these two indicators in terms of corresponding composing contributions.
Namely, in the case of electron densities derived from DFT calculations, they
examined how the SF and the
d
(
O
0
) decompose in terms of the canonical valence
and core Kohn-Sham MOs, or also in terms of the individual MOs.
32
For the
“synthetic” or experimental densities, given in terms of complex static X-ray
structure factors, delocalization indices are generally unavailable, unless using
the wavefunction constrained method [
100
] or, in principle, one of the proposed
forms of density matrix refinements ([
126
] and references therein). A core/valence
decomposition of the SF, formally analogous to that performed on DFT densities, is
anyhow possible. F&M used the XD2006 program suite [
59
] and the Hansen-
Coppens multipole formalism [
10
] to obtain and decompose the aspherical electron
density of each atom in terms of a spherical core and of an aspherical (spherical
O
,
þ
deformation) valence density, from which the corresponding contributions to the
atomic SF were calculated.
32
A similar SF decomposition, in terms of
MOs, was reported earlier in this chapter,
(Sect.
3.2.2
), when discussing whether the SF may in some way reflect
s
and
p
p
-electron conjugation.
