Chemistry Reference
In-Depth Information
becomes evident that presently the ED, being a formal observable, is hardly
measured but reconstructed namely by fitting sophisticated theoretical models
to the experimental data, exploiting previous chemical-empirical wisdom [
6
,
30
].
To make this clear in the following, we will talk about “experimentally derived
densities” rather than “experimental densities.” In principle, experimentally
determined electron densities could be used to analyze the shortcomings of theoret-
ical approaches, which, because of the complexity of the systems, use certain
approximations in particular with respect to electron correlation and relativistic
effects.
However, experimental electron densities can only be used to benchmark theo-
retical ones if they are only insignificantly biased by the procedures that are used to
analyze the measured quantities (i.e., angles and intensity distributions of Bragg
reflections). Indeed, various recent studies indicate that such a bias is introduced by
the Hansen-Coppens multipole formalism [
6
,
30
], which is most frequently used to
derive EDs from experimental diffraction data [
31
-
33
]. However, more sophisti-
cated approaches are also biased to some extent [
34
-
36
]. This seems to happen
because the basis sets used to describe the ED distribution are not flexible enough to
reflect details of electron densities in polar bonds. This appears to be at least partly
the reason for the differences found between experimentally and theoretically
determined topological properties of the ED at the bond critical points (BCPs)
which occur in particular at polar bonds, where the densities and Laplacian dis-
tributions are strongly different between the bond partners [
21
-
25
,
27
,
37
-
39
]. For
nonpolar bonds, experimentally and theoretically derived bond topological values
are in excellent agreement [
40
,
41
]. In most cases, experiment and theory provide
qualitatively the same results, for example, with respect to the number of BCPs or
the number of valence-shell charge concentrations (VSCCs) [
42
]. However, there
are many cases, for instance, in transition metal complexes or for weak interactions,
where the real situation is near a catastrophe point between different topologies,
different bond paths, and different numbers of BCPs. In such cases, slightly
different experimental or theoretical approaches yield qualitatively different
QTAIM-results [
6
,
43
,
44
]. A bias of experimental electron densities can also be
introduced if two or more parameter sets of the multipole model are of similar
quality in residual density and statistical quality. Such a nonuniqueness was
demonstrated, e.g., by Peres et al. [
45
]. Using experimentally derived densities
for the validation of theoretical densities is also problematic because the experi-
mental uncertainties - typically 0.1 e/
˚
3
for EDs and 4-5 e/
˚
5
for Laplacians
[
17
-
19
,
46
-
49
] - are often of the same magnitude as the differences. Frequently,
the computed EDs give even more reasonable trends than the measured ones [
50
].
However, the disagreement between experiment and theory could also point to
shortcomings in the theoretical description. The Hartree-Fock approach for
instance is well known for overestimating the polar character of chemical bonds.
Thus, only if correlation effects are taken into account reliable densities can be
calculated [
51
-
53
]. The MP2 approach, however, already predicts topological
parameters in close agreement with even more sophisticated approaches such as
MP4 or QCISD [
32
,
54
]. Similar densities are also obtained with DFT approaches if
