Chemistry Reference
In-Depth Information
hybrid functionals are used whereupon the results depend on the percentage of
exact exchange. Results obtained with gradient-corrected functionals show larger
deviations. Also, the influence of the flexibility of the AO basis sets used in the
computations was tested to some extent [
32
,
51
]. The observed basis set effects
were generally too small to explain the deviations between experimental results and
theory. However, in the recent work by Jayatilaka and Dittrich, it was found that the
differences between experiment and theory decrease if Slater-type basis functions
are used in the computations instead of Gaussian type [
55
]. In this context it is
important to mention that, with the exception of very small model systems, the
tested basis sets do not exceed triple-
quality although a sufficient number of
polarization functions is essential for convergence [
32
,
50
,
51
].
Besides the comparison of absolute numbers, an investigation of the correlations
between the topological parameters and the bonding type can also reveal important
information about the quality of the results. Such correlations are expected and are
used in many investigations [
3
,
4
,
6
,
38
,
56
]. One example is the position of the
BCP, which, as shown by Cremer and Kraka, correlates with the polarity of the
bond [
57
]. According to Bader's QTAIM approach, correlations are expected
between the density, its second derivative along the bond path (
z
l
3
), and the bond
ellipticity
, which is obtained from the second derivatives of the density perpen-
dicular to the bond paths (
e
can provide
information about the delocalization of electrons within a molecule [
39
,
52
].
Results which do not reveal the expected correlations are probably biased to
some extent. This is especially true if correlations are found for the less sensitive
parameters (e.g., density) but are missing for more sensitive ones (e.g., Laplacian values).
For the homoatomic C-C bonds of C
60
fullerene derivatives, Wagner et al. [
41
]
found the expected correlations between the density at the BCP and the bond
distances as well as between the Laplacian at the BCP and the bond distances.
This shows that high-resolution synchrotron diffraction experiments provide very
accurate densities of these nonpolar covalent bonds. However, whether this also
holds true for polar bonds is unclear.
Another uncertainty is caused by the environment. High resolution X-ray experi-
ments are nowadays feasible, but crystals of extremely high purity and quality are
required for accurate results. The surrounding of a single molecule in such a crystal
differs quite significantly from that in gas phase or within a liquid. One would
expect that the environment influences the charge density of the given molecule.
Thus, the question arises if densities measured in a crystal can be used to discuss
chemical reactivities in solvents, in vacuum or within a protein, e.g., an enzyme.
The latter surrounding is of particular importance for rational drug design whose
success strongly depends on an intimate knowledge of the interactions between
target and active compound [
58
-
62
]. According to the Hohenberg-Kohn theorem,
these interaction forces are also a function of the ED. High resolution X-ray
measurements of the EDs of the enzyme-inhibitor complexes would be an ideal
tool to study such interactions as a function of the substitution pattern of the ligands
[
17
-
19
,
63
,
64
]. However, high-resolution X-ray diffraction experiments are not yet
routine for such large complexes. According to the best of our knowledge, such
e
ΒΌ
l
1
/
l
2
1). The bond ellipticity
e
