Chemistry Reference
In-Depth Information
changes slowly. As a consequence, the value of the Laplacian is much less
influenced by details of the calculations.
While some of the differences between theory and experiment will result from
uncertainties in the measurements, the data discussed may be interpreted such that
computations are yet not good enough to predict topological properties of the
density. Hence, we have to ask if theory is appropriate to investigate more detailed
influences such as those of the environment. The slow convergence with respect to
method and basis sets is found for absolute values of the Laplacian of the density.
However, for an investigation of environmental influences, accurate predictions of
trends are sufficient. The set of molecules investigated above is ideally suited to
explore the capability of theory in this respect. Figure
3
shows the correlation of
experimentally and theoretically determined bond distances as well as densities and
Laplacians at the BCP. Figure
4
gives the correlation between the densities and the
Laplacian at the BCP with the bond distances. Table
6
collects the corresponding
linear regression parameters.
As expected, theory and experiment correlate quite nicely for the distances and
also for the densities at the BCP (Fig.
3a, b
) a moderate correlation is found. The
best linear fit for the distances is
y
¼
1.20
x
0.29 with a sample correlation
coefficient of
R
2
0.98. Experimental and theoretical densities at the BCP can
be linearly fitted with the line
y
¼
¼
0.68
x
+ 0.98. In this case, the sample correlation
coefficient is
R
2
0.68. The S1-N1 single bond of compound 3 represents an
outlier in the correlation. No correlation is found between the experimental and the
theoretical Laplacians (Fig.
3c
).
Figure
4
shows that both the experimental and the theoretical densities at the
BCP correlate with the bond distances (Fig.
4a
). The linear fit for the experimental
data is
y
¼
3.12
x
+ 7.01 with a sample correlation coefficient of
R
2
¼
¼
0.75. For
the theoretical data, the best linear fit is given through
y
¼
2.14
x
+ 5.12 (sample
correlation coefficient
R
2
0.95). For the computed Laplacians, a similar but less
unambiguous correlation exists (
y
¼
94.09
x
+ 147.90;
R
2
¼
¼
0.86). Such a corre-
lation is not
found for
the experimental counterpart
(
y
¼
16.53
x
38.09;
R
2
¼
0.05). These data indicate that, at least for the given set of molecules,
computations are well suited to investigate correlations. As the present set of
molecules is a quite difficult example due to the polar character of the S-N
bonds, we expect that this finding can be generalized to other families of com-
pounds. Please note that these calculations were performed with basis sets of
moderate size [6-311(d,p)] and the B3LYP functional. This shows that correlations
of topological parameters of the ED among themselves and with bond distances do
not require very sophisticated theoretical approaches.
The investigation indicates that the correlations within the experimental data are
less clear. Taking again into account that the S-N bonds represent quite difficult
examples, this cannot be generalized to compounds with less polar bonds. The major
reason for the lack of correlations in the experimental data seems to be in this case
experimental error bars and uncertainties in the analysis of the experimental data.
Table
5
shows whether experimental geometries can be used for the computa-
tions. Although a good correlation between experimental and theoretical values can
