Chemistry Reference
In-Depth Information
2 The Accuracy of Theoretical and Experimental Electron
Densities
In the next chapter, we will report on theoretical investigations of environmental
influences on electron densities. This is only meaningful if the computed electron
densities are sufficiently reliable. Thus, in the present chapter we review studies that
considered the dependency of absolute values and trends on the theoretical level used.
As mentioned before, previous works showed that experimental and theoretical
EDs of nonpolar bonds are in excellent agreement. However, less agreement was
found for polar bonds. As an example, theoretical and experimental EDs of a set of
molecules containing S-N bonds of varying polarity were investigated [
17
,
50
]. The
set consisted of methyl(diimido)-sulfinic acid H(NR)
2
SMe (1), methylene-
bis
(trii-
mido)sulfonic acid H
2
C{S(NR)
2
H(NR)}
2
(2), sulfurdiimide S(NR)
2
(3), and sulfur-
triimide S(NR)
3
(4). With R
t
Bu, the influence of substituents
on the computed densities was investigated. The molecular solid-state structures
are given in Fig.
1
. In the solid-state structure, the methyl(diimido)sulfinic acid
emerges as dimeric unit. To test the influence of the dimerization, a monomeric
form of 1 was also computed (1a). Similar considerations lead to the investigation
of a quasi-monomeric form of 2, where one methylene-(triimido)sulfonic acid
moiety was replaced by a methyl group. This molecule is termed 2a. Gas phase
structures of the model compounds were optimized for different substituents R
¼
H, R
¼
Me, and R
¼
¼
H,
R
t
Bu, respectively, using a great variety of theoretical methods.
Frequency calculations were performed to ensure that the optimized structures
represent stationary points. All calculations were performed with the Gaussian98
package [
85
].
Tables
1
-
4
show computed bond topological properties of some typical bonds of
the present set of model systems as a function of the method and basis set. The
S1
¼
Me, and R
¼
¼
N2 bond of compound 1a (R
¼
Me, Table
1
) was chosen as an example for a
formal S
N double bond, while the S1-N1 bond of the same compound was chosen
as a formal S-N single bond (Table
2
). As a typical example for S-C and N-C
bonds to a methyl (or butyl) group, the bond topological properties of the S-C bond
of compound 1a (R
¼
Me, Table
3
) were investigated. Table
4
shows the bond
topological properties of the formal S1-N1 bond of compound 3 (R
¼
¼
H), which
represents another formal S
N double bond, as a function of the basis set. The
tables contain the computed bond distance of the given bond, denoted as
d
, the
density,
¼
r
, at the BCP, the value of the Laplacian of the ED at the BCP denoted as
2
r
r
, and the eigenvalues of the Hessian of the density at the BCP,
l
1
,
l
2
, and
l
3
.In
accordance with the usual notation,
l
2
indicate the values associated to the
two Hessian eigenvectors that are perpendicular to the bond path direction at BCP,
while
l
1
and
l
3
denotes the curvature value along the bond axis. Note that the Laplacian
2
r
2
r
is identical to the sum of these eigenvalues
r
r
¼
l
1
+
l
2
+
l
3
. Furthermore,
the tables contain the ellipticity
1, and the distances of the BCP to
atom A,
d
(A), and to the other atom,
d
(B), as well as the ratios
d
(A)/
d
(B) and
l
jj
l
3
e
¼
l
1
/
l
2
=
. The latter is expected to be smaller than one in ionic bonds [
9
].
