Chemistry Reference
In-Depth Information
Fig. 2 Eigenvalues
i
(
empty circles
) and the densities (
filled circles
) along the bond path in 4,
R
¼t
Bu, calculated at the B3PW91/6-311++G(d,p) level of theory with fixed experimental geom-
etry. At the BCP (origin of the coordinate system), the density is r(BCP)
¼
1
.
90 e/
˚
3
, the
Laplacian (
r
l
r(BCP))
¼
8
.
26 e/
˚
5
. The positions of the sulfur and nitrogen centers are at
2
0.52
˚
and 0.92
˚
, respectively
Similar values are found for all formal S
N double bonds of the present model
systems. For the S1-N1 bond in 1a (Table
2
), ratios around 1.2 were computed,
while for the S-C bond in 1a the ratios are about 1.1. These values are typical for
formal single S-N and S-C bonds showing that going from formal S
¼
N double
bonds to formal single bonds the BCP moves away from the sulfur center toward
the middle of the bonds. The consequence for the density and for its second
derivatives with respect to the coordinates can be taken from Fig.
2
in which the
density and the
¼
l
i
values are plotted along the S1-N1 bond path in compound 4
(R
¼
t
Bu). The data were calculated at the experimental geometry. For this formal
S
l
2
are almost
constant, while the eigenvalue l
3
varies strongly with the position of the BCP.
Thus, the BCP lies in the “rampant edge” of the Laplacian. A tiny displacement
of the BCP to the right changes the sign of the Laplacian, while a tiny displace-
ment to the left leads to a strong increase of its positive value. Consequently,
already the small variations in the position of the BCP discussed above lead to
large changes in the
¼
N double bond, the BCP is located in a region where
l
1
and
l
3
value and in the Laplacian. This explains the exceptional
results of the (2d,p) set. For the 6-31G(2d,p) and the 6-311G(2d,p), the
d
(N)/
d
(S)
values are somewhat smaller than for the basis sets with 1d or 3d polarization
functions. For formal single bonds, the variations of the
l
i
values along the bond
path are similar, but the BCP is located close to the middle of the bonds where
l
3
