Chemistry Reference
In-Depth Information
hydrogenation and Diels-Alder cycloaddition (4
2). Thus, it was possible to antic-
ipate when the reaction occurs thermally and when it would take place under light
action (Woodward and Hoffmann
1970
, pp. 8-28, 52-75).
In the Hückel approximation for ethene and butadiene the parametric schemes are
built (Streitwieser
1961
):
+
α
C
α
C
β
=
(11.38a)
α
C
β
α
α
C
β
α
C
C
β
=
−
=
(11.38b)
The homogenous equation systems and the normalization conditions for the two
molecules are the following:
c
1
+
c
2
=
1
(11.38c)
c
1
+
c
2
+
c
3
+
c
4
=
1
(11.38d)
Considering the abbreviation
α
−
ε
=
K
(11.39)
β
the Hückel secular determinants result as:
=
K1
1K
0
(11.40a)
K100
1 K10
01K1
001K
=
0
.
(11.40b)
Subsequent to their solving, the following equations are obtained. For ethene
K
2
0, and for butadiene K
4
3K
2
−
1
=
−
+
1
=
0, which, by grouping the terms, it
becomes (K
2
1)(K
2
) and the
coefficient sets of molecular orbitals for the two aliphatic hydrocarbons (Table
11.1
).
The values calculated for the energy of the highest occupied molecular orbital
−
K
−
+
K
−
1)
=
0. The K values lead to the energies (
ε
(
ε
LUMO
) are correlated
with the butadiene oxidizing character and reducing one, which is stronger that
that of ethene. The graphical and mathematical models of the molecular orbitals
corresponding to the calculated energies are shown in Fig.
11.1
.
The bondonic information for molecules of Table
11.1
is reported in Table
11.2
and graphically represented in Fig.
11.2
. It provides the specific behavior:
ε
HOMO
) and the energy of the lowest free molecular orbital (
