Chemistry Reference
In-Depth Information
Fig. 6.4
Ring closure of
cis
-1
,
3
,
5-hexatriene to
cyclo
-hexadiene. In
C
2
v
symmetry there is a
symmetry mismatch between the
b
1
and
a
1
occupied orbitals. Vibronic orbital coupling requires a
concerted mechanism, based on a disrotatory ring closure, which conserves only the
σ
1
plane
ˆ
the
π
-bonds in the reagent, and the remaining
π
- and newly formed
σ
-bonds in the
product. As the diagram shows, in the common
C
2
v
point group there is a mismatch
between the symmetries. In order for the reaction to occur, the reaction coordinate
has to reduce the symmetry so that the
a
2
-orbital can interchange with an
a
1
-orbital.
This interchange is taking place via a PJT mechanism which couples the
a
2
occupied
orbital to an
a
1
virtual orbital in the reagent. As the reaction coordinate proceeds,
this coupling is intensified and leads to an interchange of both. The relevant matrix
element is thus an orbital vibronic coupling element:
a
2
a
1
H
∂Q
Γγ
∂
=
0
(6.86)
Hence, a distortion coordinate is required which transforms as
a
2
×
a
2
. The co-
ordinate with this symmetry is the one that destroys the symmetry planes but keeps
the twofold axis. This is typically a
conrotatory
reaction, where the extremal carbon
atoms rotate simultaneously in the same sense, to form the
σ
-bond. Ring closure of
substituted butadienes thus follows a conrotatory reaction stereochemistry, at least
if the reaction is concerted.
This ring-closure selection rule is further confirmed by the closure reaction for
the cis-1
,
3
,
5 hexatriene to 1
,
3-cyclohexadiene, as illustrated in Fig.
6.4
. Here, a
b
1
-
orbital has to interchange with a virtual orbital of
a
1
symmetry. The selection takes
thus place at the level of the orbital matrix element:
b
1
a
1
=
a
1
H
∂Q
Γγ
∂
=
0
(6.87)
Clearly, the distortion coordinate should now be of
b
1
×
b
1
symmetry, and
this corresponds to the
disrotatory
mode, which destroys the
C
2
axis but keeps the
vertical reflection plane.
a
1
=
