Chemistry Reference
In-Depth Information
E
(18)(1'8')
(18)
(1'8')
1'
1'
1'
1'
1
1
1
1
Z-SR'
E-SS'
E-RR'
Z-RS'
(11')(88')(99')
(18')(81')(99')
(11'88')(99')
(18'81')(99')
1
1'
1
1
1'
1
1'
1'
Z-RS'
E-RR'
E-SS'
Z-SR'
E*
(18)(1'8')*
1
1'
(18)*
(1'8')*
1
1'
1
1
1'
1'
Z-RS'
E-RR'
E-SS'
Z-SR'
(11')(88')(99')*
(18')(81')(99')*
(11'88')(99')*
(18'81')(99')*
1'
1'
1'
1'
1
1
1
1
Z-RS'
Z-SR'
E-SS'
E-RR'
Fig. 26 Effect of the permutation-inversion operators on the
syn
-folded conformation s-
C
2v
(
x
)
Table 12 Effect of permutation-inversion operators on the
syn
-folded conformation s-
C
2v
(
x
)
Permutation-inversion operators Effect on the conformation s-
C
2v
(
x
)
E
, (18
0
)(81
0
)(99
0
), (18)(1
0
8
0
)*, (11
0
)(88
0
)(99
0
)* None
a
(18)(1
0
8
0
), (11
0
)(88
0
)(99
0
),
E
*, (18
0
)(81
0
)(99
0
)* Inversion of both moieties
(18), (18
0
81
0
)(99
0
), (1
0
8
0
)*, (11
0
88
0
)(99
0
)*
E
,
Z
-Isomerization and inversion of first
moiety
(1
0
8
0
), (11
0
88
0
)(99
0
), (18)*, (18
0
81
0
)(99
0
)*
E
,
Z
-Isomerization and inversion of second
moiety
a
E
, (18
0
)(81
0
)(99
0
), (18)(1
0
8
0
)*, (11
0
)(88
0
)(99
0
)* correspond to the point group symmetry operators,
i.e.,
E
,
C
2
(
x
),
˃
(
xz
), and
˃
(
xy
)ofs-
C
2v
(
x
), respectively
as well as operators interchanging reactant and product. The symmetry operators of
s-
C
2v
(
x
) are:
E
, (18
0
)(81
0
)(99
0
), (18)(1
0
8
0
)*, and (11
0
)(88
0
)(99
0
)*. The permutation-
inversion operators (18)(1
0
8
0
), (11
0
)(88
0
)(99
0
),
E*
, and (18
0
)(81
0
)(99
0
)* result in
conformational inversion. Both sets combined correspond to the point group
D
2h
,
which is the highest possible point group for the transition state. All subgroups are
also valid possibilities. The groups of permutation-inversion operators, transition
state conformations including their point groups, the order of the point group
h
TS
,
number of versions
n
TS
, connectivity
C
, number of parallel pathways,
p
, the point
group of transient structures along the pathways, and the symmetry species of the
transition vector are listed in Table
13
.
The conformation with highest point group order, which, according to the above
symmetry considerations, may be a transition state, is p-
D
2h
. The order of the point
group is
h
TS
¼
8. There are two versions of this conformation, p
Z
and p
E
. The
connectivity (
C
¼
1), the number of pathways (
p
¼
1), and the mechanism are
schematically shown in Fig.
27
.
