Chemistry Reference
In-Depth Information
E
(18)(1'8')
(18)
(1'8')
1'
1'
1'
1'
1
1
1
1
Z-RR'
Z-SS'
E-SR'
E-RS'
(11')(88')(99')
1
1'
(18')(81')(99')
1
(11'88')(99')
(18'81')(99')
1
1
1'
1'
1'
Z-RR'
Z-SS'
E-SR'
E-RS'
E*
(18)(1'8')*
1
(18)*
(1'8')*
1
1
1
1'
1'
1'
1'
Z-RR'
E-RS'
E-SR'
Z-SS'
(11')(88')(99')*
(18')(81')(99')*
(11'88')(99')*
1'
(18'81')(99')*
1'
1'
1'
1
1
1
1
Z-SS'
Z-RR'
E-RS'
E-SR'
Fig. 22 Effect of the permutation-inversion operators on the
anti
-folded conformation a-
C
2h
(
y
)
Table 8 Effect of permutation-inversion operators on the
anti
-folded conformation a-
C
2h
(
y
)
Permutation-inversion operators Effect on the conformation a-
C
2h
(
y
)
E
, (11
0
)(88
0
)(99
0
), (18)(1
0
8
0
)*, (18
0
)(81
0
)(99
0
)* None
a
(18)(1
0
8
0
), (18
0
)(81
0
)(99
0
),
E
*, (11
0
)(88
0
)(99
0
)* Inversion of both moieties
(18), (11
0
88
0
)(99
0
), (1
0
8
0
)*, (18
0
81
0
)(99
0
)*
E
,
Z
-isomerization and inversion of first
moiety
(1
0
8
0
), (18
0
81
0
)(99
0
), (18)*, (11
0
88
0
)(99
0
)*
E
,
Z
-isomerization and inversion of second
moiety
a
E
, (11
0
)(88
0
)(99
0
), (18)(1
0
8
0
)*, (18
0
)(81
0
)(99
0
)* correspond to the point group symmetry operators,
E
,
C
2
(
y
),
˃
(
xz
), and
i
of a-
C
2h
(
y
), respectively
the symmetry operators of the conformation. Each of the cosets contains at least one
self-inverse operator. Thus all three dynamic processes are self-inverse and the
corresponding transition states may include the permutation-operators of the coset
as symmetry operators of their respective point groups [
271
].
In homomerous BAEs, the two tricyclic moieties are equivalent. Thus, the
processes (2) and (3), i.e.,
E
,
Z
-isomerization with inversion of either the first or
the second moiety, respectively, cannot be distinguished. They will be discussed
together as one dynamic process:
E
,
Z
-isomerization with inversion of one moiety.
Note that the combined mechanism has a connectivity of
C
2. Each conforma-
tion may be converted into two distinct versions by inverting either the first or the
second moiety.
¼
