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Figure 1
The Decalin Skeleton
⊗ ⊗
/ \ / \
/ \ / \
⊗ ⊗ ⊗
| | |
| | |
⊗ ⊗ ⊗
\ / \ /
\ / \ /
⊗ ⊗
------------------------------------------------------------
Figure 2
Three of the 10! numberings of
the Decalin Skeleton.
2 4 7 1 4 2
/ \ / \ / \ / \ / \ / \
/ \ / \ / \ / \ / \ / \
1 3 5 2 8 9 5 3 1
| | | | | | | | |
| | | | | | | | |
10 8 6 3 4 5 6 8 10
\ / \ / \ / \ / \ / \ /
\ / \ / \ / \ / \ / \ /
9 7 6 10 7 9
(2a) (2b) (2c)
------------------------------------------------------------
Figure 3.
Partially labelled graphs reduce
the equivalencies.
2 4 9 7 4 2
/ \ / \ / \ / \ / \ / \
/ \ / \ / \ / \ / \ / \
N1 3 5N N10 8 6N N 3 1N
| | | | | | | | |
| | | | | | | | |
10 8 6 1 3 5 6 8 10
\ / \ / \ / \ / \ / \ /
\ / \ / \ / \ / \ / \ /
9 7 2 4 7 9
(3a) (3b) (3c)
----------------------------------------------------------
Figure 5,9,Orbits in the Decalin Skeleton
⊗ ⊗
/ \ / \
/ \ / \
+ & +
| | |
| | |
+ & +
\ / \ /
\ / \ /
⊗ ⊗
-------------------------------------------------------------
Figure 6
Three Labellings of Decalin with
1 N and 9 C's.
⊗ ⊗ N ⊗ ⊗ ⊗
/ \ / \ / \ / \ / \ / \
/ \ / \ / \ / \ / \ / \
N ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ N ⊗
| | | | | | | | |
| | | | | | | | |
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
\ / \ / \ / \ / \ / \ /
\ / \ / \ / \ / \ / \ /
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
-------------------------------------------------------------
Figure 7
Labellings with 1 N, 1 S, and 8 C's.
A B C
⊗ ⊗ ⊗ ⊗
/ \ / \ / \ / \
N ⊗ ⊗ N ⊗ ⊗
7a1 | | | 7a1a | | |
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
\ / \ / \ / \ /
⊗ ⊗ ⊗ ⊗
N ⊗ N ⊗
/ \ / \ / \ / \
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
7a2 | | | 7a2 | | | this diagram
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ is not complete
\ / \ / \ / \ /
⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗
/ \ / \ / \ / \
⊗ N ⊗ ⊗ N ⊗
7a3 | | | 7a3 | | |
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
\ / \ / \ / \ /
⊗ ⊗ ⊗ ⊗
-------------------------------------------------------------
Figure 8
1 N to orbit {1,5,6,10}
⊗ ⊗
/ \ / \
/ \ / \
N ⊗ ⊗
| | |
| | |
⊗ ⊗ ⊗
\ / \ /
\ / \ /
⊗ ⊗
------------------------------------------------------------
Figure 9
Second step of case 5
N ⊗ ⊗ N
/ \ / \ / \ / \
N ⊗ ⊗ N ⊗ ⊗
9a | | | 9b | | |
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
\ / \ / \ / \ /
⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗
/ \ / \ / \ / \
N ⊗ ⊗ N ⊗ ⊗
9c | | | 9d | | |
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
\ / \ / \ / \ /
⊗ N N ⊗
------------------------------------------------------------
FIGURE 11
C↓6N↓6O↓4S↓4 The pot of atoms
Taking combinations of
6 atoms
e.g. C↓4S↓2 76 combinations possible
65 are valid for D.A. Rings
Labelling Step
C C C C 4 Rings generated
/ \ / \ / \ / \ from the example
C S C C C S C C C4S2
| | | | | | | |
C S C S C C C C
\ / \ / \ / \ /
C S S S
A total of 1176 rings generated from all the
65 combinations of 6 atoms taken from C6N6O4S4
------------------------------------------------------------
1 =C,C,O,O.
/ \
C 2
" |
C 3 (Fig. 12)
\ /
4
Group is i,r, where
(1 2 3 4) = i
(4 3 2 1) = r
orbits A1 = (1 4)
A2 = (2 3)
Case Assignment to orbit A1 Remaining Labels
1 C C S S
2 C S C S
3 S S C C
Case 1 C,C --> (1 4)
then S,S --> (2 3) 1 Labelling
(C S S C)
Case 2 C,S --> (1 4)
C --> 1
S --> 4
reduced group is i
C,S --> 2 3 2 labellings
C --> 2 & S --> 3 (C C S S)
S --> 2 & C --> 3 (C S C S)
Case 3 S,S --> (1 4) 1 labelling
then C,C --> (2 3) (S C C S)
Total of 4 possible labellings.
-----------------------------------------------------------
1
Octahedral
Skeletal 6 2
Framework
5 3
4
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