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Table 8.4 Energetic data (DFTB) for some C 20 -based hyper-graphenes HG (reference C 60 H 60 )
C 20 _hyper-graphene
C atoms
E tot (au)
E tot /C (au)
Gap (eV)
C 20 HG_11_90H 60
i.e. (C 20 ) 6 _90H 60
90
178.393
1.982
8.992
C 20 HG_22_252H 136
252
487.798
1.936
8.447
C 20 HG_44_780H 360
780
1487.55
1.907
8.191
C 20 HGCor_621_384H 192
384
737.736
1.921
8.307
C 20 HGCor_631_882H 396
882
1678.02
1.903
8.155
C 60 H 60
60
125.584
2.093
10.412
Table 8.5 Energetic data (DFTB) for some small fullerenes and hyper-cycles
C 20 _hyper-graphene
C atoms
E tot (au)
E tot /C (au)
Gap (eV)
102.185
1.703
C 60
60
1.930
C 20
20
33.429
1.671
0.731
C 24
24
40.142
1.673
1.667
C 28
28
47.101
1.682
0.351
(C 24 ) 5 _90
90
152.998
1.700
1.634
(C 20 C 28 ) 3 _114
114
192.488
1.688
0.166
(C 20 ) 5 _75H 50
75
146.956
1.959
9.969
(C 24 ) 5 _90H 60
90
175.282
1.948
9.103
(C 28 ) 5 _110H 80
110
220.185
2.002
9.270
178.393
1.982
(C 20 ) 6 _90H 60
90
8.992
(C 20 C 28 ) 3 _114H 84
114
226.346
1.985
10.278
C 60 H 60
60
125.584
2.093
10.412
C 20 H 20
20
41.659
2.083
12.295
C 24 H 24
24
49.752
2.073
12.247
C 28 H 28
28
58.301
2.082
12.384
cyclo-adducts but this is just the beginning of a more complex process that in-
volves the coalescence of quasi-spherical units of C 60 to form oligomers and finally
a polymer (see Figs. 8.6 and 8.7 ); Table 8.6 supports this idea.
Let us detail the structures participating to such a process. Two dimers with
joint face for C 60 units can be designed (Fig. 8.6 , top): C 60 P2J5_115 (J5 meaning a
pentagon identification) and C 60 P2J6_114 (J6 representing a hexagon identification).
These two dimers have the total energy per C atoms comparable to C 60 ; the HOMO-
LUMO gap of “J5”- dimer is larger than that of “J6”-dimer (even “J5” dimer has no
Kekulé structures).
 
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