Chemistry Reference
In-Depth Information
Table 8.6
Energetic data (DFTB level of theory) for the C
60
oligomers
Structure
C atoms
E
tot
(au)
E
tot
/C
Gap(eV)
−
−
C
60
60
102.185
1.703
1.930
C
60
P2J5_115
115
−
195.708
−
1.702
2.044
C
60
P2J6_114
114
−
194.183
−
1.703
1.444
C
60
P3J555_165
165
−
280.787
−
1.702
0.608
C
60
P3J556_164
164
−
281.658
−
1.717
0.333
C
60
P3_J566_163
163
−
280.238
−
1.719
0.391
C
60
P3J666_162
163
−
278.935
−
1.722
1.481
HypHex_165_330
330
−
567.506
−
1.710
0.179
HypHex_162_324
324
−
557.737
−
1.721
1.255
−
−
Le(Cor(C
20
))_165_1560
1560
2652.462
1.700
0.021
Cor(C
60
)_162_1512
1512
−
2603.270
−
1.722
1.095
Next, among the four trimers (Fig.
8.6
, middle and bottom) the most sta-
ble (see the total energy per carbon atom and gap values in Table x.5) appears
to be C
60
P3J666_162. The two highly distorted trimers (C
60
P3J556_164 and
C
60
P3J566_163) are less stable and further will not be considered.
The “J555” trimer C
60
P3J555_165 shows a lower gap probably because no Kekulé
structure can be written. This could be not an argument since the “J5”-dimer also
does not admit a Kekulé structure. At higher structures (see Fig.
8.6
) the Kekulé
structures are possible for the both J-type polymers and the J6-type joining appear
the most stable. Is no matter which one of the oligomers will be formed, the hyper-
graphene has a good chance to exist as areal structure. Note the hyper-graphene
Le(Cor(C
20
))_165_1560 was designed by applying the leapfrog
Le
map operation
(Diudea et al.
2006
) on the coronene-like structure made from the C
20
smallest
fullerene.
Comparative computations we made on small structures (see Table
8.7
). One can
see that, in general, the ordering in the three approaches is preserved, of course
with some exceptions. The main drawback of DFTB is the underestimation of the
gap values in case of
sp
2
carbon-only structures (see Table
8.7
). However, DFTB is
useful in ordering series of rather large carbon nanostructures.
8.4
Omega Polynomial in Nanostructures
Let
G
(
V, E
) be a connected bipartite graph, with the vertex set
V
(
G
) and edge set
E
(
G
). Two edges
e
=
(
x, y
) and
f
=
(
u, v
)of
G
are
codistant
(briefly:
ecof)
if
=
+
=
+
=
d
(
x
,
v
)
d
(
x
,
u
)
1
d
(
y
,
v
)
1
d
(
y
,
u
)
