Chemistry Reference
In-Depth Information
Table 8.18
Omega polynomial in the C
60
-based hypergraphene: F[6]
Omega(C
60
J6HG); F[6]: Formulas
=
(54
k
2
+
96
k
−
·
x
3
+
(18
k
2
+
12
k
−
·
x
4
1
(
C
60
J
6
HG
);
F
[6]
6)
12)
(1)
234
k
2
2
=
e
(
G
)
=
+
336
k
−
66
3
CI
(
G
)
=
54756
k
4
+
157248
k
3
+
81234
k
2
−
45408
k
+
4602
144
k
2
4
v
(C
60
J
6
HG
)
=
+
216
k
−
36
5
Hyp
[6]
=
k
2
F
[3]
=
R
[3]
=
2(
k
2
6
−
1)
36
k
2
7
R
[5]
=
F
[5]
=
+
48
k
−
12
F
[6]
=
54
k
2
8
+
76
k
−
16
3
k
2
9
No(C
60
)
=
(
F
[5])
/
12
=
+
4
k
−
1
Table 8.19
Examples, Omega polynomial in C
60
-based hyper-graphene: F[6]
k
Omega(C
60
J6HG); F[6]
CI
Atoms
Bonds
F[3]
F[5]
F[6]
144
x
3
+18
x
4
1
252,432
330
510
0
72
114
2
402
x
3
+84
x
4
2,372,802
1000
1570
6
228
352
768
x
3
+ 186
x
4
3
9,280,416
1970
3110
16
456
698
4
1242
x
3
+ 324
x
4
25,204,122
3240
5130
30
756
1152
8.6
Conclusions
In this chapter we presented two allotropes of the diamond D
5
: the dense
“anti”-diamond and the “syn”/quasi-diamond, which can form five-fold symme-
try quasi-crystals. Some substructures of these allotropes are proposed as possible
intermediates in the synthesis of hyper-graphenes and their energetics evaluated at
Hartree-Fock, DFT (B3LYP) and DFTB levels of theory. A topological description
of D
5
_anti network and derived hyper-graphenes, in terms of the net parameter and
Omega polynomial, was also given.
Acknowledgements
MVD acknowledges the financial support offered by project PN-II-ID-
PCE-2011-3-0346. BSZ acknowledges the Grant no. 133 of PCSS (Poznan, Poland). Thanks are
addressed to Professor Davide Proserpio, Universita degli Studi di Milano, Italy, for crystallographic
data.
References
Adams GB, O'Keeffe M, Demkov AA, Sankey OF, Huang Y-M (1994) Wide-band-gap Si in open
fourfold-coordinated clathrate structures. Phys Rev B 49(12):8048-8053
Aradi B, Hourahine B, Frauenheim T (2007) DFTB
+
, a sparse matrix-based implementation of
the DFTB method. J Phys Chem A 111:5678-5684
Benedek G, Colombo L (1996) Hollow diamonds from fullerenes. Mater Sci Forum 232:247-274
