Cent. Eur. J. Chem. • 11(4) • 2013 • 527-534
DOI: 10.2478/s11532-012-0191-2
Central European Journal of Chemistry
Fullerenes patched by flowers
Research Article
Raluca Pop1, Mihai Medeleanu2, Mircea V. Diudea3*,
Beata Szefler4, Jerzy Cioslowski5
National Institute for Research and Development in Electrochemistry
and Condensed Matter, 300569 Timisoara, Romania
1
2
University “POLITEHNICA” of Timisoara, Faculty of Industrial Chemistry
and Environmental Engineering, 300006 Timisoara, Romania
3
Faculty of Chemistry and Chemical Engineering,
“Babes-Bolyai” University,400028 Cluj, Romania
4
Department of Physical Chemistry, Collegium Medicum,
Nicolaus Copernicus University, 85–950 Bydgoszcz, Poland
5
Institute of Physics, University of Szczecin,
70-451 Szczecin, Poland
Received 14 August 2012; Accepted 21 November 2012
Abstract: Stability measures, such as the total energy and the HOMO-LUMO gap, calculated at the Hartree-Fock and DFT levels of theory, and
the aromatic character of five circulenes/flowers with a hexagonal core and petals consisting of 5-, 6- and 7-membered rings are
investigated. Geometric (HOMA) and magnetic (NICS) criteria are used to estimate the local aromatic character of every ring of the
investigated circulenes. The local aromaticity of the coronene and sumanene patches in two tetrahedrally spanned fullerenes were
calculated and compared with the HOMA and NICS values of the corresponding isolated circulenes.
Keywords: ab initio • HOMA • NICS • Circulenes • Fullerene patches
© Versita Sp. z o.o.
1. Introduction
A circulene is a flower-type molecule comprising a core
and its surrounding petals that has the general formula
[n:(p1,p2)n/2], where n is the folding of the core polygon
and pi are the polygonal petals. For n<6, the molecule is
bowl-shaped, whereas for n>6 it is saddle-shaped [1-3].
The bowl-shaped circulenes are potentially useful in
the direct synthesis of fullerenes [4,5] while the saddleshaped circulenes could appear as patches in foamy
structures of spongy carbon [6,7]. The idea of increasing
aromaticity/stability of fullerenes tessellated by disjoint
circulenes/flowers originates in the classical texts of
Clar [8,9] that postulated disjoint benzenoid rings (i.e.,
rings having six π-electrons localized in double-simple
alternating bonds and separated from adjacent rings by
formal single bonds) as a criterion for the full aromatic
conjugation (i.e., double-simple bond alternation)
[10].
According to the VB theory, molecular structures
exhibiting such fully resonant sextets are expected to be
extremely stable [10-12]. Patterns larger than benzene,
e.g. naphthalene or azulene (i.e., a pair of pentagonheptagon carbon rings) have been investigated in the
context of the Clar’s theory of aromaticity. By extension
[13-16], circulene supra-faces (eventually called flowers)
may also be taken into consideration [1,2].
A set of disjoint faces, built up over all atoms of the
molecule, is called a perfect Clar PC structure (Fig. 1,
middle). Only in polyhex structures, (e.g. polyhex toroids)
where the empty/full assignment can be interchanged at
two adjacent hexagons, the PC structure consists of full
π-electron, disjoint hexagons, as originally suggested by
Clar. However, the PC structures in fullerenes include
* E-mail: [email protected]
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Fullerenes patched by flowers
Figure 1.
Patches in fullerenes: [5:65] JFw in C140 (left); PC in C180 (middle); [5:65] DFw in C240 (right).
Figure 2.
Circulenes: coronene [6:66] (left); isocoronene [6:(5,7)3] (middle); sumanene [6:(5,6)3] (right).
all the odd faces (e.g. pentagons), usually assigned
to empty π-electron faces. It has been demonstrated
[10] that fullerenes show a PC structure if and only if
they have a Fries structure, which is a Kekulé structure
having the maximum possible (i.e., v/3) number of
benzenoid faces. The associated Fries structure ensures
the total resonance (i.e., conjugation) of the molecule
[15].
A joint flower JFw covering, with circulenes of the type
[n:pn], can appear either in Platonic (a single flower-type)
or Archimedean (two flower-types) tessellations. The
case [5:65] of corannulene is unique and is encountered
in the fullerene C140 (Fig. 1, left). The case [6:66] of the
coronene flower is encountered in polyhex tori.
A disjoint flower DFw tessellation is a disjoint set
of flowers, covering all the vertices in the molecular
graph. Corannulene [5:65] as DFw can be seen in
fullerene C240 (Fig. 1, right). A variety of circulene
patches can be drawn by using sequences of map
operations. The reader is invited to consult some recent
articles in this respect [17,18]. Circulenes as patches in
fullerenes have been discussed in two previous papers
[13,19]. Several circulenes have been synthesized
[20-23].
In this article, several patches of interest to the
structure elucidation and/or direct synthesis of fullerenes
or ordered schwartzites were designed and their stability
was evaluated in terms of the total energy and the
HOMO-LUMO gap as well as in terms of the HOMA and
NICS indices of aromaticity.
2. Computational details
The geometries of the polycyclic hydrocarbon molecules
have been optimized at the HF/6-31G(d) and B3LYP/631G(d) level of theory (unless otherwise specified)
with the Gaussian 09 suite of programs [24]. The NICS
indices [25] were calculated (using the GIAO method
[26]) at the ring centers (NICS(0)) and at 1 Å above
and under the centers (NICS(+1), NICS(-1)). Also, the
magnetic susceptibilities were computed using the GIAO
method [26]. The HOMA indices [27-29] were computed
with the JSChem [30] program. The circulenes herein
considered are displayed in Figs. 2 and 3. The tabulated
data represent the averaged values for each type of
face/ring.
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3. Results and discussion
3.2. Evaluation of the local aromaticity
The stability of five circulenes: coronene [6:66],
isocoronene [6:(5,7)3], sumanene [6:(5,6)3], and two
corazulenes [4:(7(5c))4] and [4:(7(5d))4] were investigated
by means of their aromatic character. Geometric (HOMA
index) and magnetic (NICS index) criteria were used for
the quantification of the circulenes’ aromaticity.
3.1. Evaluation of the global stability
In order to evaluate the stability of the considered
polycyclic compounds, the HOMO-LUMO gap and
total energy per number of C atoms were computed
(Table 1). The HOMO-LUMO gap may be considered
as an approximation to the chemical hardness and an
indicator of the molecular kinetic stability.
Larger values of the HOMO-LUMO gap are found for
coronene and sumanene (about the italicized Δ-value
in Table 1) and suggest a higher stability of these two
experimentally known molecules.
Figure 3.
Table 1.
Corazulenes: [4:(7(5c))4] (left) and [4:(7(5d))4] (right).
In order to estimate local aromaticities of the circulenes
under study, the NICS(0) and NICS(1) indices were
computed for every ring of the polycyclic hydrocarbons.
Results of these calculations are displayed in Tables 2
to 6 and evaluated below.
For coronene, the NICS data show a pronounced
aromatic character of the outer benzenic rings and
lower aromatic or even non-aromatic character of the
core hexagon. These data support these ”radialene”structures of coronene, as depicted in Fig. 2, left. The
HOMA data also show an enhanced aromaticity on the
outer rings.
It should be noted that coronene itself is not a totally
resonant hydrocarbon [15,31] because every Kekulé
structure leaves some carbon atoms outside of the
sextet rings. However, Clar [9] proposed that if the three
sextets of coronene can migrate into the neighboring
rings, an extra ring current would emerge. The sextet
migration current can be taken as an argument in favor
of the enhanced aromaticity of coronene (compared to
some other polycyclic hydrocarbons, e.g. naphthalene
and anthracene) [31].
Computations of the NICS(0) index for [6:(5,7)3]
isocoronene (Fig. 2, middle) provide close values for
the central 6-membered and the 5-membered rings
of this polycyclic structure, the rather low negative
values indicating a low aromatic character (Table 3).
The NICS(0) positive values of the 7-membered rings
suggest a non-aromatic character. The NICS(1) index
is often employed as an indicator of the π-electron
delocalization; in the case of 6- and 5-membered rings
of isocoronene, it provides ”more negative” values. The
enhanced values are attributed by Fowler et al. [32] to
the electron flow through the outside perimeter of the
rings. On the other hand, the HOMA values show a
different trend compared to both of the NICS indices,
suggesting a more pronounced aromatic character of
the central benzenic ring (see also [33]).
The values of the NICS(0) and NICS(1) indices for
sumanene (Fig. 2, right) correspond to an anti-aromatic
character of the pentagons, a strong aromatic character
of the outer benzene rings and a lower aromatic character
The total energies Etot, total energy per number of C atoms Etot/C and the HOMO-LUMO gaps Δ computed at HF/6-31G(d) level of theory.
Compound
Symmetry
Etot (au)
Etot/C (au)
Δ (eV)
[6:66] coronene
D6h
-915.95
-38.164
8.96
[6:(5,7)3] isocoronene
Cs
-915.78
-38.156
7.26
[4:(7(5d))4] corazulene
C4h
-1220.92
-38.154
7.08
[4:(7(5c))4] corazulene
C2
-1067.12
-38.111
6.54
[6:(5,6)3] sumanene
Cs
-802.19
-38.200
10.16
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Fullerenes patched by flowers
Table 2.
The NICS(0), NICS(1) and HOMA values calculated for the
B3LYP/6-31G(d) optimized geometry of coronene.
Hexagon (R6)
NICS(0)
NICS(1)
HOMA
core
-0.0086
-4.4291
0.6175
petal
-10.4056
-12.4532
0.7642
Table 3.
The NICS(0), NICS(1) and HOMA values calculated for
the B3LYP/6-31G(d) optimized geometry of isocoronene
[6:(5,7)3].
[6:(5,7)3]
Isocoronene
NICS(0)
NICS(1)
HOMA
core R[6]
-2.9079
-5.1564
0.8667
R[7]
0.3939
-2.7121
0.0127
R[5]
-3.1364
-5.6367
-0.0359
Table 4.
The NICS(0), NICS(1) and HOMA values calculated for the
B3LYP/6-31G(d) optimized geometry of sumanene.
Sumanene
NICS(0)
NICS(1)
HOMA
-2.7673
-10.3850
0.7082
R[6]
-10.0800
-16.8915
0.9248
R[5]
3.1887
-5.1915
-1.9552
core R[6]
Table 5.
The NICS(0), NICS(1) and HOMA values calculated for
the B3LYP/6-31G(d) optimized geometry of corazulene
[4:(7(5c))4].
[4:(7(5c))4]
corazulene
NICS(0)
NICS(1)
HOMA
R[4]
40.4505
25.3565
0.1292
R[7]
18.1369
10.7074
-0.0674
R[5] (1)
14.9961
6.1012
-0.5894
R[5] (2)
2.6882
3.3758
0.3317
Table 6.
The NICS(0), NICS(1) and HOMA values calculated for
the B3LYP/6-31G(d) optimized geometry of corazulene
[4:(7(5d))4].
[4:(7(5d))4]
corazulene
NICS(0)
NICS(1)
HOMA
R[4]
14.2630
7.1198
-0.2704
R[7]
-1.0914
-3.0528
-0.1554
R[5]
-7.8498
-9.6176
-0.2705
of the core R[6] ring (Table 4). The HOMA data closely
parallel their NICS counterparts.
Both the NICS(0) and NICS(1) values obtained for
the [4:(7(5c))4] corazulene non-planar structure (Fig. 3,
left) show an anti-aromatic character for all the rings.
The differences between indices of the two classes
of 5-membered cycles may be due to the non-planar
geometry of the [4:(7(5c))4] corazulene. HOMA values
show a different trend (Table 5).
The data for [4:(7(5d))4] corazulene (Fig. 3,
right) demonstrate a strong aromatic character of
the 5-membered rings, low aromatic character of
7-membered rings and an anti-aromatic character of the
cyclobutadiene-like ring (Table 6). The HOMA values
exhibit a trend different from that of both NICS indices.
The coronene and sumanene patches can be inserted
into 3D-structures such as the tetrahedrally spanned
fullerenes depicted in Fig. 4. These structures can
be derived from the fullerene C84 and were named
Cor_T_84 and Sum_T_84, respectively (to remember
the coronene=Cor and sumamene=Sum are embedded
in the (open) Tetrahedron T, while the last number
counts the atoms in the structure); they can also
be considered as junctions of nanotubes [2]. Even
though there are many tessellations for the tetrahedral
nanotube junctions, we opted for these two patches, as
they also represent real molecules. The data for these
structures are compiled in Table 7, in comparison to
those for Buckminster C60 fullerene. One can see that
the two tetrahedral structures show a pertinent stability,
when compared to that of the reference fullerene, with
Sum_T_84 being particularly stable.
The NICS(0) values in the Cor_T_84 species
(Fig. 4, left) are in good agreement with those in the
free coronene molecule (Table 2), differing only in the
slightly increased aromaticity of the core ring and the
splitting of the unique (averaged) values for the outer
hexagonal ring into two values; one larger for the free
(quasi plane) hexagons and one lower for the bound
hexagons (denoted R6,plane and R6,bound respectively, in
Table 8). The DFT data show (in general) the same trend,
with evenly increased negative values of NICS indices.
This description is in agreement with a radialene-type
structure of coronene (Fig. 2, left), with a low population
of π-electrons on the core hexagon.
The index NICS(+1) refers to the “inside” while
NICS(-1) refers to the “outside” of spanned tetrahedral
fullerenes. The NICS(+1) show negative values larger
than those provided by NICS(-1), indicating a higher
conjugation of π-electrons inside the structure.
Also, the NICS(+1) values suggest the bound
hexagons R6,bound being more aromatic than the core
hexagon (in the opposite to the NICS(-1) data).
The HOMA values calculated for the Cor_T_84
species exhibit the same trend as the NICS(-1) values,
namely the highest aromaticity of the free hexagons
R6,plane, followed by the R6,Core and finally the bound
hexagons. The HOMA index permits the calculation for
the coronene patch covering Cor_T_84 as well as for
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Figure 4.
The tetrahedrally spanned fullerenes patched by coronene (Cor_T_84, left) and sumanene (Sum_T_84, right).
Table 7. The total energies Etot, total energy per number of C atoms Etot/C and the HOMO-LUMO gaps Δ of the tetrahedrally spanned fullerenes
based on coronene and sumanene, respectively and the reference C60 fullerene.
Structure
Level of theory
Etot (au)
Etot/C (au)
Δ (eV)
Cor_T_84
HF/6-31G(d,p)
-3194.384
-33.275
7.347
Sum_T_84
HF/6-31G(d,p)
-3155.466
-38.028
7.562
C60
HF/6-31G(d,p)
-2271.830
-37.864
7.418
Cor_T_84
B3LYP/6-31G(d,p)
-3215.331
-35.333
2.268
Sum_T_84
B3LYP/6-31G(d,p)
-3214.968
-38.273
2.520
C60
B3LYP/6-31G(d,p)
-2286.174
-38.103
2.760
the whole molecule (Table 8). However, these values
are meaningless when ordering the molecules by their
aromaticity is attempted.
In the Sum_T_84 structure (Fig. 4, right), all the
NICS values exhibit the highest aromaticity of the outer
R6 rings in comparison to the core hexagon (see also
Table 4). The pentagons appear rather anti-aromatic by
NICS(-1) values but still aromatic by NICS(+1) values,
(with lower values in comparison to the core hexagon).
The NICS description is in agreement with a triphenylene
picture of the sumanene patch.
In case of HF-data, the HOMA values follow the
trend of NICS(0) and NICS(-1) values, while in the DFToptimized structure, the trend of HOMA values were
different from that of NICS indices.
The extent of strain, as given by POAV1 theory
[34,35], varies among the rings. It has the greatest
value for the bound-hexagons in Cor_T_84 and for the
core hexagon and pentagons in Sum_T_84, but these
values are even lower than those for the C60 fullerene
(8.256 kcal mol-1) because the present structures are
“opened fullerenes”. The extent of strain for the patch
and the whole molecule are again irrelevant.
Since the NICS and HOMA calculations indicated
the presence of some antiaromatic substructures,
we found necessary to recalculate the basic flowers:
coronene, isocoronene and sumanene, both in singlet
and multiplet states (Table 9).
There were no important differences in HOMO-LUMO
(Δ) gap values between the alpha and beta orbitals of
the triplet states (in italics) of coronene and isocoronene
molecules, as the conjugacy of the pi-electron was not
deeply affected.
The sumanene triradical should be non-planar.
Planarization induces in-plane symmetry breaking; as
a consequence, the sumanene gap value presented
in Table 1 is overestimated. The differences in HOMOLUMO gap of the alpha and beta orbitals, in the higher
multiplicity state, clearly indicates a lower conjugasy
(and a lower aromaticity) for the sumanene structure.
As a substructure of Sum_T_84, the sumanene patch
appears to be stabilized in comparison to the free
molecule (compare the data in Tables 7 and 9).
In addition to the evaluation of the local aromatic
character, the exaltation of the magnetic susceptibility
–as a measure of pi-electron delocalization- has
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Table 8. Aromaticities (in terms of the HOMA and NICS indices) of the coronene and sumanene patches in the tetrahedrally spanned fullerenes,
optimized at HF/6-31G(d,p) and B3LYP/ 6-31(d,p) levels of theory, respectively.
Structure
Substructure
HOMA
POAV1 (kcal mol-1)
NICS(+1)
NICS(0)
NICS(-1)
Cor_T_84
HF
B3LYP
R6,Core
0.525
0.387
-5.258
-0.789
-5.257
R6,plane
0.908
0.709
-16.429
-11.928
-11.342
R6,bound
0.047
2.699
-13.533
-4.5178
-1.812
patch
0.374
2.053
molecule
0.348
1.477
R6,Core
0.529
0.474
-9.184
-1.749
-2.808
R6,plane
0.804
0.765
-16.555
-12.123
-11.443
R6,bound
0.162
2.543
-14.554
-5.532
-2.259
patch
0.422
1.938
molecule
0.392
1.435
R6,Core
0.849
2.488
-11.775
-2.313
-2.078
R6
0.896
1.169
-16.264
-11.349
-9.801
R5
-1.685
2.357
-7.314
1.773
2.203
Sum_T_84
HF
B3LYP
patch
-0.548
1.684
molecule
-0.476
1.685
R6Core
0.889
3.158
-11.807
-2.437
-1.798
R6
0.850
1.408
-16.177
-11.067
-9.047
R5
-1.162
2.568
-7.006
2.779
2.117
patch
-0.296
1.832
molecule
-0.229
1.833
Table 9. The total energies Etot, total energy per number of C atoms Etot/C and the HOMO-LUMO gaps Δ computed at HF and DFT levels of theory
(see text), for the singlet and multiplet states.
Structure
HF; Etot (au)
HF; Etot/C au) HF; Δ (eV) DFT; Etot (au)
DFT; Etot/C (au)
DFT; Δ (eV)
[6:66]coronene
-915.640
-38.151
8.956
-922.071
-38.420
4.026
Coronene_3
-915.531
-38.147
6.401
-921.966
-38.415
1.156
6.619
1.144
[6:(5,7)3] isocoronene
-915.427
-38.143
7.032
-921.909
-38.413
1.933
Isocoronene_3
-915.416
-38.142
6.598
-921.878
-25.608
1.073
-805.640
-38.364
1.619
-805.588
-38.361
7.151
[6:(5,6)3] sumanene_2
-800.033
-38.097
[6:(5,6)3] sumanene_4
-
-
8.378
1.061
8.347
-
2.838
3.520
1.408
been computed. According to the theory [38,39],
the aromatic systems will show negative values of
the magnetic susceptibility exaltation, while positive
Λ values are attributed to antiaromatic compounds.
The results are given in Table 10, along with the
computed isotropic (χiso) and anisotropic (χaniso)
magnetic susceptibilities [40] according to the equations
below:
The exaltation of the magnetic susceptibility in
coronene may be compared to the existing literature
data: -117 ppm (HF/6-31G*, CSGT method) [40],
-103 ppm (experimental value) [41]. The computation
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Table 10. Calculated isotropic (χiso), anisotropic (χiso) and exaltation (Λ) of magnetic susceptibilities (B3LYP/6-31G(d), [ppm cgs]).
Structure
[6:66] coronene
χiso
χaniso
Λ (*1)
Λ (*2)
-260.2
222.1
-127.3
-120.4
[6:(5,7)3] isocoronene
-174.2
90.1
-41.4
-34.4
[4:(7(5d))4] corazulene
-243.3
139.8
-66.2
-56.9
-8.3
-187.5
145.0
151.7
-176.9
77.3
-60.4
-52.3
[4:(7(5c))4] corazulene
[6:(5,6)3] sumanene
(*1)The magnetic susceptibility exaltation (Λ) is calculated as the difference between the computed magnetic susceptibility (at B3LYP/6-31G(d) level of
theory) and the susceptibility derived from an additive scheme of increments (Λ = χ – χcalc) [36,37].
(*2) Λ is estimated as the change in the magnetic susceptibility of a hypothetical reaction that implies the corresponding circulene, butadiene and
ethylene (see the supporting information).
of Λ based on the hypothetical reaction appears
to be more appropriate than the variant based on
increments. The exaltation of magnetic susceptibility
of [6:(5,7)3] isocoronene is a little higher than the value
of -64.9 ppm, reported by Ciesielski [32] (obtained at
HF/6311G** level, CSGT method), so our results lead
to a greater difference between the aromatic character
of coronene and isocoronene. The only circulene that
shows positive value of Λ and, therefore, a strong
antiaromatic character is [4:(7(5c))4] corazulene; the
results seem to agree the NICS and HOMA computations
(see Table 5).
hydrocarbons in question (or their corresponding
patches) were quantified with the magnetic and
geometric criteria, namely the NICS and HOMA indices.
The properties of the coronene and sumanene patches
in two tetrahedrally spanned fullerenes (i.e., nanotube
junctions) were calculated and compared to those in
the isolated circulenes. The evaluation of aromatic
character may be helpful in explaining various aspects
related to the stability/reactivity of these molecules. The
data presented herein suggested the coronene and
sumanene patched tetrahedral structures as potential
candidates for laboratory synthesis.
4. Conclusions
Acknowledgements
Stability of five different circulenes were evaluated
according to their total energy and the HOMO-LUMO gap
values, computed on optimized structures at HF and DFT
levels of theory. The local aromaticities of the polycyclic
The work was supported in part by the Romanian
CNCSIS-UEFISCSU project PN-II IDEI 129/2010 and
in part by the Computational grant no. 133, PCSS
(Poznań, Poland).
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