Fullerene Dimers Connected through C_{24} and C_{36} Bridge Cages

Bulletin of the Korean Chemical Society.
2014.
Apr,
35(4):
1005-1010

- Received : September 07, 2013
- Accepted : December 05, 2013
- Published : April 20, 2014

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We have performed DFT calculations to devise some possible fullerene dimers (from C
_{ 60}
and C
_{80}
) connected through C
_{24}
and C
_{36}
bridge cages with the face-to-face linking model. The fullerene dimers with C
_{36}
bridges have lower binding energies and greater HOMO-LUMO gaps than those of the fullerene dimers with C
_{24}
bridges. Also, the replacement of C
_{60}
cages with C
_{80}
ones always leads to an increase in binding energies and HOMO-LUMO gaps in these systems. Dimerization of C
_{60}
and C
_{80}
fullerenes with C
_{24}
and C
_{36}
results in a significant decrease in antiaromaticity of the antiaromatic cages C
_{24}
and C
_{80}
, and an increase in the aromaticity of the aromatic cages C
_{36}
and C
_{60}
. Therefore, DFT results indicate that those fullerene dimers involving the initially harshly antiaromatic C
_{24}
or C
_{80}
cages are more energetically favorable configuration than the fullerene dimers involving the aromatic C
_{36}
and C
_{60}
cages.
_{60}
),
^{1}
and other smaller and larger fullerenes would lead to the synthesis of a large number of fullerene derivatives whose properties and applications have been extensively investigated from many viewpoints.
^{1-5}
One of the unique aspects of fullerenes in this field is the formation of interfullerene bondings, which makes a rich variety of nanoscale network structures such as dimers, oligomers, and one- and two-dimensional fullerene polymeric materials
^{6-11}
In general, it has been suggested that interaction between two fullerene cages can arise through one of the four possible approaches: C-C bond between C
_{60}
cages forming a [1+1] dimer (point-point mode); C=C bond forming a [2+2] dimer (side-side mode); forming a [5+5] dimer by face-face mode between two pentagons; and forming a [6+6] dimer by faceface mode between two hexagons.
^{12}
In recent years, more attention has been paid to fullerene dimers because their unique physical and chemical properties provide intriguing possibilities as model compounds for nano- and polymer science, and offer potential access to novel molecular electronic devices.
^{13,14}
In this respect, a series of fullerene dimers have been produced, such as C
_{120}
,
^{15}
the carbon-bridged dimers: C
_{121}
,
^{16-19}
C
_{140}
, C
_{131}
,
^{20}
and C
_{122}
,
^{15,19,21}
and the heteroatom bridged dimer: C
_{120}
O,
^{22-24}
which could be used as the basic units of fullerene chain structures. The simplest fullerene dimer C
_{120}
, (C
_{60}
)
_{2}
, has been prepared by solid-state
^{25}
and by chemical methods. On the other hand, Osterodt and Vogtle,
^{26}
Fabre
et al.
,
^{27}
and Dragoe
et al.
^{28}
isolated the C
_{122}
consisting of C
_{60}
fullerenes joined by a (C=C) bridge with
sp
^{2}
-hybridized C atoms which are added across C
_{60 }
bonds shared by two hexagons (hexagon-hexagon bonds). Forman
et al.
^{29}
reported the first experimental synthesis and characterization of five [2+2] structural isomers of fullerene dimers C
_{140.}
The C
_{131}
is the first hybrid type of the dumbbell-like fullerene dimer that consists of two different sizes of cages, C
_{60 }
and C
_{70}
, with a central atom-bridge.
^{20}
Its formation, structure and properties may be more complicated and interesting than those of C
_{121}
or C
_{141.}
^{16-20 }
Shvartsburg
et al.
^{30}
used the chain of C2 units to design dimers of original fullerenes (C
_{60}
or C
_{70}
). Finally, Manaa,
^{31}
and Anafcheh and Ghafouri
^{32}
proposed carbon and BN hexagons (benzene-like unit) as a building block for connecting between two C
_{60}
fullerene cages in order to yield unique electronic properties.
As mentioned above, it has been shown that fullerenes also react with themselves to generate fullerene dimers. Since carbon cages smaller than C
_{60}
violate the isolated pentagon rule (IPR), they have higher strain and reactivity due to the adjacent pentagons, thus they are good candidates to form dimers, polymers and solids.
^{33}
With this initial thought in mind, in this article we consider small fullerenes such as C
_{24 }
and C
_{36}
as molecular bridges for joining higher fullerenes such as C
_{60}
and C
_{80}
, for the first time, see
Figure 1.
Then we investigate their electronic and magnetic properties in comparison to those of their parents by calculating HOMO―LUMO gaps, binding energies, and NICS indices. In fact, the synthesis and characterization of such fullerene dimers are of main interest due to their unique structural, magnetic, superconducting and mechanical properties,
^{7,9}
which are considerably different from those of other carbon nanostructures such as carbon nanotubes and fullerene cages. Since the considered fullerenes in this study are borderless polycyclic conjugated systems with internal cavities, endohedral
^{3}
He NMR chemical shifts have proven to be a useful tool for characterizing them and their derivatives.
^{34-36}
Determining the chemical shift of encapsulated
^{3}
He nucleus into a fullerene cage and comparing with the
^{3}
He chemical shift outside gets a direct measure of the shielding of the magnetic field by the fullerene; such experiments are well known for fullerenes. Providing a good prediction for the endohedral
^{3}
He NMR chemical shift, nucleus independent chemical shift (NICS) was proposed by Schleyer
et al.
in 1996.
^{37}
Therefore, in order to probe the local effects of magnetic field inside each fullerene cage we employ grid distribution of NICS inside these molecular clusters and their parents. Magnetic field inside each cage is a consequence of diamagnetism and is related to the induced ring current in the fullerene molecular orbitals, which causes extra stabilization/destabilization in the case of aromatic/ antiaromatic compounds.
^{38}
Therefore, it can provide better insights of the electron delocalization, diamagnetic susceptibilities, molecular aromaticity and magnetic properties.
Schematic diagram of fullerene dimers together with the optimized geometries of C_{60}-C_{36}-C_{60} (C_{156}) and C_{80}-C_{24}-C_{80} (C_{184}).
Computational Methods.
All density functional theory (DFT) quantum calculations are performed using Gaussian 98 program package.
^{39}
We consider small fullerenes C
_{24 }
and C
_{36}
as molecular bridges for joining higher fullerenes C
_{60}
and C
_{80}
, see
Figure 1.
Therefore, the structural geometries of six different configurations of the considered models are allowed to relax by all-atomic optimization. Because of the large sizes of the investigated systems optimization method is qualified step by step as follows: first C
_{24}
, C
_{36}
, C
_{60}
and C
_{80}
fullerene cages considered as the starting points for the design of these compounds are optimized at the B3LYP/6- 31G(d) level of theory.
^{40}
In the next step the geometries obtained in step 1 are used to create initial geometries of the fullerene dimers, 𝑖.𝑒., smaller fullerenes, C
_{24 }
and C
_{36}
, are located between two cages with approximate interlayer bond length of 1.6 Å (based on reported CC bond lengths for the fullerene dimers
^{15,32}
); then optimization is first performed with 3-21G basis set for the resulted molecules and finally optimal geometries and normal mode frequencies for all the structures are obtained using standard 6-31G(d) basis set. The coordinates of all the optimized structures can be found in supplementary material. The standard 6-31G(d) basis set is employed due to being affordable and accurate enough for geometry optimization of even large molecules.
^{40,41}
Real frequencies obtained from frequency calculations confirm that all of them are minimum energy structures.
Ionization energy (eV) for the fullerene dimers.
As a stability criterion of different configurations, binding energies per atom have been calculated according to the following expression:
where E
_{T}
is the total energy of the fullerene dimers. Systems with larger binding energies are more stable. To calculate the NICS, ghost atoms are placed along the principal axes of the considered fullerene dimers and their parents with a step size of 0.5Å. The zero point of the coordinate system is positioned at the bridge centers of the optimized structures of the considered fullerene dimers.
_{60}
and C
_{80}
cages as parent molecules, which are fully optimized at the B3LYP/6-31G* level. The obtained structure of C
_{60}
is consistent with the literature; the prediction of bond lengths of the hexagon-hexagon (h-h) and hexagonpentagon (h-p) junctions (1.452 and 1.393 Å, respectively) is in excellent agreement with the experimental values (1.458 and 1.401 Å, respectively).
^{42,43}
The C
_{36}
and C
_{24 }
fullerene cages are chosen as bridges between two fullerene cages. The structure of C
_{24}
can be regarded as a [12]trannulene44 capped with two hexagonal terminal caps. Its optimized structure is indeed affirmative of such a consideration with the uniform C-C bond lengths (1.420 Å) of the hexagonal terminal caps and the much longer C-C bond lengths of 1.530 Å between the hexagonal caps and the central [12]trannulenic ring. Moreover, the localized C=C bond lengths of 1.365 Å and C-C bond lengths of 1.462 Å in the central [12]trannulenic ring are in excellent agreement with the reported experimental values (1.365 and 1.463 Å, respectively).
^{44,45}
The structure of C
_{36}
fullerene cage has been described in our previous work.
^{46}
In this work, we use the face-to-face linking model to create six types of fullerene dimers with C
_{24 }
and C
_{36}
bridges, see
Figure 1.
When two neighboring carbon cages share their hexagonal caps with the face-to-face pattern,
sp
^{2}
hybridization transfers to
sp
^{3}
hybridization for the carbon atoms in the merged region. As the structures are being reported for the first time, their geometrical characteristics are discussed briefly with the aim of giving better interpretations of these clusters. Based on the optimized structures, the intercage bond lengths of six fullerene dimer are in the range 1.603- 1.622 Å, which can be compared with the intercage bond lengths of 1.60 Å reported by Fowler et al.
^{47}
for a linear chain of
D_{6h}
-C
_{36}
cages, and the electron-diffraction pattern of C36-based solid which suggested an intercage distance shorter than 1.7 Å. Moreover, the calculated C-C bond lengths of 1.657-1.660 Å in the two hexagonal terminal caps of C
_{24}
bridge cages are slightly longer than the corresponding C-C bond lengths (1.522-1.604 Å) in the C
_{36}
bridge cages
Total energy (E_{T}), Binding energy (E_{bin}), and HOMO-LUMO energy gaps (E_{g}) in the fullerene dimers
To compare the obtained results with those available in the literature, binding energies per atom are calculated for the C
_{36}
and C
_{60}
fullerenes to be 8.880 and 7.820 eV/atom, which are in agreement with the previously reported values (8.55 and 7.72 eV/atom).
^{2,45}
The little difference observed can be due to the different computational methods used. We first note that binding energies for the fullerene dimers with C
_{36}
bridges are always lower than those of the fullerene dimers with C
_{24}
bridges. Secondly, the replacement of C
_{60}
cages with C
_{80}
ones (increasing the size of fullerene cage) leads to an increase in binding energy in these systems, see
Table 1.
The energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), E
_{g}
, indicates that C
_{36}
and C
_{60}
are semiconductors with the E
_{g}
of 1.02 and 1.66 eV, respectively, which are in agreement with the reported values in the literature (0.8 and 1.8 eV).
^{45,48}
As can be seen in
Table 1
, in contrast to binding energies, the E
_{g }
values of the fullerene dimers with C
_{36}
bridges are larger than those of the fullerene dimers with C
_{24}
bridges. This occurrence may bring about a change in the related electrical conductivity since it is well known that the E
_{g}
(or band gap in the bulk materials) is a major factor that determines the electrical conductivity of the material. A classic relation between them is as follows
^{49}
:
where σ is the electrical conductance and
k
is the Boltzmann’s constant. According to the equation, smaller E
_{g}
leads to higher conductance at a given temperature. Therefore, all of the considered models in this study are semiconductors with Eg values of 1.05-1.26 eV when C
_{36}
cage is located between two fullerene cages and 0.78-0.88 eV when C
_{24}
is sandwiched between two fullerene cages. Moreover, it is also found that band gaps increase with increasing the size, 𝑖.𝑒., replacing C
_{60}
with C
_{80}
leads to larger HOMO-LUMO gap for each group of fullerene dimers, see
Table 1.
The first ionization potentials (IP) are calculated under the Koopmans’ theorem for closed-shell molecules, based on the frozen orbital approximations and the finite difference approach. In the other words, they are expressed in terms of the highest occupied molecular orbital (HOMO) energies, E
_{HOMO}
: IP ≈ −E
_{HOMO}
. At this point it is necessary to mention that the focus is not to find precise ionization potential values; instead, the primary purpose is to study the evolution and the trend of IP in the considered models, and this is just an approximate comparison.
Figure 2
depicts the trend of ionization potential for the considered models. The IP plot indicates that the fullerene dimers with C
_{36 }
bridges have higher ionization potentials compared to the fullerene dimers with C
_{24}
bridges, and are thus harder to oxidize (oxidation). Meanwhile, replacement of C
_{60}
cages with C
_{80}
ones (increasing the size of fullerene cage) leads to an increase in ionization potential in these systems.
NICS Characterization.
Aromaticity describes molecules that benefit energetically from the presence of cyclic or spherical electron delocalization in closed circuits of mobile electrons. It is well known that the stability is not directly related to aromatic stabilization but with strain reduction. This is consistent with the high aromaticity of C
_{36}
compared to the antiaromaticity of C
_{24}
, as it is measured by the magnetic aromaticity index of nucleus independent chemical shift (NICS) evaluated at the center of the cages.
Since the aromaticity is not an observable characteristic, there is no magnitude that defines it clearly, and so it is generally evaluated indirectly on the basis of energetic, geometric, or electronic criteria. Especially, it can be followed by obtaining information from the magnetic properties. In fact, the most important methods among several ones to evaluate aromaticity are based on NMR chemical shifts and diamagnetic susceptibilities. Compounds with considerably exalted diamagnetic susceptibility are considered as aromatic structures. The ring currents generated in such molecules by an external magnetic field result in special properties such as “exalted” magnetic susceptibilities and NMR chemical shifts displaced from their normal ranges.
^{37,38}
Such particular magnetic influences typically are especially large inside aromatic cyclic or cage-like molecules. To match the familiar NMR convention, NICS indices correspond to the negative of the magnetic shielding, a well-defined property of electronic systems, computed at chosen points designated using the Bq ghost atoms. Significantly negative NICS values in interior positions of cages (magnetically shielded) indicate the presence of induced diatropic ring currents or aromaticity.
On the other hand, antiaromatic cages are identified by their positive NICS values (magnetically deshielded), indicating paratropic ring currents.
Computed NICS values (ppm) along the principal axes of fullerene dimers connected through C_{24} and C_{36} bridge cages. The zero point of the coordinate system is positioned at the centers of bridge cages.
As mentioned above, C
_{24 }
cage can be regarded as a [12]trannulene capped with two benzene rings at both sides. The local ring currents are diatropic within the six membered rings and, in sharp contrast, paratropic within the [12]trannulenic ring. Compensation of these two local effects results in NICS value of 37.89 ppm at the cage center,
^{50}
so C
_{24}
fullerene is antiaromatic at all. The C
_{36}
fullerene cage can be viewed as being made of a zigzag (6, 0) tubular belt, six-membered cyclic polyacene, joined to hexagonal terminal caps, which results in the high aromaticity of the C
_{36}
with the calculated NICS value of −26.52,
^{50}
in agreement with the experimental value of −28.8 ppm previously reported by Saunders
et al..
^{45}
Figure 3
depicts variations of NICS values
versus
distances from the bridge center for the considered compounds and their parent cages (The calculated NICS values for the fullerene dimers have been shown in
Table S1
of the Supplementary material). Dimerization of C
_{60}
and C
_{80}
fullerenes with C
_{24 }
and C
_{36}
significantly change their aromatic characters, leading to a decrease in antiaromaticity of the C
_{24}
and C
_{80}
with paratropic characters, while an increase in the aromaticity of the aromatic C
_{36}
and C
_{60}
cages. In other words, NICS values reflect substantial differences in magnetic properties at the cage centers of fullerene dimers. For example, weakly diatrophic (aromatic) C
_{60}
has a moderate NICS value of −2.82 ppm,
^{50}
while it receives more aromaticity with NICS value of −7.35 ppm in the fullerene dimer C
_{156}
(C
_{60}
-C
_{36}
-C
_{60}
). In this compound NICS in aromatic fullerene C
_{36}
changes from −26.52 ppm to the value of −29.76 ppm, 𝑖.𝑒., aromaticity increases. The inverse behavior is observed for C
_{24}
and C
_{80}
which are severely antiaromatic with high positive NICS values of 37.89 and 53.22 ppm, respectively. Compensation between diatropic and paratropic ring currents leads to a decrease in NICS values to 7.16 and 0.93 ppm at the cage centers of C
_{24}
and C80, respectively, in the fullerene dimer C
_{184}
(C
_{80}
-C
_{24}
-C
_{80}
). These trends reveal that fullerene dimerization causes major changes in the magnetic properties at the cage centers.
Now we are interested to make an attempt to correlate the stability of fullerene dimers with their aromaticity character. DFT results indicate that those fullerene dimers involving the initially harshly antiaromatic C
_{24}
or C
_{80}
cages are more energetically favorable configuration, with the binding energies of 8.14-9.03 eV/atom, than the fullerene dimers involving C
_{36}
and C
_{60}
, with the binding energies of 3.06-3.96 eV/ atom. It is noted that the Ebin of the fullerene dimer C
_{184}
(C
_{80}
- C
_{24}
-C
_{80}
) with three antiaromatic cage is larger than those of the other fullerene dimers. Hence, a change in aromaticity character, especially decrease of antiaromaticity, plays a major role in the stability of fullerene dimer. In fact, decrement of antiaromatic character (NICS) inside the joined antiaromatic fullerene cages leads to an increase in the ability of these compounds to sustain an induced ring current, which causes extra stabilization in the case of fullerene dimers of C
_{80}
fullerene with C
_{24}
bridge cages. Therefore, it seems that the results of this section and those of stability character in previous section mostly support each other.
_{60}
and C
_{80}
connected through C
_{24}
and C
_{36}
bridge cages with the face-to-face linking model. By comparing the results obtained in the present investigation, we emphasize the following points. First, binding energies for the fullerene dimers with C
_{36}
bridges are lower than those of the fullerene dimers with C
_{24}
bridges. Second, replacement of C
_{60}
cages with C
_{80}
ones always leads to the increase of binding energy in these systems. Third, HOMO-LUMO gaps, E
_{g}
, of the fullerene dimers with C
_{36}
bridges are larger than those of the fullerene dimers with C
_{24}
bridges and also replacement of C
_{80}
cage for C
_{60}
leads to larger E
_{g}
for the fullerene dimer. Fourth, variations of NICS values versus distances from the bridge center for the considered compounds and the parent cages indicate that dimerization of C
_{60}
and C
_{80}
fullerenes with C
_{24}
and C
_{36}
leads to a significant decrease in antiaromaticity of the antiaromatic cages C
_{24}
and C
_{80}
, and an increase in the aromaticity of the aromatic cages C
_{36}
and C
_{60}
. Finally, fullerene dimers involving the initially harshly antiaromatic C
_{24}
or C
_{80}
cages are more energetically favorable configurations than the fullerene dimers involving C
_{36}
and C
_{60}
.

Introduction

The understanding of chemical reactivity of buckminsterfullerene (C
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Results and Discussion

Geometrical and Stability Properties. We have chosen the C
Total energy (ET), Binding energy (Ebin), and HOMO-LUMO energy gaps (Eg) in the fullerene dimers

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Conclusion

We have performed a DFT theoretical description to evaluate the electronic and magnetic properties of fullerene dimers of C
Acknowledgements

Publication cost of this paper was supported by the Korean Chemical Society.

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Citing 'Fullerene Dimers Connected through C_{24} and C_{36} Bridge Cages
'

@article{ JCGMCS_2014_v35n4_1005}
,title={Fullerene Dimers Connected through C_{24} and C_{36} Bridge Cages}
,volume={4}
, url={http://dx.doi.org/10.5012/bkcs.2014.35.4.1005}, DOI={10.5012/bkcs.2014.35.4.1005}
, number= {4}
, journal={Bulletin of the Korean Chemical Society}
, publisher={Korean Chemical Society}
, author={Anafcheh, Maryam
and
Ghafouri, Reza}
, year={2014}
, month={Apr}