Journal of Nanomaterials

Volume 2013 (2013), Article ID 451920, 8 pages

http://dx.doi.org/10.1155/2013/451920

Research Article

Thermodynamic and Theoretical Study of the Preparation of New Buckyballs from Corannulene, Coronene, and Circulene

Hasan R. Obayes,¹ Ghadah H. Alwan,² Ahmed A. Al-Amiery,1,3 Abdul Amir H. Kadhum,³ and Abu Bakar Mohamad³

¹Applied Chemical Division, Applied Science Department, University of Technology, Baghdad, Iraq

²Ministry of Sciences and Technology, Industrial Research & Development Directorate, Industrial Applications Center, Baghdad, Iraq

³Department of Chemical and Process Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 29 July 2013; Revised 16 September 2013; Accepted 7 October 2013

Academic Editor: Mohammad Taghi Ahmadi

Copyright © 2013 Hasan R. Obayes et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

We applied density functional theory (DFT) to study three polycyclic aromatic compounds (PAHs), corannulene, coronene, and circulene, for the preparation of twelve new buckyballs with molecular dimensions of less than a nanometer. The results showed that the corannulene molecule is bowl-shaped, the coronene molecule is planar, and the circulene molecule has a unique saddle-shaped structure. Cyclic polymerization of the three molecules can be used to prepare new buckyballs, and this process produces hydrogen molecules. The most symmetric buckyball is also the most stable based on the values of the HOMO energy levels and has the most efficient gap energy, making it potentially useful for solar cell applications.

1. Introduction

Polycyclic aromatic hydrocarbons (PAHs) are a class of unique compounds that consist of fused, conjugated aromatic rings that do not contain heteroatoms or carry substituents [1]. Alternate PAHs contain only six-membered rings, and certain alternant PAHs are called “benzenoid” PAHs. “Small” and “large” PAHs contain up to or more than six fused aromatic rings, respectively. Most research has focused on small PAHs due to their availability [2]. Corannulene has the shape of a bowl because it contains a five-membered ring, which inverts rapidly. In addition to its nonstandard geometry and dynamic behavior, this molecule has attracted considerable interest as an important building block for the synthesis of C₅₃. Additionally, the solid state packing behavior of corannulene is interesting [3]. As discussed in detail by Kawasa and Kurata, [4] not only bowl-shaped but also ball- and belt-shaped aromatic systems provide an exciting opportunity to study concave-convex interactions. Coronene (6-circulene) is an aromatic planar symmetric molecule, which has been studied, synthesized, and well characterized [5]. Both corannulene and coronene have interesting conductive properties due to their large electronic resonance. Circulene, the next member of this molecular family, consists of a central cyclooctatetraene fragment surrounded by phenyl rings. Despite the efforts of researchers [6], circulene has not yet been synthesized. Several theoretical studies [7], but no detailed studies, have been carried out on the structure of this molecule. Theoretical predictions of the existence of buckyball molecules appeared in the late 1960s and early 1970s, but these predictions were largely unnoticed. The discovery of buckyballs was unexpected because the scientists were producing carbon plasmas to replicate and characterize unidentified interstellar matter. Mass spectrometry analysis of their product indicated the formation of spheroidal carbon molecules [8].

2. The Calculation Method

To calculate ground-state geometries, Gaussian 03, Revision C.01 [9] was optimized to a local minimum without symmetry restrictions using basis set 6-31 G [10, 11]. The combination of the Becke three-parameter hybrid (B3) [12, 13] exchange functional and the Lee-Yang-Parr (LYP) [14] correlation functional (B3LYP) [15, 16] was used for all geometry optimizations, thermodynamic functions (at 298.150 Kelvin and 1.0 atm), Highest Occupied Molecular Orbital Energies (EHOMO), Lowest Unoccupied Molecular Orbital Energies (ELUMO), and physical properties for the molecules in this study.

3. Results and Discussion

Previous studies have shown that not all polycyclic aromatic hydrocarbons (PAHs) are flat molecules. We selected aromatic compounds known as circulenes for this study. The circulenes include 5-circulene (corannulene), 6-circulene (coronene), and 7-circulene (circulene). According to Density Function Theory (DFT) calculations, not all of these molecules are flat, as shown in Figure 1. Corannulene is bowl-shaped, coronene is planar, and circulene has a unique saddle-shaped structure, which are consistent with the literature.

Figure 1: B3LYP/6-31G optimized structures of corannulene, coronene, and circulene.

3.1. Density Function Theory (DFT)

A DFT calculation introduces an additional step to each major phase of a Hartree-Fock calculation. This additional step is a numerical integration of the functional (or various derivatives of the functional). Thus, in addition to the sources of numerical error in Hartree-Fock calculations (integral accuracy, SCF convergence, and CPHF convergence), the accuracy of DFT calculations also depends on the number of points used in the numerical integration. The “fine” integration grid is the default in Gaussian 03. This grid greatly enhances the calculation accuracy at minimal additional cost. We do not recommend using a smaller grid in production DFT calculations. It is important to use the same grid for all calculations when energies will be compared (e.g., computing energy differences, heats of formation, and so forth). Larger grids are available, for example, for tight optimization of certain systems. An alternate grid may be selected in the route section [17–20].

To prepare new buckyballs, a fundamental understanding of the polymerization of polycyclic aromatic hydrocarbons (PAHs) is important. The polymerization process for new buckyballs revealed the production of hydrogen molecules [21, 22], and the general reaction of formation of new buckyballs from three molecules of polycyclic aromatic hydrocarbons (PAHs) is as follows,

where is number of carbon atoms, is , is 2 in corannulene and circulene, and is 0 in coronene.

3.1.1. The Cyclic Polymerization of Three Corannulene Molecules

Scheme 1 shows all possible cyclic polymerization reactions of three molecules of corannulene. Reaction (1) produced a new buckyball C₆₀H₂ (I) by forming five butagons, three pentagons, three hexagons, and two decagon cycles from three corannulene molecules. Reaction (2) produced a new buckyball C₆₀H₂ (II) through the formation of three butagons, five pentagons, three hexagons, and two nonagon cycles. Reaction (3) produced a new buckyball C₆₀H₂ (III) by forming three butagons, three pentagons, five hexagons, and two octagon cycles. Reaction (4) produced a new buckyball C₆₀H₂ (IV) by forming eleven pentagons and two nonagon cycles. Thirteen different cycles were formed in these four reactions. All of these reactions are spontaneous and exothermic according to the values of the entropy change (), the Gibbs energy change (), and the enthalpy change (). The results for the EHOMO (the Energy of High Occupied Molecular Orbital) and the total energy for the four reaction products in Table 1 reveal that the products are stable, that the new buckyball C₆₀H₂ (IV) is the most stable among the four, and that the increase in the EHOMO for C₆₀H₂ (IV) is (−0.4530 eV), (−0.6177 eV), and (−0.6236 eV) relative to C₆₀H₂ (I), C₆₀H₂ (II), and C₆₀H₂ (III) respectively. Additionally, the increase in the total energy is −0.1978 a.u or −124.121 KCalmol⁻¹, −0.1365 a.u or −85.655 KCalmol⁻¹, and −0.2260 a.u or −141.817 KCalmol⁻¹ for C₆₀H₂ (I), C₆₀H₂ (II), and C₆₀H₂ (III), respectively. The structures of the four new buckyballs are shown in Figure 2.

Table 1: Physical values of all new buckyballs were calculated with B3LYP/6-31G.

Molecules
Total energy a.u.
Enthalpy () Kcal·mol⁻¹
Entropy () Cal·mol⁻¹·K⁻¹
EHOMO eV
ELUMO eV
Gap energy () eV

Hydrogen molecule (H₂)
−1.1755
7.847
31.132
−11.8086
+2.7235
14.5321

Corannulene
−767.9696
154.105
103.100
−6.0170
−1.5783
4.4387

Buckyball C₆₀H₂ (I)
−2286.0419
273.343
144.707
−5.4453
−3.9097
1.5356

Buckyball C₆₀H₂ (II)
−2286.1032
274.146
141.115
−5.2806
−3.9288
1.3518

Buckyball C₆₀H₂ (III)
−2286.0137
271.613
143.457
−5.2747
−4.2510
1.0237

Buckyball C₆₀H₂ (IV)
−2286.2397
277.261
139.157
−5.8983
−3.7968
2.1015

Coronene
−921.6885
185.772
115.845
−5.4880
−1.4049
4.0831

Buckyball C₂₇ (I)
−2741.7592
304.289
157.722
−4.9922
−3.9154
1.0768

Buckyball C₂₇ (II)
−2742.1237
315.328
151.394
−5.2425
−4.1043
1.1382

Buckyball C₂₇ (III)
−2741.9284
316.535
149.671
−5.0902
−4.2567
0.8335

Buckyball C₂₇ (IV)
−2742.1856
316.159
150.231
−5.7024
−3.3212
2.3812

Circulene
−1075.2072
216.027
132.547
−5.1430
−1.4348
3.7082

Buckyball C₈₄H₂ (I)
−3199.7795
372.282
180.179
−5.2175
−3.6338
1.5837

Buckyball C₈₄H₂ (II)
−3199.9262
374.865
176.142
−5.2404
−3.7780
1.4624

Buckyball C₈₄H₂ (III)
−3199.9163
374.917
174.315
−5.0417
−4.0741
0.9676

Buckyball C₈₄H₂ (IV)
−3200.2067
381.333
170.827
−5.7372
−3.8110
1.9262

Scheme 1: The reaction of formation of buckyball C₆₀H₂ from three molecules of corannulene and the values of the change of enthalpy (), the change of entropy (), and the change of Gibbs energy ().

(a)

(b)

(c)

(d)

Figure 2: B3LYP/6-31G optimized structures of four new buckyballs: C₆₀H₂ (I), C₆₀H₂ (II), C₆₀H₂ (III), and C₆₀H₂ (IV).

The molecular dimensions of the four new buckyballs are as follows: C₆₀H₂ (I)—(0.85 -axis, 0.75 -axis, and 0.52 -axis) nm, C₆₀H₂ (II)—(0.83 -axis, 0.73 -axis, and 0.49 -axis) nm, C₆₀H₂ (III)—(0.84 -axis, 0.72 -axis, and 0.48 -axis) nm, and C₆₀H₂ (IV)—(0.84 -axis, 0.73 -axis, and 0.48 -axis) nm.

3.1.2. The Cyclic Polymerization of Three Molecules of Coronene

Scheme 2 shows all possible cyclic polymerization reactions of three molecules of coronene. Reaction (1) produced a new buckyball C₇₂ (I) and forms nine butagons, six hexagons, and two nonagon cycles from the three coronene molecules. Reaction (2) produced a new buckyball C₇₂ (II) by forming three butagons, ten pentagons, two hexagons, and two octagon cycles. Reaction (3) produced a new buckyball C₇₂ (III) and formed two butagons, ten pentagons, three hexagons, and two heptagon cycles. Reaction (4) produced a new buckyball C₇₂ (IV) and formed six butagons, and eleven hexagon cycles. Seventeen cycles were formed in each reaction. Every reaction is spontaneous and exothermic according to the values of , , and . The EHOMO and the total energy for the four reaction products in Table 1 reveal that the products are stable, that the new buckyball C₇₂ (IV) is the most stable among the four, and that the increase in EHOMO for C₇₂ (IV) is (−0.7102 eV), (−0.4599 eV), and (−0.6122 eV) relative to new buckyballs C₇₂ (I), C₇₂ (II) and C₇₂ (III), respectively. Additionally, the increases in total energy are −0.4264 a.u or −267.570 KCalmol⁻¹, −0.0619 a.u or −38.843 KCalmol⁻¹, and −0.2572 a.u or −161.395 KCalmol⁻¹ for new buckyballs C₇₂ (I), C₇₂ (II), and C₇₂ (III), respectively. The structures of the four new buckyballs are shown in Figure 3.

Scheme 2: The reaction of formation of buckyball C₇₂ from three molecules of coronene and the values of , and .

(a)

(b)

(c)

(d)

Figure 3: B3LYP/6-31G optimized structures of new buckyballs C₇₂ (I), C₇₂ (II), C₇₂ (III), and C₇₂ (IV).

The molecular dimensions of all four new C₇₂ buckyballs are as follows: C₇₂ (I)—(0.82 -axis, 0.80 -axis, and 0.52 -axis) nm, C₇₂ (II)—(0.83 -axis, 0.78 -axis, and 0.55 -axis) nm, C₇₂ (III)—(0.88 -axis, 0.77 -axis, and 0.55 -axis) nm, and C₇₂ (IV)—(0.82 -axis, 0.79 -axis, and 0.56 -axis) nm.

3.1.3. The Cyclic Polymerization for Three Molecules of Circulene

Scheme 3 shows all possible cyclic polymerization reactions of three molecules of circulene. Reaction (1) produced a new buckyball C₈₄H₂ (I) by forming seven butagons, five pentagons, five hexagons, and two decagon cycles from three circulene molecules. Reaction (2) produced a new buckyball C₈₄H₂ (II) by forming five butagons, seven pentagons, five hexagons, and two nonagon cycles. Reaction (3) produced a new buckyball C₈₄H₂ (III) and formed five butagons, five pentagons, seven hexagons, and two octagon cycles. Reaction (4) produced a new buckyball C₈₄H₂ (IV), seventeen pentagons, and two nonagon cycles. Nineteen different cycles were formed in each reaction. All of these reactions are spontaneous and exothermic according to the values of the change of entropy (), the change of Gibbs energy (), and the change of enthalpy (). However, the the Energy of the Highest Occupied Molecular Orbital (EHOMO) and the total energy for the reaction products in Table 1 reveal that the product has more stability, in this state the product new buckyball C₈₄H₂ (IV), most stable among the four new buckyballs, was C₈₄H₂ (IV) with an increase in the EHOMO, that is (−0.5197 eV), (−0.4968 eV), and (−0.6955 eV) relative to C₈₄H₂ (I), C₈₄H₂ (II), and C₈₄H₂ (III), respectively. Additionally, the increases in total energy are −0.4272 a.u or −268.072 KCalmol⁻¹, −0.2805 a.u or −176.016 KCalmol⁻¹, and −0.2904 a.u or −182.228 KCalmol⁻¹ relative to C₈₄H₂ (I), C₈₄H₂ (II) and C₈₄H₂ (III), respectively. The structures of the four new C₈₄H₂ buckyballs are shown in Figure 4. The molecular dimensions of all four new C₈₄H₂ buckyballs are as follows: C₈₄H₂ (I)—(0.86 -axis, 0.85 -axis, and 0.66 -axis) nm, C₈₄H₂ (II)—(0.90 -axis, 0.88 -axis, and 0.61 -axis) nm, C₈₄H₂ (III)—(0.89 -axis, 0.87 -axis, and 0.60 -axis) nm, and C₈₄H₂ (IV)—(0.90 -axis, 0.87 -axis, and 0.60 -axis) nm.

Scheme 3: The reaction of formation of C₈₄H₂ buckyballs from three molecules of circulene and the values of , and .

(a)

(b)

(c)

Figure 4: B3LYP/6-31G optimized structures of new buckyballs C₈₄H₂ (I), buckyballs C₈₄H₂ (II), C₈₄H₂ (III), and C₈₄H₂ (IV).

3.2. Energy Gap

The energy gap, which is also called the band gap, is an energy range in a solid where no electron states can exist. The gap energy generally refers to the energy difference (in electron volts) between the Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO) in insulators and semiconductors. This gap energy is equivalent to the energy required to free an outer shell electron from its orbit about the nucleus to become a mobile charge carrier that moves freely within the solid material. The band gap is a major factor that determines the electrical conductivity of a solid. Substances with large gap energies are generally insulators, materials with smaller gap energies are semiconductors, and conducting materials have very small or no gaps energies. The Shockley-Queisser limit gives the maximum possible efficiency of single junction solar cells under unconcentrated sunlight as a function of the semiconductor band gap. If the band gap is too high, then the material cannot absorb most daylight photons; if the band gap is too low, then most photons have much more energy than is necessary to excite electrons across the band gap, and the rest is wasted. The semiconductors that are used commonly in commercial solar cells have band gaps near the peak of this curve shown in Figure 5.

Figure 5: The Shockley-Queisser limit for the energy efficiency of a gap.

In Table 1, the values of the energy gaps for all buckyballs in the (0.8335–2.3812) eV range, arranged by the increases in energy gap, are as follows:

4. Conclusions

A quantum chemistry calculation is performed using the Density Function Theory (DFT) method to study the preparation of twelve new buckyballs from the cyclic polymerization of three polycyclic aromatic hydrocarbons (PAHs), corannulene, coronene, and circulene, and the production of hydrogen molecules. The results obtained for the new buckyballs show that the most symmetric buckyball is the most stable, depending on the values of EHOMO. The molecular dimensions of all the new buckyballs are less than a nanometer, and the new buckyballs are characterized by the high efficiency of their energy gaps.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

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