# Ih Symmetrical (4,6)-Fullerenes and Their Local Ring Aromaticity: A First Principle Study

Authors: Jing Wang; Haigang Lu; Yingfang Fan; Si-Dian Li
Journal: Journal of Nanomaterials
 (2015)

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## Abstract

As the natural extension of carbon fullerene, a series of Ih symmetrical (4,6)-fullerenes were constructed and investigated using first principle methods. These Ih (4,6)-fullerenes consist of many four- and six-membered rings and are classified into two types: (1) those with isolated four- and six-membered rings and (2) those with connected four- and/or six-membered rings. Though these (4,6)-fullerenes are less stable than Ih C60 and C240 (5,6)-fullerene, it is possible to synthesize them from their elemental unit, antikekulene, which was nearly synthesized experimentally. Though the (4,6)-fullerenes are mainly spherical and antiaromatic compounds, the local aromatic indexes indicate that all of the planar π-conjugated rings have local aromaticity in fullerenes, which provides reasonable delocalization, which is consistent with our chemical intuition. Because of the huge cavities and suitable pore sizes present in the (4,6)-fullerenes, they can be taken as potential nanocontainers for the storage of small molecules.


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## Body

## 1. Introduction

Since the striking developments of carbon fullerenes, many fullerenes with novel topology have been proposed theoretically in the search for new materials [1–6]. The famous Ih C60 fullerene consists of 20 six-membered rings (6-MR) and 12 five-membered rings (5-MR) made up of sp2-hybridized carbon atoms. Recently, cubane-like D
2
d B40 and C3 B39 fullerenes have been discovered using both experimental and theoretical methods [7, 8]. In the experiments, benzene-like antikekulene, which consists of six 6-MRs connected by six four-membered rings (4-MR), has been nearly synthesized [9]. Just like the 6-MR and 5-MR, the 4-MR should also be regarded as an elemental unit that can be used for the construction of low-dimensional carbon materials. Therefore, it is natural to consider the carbon fullerenes that consist of some 6-MRs and 4-MRs, the so-called (4,6)-fullerenes.The topological rules of (4,6)-fullerenes have now been systematically deduced by Ashrafi and Mehranian [10]. Two-dimensional carbon materials made up of 6-MRs and 4-MRs have been proposed theoretically [11, 12], from which the (4,6)-fullerenes can be formed by rolling up these materials. Fullerenes with 4-MRs can also be investigated for storage of noble gas and hydrogen [13, 14]. However, there is no systematical investigation reported to date on the three-dimensional geometrical and electronic structures of (4,6)-fullerenes. Among the large number of the (4,6)-fullerenes, the Ih symmetrical derivatives are the most important and will be taken as the model compounds to be investigated in this work.In the polycyclicπ carbon system, the aromaticity is one of the most important properties to understand their geometrical and electronic structures. For two-dimensional carbon materials, the aromaticity of graphene is localized with two π-electrons delocalized over every 6-MR [15], while two-dimensional (4,6) graphenylene is composed of cyclohexatriene units with two quite distinct C-C bonds within a 6-MR [11]. The spherical aromaticity [16–18] and nucleus-independent chemical shift (NICS) [19, 20] value at the cage center are proposed for the fullerenes. The sphere currents of fullerene provide the global and local descriptive views of the aromaticity on the surface [21]. The C60 fullerene displays only weak spherical aromaticity because its absolute diamagnetic and paramagnetic currents almost cancel each other out. The ring aromaticity of the fullerenes has been investigated using several approaches [22]. To quantitatively describe the electron delocalization in the rings of the fullerenes, a local aromatic index will be proposed using natural bonding orbital (NBO) and natural chemical shielding (NCS) analyses [23, 24].


## 2. Computational Methods

A series of Ih (4,6)-fullerenes were constructed in three steps: (1) construction of the symmetrical unique fragments with respect to the icosahedron, (2) formation of the other symmetrically equivalent atoms, and (3) optimization of the original geometrical structures using density functional theory (DFT). The geometry optimizations were carried out using Becke’s three-parameter functional (20% Hartree-Fock nonlocal exchange) [25] with the nonlocal Lee-Yang-Parr correlation functional [26] (B3LYP) in the standard 6-31G
∗ basis set (B3LYP/6-31G
∗). The NICS values were calculated using the gauge-independent atomic orbital (GIAO) [27] method at the B3LYP/6-31G
∗ level. The first principle calculations were carried out using the Gaussian 09 program [28]. The NBOs and natural chemical shifts (NCS) were analyzed using a combination of the Gaussian 09 package and NBO 6.0 software [29].


## 3. Results and Discussion

As shown in Figures1 and 2, sp2-hybridized carbon atoms can form a series of Ih (4,6)-fullerenes that can be classified into two types: (1) those with isolated 4- and 6-MRs (Ih C120, C240, C360, and C480, Figure 1) and (2) those with connected 4- and 6-MRs (Ih C300 and C
360
′, Figure 2). The C120 (4,6)-fullerene, which displays minimum Ih symmetry, was formed by substituting each atom at C20 with cyclohexatriene. The larger fullerenes were formed by the addition of some 4-MRs and/or 6-MRs to each of the equivalent fragments with respect to the icosahedron. In contrast to the buckyball (5,6)-fullerenes, there are many large rings on the surface of the (4,6)-fullerenes, such as 8-, 9-, 10-, and 12-membered rings.Figure 1
The geometrical structures of the Ih C120 (a), C240 (b), C360 (c), and C480 (d) (4,6)-fullerenes with isolated four- and six-membered rings. The dashed triangles show the symmetrically unique fragments of the fullerenes with respect to the icosahedron.
(a)
(b)
(c)
(d)Figure 2
The geometrical structures of the Ih C300 (a) and C
360
′ (b) (4,6)-fullerenes with connected four- and/or six-membered rings. The dashed triangles show the symmetrically unique fragments of the fullerenes with respect to the icosahedron.
(a)
(b)To investigate the stability of the (4,6)-fullerenes studied, we evaluated their binding energiesE
b
=
E
f
-
E
a
t
o
m, where E
f and E
a
t
o
m are the energies per atom in the fullerenes and in the free state, respectively (Table 1). The difference in the binding energy of the C60 and C120 fullerenes was only 0.02 eV/atom between the B3LYP/6-31G
∗ and MP2/6-31G
∗ levels [30]. Then, the B3LYP/6-31G
∗ level was used to investigate the stability of a series of fullerenes. Obviously, the (4,6)-fullerenes were about 0.13–0.32 eV/atom less stable than C60 fullerene and about 0.38–0.57 eV/atom less stable than C
240
′ (5,6)-fullerene. In addition, the HOMO-LUMO gaps of all the (4,6)-fullerenes studied were less than those of C60 and C
240
′ (5,6)-fullerene. Both of these results indicate that the (4,6)-fullerenes are energetically less favorable when compared to the buckyball (5,6)-fullerenes. However, antikekulene was nearly synthesized experimentally [8] and can be taken as an elemental fragment of the (4,6)-fullerenes. Therefore, it is possible to synthesize these Ih (4,6)-fullerenes from the synthetic pathway used to prepare antikekulene.Table 1
The geometrical, energetic, and electronic properties of the fullerenesa.
n
D
f
D
r
D
p
E
b
E
g
NICS
NIC
S
m
+
C
60
5, 6
6.98
2.73
−2.7
C
240
′
5, 6
7.24
2.23
−13.9
C
12
0
4, 6, 10
10.5
4.5
2.2
6.67
1.89
9.3
−35.46+
C
24
0
4, 6, 8, 10
15.1
4.5
2.2
6.69
1.57
13.8
−5.310+
C
360
4, 6, 10, 12
19.0
5.5
3.2
6.69
1.21
2.7
−22.08+
C
480
4, 6, 10, 12
22.6
5.5
3.2
6.70
1.66
2.0
−23.410+
C
30
0
4, 6, 9, 10
16.4
4.5
2.2
6.75
0.51
6.8
−3.210+
C
36
0
′
4, 5, 6, 10
18.5
4.5
2.2
6.86
1.94
−4.2
−17.78+
aThe n-ring in the carbon fullerenes (n), the diameter of the fullerenes (D
f, Å), the diameter of the maximum n-rings (D
r, Å), the diameter of the maximum pores (D
p, Å), binding energy (E
b, eV/atom), HOMO-LOMO energy gap (E
g, eV), and spherical NICS values for the fullerenes (NICS, ppm) and their m+ charged ions (NIC
S
m
+).Similar to graphenylene, the surface of the (4,6)-fullerenes has some pores available to transport small gas molecules. The ring diameters of the 10-MRs and 12-MRs are from 4.5 to 5.5 Å on the surface and their pore sizes are from 2.2 to 3.2 Å, which are suitable for small molecules to pass through. In particular, the pore size of the 12-MR (about 3.2 Å) is, in principle, larger than the kinetic diameter of H2 (2.89 Å), but smaller than those of CO (3.76 Å), N2 (3.65 Å), CO2 (3.30 Å), and CH4 (3.80 Å). Therefore, the 12-MR provides a selective channel that allows H2 molecules to access the cavity. In addition, the (4,6)-fullerenes have spherical cavities with diameters from 10.5 to 22.6 Å. Theoretically, these (4,6)-fullerenes have potential as nanocontainers to store small molecules using their huge spherical cavities and suitable pore sizes on their surface.As the polycyclicπ systems of sp2-hybridized carbon atoms, (4,6)-fullerenes have many conjugated π bonds. As shown in Figures 1 and 2, the 6-, 10-, and 12-MRs are π-conjugated rings, while most of the 4-MRs consist of only four single σ bonds and no π bond. To understand the electronic characteristics of the (4,6)-fullerenes, it is necessary to investigate their aromaticity.NICS has proved to be a simple and efficient aromaticity probe. Spherical fullerenes represent a special group of polycyclicπ systems, whose aromaticity can be described as spherical aromaticity. Because the electron number does not follow the 2
N
+
1
2 rule for spherical aromaticity [16], the Ih C60 and C
240
′ (5,6)-fullerenes display weak spherical aromaticity. However, most of the Ih (4,6)-fullerenes display weak spherical antiaromaticity, except the C
360
′ derivative (Table 1). However, after losing some electrons, most of the (4,6)-fullerenes (C120, C240, C360, and C
360
′) show spherical aromaticity (Table 1). This indicates that the (4,6)-fullerenes should become more stable when losing some electrons via chemical modification, such as halogenation [31].Because the absolute diamagnetic and paramagnetic currents partly cancel each other out in the three-dimensional cages [21], their global NICS, which is calculated directly, only partially describes the aromaticity of the electron delocalization in the π-conjugated rings. For instance, the π-conjugated 6-MRs are nonaromatic (NICS (1) = −0.5) in the C60 fullerenes, which cannot describe their high local diamagnetic and paramagnetic currents.To describe the local aromaticity of the rings, we propose a local NICS value based on the NBOs and natural chemical shielding (NCS) analyses. There were three steps used to calculate the local NICS value of a ring: (1) calculation of the global NICS on the ring, (2) decomposition of the global NICS into the individual NBO contributions, and (3) adding all the contributions from the core and bonding NBO on the ring. In addition, because of the different chemical environments in the exterior and interior of fullerene, the average NICS values at 1 Å above and below a ring were used to represent their local ring aromaticity (Figure3).Figure 3
The geometrical structures of benzene (a), antikekulene (b), Ih C60 fullerene (c), and Ih C120 (4,6)-fullerene (d). The purple spheres indicate the sites of the ghost atoms in the NICS calculations.
(a)
(b)
(c)
(d)The global and local NICS values of some typicalπ-conjugated systems are given in Table 2. Obviously, the local NICS values are always less than the global ones because the gross contribution of the other atoms is antiaromatic.Table 2
The global and local NICS values of the individualn-rings in some typical π-conjugated systemsa.
n
NICS(1)
NICS(1)L
NICS(−1)
NICS(−1)L
NICS0
NICS0L
C6H6
6
−11.2
−12.0
Antikekulene
4
4.7
−4.3
6
−1.8
−7.1
12
3.8
−4.1
C
60
5
6.4
1.0
3.1
−3.6
4.8
−1.3
6
−0.5
−8.6
−5.2
−6.6
−2.9
−7.6
C
120
4
5.1
−3.9
11.6
3.7
8.4
−0.1
6
0.8
−9.4
6.8
−3.1
3.8
−6.3
10
2.2
−4.6
7.2
−3.7
4.7
−4.2
aThe n-ring (n), the global NICS values at 1 Å above (NICS(1)) and below (NICS(−1)) the ring, the local NICS values at 1 Å above (NICS(1)L) and below (NICS(−1)L) the ring, and the average values for the global NICS (NICS0) and local NICS (NICS0L).In benzene, the local NICS for the six carbon atoms was nearly equal to its global value. Because benzene is the model of aromaticity, its local NICS (−12.0) can be taken as a standard value of local ring aromaticity. In antikekulene, all of the 4-, 6-, and 12-MRs areπ-conjugated, in which the 6-MR displays local aromaticity (NICS = −7.1) and the 4- and 12-MRs show weak aromaticity (NICS = −4.3 and −4.1, resp.).In the C60 fullerene, the 6-MR is a π-conjugated aromatic (NICS = −7.6), while the 5-MR is nonaromatic (NICS = −1.1) due to the absence of a π bond(s). In the Ih C120 (4,6)-fullerene, the π-conjugated 6- and 10-MRs are aromatic (NICS = −6.3) and weakly aromatic (NICS = −4.2), respectively. Similarly, its 4-MR is nonaromatic because it only consists of single bonds and no π bond.In general, theπ-conjugated 6-MR is aromatic, the other π-conjugated rings are weakly aromatic, and the rings without π bonds are nonaromatic, which is consistent with our chemical intuition. In addition, the aromaticity of the 6-MRs in the fullerenes is obviously less than that of benzene, which provides a quantitative description of the difference between benzene and the π-conjugated rings in the fullerenes.


## 4. Conclusions

In summary, a series of Ih symmetrical (4,6)-fullerenes were constructed and investigated using first principle methods. These Ih (4,6)-fullerenes consist of many 4- and 6-MRs that can be classified into two types: (1) those with isolated 4- and 6-MRs and (2) those with connected 4- and 6-MRs. Though the (4,6)-fullerenes are about 0.13–0.32 eV/atom less stable than the Ih C60 and about 0.38–0.57 eV/atom less than the C240 (5,6)-fullerene, it is possible to synthesize them from their elemental fragment, antikekulene, which has been nearly synthesized experimentally. Though the (4,6)-fullerenes are mainly spherical and antiaromatic compounds, their local NICS values indicate that the planar π-conjugated rings are aromatic, which provides some reasonable electronic delocalization, which is consistent with our chemical intuition. The C360 and C480 (4,6)-fullerenes have pore sizes of 3.2 Å so that only hydrogen gas molecules can easily access their cavities. Consequently, the C360 and C480 (4,6)-fullerenes can be regarded as potential nanocontainers for hydrogen storage.



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