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

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 fourand six-membered rings and are classified into two types: (1) those with isolated fourand six-membered rings and (2) those with connected fourand/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.


Introduction
Since the striking developments of carbon fullerenes, many fullerenes with novel topology have been proposed theoretically in the search for new materials [1][2][3][4][5][6].The famous I h C 60 fullerene consists of 20 six-membered rings (6-MR) and 12 five-membered rings (5-MR) made up of sp 2 -hybridized carbon atoms.Recently, cubane-like D 2d B 40 and C 3 B 39 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].Twodimensional 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 I h symmetrical derivatives are the most important and will be taken as the model compounds to be investigated in this work.
In the polycyclic  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 -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][17][18] and nucleusindependent 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 C 60 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].

Computational Methods
A series of I h (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].

Results and Discussion
As shown in Figures 1 and 2, sp 2 -hybridized carbon atoms can form a series of I h (4,6)-fullerenes that can be classified into two types: (1) those with isolated 4-and 6-MRs (I h C 120 , C 240 , C 360 , and C 480 , Figure 1) and ( 2) those with connected 4-and 6-MRs (I h C 300 and C 360  , Figure 2).The C 120 (4,6)fullerene, which displays minimum I h symmetry, was formed by substituting each atom at C 20 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.
To investigate the stability of the (4,6)-fullerenes studied, we evaluated their binding energies   =   −  atom , where   and  atom are the energies per atom in the fullerenes and in the free state, respectively (Table 1).The difference in the binding energy of the C 60 and C 120 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 0.13-0.32eV/atom less stable than C 60 fullerene and about 0.38-0.57eV/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 C 60 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 I h (4,6)-fullerenes from the synthetic pathway used to prepare antikekulene.
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 H 2 (2.89 Å), but smaller than those of CO (3.76 Å), N 2 (3.65 Å), CO 2 (3.30Å), and CH 4 (3.80 Å).Therefore, the 12-MR provides a selective channel that allows H 2 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 polycyclic  systems of sp 2 -hybridized carbon atoms, (4,6)-fullerenes have many conjugated  bonds.As shown in Figures 1 and 2, the 6-, 10-, and 12-MRs are conjugated rings, while most of the 4-MRs consist of only four single  bonds and no  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 polycyclic  systems, whose aromaticity can be described as spherical aromaticity.Because the electron number does not follow the 2( + 1) 2 rule for spherical aromaticity [16], the I h C 60 and C 240  (5,6)-fullerenes display weak spherical aromaticity.However, most of the I h (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 (C 120 , C 240 , C 360 , 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 -conjugated rings.For instance, the conjugated 6-MRs are nonaromatic (NICS (1) = −0.5) in the C 60 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 (Figure 3).
The global and local NICS values of some typical -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.
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  In the C 60 fullerene, the 6-MR is a -conjugated aromatic (NICS = −7.6),while the 5-MR is nonaromatic (NICS = −1.1)due to the absence of a  bond(s).In the I h C 120 (4,6)-fullerene, the -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  bond.
In general, the -conjugated 6-MR is aromatic, the other -conjugated rings are weakly aromatic, and the rings without  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 -conjugated rings in the fullerenes.

Conclusions
In summary, a series of I h symmetrical (4,6)-fullerenes were constructed and investigated using first principle methods.These I h (4,6)-fullerenes consist of many 4-and 6-MRs that can be classified into two types: (1) those with isolated 4and 6-MRs and (2) those with connected 4-and 6-MRs.Though the (4,6)-fullerenes are about 0.13-0.32eV/atom less stable than the I h C 60 and about 0.38-0.57eV/atom less than the C 240 (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 -conjugated rings are aromatic, which provides some reasonable electronic delocalization, which is consistent with our chemical intuition.The C 360 and C 480 (4,6)-fullerenes have pore sizes of 3.2 Å so that only hydrogen gas molecules can easily access their cavities.Consequently, the C 360 and C 480 (4,6)fullerenes can be regarded as potential nanocontainers for hydrogen storage.

Figure 1 :Figure 2 :
Figure 1: The geometrical structures of the I h C 120 (a), C 240 (b), C 360 (c), and C 480 (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.

Figure 3 :
Figure 3: The geometrical structures of benzene (a), antikekulene (b), I h C 60 fullerene (c), and I h C 120 (4,6)-fullerene (d).The purple spheres indicate the sites of the ghost atoms in the NICS calculations.

Table 1 :
The geometrical, energetic, and electronic properties of the fullerenes a .The -ring in the carbon fullerenes (), the diameter of the fullerenes (  , Å), the diameter of the maximum -rings (  , Å), the diameter of the maximum pores (  , Å), binding energy (  , eV/atom), HOMO-LOMO energy gap (  , eV), and spherical NICS values for the fullerenes (NICS, ppm) and their + charged ions (NICS + ).

Table 2 :
The global and local NICS values of the individual n-rings in some typical -conjugated systems a .