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Nonclassical fullerene C22H22 doped with transition metal atoms (ScNi): Density functional calculations
Computational and Theoretical Chemistry 999 (2012) 225–230
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Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
Nonclassical fullerene C22H22 doped with transition metal atoms (ScANi): Density functional calculations Chunmei Tang ⇑, Wei Guo, Weihua Zhu, Kaixiao Zhang, Aimei Zhang, Jiangfeng Gong, Hui Wang College of Science, Hohai University, Nanjing, Jiangsu 210098, China
a r t i c l e
i n f o
Article history: Received 15 April 2012 Received in revised form 30 August 2012 Accepted 5 September 2012 Available online 14 September 2012 Keywords: C22H22 M@C22H22 Geometric structure Electronic properties Magnetic moments Density functional theory
a b s t r a c t Geometric structures, electronic properties, hydrogen storage, optical absorption spectra, and magnetic properties of the nonclassical fullerenes M@C22H22 (M@ScANi) have been systematically studied using the density functional theory. The energy gap (5.77 eV) of the most stable C22H22 isomer has been multiplied up almost eight times compared with that of the pristine C22 cage (0.68 eV). The M@C22H22 (M@ScANi) cages with one four-membered ring are calculated the most stable. The new nanomaterials based on M@C22H22 could be excellent electron acceptors for potential photonic/photovoltaic applications in consequence of the increased VIP compared with that of C22H22. The optical properties of M@C22H22 can be tuned broadly in the ultraviolet–visible region. This is important for optoelectronic applications. Doping the transition metal atoms into the C22H22 cage can tune the magnetic properties. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Fullerenes are attracting much interest among carbon-based molecules due to their structural and electronic features [1]. All classical fullerenes are trivalent polyhedral carbon cages made up entirely of pentagonal and hexagonal rings. They are generally more stable than the nonclassical fullerenes, which include three-, four-, seven-membered, or larger rings. However, recent theoretical and experimental observations have found some exceptions. Such as, Fowler et al. [2] have suggested the inclusion of one or more four-membered rings into fullerene cage can lead to energetically competitive isomers. Qian et al. [3] have used density functional theory (DFT) and X-ray crystallography to find an isomer of C62 with a four-membered ring. Tendero et al. [4] have explored that the most stable isomer of C2þ 52 contained a fourmembered ring. Calculations [5] have suggested that cages with a heptagonal ring fell in the energy range of classical fullerene, confirmed by the isolation of C58F18 and C58F17CF3, which both contain a seven-membered ring [6]. The smallest classical fullerene is C20, which is composed of twelve pentagons [7,8]. The D6-symmetrical ground-state structure of the next smallest classical fullerene C24 has been reported [9,10]. Imaginably, the exclusive member between C20 and C24 should be C22. Previous experimental study [11] has suggested that the ground-state structure of C22 was a monocyclic ring. However, Jones et al. [12,13] have identified a ser-
⇑ Corresponding author. E-mail address: [email protected] (C. Tang). 2210-271X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2012.09.003
ies of C22 clusters, which contained both cage and noncage isomers. Killblane et al. [14] have computed that the cage structures were more stable than the ring and the bowl structures for C22, moreover, the lowest-energy structure of C22 has been predicted to be a cage with one four-membered ring, which has been confirmed by our previous research [15]. The experimental deeper researches for these nonclassical small fullerene were impeded mainly because of their high chemical activity. However, the perhydrogenatation of these nonclassical fullerenes can improve the stability and induce the experimental isolation. For example, the synthesis of C20 has been achieved by high voltage dehydrogenation of C20H20, which was considered as the dramatic experiment [16]. Saunders [17] have calculated that C60H60 was more stable than C60. Linnolahti et al. [18] have theoretically demonstrated that the icosahedral C80H80 and C180H180 fullerenes were more stable than the pristine C80 and C180. The endohedral metalfullerenes (metals encapsulated by fullerene cages) have attracted special attention as a new class of technologically relevant materials [19]. They have potential applications in diverse fields from medicine to electronics and quantum computing [20,21]. By endohedral–exohedral doping of C28 fullerene, cage species such as Ti@C28H4 has been found stable and magnetic [22]. In addition, thermodynamic factors have been discovered quite favorable for the formation of experimentally observed Zr@C28 and Sc@C28, which had different magnetic moments and ground states [23]. Sun et al. [24] have computed that M@C24H12 (M@Ti, Zr and Hf) displayed high symmetry and kinetic stability. Moreover, Wu et al. [25] have reported M@C24H12 (M@Cr, Mo and W) had high thermodynamic and kinetic stabilities.
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We have reported theoretical predictions of the geometrical and electronic properties of the lowest-energy structure of M@C22 (M@ScANi) in our previous paper [15], the results showed that the ground-state structure of the nonclassical fullerene C22 was a singlet-state cage with one four-membered ring, and the doping of transitional metal atom (TMA) into the cage of C22 could obviously enhance the stability and magnetism. As calculated, the energy gap (5.77 eV) of the most stable C22H22 isomer has been multiplied up almost eight times compared with that of the pristine C22 cage (0.68 eV) and 3.6 times of that of C60 cage (1.60 eV). Therefore, C22H22 is very stable, furthermore, we will present a systemic theoretical study of perhydrogenated endohedral fullerenes M@C22H22 (M@ScANi) in this article. This work will examine all possible cage isomers of C22H22 with one, two, three, and three four-membered rings respectively. There are two main aims in this study. Firstly, the ground-state structures of C22H22 and M@C22H22 (M@ScANi) fullerenes will be given out. Secondly, inspired by the researches on the transitional metal doped clusters [17,25,26], many properties such as electronic properties, hydrogen storage, optical absorption spectra, and magnetic moments of M@C22H22 (M@ScANi) will be presented. This paper is organized as follows. We describe our computational details in Section 2 and present the results and discussion in Section 3. Finally the conclusion is given in Section 4. 2. Computational details The DFT approach, has become one of the most popular calculation routines for large systems [27]. It has been found that the generalized gradient approximation (GGA) was more accurate than the local density approximation (LDA) in the calculations of the bond length and binding energy [28]. Therefore, GGA [28] based on DFT [27] was adopted in this paper. We chose the Becke–Lee– Yang–Parr (BLYP) correlation exchange functional, a combination of the Becke exchange functional [29] coupled with the Lee– Yang–Parr (LYP) correlation potential [30] as implemented in DMol3 package [27]. The basis sets used were double-numerical quality basis sets with polarization functions (DNP), comparable to Gaussian 6-31G sets. The real space cutoff of 5.5 was chosen. Electronic structure was obtained by solving the spin-polarized Kohn–Sham (KS) equations [31] self-consistently. DFT semicore pseudo potential (DSPP) [32] for TMAs was adopted. Self-consistent field procedures were carried out with a convergence criterion of 106 a.u. on the energy and electron density. Geometry optimizations were performed using the Broyden–Fletcher–Goldfarb– Shanno (BFGS) algorithm [33] with a convergence criterion of 103 a.u. on the displacement and 105 a.u. on the energy. All structures were fully optimized with no symmetry restriction. We confirmed the stability of the lowest-energy structure as minima of the potential energy surface by considering vibrational frequency. There was no imaginary frequency for structures reported here. In addition, for geometry optimization of each isomer, the spin multiplicity was considered at least 1, 3, 5 for even-electron clusters (Ti, Cr, Fe, and Ni) and 2, 4, 6 for odd-electron clusters (Sc, V, Mn, and Co). The optical absorption spectra were calculated in the dipole approximation using the dipole transition between the ground state and excited state. The DMol3 have assumed the ground state was a Slater determinant formed by the occupied KS orbitals. The intensity of the absorption, or the height of the absorption peak, was the square of the transition dipole moment associated with the transition energy. With this method, the optical absorption spectra of different Au32 isomers [34] and Sn12M (M@Ti, V, Cr, Mn, Fe, Co, and Ni) clusters [26] have been successfully calculated and used to identify their geometric structures.
3. Results and discussion 3.1. Geometric structures and stabilities Killblane et al. [24] have computed that there were four cages within the energy-cutoff criteria (0.6 eV) in the total isomers of C22 had the lowest energies. Furthermore, at both the PBE1PBE and MP2 levels, the cage isomer with one four-membered ring was confirmed to be the ground-state structure, therefore, these four stable C22 cages are considered for perhydrogenation in this paper. They contain one, three, two, and three four-membered rings respectively. Fig. 1 shows the geometric structures of these four isomers, which are named as C22H22-1, C22H22-2, C22H22-3 and C22H22-4 respectively. Commonly, the thermodynamic stability of a fullerene is mainly determined by its binding energy (Eb), which is defined as the absolute value of the difference between the total energy of the whole molecule and the energy sum of all the free atoms constituting the molecule [35]. The larger Eb indicates the better stability. The calculated Ebs of them is 225.35, 223.61, 223.62 and 224.55 eV respectively, so C22H22-1 has the best thermodynamic stability. Therefore, the most stable structure of C22H22 is formed by perhydrogenation of the most stable C22 cage. Additionally, the energy gaps (Egs) between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) for them are also computed. As we know, the kinetic stability of a fullerene derivative is often correlated with the Eg [36,37]. From calculation we can see that the Eg (5.77 eV) of C22H22-1 has been multiplied up almost eight times compared with that of C22-1 (0.68 eV). Thus, C22H22-1 has the dramatically enhanced kinetic stability. Next, we will pay attention to the stabilities of the TMA doped M@C22H22 (M@ScANi) structures. For each doped M atom, it is found that structure with one four-membered ring is the most stable by comparing the Ebs of four different symmetric isomers. The ground-state structures of M@C22H22 are discovered singlet state for Ti, Cr, Fe, Ni and doublet state for Sc, V, Mn, Co. Therefore, the most stable M@C22H22 is gotten by encaging M into the most stable C22H22, different from the case for La2@C72 [38]. Table 1 lists the doping energies (DEs), Egs, HCPs, LCPs, vertical ionization potentials (VIPs), and adsorption energies (Eadss) of M@C22H22 (M@ScANi). Here, the HCPs and LCPs are the percentages of M in the component of HOMO and LUMO. The geometric structures of M@C22H22 are simply presented in Fig. 2. The DE is defined as the energy difference between the M@C22H22 and the sum of the isolated C22H22 and M [39]. The positive DE means the exothermic reaction. The higher the DE is, the greater the stability of the resultant will be. The computed DEs of eight derivatives shown in Table 1 indicate the formations of M@C22H22 (M@Ti, Cr, Fe, Co, and Ni) are exothermic and energetically favored, however, the DEs of Sc@C22H22 and V@C22H22 are negative, while that of Mn@C22H22 is positive of 0.56 eV, indicating that Sc, V, and Mn cannot stably locate inside the C22H22 cage, which is in consistent with the observation from Fig. 2 that these three atoms shift to the surface of the cage and dramatically destroy the cage structure after optimization. In order to investigate the effect on the geometric structure of C22 brought by perhydrogenation and the doped M atom, the geometric parameters will be discussed in the following. We define the maximum distance between two C atoms along three rectangular coordinate axes as the corresponding axial diameter (Da), the Da along x, y, and z axes are named as X-Da, Y-Da, and Z-Da. The calculated X-Da, Y-Da, and Z-Da for the most stable C22 cage are 4.01, 4.00 and 4.44 Å respectively, while that of C22H22-1 extends by 13.12%, 4.61% and 2.93%, indicating that the perhydrogenation draw the cage outward to some degree. For the five closed
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Fig. 1. The ground-state geometric structures of four C22H22 cages.
Table 1 The DEs, Egs, HMPs, LMPs, VIP and Eadss of M@C22H22 (M@ScANi). HCPs and LCPs are the component percentages of M of HOMO and LUMO.
DE (eV) Eg (eV) HCP (%) LCP (%) VIP (eV) Eads (eV)
Sc@C22H22
Ti@C22H22
V@C22H22
Cr@C22H22
Mn@C22H22
Fe@C22H22
Co@C22H22
Ni@C22H22
1.61 0.44 35 28 4.66 3.39
4.48 0.43 81 88 3.23 3.38
1.47 1.67 99 85 0.40 3.07
5.86 0.38 59 67 4.63 3.14
0.56 0.69 99 98 0.95 3.18
5.15 0.95 87 93 3.00 3.25
4.14 0.47 84 99 4.33 3.35
9.76 1.52 99 73 4.80 3.48
Fig. 2. The optimized geometric structures of M@C22H22 (M@ScANi).
M@C22H22 (Ti, Cr, Fe, Co, and Ni) cages, when compared with that of C22H22-1, the X-Da increases 3.00%, 1.97%, 2.70%, 2.87% and 2.34%, the Y-Da elongates 3.79%, 4.13%, 2.02%, 1.38% and 1.38%, the Z-Da rises 7.08%, 0.72%, 6.44%, 6.18% and 6.48%, respectively. This indicates the encapsulation of M expands the cage outward once again. It is observed from Fig. 2 that the M atom somewhat shifts to the four-membered ring in the optimized M@C22H22 (Ti, Cr, Fe, Co, and Ni) cages. The bond lengths of C16–C20, C17–C21, C16–C17 and C20–C21 in the four-membered ring of C22, shorten as L (C16–C20), L (C17–C21), L (C16–C17), and L (C20–C21), are calculated 1.40, 1.40, 1.55, and 1.55 Å respectively, but that of C22H221 are equal of 1.56 Å and respectively elongates 11.41%, 11.41%, 1.10%, and 1.10%. For all the M@C22H22 cages, when compared with that of C22H22, L (C16–C20) increases 3.39%, 1.54%, 1.60%, 2.05% and 1.54%, L (C17–C21) lengthens 3.39%, 1.54%, 1.60%, 2.05% and 1.54%, L (C16–C17) rises 0.06%, 0.90%, 0.45%, 0.32% and 0.45%, L (C20–C21) elongates 0.06%, 0.90%, 0.45%, 0.32% and 0.45%. There-
fore, two relative long bonds of the four-membered ring are elongated while the other two short bond length of it are shortened. Furthermore, for the Sc and V doping, we find that the four-membered ring is completely distorted and becomes an open hole, where the encaged atom can shift outward, while for the Mn doping, the Mn atom moves to the outside through the hexagon, keep the four-membered ring of the cage intact. The smallest CAM bond lengths of M@C22H22 are 2.21, 2.22, 2.10, 2.19, 2.05, 2.14, 2.14 and 2.14 Å, respectively larger than the sum of the atom radius of C and M, 2.21, 2.09, 1.99, 1.95, 1.94, 1.94, 1.93 and 1.92 Å. The difference charge densities for M@C22H22 are defined as dqðrÞ ¼ qM@C 22 H22 ðrÞ ½qC 22 H22 1 ðrÞþ qM ðrÞ [40]. Here, dq(r) are the difference charge densities of M@C22H22 at r, qM@C 22 H22 ðrÞ; qC 22 H22 1 ðrÞ and qM(r) are the total charge densities of M@C22H22, C22H22-1 and M separately. Fig. 3 shows the difference charge densities for Ti@C22H22 as an example. There is no difference charge density distributes between Ti and C.
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the abilities for detaching electrons of M@C22H22 are increased compared with that of C22H22. 3.3. Hydrogen storage
Fig. 3. The difference charge densities of Ti@C22H22.
3.2. Electronic properties In quantum chemistry, the reactivity of a molecule can be correlated with its frontier orbitals and VIP. Commonly, the atom which contributes more to the HOMO should have the stronger ability for detaching electrons, whereas, the atom which occupies the main component of the LUMO should be easier to gain electrons [41]. Fig. 4 shows the wave functions of HOMOs and LUMOs of M@C22H22, where the blue and yellow represents the negative and positive parts of the wave functions. The calculated Egs of M@C22H22 known from Table 1 are all much smaller than that of C22H22-1. Thus, the doped M dramatically decreases the kinetic stability of the pristine cage. It is noted that the Eg and DE of Ni@C22H22, 1.52 and 9.76 eV, both are the largest of all, indicating that Ni@C22H22 should be the most stable of all. Not only known from the considerable contributions of M to the HOMO and LUMO in the form of percentage listed in Table 1, but also observed from Fig. 4 that the wavefunctions of HOMOs and LUMOs of the cage partly distribute on the M, the new nanomaterials based on M@C22H22 can serve as excellent acceptors with potential photonic/photovoltaic applications. The VIP is defined as the total energy difference between the one electron positively charged and neutral clusters. As Table 1 lists, the calculated VIP of C22H22-1 is 8.11 eV, whereas that of M@C22H22 become smaller, indicating
Fig. 4. The wave functions of HOMOs and LUMOs of M@C22H22 (M@ScANi).
We next study the possibilities for hydrogen storage of M@C22H22 clusters. The most crucial question in relation to hydrogen storage is whether the storage material has the good performance of both hydrogen adsorbing and releasing. The Eads of each H is defined as: Eads ¼ ½EðM@C 22 Þ þ 22EðHÞ EðM@C 22 H22 Þ=22 [42], which is an important indicator to measure the capacity of hydrogen adsorbing [42]. Here, EðM@C 22 H22 Þ; EðM@C 22 Þ and E(H) are the total energies of M@C22H22, M@C22 and H atom respectively. Table 1 presents that the calculated Eadss for each H atom adsorbed on the M@C22 surface are greater than 3 eV, similar to the Eads of 3.22 eV for each H atom adsorbed on the C22 cage [43], exploring that the H adsorption should be chemical adsorption. Previous findings indicate that the adsorption of H2 to the material ensures retrievable hydrogen storage should be with a desirable Eads in the range of 0.2–0.6 eV/H2 [44]. Therefore, the Eads value of an isolated H atom adsorbed on the M@C22 cage is so large that the hydrogen releasing may be difficult. Otherwise, using first-principles molecular dynamics calculations [45] up to 5 ps time scale, we found that, at high temperature (800 K), the cage structures of M@C22H22 are retained and the H atom remain attached to the cages. We have also investigated the Eadss for each H2 molecule adsorbed on the M@C22 cage. The calculated Eadss for each H2 molecule of M@C22 (H2)22 are from 0.007 to 0.028 eV, therefore, the adsorption of H2 on the cages should be physical, moreover, the binding of H2 molecules on M@C22 is so weak that storage at ambient conditions is not feasible. However, the hydrogen storage ability can be improved through some approaches such as coated by metal atom, and similar to the case of Li12@C60 [46]. 3.4. Optical absorption spectra Fig. 5 shows the calculated optical absorption spectra of C22H22 and M@C22H22 (M@ScANi). The optical gaps (OGs) are also shown in each panel. The spectra are described by a Lorenzian expansion of the obtained data. The broadening width parameter is chosen to be 0.06 eV. It is discovered that most of the absorption peaks in Fig. 5 locate in the visible and near-UV regain, easily detected by further experimental measurements. The spectra of C22H22-1 exhibit rich structures in the range from 9 to 15 eV, where well-resolved peaks are observed. However, the spectra of eight
Fig. 5. The optical absorption spectra of C22H22 and M@C22H22 (M@ScANi).
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C. Tang et al. / Computational and Theoretical Chemistry 999 (2012) 225–230 Table 2 The magnetic moments of M and M@C22H22 (M@ScANi)(unit: lB).
Fig. 6. The partial density of states (PDOS) of Cr and C22H22 of the Cr@C22H22 cluster. The PDOS of Cr is multiplied by 10 times in the figure.
M@C22H22 structures show continuous peaks in the broad range from 0 to 8 eV besides 9 to 15 eV. These spectra are more or less different from each other. Therefore, the doped M dramatically disturbs the optical absorption spectra of the bare C22H22-1 cage. To find out whether the origins of peaks in the energy range from 0 to 8 eV come from the doped M atom, we take Cr@C22H22 as an example. It is found that the absorption peak at 0.96 eV of the optical absorption spectra of Cr@C22H22 is formed by the electron transition from the energy level at 13.56 eV to that at 13.25 eV. We present the partial density of states (PDOSs) of Cr and C22H22 of Cr@C22H22 fullerene respectively in Fig. 6. The PDOS is obtained by a Lorentzian expansion of the discrete energy levels with weights being the orbital populations in the levels and a summation over them. The broadening width parameter is chosen to be 0.15 eV. The PDOS of Cr is so small that it is multiplied by 10 times in the figure. Because these two energies are too close to each other, therefore, only the PDOS at 13.25 eV is given in the figure. The figure shows that the PDOS at 13.25 eV for the Cr atom is only 2.21, which can be ignored, whereas that for C22H22 at 13.25 eV is 181. So the peak at 13.25 eV in the optical absorption spectra of Cr@C22H22 is derived from the C22H22. Therefore, the new peaks appear between 0 and 8 eV are not only from the doped M atom, moreover, the optical absorption spectra of the bare C22H22 cage are completely disturbed and redistributed in a wider energy range. In order to better understand the absorption properties, we further analyze the OGs and the lowest-energy absorption features of these clusters in each spectrum. It is calculated that the OGs of M@C22H22 vary from 1.00 to 2.71 eV, much smaller than that of C22H22, 9.19 eV, thus, the OGs of the M@C22H22 are red-shifted compared to that of C22H22. The irregularity of the curve illustrates that the OGs and spectral properties of M@C22H22 are apparently composition dependent after endohedral doping. Therefore, the optical properties of M@C22H22 can be tuned broadly in the ultraviolet–visible region. This is important for optoelectronic applications. 3.5. Magnetic moment Mulliken population analysis is one of the most widely used methods to obtain the atomic spin. Therefore, we employed this method to investigate the magnetic moments of M and M@C22H22, which are summarized in Table 2. The total magnetic moment is obtained by counting the unpaired spins below the Fermi level. From the table, one may see that only the M@C22H22 (Sc, V, Cr, Mn, and Co) clusters are magnetic. Amongst, for Sc, Cr and Co doped structures, the total magnetic moment of the cage is interestingly identical to the moment of the corresponding isolated M
M@C22H22
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
M moment Molecular moment
1 1
0 0
4 5
5 6
3 3
0 0
1 1
0 0
atom. Take Cr@C22H22 as an example, Cr is considered as a special case, different from other 3d TMAs with a half filled 4s level electronic configuration. The magnetic moment of an isolated Cr atom is 6 lB. When the Cr atom is doped into the C22H22 cage, the magnetic moment of it is reduced to 5 lB and the total magnetic moment of the Cr@C22H22 is 6 lB, owing to the electron transference. It should be noticed that the magnetic moments of M@C22H22 (M@Ti, Fe, and Ni) are all zero, therefore, doping of these three atoms can lead to the magnetism vanishing of the fullerene. Theoretically, the 3d electron delocalization and the exchange splitting of 3d orbital both play an important role in the magnetic moments [47]. Similarly, the doped M affects the orbital hybridization and the electronic population of the 3d orbital, resulting in the new spin state of the M@C22H22 clusters. Therefore, we can come to the conclusion that the magnetic moments of the M@C22H22 clusters vary from 0 to 6 lB, and doping the TMA into the C22H22 cage could tune the magnetic properties of the clusters. 4. Conclusion We have used the DFT to study the geometric structures, electronic properties, hydrogen storage, optical absorption spectra, and magnetic moments of nonclassical fullerene M@C22H22 (M@ScANi). The C22H22 cage with one four-membered ring has the largest thermodynamic and kinetic stability. The Eg of the most thermodynamic stable C22H22 cage is large, multiplied up almost eight times when compared with the pristine cage. Afterwards, the M@C22H22 (M@ScANi) cages with one four-membered ring are calculated the most stable known from the Ebs. The optimization process shows Ti, Cr, Fe, Co, and Ni can stably locate inside the C22H22 cage, while Sc, V, and Mn prefer the site near the surface of the cage and dramatically destroy the cage structure. It can be concluded from the difference charge densities that the CAM bond mainly has the ionic character. Further investigations show that the new nanomaterials based on M@C22H22 could be excellent electron acceptors for potential photonic/photovoltaic applications in consequence of the increased VIP compared with that of the most stable C22H22. The Eadss explore M@C22H22 possess poor hydrogen releasing performance. The optical properties of M@C22H22 can be tuned broadly in the ultraviolet–visible region. This is important for optoelectronic applications. The magnetic moments of M@C22H22 vary from 0 to 6 lB, indicating that doping the TMA into the C22H22 cage could tune the magnetic properties of the clusters. Acknowledgements Project supported by the Special Foundation of National Natural Science (Grant Nos. 11104062, 10947132, 11004047), the Excellent Innovation Personal Support Plan of Hohai University, and the Fundamental Research Funds for the Central Universities (Grant No. 2012B12914). References [1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, C60: buckminsterfullerene, Nature 318 (1985) 162–163. [2] P.W. Fowler, T. Heine, D.E. Manolopoulos, D. Mitchell, G. Orlandi, R. Schmidt, G. Seifert, F. Zerbetto, Energetics of fullerenes with four-membered rings, J. Phys. Chem. 100 (1996) 6984–6991.
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Nonclassical fullerene C22H22 doped with transition metal atoms (ScANi): Density functional calculations Chunmei Tang ⇑, Wei Guo, Weihua Zhu, Kaixiao Zhang, Aimei Zhang, Jiangfeng Gong, Hui Wang College of Science, Hohai University, Nanjing, Jiangsu 210098, China
a r t i c l e
i n f o
Article history: Received 15 April 2012 Received in revised form 30 August 2012 Accepted 5 September 2012 Available online 14 September 2012 Keywords: C22H22 M@C22H22 Geometric structure Electronic properties Magnetic moments Density functional theory
a b s t r a c t Geometric structures, electronic properties, hydrogen storage, optical absorption spectra, and magnetic properties of the nonclassical fullerenes M@C22H22 (M@ScANi) have been systematically studied using the density functional theory. The energy gap (5.77 eV) of the most stable C22H22 isomer has been multiplied up almost eight times compared with that of the pristine C22 cage (0.68 eV). The M@C22H22 (M@ScANi) cages with one four-membered ring are calculated the most stable. The new nanomaterials based on M@C22H22 could be excellent electron acceptors for potential photonic/photovoltaic applications in consequence of the increased VIP compared with that of C22H22. The optical properties of M@C22H22 can be tuned broadly in the ultraviolet–visible region. This is important for optoelectronic applications. Doping the transition metal atoms into the C22H22 cage can tune the magnetic properties. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Fullerenes are attracting much interest among carbon-based molecules due to their structural and electronic features [1]. All classical fullerenes are trivalent polyhedral carbon cages made up entirely of pentagonal and hexagonal rings. They are generally more stable than the nonclassical fullerenes, which include three-, four-, seven-membered, or larger rings. However, recent theoretical and experimental observations have found some exceptions. Such as, Fowler et al. [2] have suggested the inclusion of one or more four-membered rings into fullerene cage can lead to energetically competitive isomers. Qian et al. [3] have used density functional theory (DFT) and X-ray crystallography to find an isomer of C62 with a four-membered ring. Tendero et al. [4] have explored that the most stable isomer of C2þ 52 contained a fourmembered ring. Calculations [5] have suggested that cages with a heptagonal ring fell in the energy range of classical fullerene, confirmed by the isolation of C58F18 and C58F17CF3, which both contain a seven-membered ring [6]. The smallest classical fullerene is C20, which is composed of twelve pentagons [7,8]. The D6-symmetrical ground-state structure of the next smallest classical fullerene C24 has been reported [9,10]. Imaginably, the exclusive member between C20 and C24 should be C22. Previous experimental study [11] has suggested that the ground-state structure of C22 was a monocyclic ring. However, Jones et al. [12,13] have identified a ser-
⇑ Corresponding author. E-mail address: [email protected] (C. Tang). 2210-271X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2012.09.003
ies of C22 clusters, which contained both cage and noncage isomers. Killblane et al. [14] have computed that the cage structures were more stable than the ring and the bowl structures for C22, moreover, the lowest-energy structure of C22 has been predicted to be a cage with one four-membered ring, which has been confirmed by our previous research [15]. The experimental deeper researches for these nonclassical small fullerene were impeded mainly because of their high chemical activity. However, the perhydrogenatation of these nonclassical fullerenes can improve the stability and induce the experimental isolation. For example, the synthesis of C20 has been achieved by high voltage dehydrogenation of C20H20, which was considered as the dramatic experiment [16]. Saunders [17] have calculated that C60H60 was more stable than C60. Linnolahti et al. [18] have theoretically demonstrated that the icosahedral C80H80 and C180H180 fullerenes were more stable than the pristine C80 and C180. The endohedral metalfullerenes (metals encapsulated by fullerene cages) have attracted special attention as a new class of technologically relevant materials [19]. They have potential applications in diverse fields from medicine to electronics and quantum computing [20,21]. By endohedral–exohedral doping of C28 fullerene, cage species such as Ti@C28H4 has been found stable and magnetic [22]. In addition, thermodynamic factors have been discovered quite favorable for the formation of experimentally observed Zr@C28 and Sc@C28, which had different magnetic moments and ground states [23]. Sun et al. [24] have computed that M@C24H12 (M@Ti, Zr and Hf) displayed high symmetry and kinetic stability. Moreover, Wu et al. [25] have reported M@C24H12 (M@Cr, Mo and W) had high thermodynamic and kinetic stabilities.
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We have reported theoretical predictions of the geometrical and electronic properties of the lowest-energy structure of M@C22 (M@ScANi) in our previous paper [15], the results showed that the ground-state structure of the nonclassical fullerene C22 was a singlet-state cage with one four-membered ring, and the doping of transitional metal atom (TMA) into the cage of C22 could obviously enhance the stability and magnetism. As calculated, the energy gap (5.77 eV) of the most stable C22H22 isomer has been multiplied up almost eight times compared with that of the pristine C22 cage (0.68 eV) and 3.6 times of that of C60 cage (1.60 eV). Therefore, C22H22 is very stable, furthermore, we will present a systemic theoretical study of perhydrogenated endohedral fullerenes M@C22H22 (M@ScANi) in this article. This work will examine all possible cage isomers of C22H22 with one, two, three, and three four-membered rings respectively. There are two main aims in this study. Firstly, the ground-state structures of C22H22 and M@C22H22 (M@ScANi) fullerenes will be given out. Secondly, inspired by the researches on the transitional metal doped clusters [17,25,26], many properties such as electronic properties, hydrogen storage, optical absorption spectra, and magnetic moments of M@C22H22 (M@ScANi) will be presented. This paper is organized as follows. We describe our computational details in Section 2 and present the results and discussion in Section 3. Finally the conclusion is given in Section 4. 2. Computational details The DFT approach, has become one of the most popular calculation routines for large systems [27]. It has been found that the generalized gradient approximation (GGA) was more accurate than the local density approximation (LDA) in the calculations of the bond length and binding energy [28]. Therefore, GGA [28] based on DFT [27] was adopted in this paper. We chose the Becke–Lee– Yang–Parr (BLYP) correlation exchange functional, a combination of the Becke exchange functional [29] coupled with the Lee– Yang–Parr (LYP) correlation potential [30] as implemented in DMol3 package [27]. The basis sets used were double-numerical quality basis sets with polarization functions (DNP), comparable to Gaussian 6-31G sets. The real space cutoff of 5.5 was chosen. Electronic structure was obtained by solving the spin-polarized Kohn–Sham (KS) equations [31] self-consistently. DFT semicore pseudo potential (DSPP) [32] for TMAs was adopted. Self-consistent field procedures were carried out with a convergence criterion of 106 a.u. on the energy and electron density. Geometry optimizations were performed using the Broyden–Fletcher–Goldfarb– Shanno (BFGS) algorithm [33] with a convergence criterion of 103 a.u. on the displacement and 105 a.u. on the energy. All structures were fully optimized with no symmetry restriction. We confirmed the stability of the lowest-energy structure as minima of the potential energy surface by considering vibrational frequency. There was no imaginary frequency for structures reported here. In addition, for geometry optimization of each isomer, the spin multiplicity was considered at least 1, 3, 5 for even-electron clusters (Ti, Cr, Fe, and Ni) and 2, 4, 6 for odd-electron clusters (Sc, V, Mn, and Co). The optical absorption spectra were calculated in the dipole approximation using the dipole transition between the ground state and excited state. The DMol3 have assumed the ground state was a Slater determinant formed by the occupied KS orbitals. The intensity of the absorption, or the height of the absorption peak, was the square of the transition dipole moment associated with the transition energy. With this method, the optical absorption spectra of different Au32 isomers [34] and Sn12M (M@Ti, V, Cr, Mn, Fe, Co, and Ni) clusters [26] have been successfully calculated and used to identify their geometric structures.
3. Results and discussion 3.1. Geometric structures and stabilities Killblane et al. [24] have computed that there were four cages within the energy-cutoff criteria (0.6 eV) in the total isomers of C22 had the lowest energies. Furthermore, at both the PBE1PBE and MP2 levels, the cage isomer with one four-membered ring was confirmed to be the ground-state structure, therefore, these four stable C22 cages are considered for perhydrogenation in this paper. They contain one, three, two, and three four-membered rings respectively. Fig. 1 shows the geometric structures of these four isomers, which are named as C22H22-1, C22H22-2, C22H22-3 and C22H22-4 respectively. Commonly, the thermodynamic stability of a fullerene is mainly determined by its binding energy (Eb), which is defined as the absolute value of the difference between the total energy of the whole molecule and the energy sum of all the free atoms constituting the molecule [35]. The larger Eb indicates the better stability. The calculated Ebs of them is 225.35, 223.61, 223.62 and 224.55 eV respectively, so C22H22-1 has the best thermodynamic stability. Therefore, the most stable structure of C22H22 is formed by perhydrogenation of the most stable C22 cage. Additionally, the energy gaps (Egs) between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) for them are also computed. As we know, the kinetic stability of a fullerene derivative is often correlated with the Eg [36,37]. From calculation we can see that the Eg (5.77 eV) of C22H22-1 has been multiplied up almost eight times compared with that of C22-1 (0.68 eV). Thus, C22H22-1 has the dramatically enhanced kinetic stability. Next, we will pay attention to the stabilities of the TMA doped M@C22H22 (M@ScANi) structures. For each doped M atom, it is found that structure with one four-membered ring is the most stable by comparing the Ebs of four different symmetric isomers. The ground-state structures of M@C22H22 are discovered singlet state for Ti, Cr, Fe, Ni and doublet state for Sc, V, Mn, Co. Therefore, the most stable M@C22H22 is gotten by encaging M into the most stable C22H22, different from the case for La2@C72 [38]. Table 1 lists the doping energies (DEs), Egs, HCPs, LCPs, vertical ionization potentials (VIPs), and adsorption energies (Eadss) of M@C22H22 (M@ScANi). Here, the HCPs and LCPs are the percentages of M in the component of HOMO and LUMO. The geometric structures of M@C22H22 are simply presented in Fig. 2. The DE is defined as the energy difference between the M@C22H22 and the sum of the isolated C22H22 and M [39]. The positive DE means the exothermic reaction. The higher the DE is, the greater the stability of the resultant will be. The computed DEs of eight derivatives shown in Table 1 indicate the formations of M@C22H22 (M@Ti, Cr, Fe, Co, and Ni) are exothermic and energetically favored, however, the DEs of Sc@C22H22 and V@C22H22 are negative, while that of Mn@C22H22 is positive of 0.56 eV, indicating that Sc, V, and Mn cannot stably locate inside the C22H22 cage, which is in consistent with the observation from Fig. 2 that these three atoms shift to the surface of the cage and dramatically destroy the cage structure after optimization. In order to investigate the effect on the geometric structure of C22 brought by perhydrogenation and the doped M atom, the geometric parameters will be discussed in the following. We define the maximum distance between two C atoms along three rectangular coordinate axes as the corresponding axial diameter (Da), the Da along x, y, and z axes are named as X-Da, Y-Da, and Z-Da. The calculated X-Da, Y-Da, and Z-Da for the most stable C22 cage are 4.01, 4.00 and 4.44 Å respectively, while that of C22H22-1 extends by 13.12%, 4.61% and 2.93%, indicating that the perhydrogenation draw the cage outward to some degree. For the five closed
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Fig. 1. The ground-state geometric structures of four C22H22 cages.
Table 1 The DEs, Egs, HMPs, LMPs, VIP and Eadss of M@C22H22 (M@ScANi). HCPs and LCPs are the component percentages of M of HOMO and LUMO.
DE (eV) Eg (eV) HCP (%) LCP (%) VIP (eV) Eads (eV)
Sc@C22H22
Ti@C22H22
V@C22H22
Cr@C22H22
Mn@C22H22
Fe@C22H22
Co@C22H22
Ni@C22H22
1.61 0.44 35 28 4.66 3.39
4.48 0.43 81 88 3.23 3.38
1.47 1.67 99 85 0.40 3.07
5.86 0.38 59 67 4.63 3.14
0.56 0.69 99 98 0.95 3.18
5.15 0.95 87 93 3.00 3.25
4.14 0.47 84 99 4.33 3.35
9.76 1.52 99 73 4.80 3.48
Fig. 2. The optimized geometric structures of M@C22H22 (M@ScANi).
M@C22H22 (Ti, Cr, Fe, Co, and Ni) cages, when compared with that of C22H22-1, the X-Da increases 3.00%, 1.97%, 2.70%, 2.87% and 2.34%, the Y-Da elongates 3.79%, 4.13%, 2.02%, 1.38% and 1.38%, the Z-Da rises 7.08%, 0.72%, 6.44%, 6.18% and 6.48%, respectively. This indicates the encapsulation of M expands the cage outward once again. It is observed from Fig. 2 that the M atom somewhat shifts to the four-membered ring in the optimized M@C22H22 (Ti, Cr, Fe, Co, and Ni) cages. The bond lengths of C16–C20, C17–C21, C16–C17 and C20–C21 in the four-membered ring of C22, shorten as L (C16–C20), L (C17–C21), L (C16–C17), and L (C20–C21), are calculated 1.40, 1.40, 1.55, and 1.55 Å respectively, but that of C22H221 are equal of 1.56 Å and respectively elongates 11.41%, 11.41%, 1.10%, and 1.10%. For all the M@C22H22 cages, when compared with that of C22H22, L (C16–C20) increases 3.39%, 1.54%, 1.60%, 2.05% and 1.54%, L (C17–C21) lengthens 3.39%, 1.54%, 1.60%, 2.05% and 1.54%, L (C16–C17) rises 0.06%, 0.90%, 0.45%, 0.32% and 0.45%, L (C20–C21) elongates 0.06%, 0.90%, 0.45%, 0.32% and 0.45%. There-
fore, two relative long bonds of the four-membered ring are elongated while the other two short bond length of it are shortened. Furthermore, for the Sc and V doping, we find that the four-membered ring is completely distorted and becomes an open hole, where the encaged atom can shift outward, while for the Mn doping, the Mn atom moves to the outside through the hexagon, keep the four-membered ring of the cage intact. The smallest CAM bond lengths of M@C22H22 are 2.21, 2.22, 2.10, 2.19, 2.05, 2.14, 2.14 and 2.14 Å, respectively larger than the sum of the atom radius of C and M, 2.21, 2.09, 1.99, 1.95, 1.94, 1.94, 1.93 and 1.92 Å. The difference charge densities for M@C22H22 are defined as dqðrÞ ¼ qM@C 22 H22 ðrÞ ½qC 22 H22 1 ðrÞþ qM ðrÞ [40]. Here, dq(r) are the difference charge densities of M@C22H22 at r, qM@C 22 H22 ðrÞ; qC 22 H22 1 ðrÞ and qM(r) are the total charge densities of M@C22H22, C22H22-1 and M separately. Fig. 3 shows the difference charge densities for Ti@C22H22 as an example. There is no difference charge density distributes between Ti and C.
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the abilities for detaching electrons of M@C22H22 are increased compared with that of C22H22. 3.3. Hydrogen storage
Fig. 3. The difference charge densities of Ti@C22H22.
3.2. Electronic properties In quantum chemistry, the reactivity of a molecule can be correlated with its frontier orbitals and VIP. Commonly, the atom which contributes more to the HOMO should have the stronger ability for detaching electrons, whereas, the atom which occupies the main component of the LUMO should be easier to gain electrons [41]. Fig. 4 shows the wave functions of HOMOs and LUMOs of M@C22H22, where the blue and yellow represents the negative and positive parts of the wave functions. The calculated Egs of M@C22H22 known from Table 1 are all much smaller than that of C22H22-1. Thus, the doped M dramatically decreases the kinetic stability of the pristine cage. It is noted that the Eg and DE of Ni@C22H22, 1.52 and 9.76 eV, both are the largest of all, indicating that Ni@C22H22 should be the most stable of all. Not only known from the considerable contributions of M to the HOMO and LUMO in the form of percentage listed in Table 1, but also observed from Fig. 4 that the wavefunctions of HOMOs and LUMOs of the cage partly distribute on the M, the new nanomaterials based on M@C22H22 can serve as excellent acceptors with potential photonic/photovoltaic applications. The VIP is defined as the total energy difference between the one electron positively charged and neutral clusters. As Table 1 lists, the calculated VIP of C22H22-1 is 8.11 eV, whereas that of M@C22H22 become smaller, indicating
Fig. 4. The wave functions of HOMOs and LUMOs of M@C22H22 (M@ScANi).
We next study the possibilities for hydrogen storage of M@C22H22 clusters. The most crucial question in relation to hydrogen storage is whether the storage material has the good performance of both hydrogen adsorbing and releasing. The Eads of each H is defined as: Eads ¼ ½EðM@C 22 Þ þ 22EðHÞ EðM@C 22 H22 Þ=22 [42], which is an important indicator to measure the capacity of hydrogen adsorbing [42]. Here, EðM@C 22 H22 Þ; EðM@C 22 Þ and E(H) are the total energies of M@C22H22, M@C22 and H atom respectively. Table 1 presents that the calculated Eadss for each H atom adsorbed on the M@C22 surface are greater than 3 eV, similar to the Eads of 3.22 eV for each H atom adsorbed on the C22 cage [43], exploring that the H adsorption should be chemical adsorption. Previous findings indicate that the adsorption of H2 to the material ensures retrievable hydrogen storage should be with a desirable Eads in the range of 0.2–0.6 eV/H2 [44]. Therefore, the Eads value of an isolated H atom adsorbed on the M@C22 cage is so large that the hydrogen releasing may be difficult. Otherwise, using first-principles molecular dynamics calculations [45] up to 5 ps time scale, we found that, at high temperature (800 K), the cage structures of M@C22H22 are retained and the H atom remain attached to the cages. We have also investigated the Eadss for each H2 molecule adsorbed on the M@C22 cage. The calculated Eadss for each H2 molecule of M@C22 (H2)22 are from 0.007 to 0.028 eV, therefore, the adsorption of H2 on the cages should be physical, moreover, the binding of H2 molecules on M@C22 is so weak that storage at ambient conditions is not feasible. However, the hydrogen storage ability can be improved through some approaches such as coated by metal atom, and similar to the case of Li12@C60 [46]. 3.4. Optical absorption spectra Fig. 5 shows the calculated optical absorption spectra of C22H22 and M@C22H22 (M@ScANi). The optical gaps (OGs) are also shown in each panel. The spectra are described by a Lorenzian expansion of the obtained data. The broadening width parameter is chosen to be 0.06 eV. It is discovered that most of the absorption peaks in Fig. 5 locate in the visible and near-UV regain, easily detected by further experimental measurements. The spectra of C22H22-1 exhibit rich structures in the range from 9 to 15 eV, where well-resolved peaks are observed. However, the spectra of eight
Fig. 5. The optical absorption spectra of C22H22 and M@C22H22 (M@ScANi).
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C. Tang et al. / Computational and Theoretical Chemistry 999 (2012) 225–230 Table 2 The magnetic moments of M and M@C22H22 (M@ScANi)(unit: lB).
Fig. 6. The partial density of states (PDOS) of Cr and C22H22 of the Cr@C22H22 cluster. The PDOS of Cr is multiplied by 10 times in the figure.
M@C22H22 structures show continuous peaks in the broad range from 0 to 8 eV besides 9 to 15 eV. These spectra are more or less different from each other. Therefore, the doped M dramatically disturbs the optical absorption spectra of the bare C22H22-1 cage. To find out whether the origins of peaks in the energy range from 0 to 8 eV come from the doped M atom, we take Cr@C22H22 as an example. It is found that the absorption peak at 0.96 eV of the optical absorption spectra of Cr@C22H22 is formed by the electron transition from the energy level at 13.56 eV to that at 13.25 eV. We present the partial density of states (PDOSs) of Cr and C22H22 of Cr@C22H22 fullerene respectively in Fig. 6. The PDOS is obtained by a Lorentzian expansion of the discrete energy levels with weights being the orbital populations in the levels and a summation over them. The broadening width parameter is chosen to be 0.15 eV. The PDOS of Cr is so small that it is multiplied by 10 times in the figure. Because these two energies are too close to each other, therefore, only the PDOS at 13.25 eV is given in the figure. The figure shows that the PDOS at 13.25 eV for the Cr atom is only 2.21, which can be ignored, whereas that for C22H22 at 13.25 eV is 181. So the peak at 13.25 eV in the optical absorption spectra of Cr@C22H22 is derived from the C22H22. Therefore, the new peaks appear between 0 and 8 eV are not only from the doped M atom, moreover, the optical absorption spectra of the bare C22H22 cage are completely disturbed and redistributed in a wider energy range. In order to better understand the absorption properties, we further analyze the OGs and the lowest-energy absorption features of these clusters in each spectrum. It is calculated that the OGs of M@C22H22 vary from 1.00 to 2.71 eV, much smaller than that of C22H22, 9.19 eV, thus, the OGs of the M@C22H22 are red-shifted compared to that of C22H22. The irregularity of the curve illustrates that the OGs and spectral properties of M@C22H22 are apparently composition dependent after endohedral doping. Therefore, the optical properties of M@C22H22 can be tuned broadly in the ultraviolet–visible region. This is important for optoelectronic applications. 3.5. Magnetic moment Mulliken population analysis is one of the most widely used methods to obtain the atomic spin. Therefore, we employed this method to investigate the magnetic moments of M and M@C22H22, which are summarized in Table 2. The total magnetic moment is obtained by counting the unpaired spins below the Fermi level. From the table, one may see that only the M@C22H22 (Sc, V, Cr, Mn, and Co) clusters are magnetic. Amongst, for Sc, Cr and Co doped structures, the total magnetic moment of the cage is interestingly identical to the moment of the corresponding isolated M
M@C22H22
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
M moment Molecular moment
1 1
0 0
4 5
5 6
3 3
0 0
1 1
0 0
atom. Take Cr@C22H22 as an example, Cr is considered as a special case, different from other 3d TMAs with a half filled 4s level electronic configuration. The magnetic moment of an isolated Cr atom is 6 lB. When the Cr atom is doped into the C22H22 cage, the magnetic moment of it is reduced to 5 lB and the total magnetic moment of the Cr@C22H22 is 6 lB, owing to the electron transference. It should be noticed that the magnetic moments of M@C22H22 (M@Ti, Fe, and Ni) are all zero, therefore, doping of these three atoms can lead to the magnetism vanishing of the fullerene. Theoretically, the 3d electron delocalization and the exchange splitting of 3d orbital both play an important role in the magnetic moments [47]. Similarly, the doped M affects the orbital hybridization and the electronic population of the 3d orbital, resulting in the new spin state of the M@C22H22 clusters. Therefore, we can come to the conclusion that the magnetic moments of the M@C22H22 clusters vary from 0 to 6 lB, and doping the TMA into the C22H22 cage could tune the magnetic properties of the clusters. 4. Conclusion We have used the DFT to study the geometric structures, electronic properties, hydrogen storage, optical absorption spectra, and magnetic moments of nonclassical fullerene M@C22H22 (M@ScANi). The C22H22 cage with one four-membered ring has the largest thermodynamic and kinetic stability. The Eg of the most thermodynamic stable C22H22 cage is large, multiplied up almost eight times when compared with the pristine cage. Afterwards, the M@C22H22 (M@ScANi) cages with one four-membered ring are calculated the most stable known from the Ebs. The optimization process shows Ti, Cr, Fe, Co, and Ni can stably locate inside the C22H22 cage, while Sc, V, and Mn prefer the site near the surface of the cage and dramatically destroy the cage structure. It can be concluded from the difference charge densities that the CAM bond mainly has the ionic character. Further investigations show that the new nanomaterials based on M@C22H22 could be excellent electron acceptors for potential photonic/photovoltaic applications in consequence of the increased VIP compared with that of the most stable C22H22. The Eadss explore M@C22H22 possess poor hydrogen releasing performance. The optical properties of M@C22H22 can be tuned broadly in the ultraviolet–visible region. This is important for optoelectronic applications. The magnetic moments of M@C22H22 vary from 0 to 6 lB, indicating that doping the TMA into the C22H22 cage could tune the magnetic properties of the clusters. Acknowledgements Project supported by the Special Foundation of National Natural Science (Grant Nos. 11104062, 10947132, 11004047), the Excellent Innovation Personal Support Plan of Hohai University, and the Fundamental Research Funds for the Central Universities (Grant No. 2012B12914). References [1] H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, C60: buckminsterfullerene, Nature 318 (1985) 162–163. [2] P.W. Fowler, T. Heine, D.E. Manolopoulos, D. Mitchell, G. Orlandi, R. Schmidt, G. Seifert, F. Zerbetto, Energetics of fullerenes with four-membered rings, J. Phys. Chem. 100 (1996) 6984–6991.
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