Quantum Chemical Studies of Endofullerenes (M@C60) Where M = H2O, Li+, Na+, K+, Be2+, Mg2+, and Ca2+

Quantum chemical calculations were performed to investigate the structural and electronic properties of seven endofullerenes. The interaction energies indicated that all of the chemical species are stable inside the fullerene for each complex. The ionization potential and electron affinity values suggest that the endofullerenes consisting of alkaline earth ions are the most reactive and that the dipole moment decreased according to the following order: Be2+@C60 (4.75) > Mg2+@C60 (3.14) > Ca2+@C60 (2.24) > Li+@C60 (1.26) > Na+@C60 (0.76) > H2O@C60 (0.24) > K+@C60 (0.00 Debye). These results imply that the solubility of endofullerenes in a polar solvent may increase from H2O@C60 to Be2+@C60. The energetic gaps indicate that Be2+@C60 and Mg2+@C60 possess a higher electrical conductivity, and the UV spectra show a shift in the bands to the visible light region. The results of this work may be useful for the development of new endofullerenes.


Introduction
Fullerene (C 60 ), which was discovered in 1985 by Kroto et al., is the third allotropic form of carbon [1]. The most well-known structure of C 60 is the Buckminsterfullerene, which consists of 20 hexagonal rings and 12 pentagonal rings that form a geometric structure with 32 faces, which form a closed cage. Each carbon atom is bonded to three others with sp 2 hybridization, and C 60 tends to react readily with electron rich species due its poor electron delocalization. Since the discovery of C 60 [1], the literature has reported the development of sev-eral fullerene derivatives based on the functionalization of the C 60 cage aiming to produce new properties and/or improve their existing properties. Other important studies involve the use of C 60 derivatives in biological systems [2]- [4], solar cells [5]- [8] and superconductors [9]- [11]. Another class of C 60 derivatives has been achieved by the encapsulation of small molecules, metals and ions inside the C 60 cage. This type of system is known as an endofullerene (nomenclature proposed by Chai et al.) [12]. This representation is referred to as A@C n , where A and n are the chemical species and the number of carbon atoms, respectively. Among the endofullerenes, those based on C 60 have attracted much attention due their potential applications in superconductivity and materials science [13]- [15]. The first evidence of metal trapped inside C 60 was obtained by Heath and collaborators [16], who reported the formation of the La@C 60 complex. In the same laboratory, an air-stable film of La@C 60 was obtained [12]. Li + @C 60 was the first endohedral to be isolated, characterized and its crystal structure elucidated [17] [18]. Other non-metal C 60 endofullerenes have been experimentally determined including H 2 @C 60 [19] [20], N 2 @C 60 [21], noble gas [22] [23], and, more recently, H 2 O@C 60 [24]- [26].
C 60 endofullerenes can be obtained using three different experimental methods [27] including 1) the vaporization of graphite, 2) the insertion of the atoms through the fullerene cages, and 3) chemical routes that involve opening the fullerene cage. However, this method involves the use of extreme conditions, such as high temperature and treatment with high pressure. The increased energy expenditure results in endofullerene synthesis having high costs. Theoretical methods based on quantum chemistry are useful for predicting important properties that, in general, confirm the experimental data. Several theoretical studies of C 60 endofullerenes have been reported. Among these studies, quantum chemistry has been employed to study 1) the structural and optical properties of endofullerenes [28], 2) the mechanism of alkali-metal insertion into C 60 [29], 3) electronic structures [30] [31], 4) the charge transfer from the metal to C 60 [32] [33], 5) the insertion of Be into C 60 [34], and 6) the photoionization cross section in Mg 2+ @C 60 [35]. Although some alkali and alkaline earth ions have been studied using quantum chemical methods [28]- [35], the reactivity parameters of the current endofullerenes have not been predicted. However, some properties are very important in the chemical synthesis. Therefore, the goal of the current work was to investigate the electronic and structural properties of M@C 60 (where M = H 2 O, Li + , Na + , K + , Be 2+ , Mg 2+ , and Ca 2+ ) using quantum chemical methods. We have considered H 2 O@C 60 and pure C 60 to be reference systems when comparing the properties of a non-metallic endofullerene with the metallic ions complexes. Here, we are interested in predicting the reactivity parameters, electrical conductivity, absorption spectra, polarization and charge transfer process.

Computational Details
The C 60 structure was retrieved from the Library of 3-D Molecular Structures [http://www.nyu.edu/pages/mathmol/library/]. The endofullerenes were initially constructed by inserting the chemical species into the center of the fullerene using PyMOL [http://www.pymol.org/]. In sequential calculations, all of the structures were initially optimized using semi-empirical PM7 Hamiltonian [36], as implemented in the MOPAC package [37]. The final structures from these calculations were re-optimized using the GAMESS-US software [38] using DFT/B3LYP hybrid functional [39] [40] with the 6-31G(2d,2p) basis set. All of the stationary points were characterized as a point of minimum energy using the harmonic vibrational and ZPE correction calculations with the 6-31G(2d,2p) basis set. The absorption spectra were calculated using the TDDFT method with the 6-31G basis set, as implemented in the GAMESS-US software [38]. This basis set was used to reduce the high computational cost of the TDDFT calculations, and the polarizable continuum model (PCM) [41] of solvation was employed to account for the solvent (toluene) effects.

Results and Discussion
At the end of the optimizations, which were conducted using different methodologies, the spatial structures were aligned, and the RMSD (root mean square deviation) was calculated based on the DFT optimized structure, which was used as a reference. Surprisingly, the RMSD values were lower than 0.001 Å for all of the endofullerenes except Be 2+ @C 60 and Mg 2+ @C 60 , for which the RMSD was 0.01 Å. These small values indicate that the endofullerene structures obtained using the semi-empirical PM7 and DFT methods are very similar. Therefore, these methods possessed similar accuracies for the prediction of the current endofullerene structures. However, all of the reported results have been extracted from the DFT optimized structures (Figure 1).
The results in Figure 1 indicate that in all of the endofullerenes except H 2 O@C 60 and K + @C 60 , the ions are located in an off-center position in the C 60 . In addition, these ions are near the six-membered ring, with a distance of 2.3, 2.8, 1.8 and 2.6 Å for Li + , Na + , Be 2+ and Ca 2+ ions, respectively. The Li + ...C distance in the crystallographic structure (2.3 Å) [17] and our optimized molecule are the same, which demonstrates the accuracy of the current theoretical protocols. In K + @C 60 , the K + ion is located in the center of the C 60 cage, which is in agreement with the results from previous calculations [42]. This behavior can be attributed to the high ionic size of K + compared with the other studied ions. In all of the optimized structures, the encapsulation of the chemical species is favorable (negative values of ∆E). Table 1 summarizes some of the electronic properties obtained from the calculations.
According to Koopmans' theorem, the ionization potential (IP) of a molecule is the highest orbital molecular orbital (HOMO) energy (ε HOMO ) multiplied by −1, and the lowest unoccupied molecular orbital (LUMO) energy (ε LUMO ) multiplied by −1 represents the electron affinity (EA) or the capacity of a molecule to accept electrons. In a simplistic reaction model, the LUMO would be expected to accept electrons from the HOMO of another molecule. The results in Table 1 indicate that the endofullerenes containing ions in the same family have a similar IP, with values of ~9.20 and ~12.36 eV for alkali and alkaline earth ions, respectively. Therefore, the size of ionic radius and the IP of the ions in the same family do not effectively contribute to the IP of C 60 endofullerenes. However, the IP of endofullerenes increases by ~31% when alkali ions are replaced by alkaline earth ions. This increase is due to the high IP values of the alkaline earth ions compared with the alkali ions. Interestingly, the presence of the water molecule in the C 60 decreased its IP, which indicated that the C 60 endofullerene is more electron donor than the pure C 60 . In contrast, an increase in the IP was observed for the metal endofullerenes because they are more electron acceptor than C 60 . Therefore, in both cases, the ions transfer their ionic character to C 60 in the encapsulation process. The same behavior was observed for the electron affinity (LUMO orbital energy), as shown in Table 1. The EA is more negative for all of the C 60 endofullerenes studied than it is for pure C 60 , which indicated that the endofullerenes are more electron accepting compared with pure fullerene. Other chemical properties that can be estimated from the ε LUMO and ε HOMO include the chemical potential, µ ((ε LUMO + ε HOMO )/2), and the chemical hardness, η((ε LUMO − ε HOMO )/2). µ and η measure the tendency of an electron to escape from a particular field [43] and the resistance to modification of the electronic density [44], respectively. Therefore, the low values of µ and η for the alkaline earth ion C 60 endofullerenes indicated that these complexes are more resistant to donating an electron and that their electronic density is more easily modified compared with the other endofullerenes. In other words, the endofullerenes based on alkaline earth ions are more reactive than are the other endofullerenes studied. Among the M@C 60 complexes, Mg 2+ @C 60 exhibited the lowest values of µ (−11.66 eV) and η (0.70 eV), which is expected to result in high reactivity. The degree of fullerene polarization was characterized by the dipole moment. Except for K + @C 60 , all of the studied chemical species increased the C 60 polarizability, and the dipole moment values increased with the decreasing binding energies (∆E) ( Table 1). The K + ion did not increase the dipole of C 60 due to the large distance between the carbon atoms and this ion. The dipole moment for H 2 O@C 60 was 0.34 D. Therefore, the water molecule transferred its partial dipole to C 60 . The calculated dipole moment for pure water obtained using the same theoretical level as that employed for all of the endofullerenes was 2.04 D. By comparing the dipole moment of pure H 2 O and H 2 O@C 60 , a decrease of 83% was observed, which is in agreement with the ab initio results reported by Shameema [45]. However, Kurotobi and Murata [24] predicted an increase in the dipole moment of 0.05% in H 2 O@C 60 relative to pure water using the MX06-2X functional. This discrepancy may be due to the different functionals used. The dipole moment of the endofullerenes decreased in the following order: Be 2+ @C 60 (4.75 D) > Mg 2+ @C 60 (3.14 D) > Ca 2+ @C 60 (2.24 D) > Li + @C 60 (1.26 D) > Na + @C 60 (0.76 D) > H 2 O@C 60 (0.24 D) > K + @C 60 (0.00 D). This sequence indicates that the solubility of endofullerene in water or other polar solvents may increase from H 2 O@C 60 to Be 2+ @C 60 . Therefore, the presence of these chemical species, except for K + , in the C 60 cage can improve its solubility. The dipole moment observed for these fullerenes was due to the charge transfer from the chemical species to the fullerene ( Table 1). Except for water, all of the chemical species positively increased the fullerene charge. For single water, the ChelpG charge of the O and H atoms were −0.72 and 0.36, respectively. In H 2 O@C 60 , the charge of the oxygen increased to −0.46, and the charge of the hydrogen atoms decreased to 0.33 and 0.32. Therefore, a portion of the water charge was transferable to C 60 , which resulted in a negative charge of −0.19 ( Table 1). For all of the systems, the carbon atoms nearest the ions acquired a negative charge, while the positive charge was distributed over the C 60 surface that was far from the metal ions. In general, the charge transfer from the cation to C 60 increased as the binding energy decreased due to cation-pi electronic interactions. Therefore, Be 2+ transferred 82% of its charge to the fullerene, and this endofullerene possessed the lowest binding energy (−11.96 kcal/mol). Electronic conductivity is another interesting and important property of the new materials. This property can be estimated from the difference between the calculated HOMO and LUMO energies using Equation (1).
where σ is the electric conductivity, E g is the band gap energy, k b is Boltzmann's constant and T is the temperature. This equation indicates that a higher electric conductivity is due to a decrease in E g . Figure 2 shows the HOMO and LUMO energies and their surface representations obtained from DFT calculations. C 60 acts as a semiconductor with an experimental band gap of 2.3 -2.7 eV [46]- [49]. Therefore, the value (2.90 eV) that we obtained using the approximation |HOMO − LUMO| (Figure 2) is close to the experimental data. It is interesting to note that for all of the endofullerenes, the calculated energy gap is less than that of pure C 60 . Based on Equation (1) and the low band gap energy of Be 2+ @C 60 (1.98 eV) and Mg 2+ @C 60 (1.38 eV), we suggest that these endofullerenes are more conductive than C 60 and the other studied endofullerenes.
Another important property in the development of new materials is the capacity of a material to absorb in the visible region. Figure 3 shows the UV spectra of all of the studied compounds.  According to Prylutskyy [50], fullerene in toluene solvent possesses two intense broad absorption bands (i.e., 269 and 335 nm) and allowed transitions. In the current work, the band of major interest is near the UV-visible region (335 nm) because we believe that the presence of ions in C 60 can shift this band to the visible region. In our calculations, we observed a band centered at 310 nm for a single C 60 . Because our calculations were performed using PCM [41] with average basis sets, the calculated UV spectra are in reasonable agreement with the experimental data. However, the band at 310 nm for pure C 60 is in agreement with previous theoretical calculations [51] [52]. In Figure 3, the absorption and band intensity of H 2 O@C 60 and K + @C 60 are similar to those of pure C 60 , which is due to the low interaction energy between these species and C 60 ( Table 1). For Li + @C 60 and Na + @C 60 , the same wavelength (308 nm) with a relative intensity of 0.34 and a small shoulder at 343 nm was also observed. Interestingly, two bands at 343 (small shoulder) and 350 nm (large shoulder) were observed for Ca 2+ @C 60 and Be 2+ @C 60 , respectively. However, the largest shoulder with a band centered at 356 nm with the lowest relative intensity (0.09) was observed for Mg 2+ @C 60 . This result reinforces the hypothesis that the presence of Mg 2+ in C 60 can shift the absorption spectra to the visible region (Figure 3).