Fullerene (C₆₀), which was discovered in 1985 by Kroto et al., is the third allotropic form of carbon [1] . The most well-known structure of C₆₀ 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 sp² hybridization, and C₆₀ tends to react readily with electron rich species due its poor electron delocalization. Since the discovery of C₆₀ [1] , the literature has reported the development of several fullerene derivatives based on the functionalization of the C₆₀ cage aiming to produce new properties and/or improve their existing properties. Other important studies involve the use of C₆₀ derivatives in biological systems [2] -[4] , solar cells [5] -[8] and superconductors [9] -[11] . Another class of C₆₀ derivatives has been achieved by the encapsulation of small molecules, metals and ions inside the C₆₀ 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 C₆₀ have attracted much attention due their potential applications in superconductivity and materials science [13] -[15] . The first evidence of metal trapped inside C₆₀ was obtained by Heath and collaborators [16] , who reported the formation of the La@C₆₀ complex. In the same laboratory, an air-stable film of La@C₆₀ was obtained [12] . Li⁺@C₆₀ was the first endohedral to be isolated, characterized and its crystal structure elucidated [17] [18] . Other non-metal C₆₀ endofullerenes have been experimentally determined including H₂@C₆₀ [19] [20] , N₂@C₆₀ [21] , noble gas [22] [23] , and, more recently, H₂O@C₆₀ [24] -[26] .

C₆₀ 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 C₆₀ 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 C₆₀ [29] , 3) electronic structures [30] [31] , 4) the charge transfer from the metal to C₆₀ [32] [33] , 5) the insertion of Be into C₆₀ [34] , and 6) the photoionization cross section in Mg²⁺@C₆₀ [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@C₆₀ (where M = H₂O, Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, and Ca²⁺) using quantum chemical methods. We have considered H₂O@C₆₀ and pure C₆₀ 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.

The C₆₀ 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.

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 Be²⁺@C₆₀ and Mg²⁺@C₆₀, 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 H₂O@C₆₀ and K⁺@C₆₀, the ions are

located in an off-center position in the C₆₀. 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⁺, Be²⁺ and Ca²⁺ 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⁺@C₆₀, the K⁺ ion is located in the center of the C₆₀ 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. For the optimized H₂O@C₆₀ complex, the shortest H...C and O...C distances are 2.70 and 3.45 Å, respectively, which is consistent with the crystallographic structure [26] , where the H...C and O...C interatomic distances are 2.60 and 3.55 Å, respectively. In addition, we performed an optimization with a single water molecule using the same theoretical level to compare the various properties obtained with the water molecule encapsulated in C₆₀. In this calculation, the H-O bonds had the same distance (0.96 Å). However, the H-O-H angle was different (i.e., H₂O@C₆₀ = 103.72˚ and pure water = 104.13˚). A decrease of 0.4% in this angle was most likely due to electronic repulsion between the hydrogen and carbon atoms. The endofullerene stability was based on the total energy (in hartree) obtained by DFT optimizations. The stability of the endofullerenes increased in the following order: C₆₀ (−2284.8) > Li⁺@C₆₀ (−2292.2) > Be²⁺@C₆₀ (−2298.9) > H₂O@C₆₀ (−2361.2) > Na⁺@C₆₀ (−2446.9) > Mg²⁺@C₆₀ (−2484.2) > K⁺@C₆₀ (−2884.5) > Ca²⁺@C₆₀ (−2961.8).

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 C₆₀ 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 C₆₀ decreased its IP, which indicated that the C₆₀ endofullerene is more electron donor than the pure C₆₀. In contrast, an increase in the IP was observed for the metal endofullerenes because they are more electron acceptor than C₆₀. Therefore, in both cases, the ions transfer their ionic character to C₆₀ 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 C₆₀ endofullerenes studied than it is for pure C₆₀, 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 C₆₀ endofullerenes indicated that these

^a in kcal/mol; ^bChelpG charge of encapsulated chemical species.

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@C₆₀ complexes, Mg²⁺@C₆₀ 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⁺@C₆₀, all of the studied chemical species increased the C₆₀ polarizability, and the dipole moment values increased with the decreasing binding energies (∆E) (Table 1). The K⁺ ion did not increase the dipole of C₆₀ due to the large distance between the carbon atoms and this ion. The dipole moment for H₂O@C₆₀ was 0.34 D. Therefore, the water molecule transferred its partial dipole to C₆₀. 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 H₂O and H₂O@C₆₀, 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 H₂O@C₆₀ 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: Be²⁺@C₆₀ (4.75 D) > Mg²⁺@C₆₀ (3.14 D) > Ca²⁺@C₆₀ (2.24 D) > Li⁺@C₆₀ (1.26 D) > Na⁺@C₆₀ (0.76 D) > H₂O@C₆₀ (0.24 D) > K⁺@C₆₀ (0.00 D). This sequence indicates that the solubility of endofullerene in water or other polar solvents may increase from H₂O@C₆₀ to Be²⁺@C₆₀. Therefore, the presence of these chemical species, except for K⁺, in the C₆₀ 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 H₂O@C₆₀, 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 C₆₀, 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 C₆₀ surface that was far from the metal ions. In general, the charge transfer from the cation to C₆₀ increased as the binding energy decreased due to cation-pi electronic interactions. Therefore, Be²⁺ 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.

C₆₀ 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 C₆₀. Based on Equation (1) and the low band gap energy of Be²⁺@C₆₀ (1.98 eV) and Mg²⁺@C₆₀ (1.38 eV), we suggest that these endofullerenes are more conductive than C₆₀ 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 C₆₀ can shift this band to the visible region. In our calculations, we observed a band centered at 310 nm for a single C₆₀. 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 C₆₀ is in agreement with previous theoretical calculations [51] [52] . In Figure 3, the absorption and band intensity of H₂O@C₆₀ and K⁺@C₆₀ are similar to those of pure C₆₀, which is due to the low interaction energy between these species and C₆₀ (Table 1). For Li⁺@C₆₀ and Na⁺@C₆₀, 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 Ca²⁺@C₆₀ and Be²⁺@C₆₀, respectively. However, the largest shoulder with a band centered at 356 nm with the lowest relative intensity (0.09) was observed for Mg²⁺@C₆₀. This result reinforces the hypothesis that the presence of Mg²⁺ in C₆₀ can shift the absorption spectra to the visible region (Figure 3).

Chemical species trapped in fullerenes comprise a new class of molecules with interesting properties. Therefore, in the current work, we employed quantum chemical methods to study seven endofullerenes (i.e., H₂O@C₆₀, Li⁺@C₆₀, Na⁺@C₆₀, K⁺@C₆₀, Be²⁺@C₆₀, Mg²⁺@C₆₀ and Ca²⁺@C₆₀). Our results indicate that all of the endoful- lerenes are more stable than pure C₆₀. The total energy (in hartree) calculated using DFT optimizations is as follows: C₆₀ (−2284.8) > Li⁺@C₆₀ (−2292.2) > Be²⁺@C₆₀ (−2298.9) > H₂O@C₆₀ (−2361.2) > Na⁺@C₆₀ (−2446.9) > Mg²⁺@C₆₀ (−2484.2) > K⁺@C₆₀ (−2884.5) > Ca²⁺@C₆₀ (−2961.8). The reactivity parameters (i.e., ionization potential and electron affinity) indicate that the alkali earth ions trapped in C₆₀ are the most reactive. In our calculations, charge transfer was observed from the ions to the fullerene. Therefore, except for K⁺@C₆₀, the dipole moment increased in the following order: Be²⁺@C₆₀ (4.75 Debye) > Mg²⁺@C₆₀ (3.14 D) > Ca²⁺@C₆₀ (2.24 D) > Li⁺@C₆₀ (1.26 D) > Na⁺@C₆₀ (0.76 D) > H₂O@C₆₀ (0.24 D) > K⁺@C₆₀ (0.00 D). Therefore, the solubility of the endofullerenes in polar solvents is expected to follow the same trend. Based on the HOMO and LUMO energy difference, Be²⁺@C₆₀ and Mg²⁺@C₆₀ have the highest electrical conductivity with band gap energies of 1.98 and 1.38 eV, respectively. The UV spectra obtained is in reasonable agreement with the experimental data. The C₆₀ band centered at 310 nm shifted to 343, 350 and 356 nm for Ca²⁺@C₆₀, Be²⁺@C₆₀ and Mg²⁺@C₆₀, respectively, which confirms the previous theoretical results.

We wish to thank our institute for financial support for this study.