Computational and Theoretical Chemistry 1034 (2014) 73–79

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Computational and Theoretical Chemistry

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Theoretical studies on the interaction of some endohedral fullerenes{[X@C60]� (X = F�, Cl�, Br�) or [M@C60] (M = Li, Na, K)} with [Al(H2O)6]3+

and [Mg(H2O)6]2+ cations

http://dx.doi.org/10.1016/j.comptc.2014.01.0332210-271X/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Fax: +98 (811) 8380709.E-mail address: saleh@basu.ac.ir (S. Salehzadeh).

Sadegh Salehzadeh ⇑, Fereshteh Yaghoobi, Mehdi BayatFaculty of Chemistry, Bu-Ali Sina University, Hamedan, Iran

a r t i c l e i n f o

Article history:Received 25 October 2013Received in revised form 31 January 2014Accepted 31 January 2014Available online 23 February 2014

Keywords:Theoretical studyInteraction energyEndofullereneHydrated metal ions

a b s t r a c t

The effect of various encaged species (F�, Cl�, Br�, Li, Na and K) on the interaction of fullerene molecule with[Al(H2O)6]3+ and [Mg(H2O)6]2+ cations was theoretically studied. At first, the possibility of encapsulation ofabove species into the fullerene cage was studied. Therefore, the formation energies were calculated for allof these compounds. Then the interactions between [X@C60]� (X = F�, Cl�, Br�) or [M@C60] (M = Li, Na, K)complexes, with [Al(H2O)6]3+ and [Mg(H2O)6]2+ cations were investigated. Density functional theory (DFT),atoms-in-molecules (AIM) and natural bond orbital (NBO) calculation were applied to understand thenature of the interactions. The interaction energies were also calculated for all compounds. Generally,our computations reveal that the encapsulated atom/ion increases the interaction of the fullerene surfacewith above cations. It was shown that the negative charge of carbon atoms in [M@C60] complexes islarger than in [X@C60]� anions. However, the strength of the reactions/interactions of [Al(H2O)6]3+ and[Mg(H2O)6]2+ cations with [X@C60]� endofullerenes is considerably greater than that with [M@C60]. Thusthe results show that the total negative charge of endofullerene has significantly greater effect on the aboveinteraction than the negative charge of fullerene carbon atoms.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Since the discovery of buckminsterfullerene in 1985 [1], andespecially after the macroscopic preparation of fullerenes in 1990[2], many theoretical and experimental investigations have beencarried out on these molecules. As the radius of the C60 isapproximately 3.5 ÅA

0

, small guest species such as atoms, ions andmolecules can be placed inside its cavity to generate endohedral(inside the cage) complexes. Endohedral complexes have appearedin different areas of science and technology, ranging from medicine[3,4] and environmental protection [5] to molecular optoelectronics[6] and renewable energetic [7]. Following the first successfulenclosure of a La atom inside the C60 cage [8], a number ofendofullerene have been synthesized from alkali metal ions(especially Li+) [9–11], groups II metals (Ca, Sr, Ba) [12–14], groupsIII metals (Sc, Y, La) [14,15], all the lanthanides (Ce–Lu) [16,17],nitrogen [18], phosphorus [19], noble gases [20,21], and many otheratoms and species [22,23]. Due to the extreme difficulty inproducing macroscopic quantities and isolating pure samples,theoretical studies have been playing an important role in

investigating the structural and electronic properties of endofulle-renes and predicting their striking characteristics. Several theoret-ical studies have been made on the encapsulation of a variety ofatoms and ions inside the fullerene cage of different dimensions[22–32]. Additionally, there are some theoretical reports oninteraction between endofullerene surface and external molecules,in which charge transfer between the encaged species and C60

influences the strength of these interactions. For example the inter-action of Li@C60 with amino acids has been investigated by Jalbout[33]. Their results suggested that there is an interaction of theamino acids with the fullerene surfaces that can be attributedto some form of charge transfer effects. Other efforts in thisgroup have demonstrated that the encapsulation of metals insidefullerenes improves external interactions with small polarmolecules [34–37].

Recently, we reported a theoretical study on the interaction ofhydrated Al(III) and Mg(II) ions with C60 molecule and two otherG-systems [38]. The results showed that among the three studiedG-systems, the fullerene molecule has a stronger bondinginteraction with both the [Al(H2O)6]3+ and [Mg(H2O)6]2+ cations.In the present work, we report a theoretical study on theinteraction of [X@C60]� (X = F�, Cl�, Br�) or [M@C60] (M = Li, Na, K)endohedral fullerenes with [Al(H2O)6]3+ and [Mg(H2O)6]2+ cations.

74 S. Salehzadeh et al. / Computational and Theoretical Chemistry 1034 (2014) 73–79

We want to know which of the encaged halide anions or neutralalkaline atoms will significantly increase the interaction of fullerenesurface with the hydrated metal ions. In our previous work we usedonly the B3LYP which is a hybrid DFT method. However in presentcalculations we also used the PBE, which is one of the known pureDFT methods.

2. Computational details

Geometry optimization for all systems under investigation wascarried out using the Gaussian 03 [39] set of programs. Thegeometries of the isolated [X@C60]� (X = F�, Cl�, Br�) and [M@C60](M = Li, Na, K) endofullerenes were fully optimized at B3LYP/6-311++G** levels of theory. Single point energy calculation atMP2/6-311++G** and PBE/6-311++G** level were carried out onthe B3LYP/6-311++G** optimized geometries of isolated endofulle-renes. The geometries of {[X@C60]�. . .[Mg(H2O)6]2+}, {[M@C60]. . .

[Mg(H2O)6]2+}, {[X@C60]�. . .[Al(H2O)6]3+} and {[M@C60]. . .[Al(H2O)6]3+} (X = F�, Cl�, Br�;M = Li, Na, K) complexes were optimizedat the B3LYP/6-31G** level of theory. Then the single point calcula-tions were only carried out on above optimized Mg systems andalso related [X@C60]�, [M@C60] and [Mg(H2O)6]2+ fragments atB3LYP/6-311++G** and PBE/6-311++G** levels. The calculatedinteraction energies between the endofullerenes and [Mg(H2O)6]2+

cation were corrected for basis set superposition error (BSSE) usingthe counterpoise method [40]. The AIM 2000 package was used toobtain the bond properties. Wave function files were generatedfrom the Gaussian output files at B3LYP/6-311++G** level of theoryto perform AIM calculations [41]. Natural bond orbital analyses

Fig. 1. Optimized geometries along with selected calculated bond lengths (Å) for the {[Xcomplexes. In all of above complexes the proton transfer occurs from [Al(H2O)6]3+ to th

(NBO) have also been performed at B3LYP/6-31G** level of theory[42].

3. Results and discussion

The B3LYP/6-31G** optimized geometries of {[X@C60]�. . .

[Mg(H2O)6]2+}, {[M@C60]. . .[Mg(H2O)6]2+}, {[X@C60]�. . .[Al(H2O)6]3+} and {[M@C60]. . .[Al(H2O)6]3+} (X = F�, Cl�, Br�; M = Li,Na, K) complexes are given in Figs. 1 and 2. As can be seen inFig. 1, in all of the Al(III) complexes studied here, when the anionX� or the atom M is encapsulated in fullerene cavity, the protontransfer occurs from cation to the endohedral fullerene. Forexample, in {[X@C60]�. . .[Al(H2O)6]3+} complexes one, two andthree protons are transferred from the [Al(H2O)6]3+ cation to[F@C60]�, [Cl@C60]� and [Br@C60]� anions, respectively. On the otherhand, in the case of {[M@C60]. . .[Al(H2O)6]3+} complexes theresults show that in all cases only one proton is transferred fromthe [Al(H2O)6]3+ cation to the endofullerene molecule. Obviously,the proton transfer is the result of a very strong interaction betweenthe endofullerene and [Al(H2O)6]3+ cation. In contrast, in the case ofboth {[X@C60]�. . .[Mg(H2O)6]2+} and {[M@C60]. . .[Mg(H2O)6]2+}complexes, there is no proton transfer from the cation to the endo-fullerene (Fig. 2). As can be seen in Fig. 2, three H2O molecules of[Mg(H2O)6]2+ cations, through their hydrogen atoms, interact withthe carbon atoms of the six-membered ring in the endofullerenemolecule. What is very interesting is that, the F� ion due to its smallsize show a large off-center displacement in the C60 molecule whenthe C60 molecule interact with hydrated Al3+ and Mg2+ ions. There-fore, the motion of F� anion from the center of fullerene cage toward

@C60]�. . .[Al(H2O)6]3+} and {[M@C60]. . .[Al(H2O)6]3+} (X = F�, Cl�, Br�; M = Li, Na, K)e endofullerene.

Fig. 2. Optimized geometries along with selected calculated bond lengths (Å) for the {[X@C60]�. . .[Mg(H2O)6]2+} and {[M@C60]. . .[Mg (H2O)6]2+} (X = F�, Cl�, Br�; M = Li, Na, K)complexes.

Table 1Calculated formation energies (FE, kcal/mol) for the [M@C60] and [X@C60]�

endofullerenes.

Method Li Na K F� Cl� Br�

B3LYPa �12.83 �16.78 �33.16 �48.00 �30.19 �17.22PBEb �21.08 �27.22 �45.59 �48.51 �37.96 �29.04MP2b �33.67 �41.01 �69.59 �62.48 �78.66 �79.16

a The geometries are optimized at the B3LYP/6-311++G** level.b Single-point calculations at the PBE/6-311++G** and MP2/6-311++G** level are

performed on geometries optimized at the B3LYP/6-311++G** level.

S. Salehzadeh et al. / Computational and Theoretical Chemistry 1034 (2014) 73–79 75

the inner surface of fullerene has probably a reason for this fact thatthe interaction between the fullerene surface and the hydratedMg(P) ion is large (see next section). The average bond lengths

Table 2Calculated correcteda and uncorrected interaction energies (IE, kcal/mol) as well as thr(H2O)6]2+} complexes.b

Empty C60 M

Li Na

IE(uncorrected) �32.63 �37.57 �37.37�34.82 �40.15 �39.80

IE(corrected)b �30.34 �35.54 �35.33

�32.01 �37.71 �37.34Bond lengths 2.082 1.993 2.042

2.094 2.113 2.0572.101 2.128 2.137

a IE(corrected) = IE(uncorrected) + BSSE.b Single-point calculations at the B3LYP/6-311++G** are given as plain text and those

between the hydrogen atoms of the [Mg(H2O)6]2+ cation and thecarbon atoms of C60 molecule vary from 2.09 in {[C60]. . .[Mg(H2O)6]2+} to 1.88 ÅA

0

in {[F@C60]�. . .[Mg(H2O)6]2+} (see Table 2).The small displacement observed for other encapsulated speciesin the fullerene cavity is probably due to the larger size of thesespecies. Therefore they prefer to be in the center of the cage.

3.1. Formation energies of endohedral fullerenes

Before studying on interaction between the endohedralfullerenes and hydrated metal ions we checked the possibleformation of [X@C60]� (X = F�, Cl�, Br�) or [M@C60] (M = Li, Na, K)endofullerenes. The complexation and/or interaction energies forboth above systems have been already reported [24–30]. However,

ee OH. . .C bond lengths (Å) for the {[M@C60]. . .[Mg(H2O)6]2+} and {[X@C60]�. . .[Mg

X�

K F� Cl� Br�

�37.15 �146.07 �136.04 �135.79�39.78 �149.27 �139.04 �138.89�35.12 �143.70 �133.68 �133.52�37.35 �146.45 �136.41 �136.22

1.999 1.865 1.942 1.9212.155 1.884 1.945 1.9302.150 1.897 1.945 1.935

at PBE/6-311++G** are in bold.

-160

-140

-120

-100

-80

-60

-40

-20

0none Li Na K F¯ Cl¯ Br¯

IE

M or X¯

B3LYP/6-311++G**

PBE/6-311++G**

Fig. 3. The variation of calculated interaction energies (IE) between [X@C60]� and[M@C60] endofullerenes and [Mg(H2O)6]2+ cation.

76 S. Salehzadeh et al. / Computational and Theoretical Chemistry 1034 (2014) 73–79

we were interested to study the formation energies of these endo-fullerenes at the same theoretical level used in studying their inter-action with [Al(H2O)6]3+ and [Mg(H2O)6]2+ cations.

The formation energy (FE) for the [X@C60]� (X = F�, Cl�, Br�) or[M@C60] (M = Li, Na, K) complexes, were calculated using Eqs. (1)and (2), respectively:

FE X@C60½ �� ¼ E X@C60½ ��ð Þ � E X�ð Þ þ E C60ð Þ� �

ð1Þ

FE M@C60½ �� ¼ E M@C60½ ��ð Þ � E Mð Þ þ E C60ð Þ� �

ð2Þ

In above equations E is the electronic energy of the optimizedstructure of each species. Obviously, FE is a measure of the stabilityof the complex. If FE is negative, the compound is stable againstdecomposition into the pure components. The calculated FEs ofall [X@C60]� (X = F�, Cl�, Br�) or [M@C60] (M = Li, Na, K) complexesare listed in Table1. As it can be seen, all complexes are stable in-side C60. The observed trend using B3LYP and PBE levels of theoryshows that the stability of [X@C60]� (X = F�, Cl�, Br�) complexesdecreases with increasing the size of the ions. Thus the result ofpresent calculations is in excellent agreement with previous theo-retical studies [26,29]. It is interesting that MP2 calculations showsan inverse trend. However, it has previously confirmed that whilethe dispersion energy increases from F�@C60 to Br�@C60, but theinteraction energy decreases in this series of molecules [29]. Thusthe data of present work are in good agreement with previous dataindicating that MP2 usually overestimates the dispersion energy innon-covalent systems. On the other hand, for the [M@C60] com-plexes (M = Li, Na, K), there are almost the similar trends atB3LYP, PBE and MP2 levels of theory.

3.2. Interaction energies with hydrated metal cations

After study on possible formation of endofullerenes we investi-gated their interaction with [Mg(H2O)6]2+ and [Al(H2O)6]3+ cations.As it was mentioned above, in all of the Al(III) complexes studiedhere, the proton transfer occurs from the cation to the endofulle-rene. Thus we calculated only the energy of non-covalent interac-tion between the endofullerenes and [Mg(H2O)6]2+ cation.Interaction energy (IE) in {[X@C60]�. . .[Mg(H2O)6]2+} and{[M@C60]. . .[Mg(H2O)6]2+} complexes were calculated using Eqs.(3) and (4), respectively:

IEðuncorrectedÞ ¼ EX@C60½ �� ... Mg H2Oð Þ6½ �2þ� �

� E X@C60½ ��ð Þ þ EMgðH2OÞ6½ �2þ� �� �

ð3Þ

IEðuncorrectedÞ ¼ EM@C60½ �... Mg H2Oð Þ6½ �2þ� �

� E M@C60½ �ð Þ þ EMgðH2OÞ6½ �2þ� �� �

ð4Þ

In the above equation E is the electronic energy of each speciesin the equilibrium geometry of whole complex. The calculatedinteraction energies were also corrected for basis set superpositionerrors (BSSE).

Both the calculated IE(corrected) and IE(uncorrected) values for{[X@C60]�. . .[Mg(H2O)6]2+} and {[M@C60]. . .[Mg(H2O)6]2+} com-plexes are listed in Table 2. As can be seen in both the Table 2and Fig. 3, the B3LYP data are in good agreement to that of PBE.The interaction energies calculated using latter method are onlyslightly larger than those with B3LYP. Generally all of the calcu-lated interaction energies for the {[X@C60]�. . .[Mg(H2O)6]2+} com-plexes are considerably larger than corresponding interactionenergies for the {[M@C60]. . .[Mg(H2O)6]2+} complexes. Forexample, the interaction energy at the B3LYP level in {[F@C60]�. . .

[Mg(H2O)6]2+} is about �108.58 kcal/mol larger than in {[K@C60]

. . .[Mg(H2O)6]2+}. Indeed, among all endofullerenes studied here,[F�@C60] has the strongest interaction with [Mg(H2O)6]2+ cation.On the other hand, as can be seen in Table 2, the interactionenergies between the [X@C60]� anions and [Mg(H2O)6]2+ cationare considerably larger than that between the C60 molecule andthis cation. However, the calculated interaction energies in{[M@C60]. . .[Mg(H2O)6]2+} complexes are only slightly larger thanin {[C60]. . .[Mg(H2O)6]2+}. Thus in contrast to halide anion theencapsulated alkaline metal atom do not increase significantlythe amount of interaction of fullerene molecule with Mg(H2O)6]2+

cation.

3.3. NBO analysis

In order to evaluate the natural charges of the atoms involved inthe bonding interaction between [Mg(H2O)6]2+ cation and theendofullerene, as well as the global value of the charge transfer(DQ) from the endofullerene complexes to [Mg(H2O)6]2+ cationthe natural bond orbital (NBO) analysis was performed. At first,the natural charges of the halide anion, alkaline metal atom andsum of carbon atoms of C60 molecule in the [X@C60]� and[M@C60] endofullerenes, before the interaction with [Mg(H2O)6]2+

cation, were evaluated through NBO analysis (see Table 3). In boththe [X@C60]� and [M@C60] endofullerenes a charge transfer occursfrom the encaged atom (X) or (M) to the C60 molecule. In the seriesof [M@C60] endofullerenes, the value of charge transfer from the Li,Na and K atoms to the C60 cage, is �0.455, �0.511 and �0.753 e,respectively. Clearly, K atom donates the largest amount of elec-tronic charge to the C60 cage. Also, this can be attributed to thesmaller ionization potential of K relative to Li and Na. In the caseof [F@C60]� , [Cl@C60]� and [Br@C60]� endofullerenes, the sum ofthe natural charges of carbon atoms on C60 cage are �0.247,�0.023 and �0.033 e, respectively. Therefore, in the series of[X@C60]� endofullerenes, the maximum charge transfer from thehalide anion to the C60 cage was observed for the F� anion. Gener-ally, our calculations demonstrate the amount of charge-transferfrom the encapsulated alkaline atom to the cage of C60 is largerthan that from a encapsulated halide anion Thus a neutral alkalinemetal atom encapsulated in the C60 cage, in comparison to a halideanion, donates a larger amount of electronic charge to the C60

molecule.In the second stage, the natural charges of the X, M and C60 in

the [X@C60]� and [M@C60] endofullerenes after interaction with[Mg(H2O)6]2+ cation were investigated. The calculated naturalcharges are listed in Table 3. The changes in the natural chargeson both the atom M and anion X� upon the interaction of[M@C60] and [X@C60]� endofullerenes with the [Mg(H2O)6]2+ cat-ion are small. Interestingly, the total charge on the C60 moleculein {[M@C60]. . .[Mg(H2O)6]2+} complexes is negative but in

Table 3Natural charges for the encaged M atom or X� anion and C60 molecule and [Mg(H2O)6]2+ cation before (q or Q) and after (q0 or Q’) interaction of endofullerenes with [Mg(H2O)6]2+

cation and the Wiberg bond indices for the OH. . .C bonds.

Empty C60 M X�

Li Na K F� Cl� Br�

WBIs 0.0396 0.0609 0.0501 0.0596 0.1001 0.0705 0.07230.0388 0.0350 0.0447 0.0289 0.0932 0.0701 0.07400.0380 0.0321 0.0303 0.0311 0.0883 0.0701 0.0726

q(M or X) – 0.455 0.511 0.766 �0.753 �0.977 �0.967QC60

0.000 �0.455 �0.511 �0.766 �0.247 �0.023 �0.033QfM or X@C60g – 0.000 0.000 0.000 �1.000 �1.000 �1.000q0(M or X) – 0.453 0.508 0.763 �0.779 �0.962 �0.949Q 0C60

0.114 �0.332 �0.390 �0.646 0.081 0.177 0.173

q0Ca �0.143 �0.209 �0.192 �0.213 �0.218 �0.172 �0.184

�0.140 �0.146 �0.170 �0.121 �0.212 �0.171 �0.184�0.139 �0.125 �0.116 �0.138 �0.204 �0.171 �0.181

Q 0fM or X@C60g– 0.121 0.118 0.117 �0.698 �0.785 �0.776

Q 0½MgðH2 OÞ6 �2þ 1.886 1.879 1.882 1.883 1.698 1.785 1.776

Dq(M or X) �0.002 �0.003 �0.003 �0.026 0.015 0.018DQC60

0.114 0.123 0.115 0.114 0.276 0.200 0.206DQ ½MgðH2 OÞ6 �

2þ �0.114 �0.121 �0.118 �0.117 �0.302 �0.215 �0.224

a The charge of the carbon atoms that directly interact with the [Mg(H2O)6]2+ cation.

S. Salehzadeh et al. / Computational and Theoretical Chemistry 1034 (2014) 73–79 77

{[X@C60]�. . .[Mg(H2O)6]2+} complexes it is positive. However, in allcases the charge of the carbon atoms that directly interact with the[Mg(H2O)6]2+ cation is negative (q0C, Table 3). We know that thechange in the total charge of Mg(H2O)6]2+ cation upon the interac-tion with endofullerenes represents the amount of charge transferfrom the endofullerene to this cation. As can be seen, the amount ofcharge transfer (DQ ½MgðH2OÞ6 �

2þ ) from the endofullerene to the

[Mg(H2O)6]2+ cation in {[M@C60]. . .[Mg(H2O)6]2+} complexes issmaller than that in {[X@C60]�. . .[Mg(H2O)6]2+} complexes.For example, the amount of charge transfer in {[F�@C60]. . .

[Mg(H2O)6]2+} complex is 0.302e and in {[K@C60]. . .[Mg(H2O)6]2+}is only 0.117e. However, comparison of the charges of atom M, an-ion X�, C60 molecule and [Mg(H2O)6]2+ cation before and afterinteraction of endofullerenes with [Mg(H2O)6]2+ cation shows thatthe charge transfer occurs mainly by the electron donating of C60

molecule and not the encaged atom (compare the DqðM or XÞ;

DQC60and DQ

MgðH2OÞ6½ �2þ values). Thus the fullerene molecule pro-

tects the encaged atom/ion from the attached electron withdraw-ing [Mg(H2O)6]2+ cation. This is in agreement with the previousworks indicating that fullerene molecule acts as an electron buffer[31]. A comparison of data in Table 3 indicates that the amount ofcharge transfer between the endofullerenes and [Mg(H2O)6]2+

Table 4Bond lengths (Å), electron densities (q(BCP), e=a3

o), Laplacians (»2q(BCP), e=a3o) and a num

carbon atoms of the C60 molecule of the [X@C60]� and [M@C60] endofullerenes with three

Encaged atom/anion OH. . .C bond length q(rc) »2(qv)

Li 1.993 0.029 0.05182.113 0.0212 0.04852.128 0.0203 0.048

Na 2.042 0.0256 0.05062.057 0.0242 0.05072.137 0.0199 0.0476

K 1.999 0.0286 0.05182.15 0.0197 0.04672.156 0.0196 0.0476

F� 1.865 0.0394 0.05021.884 0.0376 0.05121.8974 0.0364 0.0518

Cl� 1.944 0.0321 0.05421.945 0.0319 0.05421.942 0.0319 0.0542

Br� 1.921 0.0334 0.0541.93 0.033 0.05381.935 0.0325 0.0538

cation has a significant effect on the strength of interaction be-tween these species. Thus the largest and the smallest interactionenergies are calculated for {[F@C60]�. . .[Mg(H2O)6]2+} and {[K@C60]. . .[Mg(H2O)6]2+} complexes that among all compounds show themaximum and minimum amount of charge transfer, respectively.The Wiberg bond indices (WBI) are also given in Table 3. The cal-culated Wiberg bond indices for the {[X@C60]�. . .[Mg(H2O)6]2+}complexes are greater than those for the {[M@C60]. . .[Mg(H2O)6]2+}complexes. Thus the values of the calculated Wiberg bond indicesand also the charge transfers between endofullerenes and cationsare in good agreement with the calculated bond lengths and theinteraction energies.

3.4. AIM analysis

We used AIM theory [41] to investigate the bond critical points(BCPs) of three interactions between three carbon atoms of the C60

molecule of the [X@C60]� and [M@C60] endofullerenes with threehydrogen atoms of [Mg(H2O)6]2+ cation, in order to evaluate thenature of these interactions. The values of topological propertiesof the interactions calculated at the BCPs are given in Table 4.The small values of the electron density (q), the positive values

ber of other AIM topological parameters at BCPs of three interactions between threehydrogen atoms of [Mg(H2O)6]2+ cation.

�k1 �k2 k3 |k1|/k3 �Gc/Vc e

0.0355 0.0334 0.1207 0.2941 0.8649 0.06090.0237 0.0205 0.0927 0.2557 1.0277 0.16030.0222 0.0185 0.0887 0.2503 1.051 0.20070.0301 0.028 0.1086 0.2772 0.9275 0.07660.0282 0.0251 0.104 0.2712 0.9573 0.12160.0221 0.0174 0.0871 0.2537 1.0771 0.2720.0348 0.0329 0.1194 0.2914 0.8709 0.0590.0212 0.0184 0.0863 0.2456 1.0598 0.15060.0217 0.0151 0.0844 0.2571 1.0907 0.43380.0537 0.0497 0.1536 0.3496 0.7303 0.08140.0506 0.0463 0.1481 0.3417 0.7507 0.0930.0484 0.0439 0.1441 0.3359 0.7655 0.10230.0402 0.0364 0.1309 0.3071 0.8272 0.10680.04 0.0361 0.1303 0.307 0.8293 0.10950.04 0.0361 0.1303 0.307 0.8293 0.10840.043 0.0388 0.1358 0.3166 0.8072 0.10730.0423 0.0376 0.1337 0.3164 0.8148 0.12650.0412 0.0375 0.1326 0.3107 0.819 0.0993

78 S. Salehzadeh et al. / Computational and Theoretical Chemistry 1034 (2014) 73–79

of the Laplacian »2q > 0 and |k1|/k3 < 1 at the BCPs indicate thatthese interactions correspond to closed shell interactions. Amongall the compounds investigated here, the BCPs between [X@C60]�

and [Mg(H2O)6]n+ cation have the greatest density. The values of»2q and �Gc/Vc have been used to study the nature of the interac-tion [43,44]. The data show that the interactions of [Mg(H2O)6]2+

cation with both the [X@C60]� and [M@C60] endoherdal fullerenesare partly covalent (»2q > 0 and �Gc/Vc < 1). The ellipticity valuesof the {[X@C60]�. . .[Mg(H2O)6]2+} complexes are also smaller thanthose for the other complexes studied here, and this is in goodagreement with the above results indicating that the interactionenergies between [X@C60]� and the [Mg(H2O)6]2+ cation are largerthan those between [M@C60] and [Mg(H2O)6]2+ cation.

4. Conclusions

A theoretical study on the effect of encapsulation of various spe-cies (F�, Cl�, Br�, Li, Na and K) into the cavity of C60 on the interac-tion of fullerene surface with [Al(H2O)6]3+ and [Mg(H2O)6]2+

cations was reported. The results indicated that the encapsulatedatom/ion increases the interaction of the fullerene surface withboth the above cations. In all of the Al(III) complexes studied here,when the anion X� or the atom M is encapsulated in fullerene cav-ity, the proton transfer occurs from [Al(H2O)6]3+ cation to the endo-fullerene. For example, in{[X@C60]�. . .[Al(H2O)6]3+} complexes one,two and three protons are transferred from the [Al(H2O)6]3+ cationto [F@C60]�, [Cl@C60]� and [Br@C60]� anions, respectively. On theother hand, in the case of Mg(II) complexes the encaged atomhas significantly increased the amount of interaction, but the pro-ton transfer is not occurred. It was shown that the negative chargeof carbon atoms in [M@C60] complexes is larger than that in[X@C60]� endofullerenes. However, the strength of the reactions/interactions of [Al(H2O)6]3+ and [Mg(H2O)6]2+ cations with[X@C60]� compounds is considerably greater than that with[M@C60] endofullerenes. Thus the results show that the total neg-ative charge of whole endofullerene has significantly greater effecton the above interaction than the total negative charge of fullerenecarbon atoms.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.comptc.2014.01.033.

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