Theoretical Insight for the Metal Insertion Pathway of Endohedral

Article pubs.acs.org/JPCA

Theoretical Insight for the Metal Insertion Pathway of Endohedral Alkali Metal Fullerenes Hema Malani and Dawei Zhang* Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore ABSTRACT: We have investigated the mechanism of alkali metal incorporation into C60 fullerene by density functional theory (DFT) at the UB3LYP/6-31G* level of theory. Calculations were performed to study the insertion pathways of Li+, Na+, and K+ through six- or five-membered rings of fullerene, and the computed energy barriers of metal ion insertion are compared with the available experimental data. Between the two possible insertion pathways, metal ion insertion through [2 + 2 + 2] ring opening of the six-membered ring is found to be more favored than the insertion through the ring opening of the five-membered ring. The size of the ring openings generated by the three metal ions is likely to be correlated with their ionic size, which shows the smallest opening for Li+ and the largest for K+ cation. The insertion energy barriers of the ions are found to be increased in the order of Li+ < Na+ < K+ in line with the experimental results. The ring opening made by breaking of C−C bonds during the metal ion insertion in sixor five-membered rings can cause the ring to be rearranged and convert back into a closed fullerene cage to form a stable endohedral metal-fullerene complex.

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INTRODUCTION The discovery of Buckminsterfullerene in 1985 opened a new pathway for studying the chemical properties of C60 and other carbon clusters such as C70, C76, C78, and C84.1 The first method used for production of fullerenes was laser vaporization of carbon in an inert atmosphere, but this produced only microscopic amounts of fullerenes. The large scale production of C60 was achieved by Krätschmer et al. in 1990, by using an arc discharge to vaporize graphite in helium atmosphere.2,3 Due to the fact that C60 and higher fullerenes are able to hold host atoms in their interior, new experiments were rapidly devised to enclose a metal atom inside their cage structures. The first experimental evidence of the existence of metal fullerenes was reported with the finding of La@C60,4 followed by the successful isolation and purification of Sc@C82,5 Y@C82,6 Gd@C82,7 and La@C828 in large quantities. In 1996, a new method for more efficient production of macroscopic amounts of endohedral alkali metal fullerenes was discovered by Tellgmann et al.9 by exposing monolayers of C60 to a beam of alkali ions at a carefully chosen energy. Recently, the complete isolation and determination of the molecular and crystal structure of polar cationic Li@C60 metallofullerene reported by Aoyagi et al. gave a direct experimental observation of Li ion encapsulated in C60 cage.10,11 As one of the most exciting findings in fullerene science, encapsulation of metal atoms inside fullerene cages can tune the properties of fullerenes and therefore has been developed into an entirely new branch of chemistry, with consequences in such diverse areas such as superconductivity and materials chemistry.12−17 The discovery of superconductivity of potassiumdoped C60 by Hebard et al. in 1991 triggered a flood of interest in fullerene research.18,19 The highly paramagnetic and radioactive character of some endohedral metal fullerenes shows that © 2013 American Chemical Society

they could be used as magnetic resonance imaging (MRI) agents and therefore have a good application prospect in medical chemistry.20−22 Furthermore, these materials are very important for their potential application as organic ferromagnets, nonlinear optical materials, and functional molecular devices, which could have great influence over electronics, optics, and electromagnetics. It is an interesting challenge to disclose the formation and structural modifications of fullerene upon metal insertion from the theoretical point of view. The ab initio calculations of electronic structures on the C60 cage and its endohedral complexes were reported by Cioslowski et al. in 1991.23,24 They observed that placing ions at the center of the C60 cage results in a net stabilization and negatively charged ionic guests such as F− decrease the cage radii, while positively charged guests such as Na+, Mg2+, Al3+ increase the cage radii. Furthermore, it has been found that the minimum energy position of Na+ in Na@C60 is not at the center of the cage but the position 0.66 Å from the center of C60 cage. This finding was further confirmed by Dunlap et al. in 1992, which showed that the equilibrium position of Li+ and Na+ are displaced radially outward by 1.40 Å and 0.70 Å from the center of the cage of Li@C60 and Na@C60, while K+ is located in the center of the cage of [email protected] In other studies, interactions of Na atom and Na+ ion with C60 molecule were investigated by Hartree−Fock theory, and possibilities of significant charge transfer from the metal to the C60 molecule and subsequent decrease in the HOMO−LUMO gaps of C60 were discovered.26 Quantum chemical calculations of Li@C60 Received: January 23, 2013 Revised: March 28, 2013 Published: March 29, 2013 3521

dx.doi.org/10.1021/jp4007697 | J. Phys. Chem. A 2013, 117, 3521−3528

The Journal of Physical Chemistry A

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(IRC) calculations were carried out using Gaussian09 program.33 IRC pathway is the minimum energy path connecting the reactants to products via the transition state. Starting from the transition state, the IRC calculation goes forward and backward down the steepest descent path leading to energy minimum in reactant and products. In this work, IRC calculations were used to verify the calculated transition state by observing whether it correctly lead toward the reactants in one direction and products in the other direction.

by Pavanello et al. showed that when Li atom is inserted into the C60 system, a charge of nearly +1 is donated to the surface yielding a structure with Li+@C60− electron configuration. In addition, it has been found that fullerene cage acts as an electron buffer and accommodates excess electrons.27 The character of the bond between encapsulated atoms and the enclosing C60 shell in M@C60 complexes was studied using DFT, and it suggested that the M-C60 bond may be purely ionic in encapsulated K and partly ionic in the case of Li.28 In a recent first principle study, cation-π interactions between Li+, Na+, and K+ and pristine C24 fullerenes were investigated, and interaction energies are found to be decreased in the order of Li+ > Na+ > K+ with values of −1.38, −0.97, and −0.68 eV.29 Despite the success in experimental and theoretical procedures to investigate the properties of endohedral metal fullerenes, the theoretical underpinning of how metal is trapped inside fullerene is still not well understood. The first proposed mechanism for the formation of endohedral metal fullerene is the opening window mechanism, in which metal atoms penetrate into empty carbon cage through an opening window. Saunders et al. suggested that metal ions can penetrate into the carbon cage without destroying it through this opening.30 Ab initio molecular dynamics simulations were also used to study the collision between C60 and alkali metal ions. Ohno et al. observed that Li@C60 is created when Li+ with the kinetic energy of 5 eV hits the center of a six-membered ring of C60.31 If either the kinetic energy is lower or the collision occurs off the center, the Li+ ion stays outside and the C60 is deformed by the shock. In another recent DFT molecular dynamics simulation, a possible dynamical formation mechanism of Ni-doped fullerenes was explored and Ni@C60 is found to be formed by a push-through mechanism by ring opening upon impingement and subsequent ring closure.32 Since clarification of metal insertion pathway into fullerenes is still not very clearly unveiled, further quantum chemical studies are indispensable to understand the energetics of metal insertion barriers, the structural features of C60 during metal insertion, and the electronic interactions in details. In this investigation, calculations based on unrestricted DFT were performed to address the interactions of Li+, Na+, and K+ with C60 to form alkali metal endohedral fullerenes Li@C60, Na@C60, and K@ C60 in order to gain theoretical insight of the metal insertion process through the wall of C60.

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RESULTS AND DISCUSSION Formation Pathway of Li@C60. The potential energy profile for Li+ insertion through the six- or five-membered ring of C60 is given in Figure 1, and the calculated interaction energies at

Figure 1. Potential energy profile for Li+ insertion through six- and fivemembered rings.

each position along the pathway and the size of the opening formed on the surface of C60 are presented in Table 1, with the energy maxima and the corresponding ring size shown in bold font for both insertion pathways. The insertion started from the outside of C60 center and approached to the surface of C60 with a step of 0.25 Å. As can be seen, the interaction energy increases gradually from the original negative to more positive when closer to the surface. The calculated energy barrier through the sixmembered ring is 5.83 eV, while the barrier through the fivemembered ring is 9.75 eV, showing that Li+ insertion through a hexagon is energetically more favorable than through a pentagon. The barrier of 5.83 eV for Li+ insertion through the sixmembered ring agrees well with the collision energy of 6.00 eV obtained by Wan et al. using collision experiment of alkali ions with C60.34,35 During the Li+ insertion through the six-membered ring, three shorter [6,6] bonds connecting two successive hexagons are kept intact and three longer [6,5] bonds joining a hexagon and a pentagon are broken leading to a [2 + 2 + 2] ring opening with the hole size of 9.58 Å as shown in Figure 2a. For the insertion through the five-membered ring, all five [6,5] bonds are broken forming a larger hole size of 9.10 Å shown in Figure 2b. After the Li+ insertion, the broken C−C bonds swiftly reconnect themselves around the opening and convert back into the closed fullerene cage. When the Li+ inserts into fullerene through hexagon, it goes through a transition state with the activation energy of about 5.83 eV. The optimized structure of the TS along the pathway through hexagon and the size of the formed hole are shown in Figure 5a. The only one imaginary frequency of the transition state is

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METHOD All the quantum chemical calculations were carried out with the Gaussian09 suite of programs, employing the UB3LYP/6-31G* method. To investigate the metal insertion mechanism, two different possible pathways through either six- or five-membered ring of C60 surface were considered respectively. Our goal is to calculate the potential energy profiles along the reaction coordinate corresponding to the motion of alkali metal ion from the outside of C60 toward the center of C60. Geometry optimizations were started by keeping the metal ion 5.50 Å from the center of C60 and then moved toward the center of C60 through either pathway with the step of 0.25 Å. Constraints were imposed on the metal ion, and half the carbon atoms of the fullerene facing toward the insertion direction were allowed to move while the rest of the carbon atoms were frozen during the optimization. Frequency calculations for the highest energy structures were carried out to identify the transition state (TS) with one imaginary frequency associated with the reaction coordinate of the metal ion insertion. In order to further verify the calculated transition state, intrinsic reaction coordinate 3522



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Table 1. Calculated Interaction Energies and Ring Size for Li+ Insertiona six-membered ring

five-membered ring

Li−center distance (Å)

interaction energy (eV)

ring size (Å)


ring size (Å)

5.50 5.25 5.00 4.75 4.50 4.25 4.00 3.75 3.50 3.30 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00

−1.555 −1.679 −1.699 −1.496 −1.024 −0.101 1.200 3.100 5.050 5.832 5.573 4.906 3.376 1.717 0.273 −0.736 −1.266 −1.421 −1.351 −1.218 −1.037 −0.919 −0.838 −0.793

8.59 8.59 8.59 8.59 8.60 8.62 8.66 8.76 9.01 9.58 9.49 9.23 9.01 8.84 8.73 8.65 8.60 8.57 8.56 8.56 8.55 8.55 8.55 8.55

−1.564 −1.629 −1.514 −1.063 −0.149 1.356 3.474 6.097 8.233 9.754 9.134 7.475 4.999 2.627 0.752 −0.499 −1.135 −1.332 −1.283 −1.136 −0.980 −0.847 −0.781 −0.740

7.30 7.29 7.28 7.27 7.26 7.25 7.23 7.18 9.06 9.10 8.85 8.46 8.04 7.75 7.56 7.43 7.36 7.31 7.29 7.28 7.28 7.27 7.27 7.27

Figure 3. Potential energy profile for Na+ insertion through six- and fivemembered rings.

Ring size has been calculated by the total bond length of the five- or six-membered ring. a

Figure 4. Potential energy profile for K+ insertion through six- and fivemembered rings.

along the IRC pathway through hexagon as shown in Figure 7. In reactant, the Li+ is positively charged with +0.50e. When the ion is approaching the C60 surface, the Li+ charge decreases gradually due to the charge transfer from the carbon atoms on the C60 surface and then reaches the minimum (−0.69e) showing the largest charge transfer at the transition state. In order to understand the strong charge transfer event at the TS, the distance between the Li+ and the [6,6] double bonds in the opening of C60 surface is measured to be 1.60 Å, showing close contact and leading to the significant charge transfer. After the insertion, the charge of Li+ changes back to +0.46e at product, indicating nonignorable charge transfer when the ion is placed inside and in the vicinity of six-membered ring on C60 surface. To illustrate the charge transfer effect, the electrostatic potential map of C60 at the TS of the Li+ insertion is shown in Figure 8a. It is visible that areas of low electrostatic potential (red) characterized by abundance of electrons are concentrated on the Li+, while areas of high electrostatic potential (green) are delocalized on the carbon atoms of C60. Formation Pathway of Na@C60. Next, the Na+ insertion mechanism through six- or five-membered rings of C60 is investigated as shown in Figure 3. Results for interaction energies at each distance and the size of the formed opening on the C60 surface are presented in Table 2, with the maximal energy and the corresponding ring size shown in bold font. Similarly, as the Na+

Figure 2. Ring-opening mechanism on C60 surface (a) on sixmembered ring and (b) on five-membered ring.

calculated as −763.24 cm−1, which verifies the transition state. Moreover, the calculated TS connecting reactant and product can be further confirmed by IRC calculations shown in Figure 6a. The IRC study shows that the Li+ is stabilized at 5.10 Å from the center before insertion and 1.48 Å from the center after insertion. This result agrees well with the finding of the equilibrium distance of Li+ inside Li@C60, in which the metal ion is stabilized by 1.40 Å from the cage center.24 Furthermore, this result agrees well with the finding of Aoyagi et al. which shows that the encapsulated Li+ is located in the vicinity of a hexagon and stabilized at 1.34 Å off-center position.10 Unfortunately, the real transition state could not be obtained for the insertion through the five-membered ring. To further investigate electronic properties of Li+ during the insertion, the charge transfer between the metal ion and fullerene is investigated by computing Mulliken atomic charges of Li+ 3523



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Figure 5. Top view of the calculated transition states during the insertion of three metal ions through the six-membered ring: (a) Li+ insertion, (b) Na+ inserion, and (c) K+ insertion. The carbon atoms in the ring opening are colored yellow, and the size of the ring opening is shown as the dotted circle.

Figure 6. Side view of the IRC optimized structures before, during, and after metal insertion through the six-membered ring: (a) Li+ insertion, (b) Na+ insertion, and (c) K+ insertion. Similarly, the carbon atoms in the ring opening are colored yellow, and the distance from the center of C60 to the metal ion is shown as the dotted line.

During the Na+ insertion through the six-membered ring, three [6,6] bonds connecting two successive hexagons are kept intact, while three [6,5] bonds shared by six- and five-membered rings are broken, leading to [2 + 2 + 2] ring opening with a hole size of 13.40 Å as shown in Figure 2a. In the case of the Na+ insertion through five-membered ring, all five [6,5] bonds joining a hexagon and pentagon are broken forming a hole size of 14.88

gets closer to the C60 surface, the interaction energy is becoming more and more positive. The calculated energy barrier through the six-membered ring is 8.86 eV, while the barrier through fivemembered ring is 16.53 eV. Same as Li+ insertion, the energy barrier for Na+ insertion through the six-membered ring is found to be lower than the insertion through the five-membered ring. 3524



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Table 2. Calculated Interaction Energies and Ring Size for Na+ Insertiona six-membered ring

Figure 7. Charge analysis of the IRC optimized structures for Li+, Na+, and K+ insertion.

Å. Although the ring-opening made in Li+ insertion is closed soon after the metal insertion, the larger ring opening made by Na+ insertion rearranges slowly into the closed fullerene cage. This phenomenon is visible in the interaction energy profile showing a high-energy flat-topped surface, which is different from the interaction energy profile of Li+. This high-energy flattopped surface corresponds to the energies of unstable C60 structures with a temporary ring opening. After that, the broken C−C bonds are transformed back to close the C60 cage, stabilizing C60 gradually as shown in descending curves in Figure 3. The optimized TS structure in the pathway of Na+ insertion through the six-membered ring and the size of the formed hole are shown in Figure 5b. The only one imaginary frequency of the transition state is calculated as −148.89 cm−1, and the transition state could be confirmed as real by viewing the vibrational motion of the frequency mode. The calculated TS could be further confirmed by the IRC calculation which shows that Na+ ion is stabilized at 5.44 Å from the center before insertion, while stabilized at 0.83 Å from the center after insertion as shown in Figure 6b. This result agrees well with the findings of equilibrium position of Na+ in Na@C60, in which Na+ is displaced 0.66−0.70 Å from the cage center.23,25 Unfortunately, the real transition state could not be obtained for the insertion pathway through the five-membered ring. For further measuring of electronic properties of Na@C60 and elucidation of the charge transfer during the insertion, Mulliken

five-membered ring

Na−center distance (Å)


ring size (Å)


ring size (Å)

5.50 5.25 5.00 4.75 4.50 4.25 4.00 3.75 3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00

−1.346 −1.303 −1.028 −0.372 0.807 2.652 5.247 8.537 8.861 8.968 8.839 8.628 8.373 8.118 3.057 1.194 −0.086 −0.742 −0.979 −1.013 −0.971 −0.924 −0.908

8.58 8.58 8.58 8.58 8.58 8.58 8.58 8.58 13.40 13.42 13.27 13.03 12.71 12.33 8.97 8.79 8.70 8.70 8.58 8.52 8.52 8.52 8.52

−1.250 −1.078 −0.579 0.406 2.001 4.192 6.806 9.592 16.535 16.700 16.859 17.007 10.098 6.700 3.630 1.401 0.037 −0.664 −0.915 −0.954 −0.916 −0.856 −0.865

7.25 7.25 7.25 7.20 7.20 7.15 7.05 7.05 14.88 14.87 14.69 14.21 8.41 8.00 7.70 7.50 7.40 7.30 7.30 7.25 7.25 7.25 7.25

Ring size has been calculated by the total bond length of the five- or six-membered ring.

a

charge analysis is carried out for the IRC optimized structures as shown in Figure 7. As we can see, Na+ is positively charged with +0.66e at the reactant before the insertion. The Na+ charge decreases when closer to the surface and changes to +0.30e in the TS of the metal insertion, showing that 0.70e charge has been transferred from C60 to the metal along the opening. Due to the larger opening on the fullerene surface, the distance between the Na+ and the [6,6] double bonds in the opening increases to 2.33 Å compared to the 1.60 Å in the Li+ insertion and thus weakens the charge transfer effect. After the insertion, the Na+ charge changes back to +0.68e at the product, which shows that 0.32e electronic charge has been transferred from the carbon cage to the encapsulated metal. Figure 8b shows the electrostatic

Figure 8. Electrostatic potential map of the transition state during the metal ion insertion through the six-membered ring: (a) Li+ insertion, (b) Na+ insertion, and (c) K+ insertion. 3525



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interaction energy profile of Na+. Here also this high-energy flattopped surface corresponds to the energies of unstable C60 structures with the hole formed by the metal insertion. Since the ring opening made by K+ insertion is larger than those for Li+ or Na+, the broken C−C bonds are transformed back more slowly to close the C60 cage. The gradual reduction of the interaction energy shows that the C60 system stabilizes more slowly with the ring closure. In Figure 5c, the optimized structure of the K@C60 transition state in the pathway through the six-membered ring and the size of the formed hole are shown. The only one imaginary frequency of the transition state is calculated at −95.35 cm−1, and it is confirmed by viewing the vibrational motion of frequency mode corresponding to the reaction coordinate. The calculated TS is further confirmed by the IRC calculation which shows that the K cation is stabilized in 5.80 Å from the center before insertion and stabilized in the center of C60 after insertion as shown in Figure 6c. This result agrees well with the equilibrium position of K+ in K@C60 determined by Dunlap et al.25 Unfortunately, the real transition state could not be calculated for the K+ insertion pathway through the five-membered ring. For further measuring of electronic properties of K@C60, Mulliken charge analysis is carried out to calculate the magnitude of the charge transfer along the IRC insertion pathway of K+. As shown in Figure 7, the K+ is positively charged with +0.84e at reactant outside of C60, showing that 0.16e electronic charge has been transferred to K+ ion from the C60 cage. With the closeness to the surface, the charge of K+ decreases and reaches a minimum of +0.56e at the TS, showing 0.44e charge has been transferred from C60 to the K+ ion. The largest opening caused by the K+ insertion further widens the gap between the K+ ion and the [6,6] double bonds in the opening to 3.08 Å, which can be attributed to the smallest charge transfer for the K+ insertion as shown in Figure 7. After the insertion into C60, the charge of K+ changes back into +0.84e at the center of the C60 cage. The difference of charge density is clearly visible in the electrostatic potential map of the TS of the K+ insertion as shown in Figure 8c, showing the low electrostatic potential (yellow) centered on the K+ ion.

potential map which illustrates the partial charges and electron densities around the atoms after the Na+ insertion. The area of low electrostatic potential (orange) characterized by abundance of electrons is concentrated on the Na+, while areas of high electrostatic potential (green) are delocalized on the carbon atoms of the C60 molecule. Formation Pathway of K@C60. Subsequently, the pathway of K+ insertion mechanism through the six- or five-membered ring of fullerene is investigated as shown in Figure 4. Results for interaction energies at each distance and size of the formed ring opening on the surface are presented in Table 3, and the highest Table 3. Calculated Interaction Energies and Ring Size for K+ Insertiona six-membered ring

five-membered ring

K−center distance (Å)

interaction energy(eV)

ring size (Å)


ring size (Å)

5.50 5.25 5.00 4.75 4.50 4.25 4.00 3.75 3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00

−0.664 −0.124 0.914 2.603 5.046 8.177 11.701 15.227 15.362 15.354 15.342 11.545 11.062 10.506 9.928 9.389 3.372 1.432 0.213 −0.382 −0.615 −0.688 −0.704

8.52 8.52 8.52 8.49 8.46 8.40 8.37 8.34 15.98 15.95 15.87 14.20 13.86 13.47 13.02 12.51 8.88 8.85 8.70 8.64 8.58 8.55 8.52

−0.358 0.400 1.718 3.612 6.010 8.686 11.970 17.735 17.942 13.548 13.393 13.067 12.631 12.121 11.585 11.072 3.616 1.532 0.281 −0.322 −0.567 −0.633 −0.653

7.25 7.20 7.15 7.10 7.05 7.00 7.00 7.00 14.53 14.41 14.27 13.96 13.58 13.09 12.53 11.83 7.60 7.45 7.35 7.30 7.30 7.25 7.25

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CONCLUSION In this study, the reaction mechanism of alkali metal incorporation through the wall of the fullerene cage and the changes of the cage geometry upon metal insertion have been investigated by unrestricted DFT method. Energy barriers for the metal insertion through the two possible pathways (either six- or five-membered rings) are reported for Li+, Na+, and K+ metal ions, respectively. On the basis of our calculations, theoretical evidence has been presented for the cage opening mechanism on the surface of C60 fullerenes. Through this mechanism, ring opening could be formed when a metal ion is passing through and fullerene could be converted back into the closed cage after the insertion. The fullerene cage itself does not undergo any significant distortion during the process, while the ring opening made by the C−C bond breaking in six- or five-membered rings on the cage surface closes, again forming a stabilized endohedral metal-fullerene system. The interaction energy barriers of the metal ion insertion are found to be increased in the order of Li+ < Na+ < K+. The difference in the barriers of three alkali metal ions can be understood in terms of the constriction encountered during their insertions due to the different ionic sizes. With the higher ionic size, K+ ion experiences much greater steric interaction when forcing its way through the fullerene surface, while the smaller Li+

a Ring size has been calculated by the total bond length of the five- or six-membered ring.

energy and the ring size are shown in bold font. The interaction energy before insertion is found to be less negative than those for Li+ and Na+ systems. When the K+ comes closer to the surface of C60, the highest energy is observed when the cation is at 3.50 Å from the center of C60. The calculated energy barrier for K+ insertion through the six-membered ring is calculated as 15.36 eV, while the energy barrier through the five-membered ring is 17.94 eV. Same as for Li+ and Na+ insertions, the interaction energy barrier for K+ insertion through the six-membered ring is found to be lower than the insertion through the five-membered ring. Unlike the [2 + 2 + 2] ring opening of Li+ and Na+ insertions through the six-membered ring as shown in Figure 2a, the breaking of both three [6,5] bonds and one [6,6] bond leads to form a relatively larger hole size of 15.98 Å. In the five-membered ring, three of five [6,5] bonds joining a hexagon and a pentagon are broken and moved apart forming a hole size of 14.53 Å. After the metal insertion, the potential energy profile shows a highenergy flat-topped surface (shown in Figure 4), the same as the 3526



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chemically well-stabilized endohedral metal-fullerene systems. Our theoretical study indicates that the incorporation of metal ion into C60 through six- or five-membered rings needs to overcome a very high-energy barrier, which is compatible with the results of high-energy collision experiments. Our study provides a theoretical explanation and a better understanding for experimental evidence that has prepared endohedral alkali metal compounds of C60 under thermal excitation.

ion encounters much less resistance to insert through the opening. Our calculations show a linear correlation between the ionic size of metal ion and the interaction energy barrier for the insertion. The calculated barrier of Li+ insertion shows a better agreement with the experimental results as shown in Table 4. Although the barriers for Na+ and K+ insertion show higher deviation from the experimental values, they are still in good agreement with the experimental trend.34,35

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Table 4. Ionic Size, Formed Hole Size, and Calculated and Experimental Energy Barriers for Li+, Na+, and K+ Insertionsa

Corresponding Author

*E-mail: [email protected].

energy barrier (eV) metal

ionic size (Å)

hole size (Å)

calcd

exptl

Li+ Na+ K+

0.76 1.02 1.38

9.61 (9.10) 13.40 (14.88) 15.98 (14.53)

5.83 (9.76) 8.86(16.54) 15.36 (17.94)

6.00 18.00 40.00

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.Z. was supported by a Nanyang Technological University start-up grant and in part by Singapore AcRF Tier 1 Grant. D.Z. also thanks the NTU HPC for support and resources.

Values for insertion through the five-membered ring are shown in parentheses.

a

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The charge transfer between C60 and three alkali metal ions at the transition state of the insertion is investigated and found to decrease in the order of Li+ > Na+ > K+, which can be attributed to the gap between the metal ion and the π bonds in the opening of C60 surface. The close contact between the Li+ and the [6,6] double- bonds in the small ring opening on the C60 surface facilitates the charge transfer, whereas the very large separation between the K+ and the [6,6] double bonds in the widened opening greatly weakens the charge transfer from the π bonds to the metal ion although K+ has the largest ionic size compared to Li+ and Na+. This observed relationship between the charge transfer and the strength of the cation-π interaction is in good agreement with the DFT study of Moradi et al. which showed the cation-π bond interaction energies of the C24-alkali metal complexes are changed in the order of Li+ > Na+ > K+.29 The investigated reaction pathways are useful for the understanding of the general formation mechanism of alkali endohedral metal fullerenes. Our calculations can coincide well with currently available experiments, for which there are several examples: (1) The calculated results correspond well with the mechanism of the formation of La-endohedral fullerene described by Hirata et al., which showed that La atoms can be encapsulated into fullerenes without causing cage deformation and the smaller La cations are more readily accepted by the fullerenes.36 (2) Our calculated energy barriers clearly show that the barrier of metal insertion depends on the size of alkali metal cations. (3) Our results agree well with the ab initio molecular dynamics (MD) simulation performed by Ohno et al., which showed that Li@C60 is created when Li+ hits the center of a sixmembered ring of C60.31 (4) Also, our results show a mechanism similar to that observed by Neyts et al. for the formation of Ni@ C60 through MD studies, which showed that Ni atom broke three C−C bonds of the six-membered ring upon impingement while the other three bonds were left intact.32 Our results showed the same mechanism with the [2 + 2 + 2] ring opening for the insertions of Li+ and Na+ through the six-membered ring. Furthermore, this work confirms the window mechanism proposed by Saunders et al. in which one or more bonds in the C60 cage are reversibly broken to open a temporary window allowing the incorporation of guests inside C60 cage.30 The C60 fullerene cage could be able to adjust the size of the ring opening to afford and facilitate alkali metal ions with different size to form

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Theoretical Insight for the Metal Insertion Pathway of Endohedral

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