Structural and Electronic Stability of Russian-Doll-Structured Sc4C2@C80

Cherno B. Kah, James Nathaniel, Kelvin Suggs, and Xiao-Qian Wang*Department of Physics and Center for Functional Nanoscale Materials, Clark Atlanta UniVersity,Atlanta, Georgia 30314

ReceiVed: May 18, 2010; ReVised Manuscript ReceiVed: June 28, 2010

Recent experimental work reported the synthesis, isolation, and characterization of a “Russian-doll”-styleendohedral fullerene, encompassing a carbon dimer within a scandium tetrahedron, all encased by a C80 cage.We have investigated the equilibrium conformations and the associated charge transfer of the endohedralfullerene Sc4C2@C80 based on first-principles density-functional calculations. Our results show that a distortedtetrahedron Sc4 cluster enfolding around the C2 dimer has the desired electronic structure that leads to efficientcharge transfer to the open-shell icosahedral C80. A detailed analysis of the charge transfer between the Sc4C2

configurations and the icosahedral C80 cage indicate that the structural stability of the Russian-doll-structuredSc4C2@C80 can be attributed to the donor-acceptor effects.

Introduction

Endohedral metallofullerenes are an expanded class offullerenes known for their novel structures and promisingapplications.1-6 Recent experimental study reported the syn-thesis, isolation, and characterization of a “Russian-doll”-stylefullerene,1 which holds three distinct nested molecules. The coreof the nested structure consists of a C2 dimer surrounded byfour scandium atoms, and the metal cluster Sc4C2 is trappedinside a C80 cage. The architectural magnificence of this Russian-doll fullerene1,2 has attracted an increasing amount of attentiondue to its feasibility for quantum information processing. Giventhe Sc4C2 cluster is relatively large in size, experimental studiesindicate the increasing possibility of encasing even larger, yetstructurally more complicated, atomic clusters in C80. Further-more, in light of quantum calculations, the inner C2 species isin an unusually high charge state,1,2 which is also of great interestin the context of forming an electronic donor-acceptor complex.

In general, metallofullerenes represent relevant novel nano-structured material for functionalization in future nanoscaleelectronic devices.7-10 The utilization of the unique structuraland electronic properties of endohedral metallofullerenes11-14

however depends upon improved understanding and control ofthe corresponding properties. The pristine C80 has seven isolated-pentagon-rule isomers, with D2, D5d, C2V, C2V′ , D3, D5h, and Ih

symmetry, respectively.15 Among them, the isomer of D2

symmetry is the most abundant C80 in pristine form.15 However,for the encapsulation of Russian-doll-structured Sc4C2 or La2

clusters, the Ih-C80 is the most favorable cage.15 This is attributedto the fact that the Ih-C80 cage has only two electrons occupiedin the 4-fold degenerate highest occupied molecular orbital(HOMO) and can accommodate an additional six electrons toform a stable closed-shell electronic state, with a largeHOMO-LUMO (the lowest unoccupied molecular orbital) gap.

In lieu of intriguing experimental advances,1 there areimportant questions that need to be addressed.2 Specifically,given the large number of atoms involved in the Sc4C2 cluster,there exist a few stable Sc4C2 conformations. While it isstraightforward to list all the combinations and calculate the

energetics of the encased fullerenes, it is highly desirable todevelop a systematic understanding of the stability on the basisof lineup of charge neutrality levels, which will be crucial forfuture development of metallofullerene-based nanodevices.

Here, we present a comprehensive study of the structural andelectronic characteristics of the Russian-doll-style Sc4C2@C80

based on first-principles density-functional calculations. Ourresults demonstrate that the detailed analysis of lineup of chargeneutrality levels16,17 is very helpful in understanding the chargetransfer and the associated structural and electronic stability ofRussian-doll-structured Sc4C2@C80. Furthermore, our calculationof the transitions among various conformations indicates thatthe Sc4C2 can hardly rotate at room temperature in connectionwith the relatively large energy barrier.

Computational Details

Our first-principles calculations were based on spin-polarizeddensityfunctionaltheory.Gradient-correctedBecke-Lee-Yang-Parr(BLYP) parametrization19,20 of the exchange-correlation wasused along with all electron double numerical plus polarization(DNP) basis sets as implemented in the DMol3 package.18 Theoptimization of atomic positions proceeded until the forces wereless than 0.01 eV/Å and the change in energy was less than5 × 10-4 eV. The approach was shown to account for thestructural, electronic, and vibrational properties reasonablywell.2,21,22 The icosahedral C80 cage was used to encapsulatethe Sc4C2 cluster.

Results and Discussion

We show in the top panel of Figure 1 a few neutral Sc4C2

structures. These structures were generated through exhaustingall the topological combinations of Sc4C2, followed by geometryoptimization using force-field-based molecular dynamics andsubsequent optimization using first-principles density functionalcalculations.18 It is worth mentioning that the energy of classicalforce-field-based calculations depends pivotally on the bondingamong the atoms. In contrast, the first-principles calculationsare independent in reference to the bond formations.

As seen from Figure 1, among various Sc4C2 structures, thereare tetrahedral shaped of Sc4 encased with a C2 dimer (Figures

* To whom correspondence should be addressed. E-mail:xwang@cau.edu.

J. Phys. Chem. C 2010, 114, 13017–13019 13017

10.1021/jp104555e 2010 American Chemical SocietyPublished on Web 07/13/2010

1c and 1d). Other structures can have a rectangular shape ofSc4 (Figure 1a), a pentagon-like structure for three of the fourscandium atoms with a slightly twisted C2 (Figure 1b), as wellas X-shaped scandium atoms (Figure 1e). On the other hand,conformations with or without the twisted carbon dimer (Figure1a vs Figure 1j) or conformations with distinctive bonding(Figure 1b vs Figure 1g) yield different stable configurations.Structures c and d are almost isoenergetic and are the lowestenergy structures among various conformations. All thesestructures can be encased into C80 and form stable structures.

We have calculated energies for various structuredSc4C2@C80. Among eight conformations studied (correspondingto the encapsulation of a-g conformations of Sc4C2, see Figure1), the slightly distorted structures c and d are nearly isoener-getic. The structure c coincides with the conformation obtainedfrom previous ab initio calculations,1,2 which was confirmedexperimentally as the Russian-doll structure.1 Summarized inTable1are thebindingenergiesandcharacteristicHOMO-LUMOgaps for a few prototype structures. The slight difference inenergies -598.66 eV for Sc4C2@C80-c) compared with previouscalculations6 (-599.26 eV for the same Sc4C2@C80-c structure)appears to be attributed to the level of integration methodemployed (higher level of integration for densities, as we usedin the present calculation, tends to have slightly higher valuein energy), which nevertheless has little impact on the relativeenergy orders. On the other hand, the underestimate of theHOMO-LUMO gap is due to the well-known limitation of thegradient-correction approximation approach. It is worth remark-ing that,although the HOMO-LUMO gap can be rectified withmore accurate methods such as hybrid functionals19,20 or many-body GW calculations (e.g., the rectified gap is 1.70 eV for themany-body GW approach, in good agreement with experimentalvalue1 of 1.56 eV), the correction to the HOMO-LUMO gapis not expected to impact greatly on the discussion of “bandalignment”,17 which is the main thrust of the present work.

While the tetrahedral Sc4C2 is the lowest energy conformationboth in the cluster itself and encased in C80, it is important to

note that there is no one-to-one correspondence for otherstructures. This can be attributed to the fact that stable structuresof Sc4C2@C80 involve charge transfers from the Sc4C2 to C80.As such, the energy order for neutral Sc4C2 cannot be used topredict that for Sc4C2@C80.

In order to understand the structural and electronic stabilityof this Russian-doll-structured fullerene, we depict in Figure 2the molecular levels of C80 (top view with the height of the barproportional to the degeneracy) the slightly distorted Sc4 C2-c,along with those for three prototype Sc4C2@C80 conformations.The molecular level for a Russian-doll-structured Sc4C2@C80

is shown in Figure 2c. The encapsulation of the core structurebreaks the icosahedral symmetry of C80; thus, all the molecularlevels are singly degenerated.

Careful examination of the “band alignment” indicates thatthe molecular level 2c is attributed to a type-I lineup of 2a and2b components. Specifically, those three levels marked witharrows (red and green arrows indicate spin up and downcomponents, respectively) in 2b shift up because the donationof six electrons to the C80. The next two close levels becomethe two occupied levels of the Russian-doll-structuredSc4C2@C80. The molecular levels of 2c and 2d are very similardue to the similar structures. On the other hand, the levels of2e are quite different simply due to the differences in thecorresponding Sc4C2 cluster and the associated distinct structuralproperties.

Closer scrutiny of the level alignment between the molecularlevels of C80 and Sc4C2 reveals that the Russian-doll-structuredSc4C2@C80 is yet another example of the quantum stability dueto registry of energy levels.16 Specifically, applying the theoryof line up of charge neutrality levels,16,17 the formation of aclosed structure of C80 requires not only the charge transfer ofsix electrons from Sc4C2 but also the registry of the relevantgaps. In this regard, the HOMO-LUMO gap of C80 matcheswell with the corresponding gap Eg

(2-3) of structure c (see Table1). The Russian-doll structure is attributed to a donor-acceptorcomplex mechanism in that the encapsulation of electropositiveSc4C2 leads to the transfer of electrons from the cluster to theelectronegative fullerene cage.

Shown in Figure 3 are the calculated charge densities of neargap states. In accordance with the level alignment argument,for structures c and d (see Figures 3a and b, respectively), theHOMO and HOMO-1 are confined at the Sc4C2 core, as a resultof the type-I alignment. The next two unoccupied levels havecharges predominantly confined at the C80, consistent with lineupof charge neutrality levels. In contrast, structure e (see Figure3c) has different charge density distributions in conformity withthe analysis shown in Figure 2.

Figure 1. Ball-and-stick presentation of a few stable conformationsof neutral Sc4C2 (a-g) in the top panel, along with the encasedSc4C2@C80 for c and d. Carbon and scandium atoms are colored ingreen and silver, respectively.

TABLE 1: Calculated Energy EB, HOMO-LUMO Gap (Eg)for Sc4C2, C80 and Sc4C2@C80, Respectivelya

structure EB (eV) Eg (eV) Eg(2-3) (eV)

Sc4C2 c -22.10 1.729 1.63Sc4C2 e -21.62 0.48 2.80C80 -573.32 1.989Sc4C2@C80 c -598.66 1.181Sc4C2@C80 d -598.65 1.178Sc4C2@C80 e -597.71 1.117

a Eg(2-3) is the energy split between HOMO-2 and HOMO-3 for

Sc4C2.

Figure 2. Calculated electronic structure of (a) C80, (b) Sc4C2 (forstructure c shown in Figure 1), and (c-e) the three isomers ofSc4C2@C80, corresponding to encased c, d, and e conformers of Sc4C2,respectively.

13018 J. Phys. Chem. C, Vol. 114, No. 30, 2010 Kah et al.

The distorted tetrahedron Sc4C2 core can assume a few stableorientations. The transition state between the stable conforma-tions is directly relevant to the rotation barrier of the Sc4C2.We have calculated the transition state between the two nearlyisoenergetic structures Sc4C2@C80 c and d. Shown in Figure 4is the transition state conformation, in reference to the two stablestructures. As can be seen from Figure 4, the potential barrierfor the transition is ∼0.57 eV, which is substantially higher thanthe thermal energy of room temperature. This indicates that thetetrahedral Sc4C2 core cannot rotate freely at room temperature.As can be seen from Figure 4, the transition state conformationinvolves displacement of the C2 dimer as well, indicating thatthe rotation is not completely along the C2 axis. This is to becontrasted to the previous calculations that only the path alongthe potential energy surface for the rotation of the tetrahedralSc4 around the C2 axis was considered.6

Conclusions

In summary, we have studied the level alignment betweenC80 and the Sc4C2 core. We have demonstrated that the structural

and electronic stability of the Russian-doll is attributed to thequantum registry effect. Moreover, the high degree of icosa-hedral symmetry of C80 is important to have the large amountof charge transfer of six electrons for a stable closed shellelectronic structure. As a result, the Russian-doll-structuredSc4C2@C80 is an efficient donor-acceptor complex. In thisregard, it is worth noting that, for other fullerenes, such as C82

and C84, such a large amount of charge transfer is not feasibledue to the limitations of the symmetry-induced level degeneracy.We have demonstrated that the charge transfer behavior can beunderstood based on the concept of alignment of chargeneutrality levels.16,17 Our approach should be particularly usefulin future design of escaped fullerenes. Furthermore, we havestudied the transition barrier of the stable Russian-doll states.Our results indicate that the rotation can hardly be achieved atroom temperature.

Acknowledgment. This work was supported by the NationalScience Foundation (Grant DMR-0934142), Army ResearchOffice (Grant W911NF-06-1-0442), and Air Force Office ofScientific Research (Grant FA9550-10-1-0254).

References and Notes

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JP104555E

Figure 3. Isodensity surfaces for the two highest occupied molecularorbitals (HOMO-1 and HOMO) and the two lowest unoccupiedmolecular orbitals (LUMO and LUMO+1) for the three isomers ofSc4C2@C80. The labels a, b, and c correspond to the electronic structureslisted in Figures 2c, d, and e, respectively.

Figure 4. Calculated transition state (TS) structure between the twonearly isoenergetic conformers of Sc4C2@C80. Carbon and scandiumatoms are colored in green and silver, respectively.

Russian-Doll Structured Sc4C2@C80 J. Phys. Chem. C, Vol. 114, No. 30, 2010 13019