J. Phys. Chem. C 2010, 114, 13017–13019
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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”-style endohedral 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 endohedral fullerene Sc4C2@C80 based on first-principles density-functional calculations. Our results show that a distorted tetrahedron Sc4 cluster enfolding around the C2 dimer has the desired electronic structure that leads to efficient charge 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-structured Sc4C2@C80 can be attributed to the donor-acceptor effects. Introduction Endohedral metallofullerenes are an expanded class of fullerenes known for their novel structures and promising applications.1-6 Recent experimental study reported the synthesis, isolation, and characterization of a “Russian-doll”-style fullerene,1 which holds three distinct nested molecules. The core of the nested structure consists of a C2 dimer surrounded by four scandium atoms, and the metal cluster Sc4C2 is trapped inside a C80 cage. The architectural magnificence of this Russiandoll fullerene1,2 has attracted an increasing amount of attention due to its feasibility for quantum information processing. Given the Sc4C2 cluster is relatively large in size, experimental studies indicate the increasing possibility of encasing even larger, yet structurally more complicated, atomic clusters in C80. Furthermore, in light of quantum calculations, the inner C2 species is in an unusually high charge state,1,2 which is also of great interest in the context of forming an electronic donor-acceptor complex. In general, metallofullerenes represent relevant novel nanostructured material for functionalization in future nanoscale electronic devices.7-10 The utilization of the unique structural and electronic properties of endohedral metallofullerenes11-14 however depends upon improved understanding and control of the corresponding properties. The pristine C80 has seven isolated′ , D3, D5h, and Ih pentagon-rule isomers, with D2, D5d, C2V, C2V 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 attributed to the fact that the Ih-C80 cage has only two electrons occupied in the 4-fold degenerate highest occupied molecular orbital (HOMO) and can accommodate an additional six electrons to form a stable closed-shell electronic state, with a large HOMO-LUMO (the lowest unoccupied molecular orbital) gap. In lieu of intriguing experimental advances,1 there are important 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 is straightforward to list all the combinations and calculate the * To whom
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energetics of the encased fullerenes, it is highly desirable to develop a systematic understanding of the stability on the basis of lineup of charge neutrality levels, which will be crucial for future development of metallofullerene-based nanodevices. Here, we present a comprehensive study of the structural and electronic characteristics of the Russian-doll-style Sc4C2@C80 based on first-principles density-functional calculations. Our results demonstrate that the detailed analysis of lineup of charge neutrality levels16,17 is very helpful in understanding the charge transfer and the associated structural and electronic stability of Russian-doll-structured Sc4C2@C80. Furthermore, our calculation of the transitions among various conformations indicates that the Sc4C2 can hardly rotate at room temperature in connection with the relatively large energy barrier. Computational Details Our first-principles calculations were based on spin-polarized densityfunctionaltheory.Gradient-correctedBecke-Lee-Yang-Parr (BLYP) parametrization19,20 of the exchange-correlation was used along with all electron double numerical plus polarization (DNP) basis sets as implemented in the DMol3 package.18 The optimization of atomic positions proceeded until the forces were less than 0.01 eV/Å and the change in energy was less than 5 × 10-4 eV. The approach was shown to account for the structural, electronic, and vibrational properties reasonably well.2,21,22 The icosahedral C80 cage was used to encapsulate the Sc4C2 cluster. Results and Discussion We show in the top panel of Figure 1 a few neutral Sc4C2 structures. These structures were generated through exhausting all the topological combinations of Sc4C2, followed by geometry optimization using force-field-based molecular dynamics and subsequent optimization using first-principles density functional calculations.18 It is worth mentioning that the energy of classical force-field-based calculations depends pivotally on the bonding among the atoms. In contrast, the first-principles calculations are independent in reference to the bond formations. As seen from Figure 1, among various Sc4C2 structures, there are tetrahedral shaped of Sc4 encased with a C2 dimer (Figures
10.1021/jp104555e 2010 American Chemical Society Published on Web 07/13/2010
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J. Phys. Chem. C, Vol. 114, No. 30, 2010
Kah et al.
Figure 1. Ball-and-stick presentation of a few stable conformations of neutral Sc4C2 (a-g) in the top panel, along with the encased Sc4C2@C80 for c and d. Carbon and scandium atoms are colored in green and silver, respectively.
TABLE 1: Calculated Energy EB, HOMO-LUMO Gap (Eg) for Sc4C2, C80 and Sc4C2@C80, Respectivelya structure
EB (eV)
Eg (eV)
E(2-3) (eV) g
Sc4C2 c Sc4C2 e C80 Sc4C2@C80 c Sc4C2@C80 d Sc4C2@C80 e
-22.10 -21.62 -573.32 -598.66 -598.65 -597.71
1.729 0.48 1.989 1.181 1.178 1.117
1.63 2.80
a (2-3) Eg is the energy split between HOMO-2 and HOMO-3 for Sc4C2.
1c and 1d). Other structures can have a rectangular shape of Sc4 (Figure 1a), a pentagon-like structure for three of the four scandium atoms with a slightly twisted C2 (Figure 1b), as well as X-shaped scandium atoms (Figure 1e). On the other hand, conformations with or without the twisted carbon dimer (Figure 1a 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 lowest energy structures among various conformations. All these structures can be encased into C80 and form stable structures. We have calculated energies for various structured Sc4C2@C80. Among eight conformations studied (corresponding to the encapsulation of a-g conformations of Sc4C2, see Figure 1), the slightly distorted structures c and d are nearly isoenergetic. The structure c coincides with the conformation obtained from previous ab initio calculations,1,2 which was confirmed experimentally as the Russian-doll structure.1 Summarized in Table 1 are the binding energies and characteristic HOMO-LUMO gaps for a few prototype structures. The slight difference in energies -598.66 eV for Sc4C2@C80-c) compared with previous calculations6 (-599.26 eV for the same Sc4C2@C80-c structure) appears to be attributed to the level of integration method employed (higher level of integration for densities, as we used in the present calculation, tends to have slightly higher value in energy), which nevertheless has little impact on the relative energy orders. On the other hand, the underestimate of the HOMO-LUMO gap is due to the well-known limitation of the gradient-correction approximation approach. It is worth remarking that,although the HOMO-LUMO gap can be rectified with more accurate methods such as hybrid functionals19,20 or manybody GW calculations (e.g., the rectified gap is 1.70 eV for the many-body GW approach, in good agreement with experimental value1 of 1.56 eV), the correction to the HOMO-LUMO gap is not expected to impact greatly on the discussion of “band alignment”,17 which is the main thrust of the present work. While the tetrahedral Sc4C2 is the lowest energy conformation both in the cluster itself and encased in C80, it is important to
Figure 2. Calculated electronic structure of (a) C80, (b) Sc4C2 (for structure c shown in Figure 1), and (c-e) the three isomers of Sc4C2@C80, corresponding to encased c, d, and e conformers of Sc4C2, respectively.
note that there is no one-to-one correspondence for other structures. This can be attributed to the fact that stable structures of Sc4C2@C80 involve charge transfers from the Sc4C2 to C80. As such, the energy order for neutral Sc4C2 cannot be used to predict that for Sc4C2@C80. In order to understand the structural and electronic stability of this Russian-doll-structured fullerene, we depict in Figure 2 the molecular levels of C80 (top view with the height of the bar proportional 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 structure breaks the icosahedral symmetry of C80; thus, all the molecular levels are singly degenerated. Careful examination of the “band alignment” indicates that the molecular level 2c is attributed to a type-I lineup of 2a and 2b components. Specifically, those three levels marked with arrows (red and green arrows indicate spin up and down components, respectively) in 2b shift up because the donation of six electrons to the C80. The next two close levels become the two occupied levels of the Russian-doll-structured Sc4C2@C80. The molecular levels of 2c and 2d are very similar due to the similar structures. On the other hand, the levels of 2e are quite different simply due to the differences in the corresponding Sc4C2 cluster and the associated distinct structural properties. Closer scrutiny of the level alignment between the molecular levels of C80 and Sc4C2 reveals that the Russian-doll-structured Sc4C2@C80 is yet another example of the quantum stability due to registry of energy levels.16 Specifically, applying the theory of line up of charge neutrality levels,16,17 the formation of a closed structure of C80 requires not only the charge transfer of six electrons from Sc4C2 but also the registry of the relevant gaps. In this regard, the HOMO-LUMO gap of C80 matches well with the corresponding gap Eg(2-3) of structure c (see Table 1). The Russian-doll structure is attributed to a donor-acceptor complex mechanism in that the encapsulation of electropositive Sc4C2 leads to the transfer of electrons from the cluster to the electronegative fullerene cage. Shown in Figure 3 are the calculated charge densities of near gap states. In accordance with the level alignment argument, for structures c and d (see Figures 3a and b, respectively), the HOMO and HOMO-1 are confined at the Sc4C2 core, as a result of the type-I alignment. The next two unoccupied levels have charges predominantly confined at the C80, consistent with lineup of charge neutrality levels. In contrast, structure e (see Figure 3c) has different charge density distributions in conformity with the analysis shown in Figure 2.
Russian-Doll Structured Sc4C2@C80
Figure 3. Isodensity surfaces for the two highest occupied molecular orbitals (HOMO-1 and HOMO) and the two lowest unoccupied molecular orbitals (LUMO and LUMO+1) for the three isomers of Sc4C2@C80. The labels a, b, and c correspond to the electronic structures listed in Figures 2c, d, and e, respectively.
J. Phys. Chem. C, Vol. 114, No. 30, 2010 13019 and electronic stability of the Russian-doll is attributed to the quantum registry effect. Moreover, the high degree of icosahedral symmetry of C80 is important to have the large amount of charge transfer of six electrons for a stable closed shell electronic structure. As a result, the Russian-doll-structured Sc4C2@C80 is an efficient donor-acceptor complex. In this regard, it is worth noting that, for other fullerenes, such as C82 and C84, such a large amount of charge transfer is not feasible due to the limitations of the symmetry-induced level degeneracy. We have demonstrated that the charge transfer behavior can be understood based on the concept of alignment of charge neutrality levels.16,17 Our approach should be particularly useful in future design of escaped fullerenes. Furthermore, we have studied the transition barrier of the stable Russian-doll states. Our results indicate that the rotation can hardly be achieved at room temperature. Acknowledgment. This work was supported by the National Science Foundation (Grant DMR-0934142), Army Research Office (Grant W911NF-06-1-0442), and Air Force Office of Scientific Research (Grant FA9550-10-1-0254). References and Notes
Figure 4. Calculated transition state (TS) structure between the two nearly isoenergetic conformers of Sc4C2@C80. Carbon and scandium atoms are colored in green and silver, respectively.
The distorted tetrahedron Sc4C2 core can assume a few stable orientations. The transition state between the stable conformations is directly relevant to the rotation barrier of the Sc4C2. We have calculated the transition state between the two nearly isoenergetic structures Sc4C2@C80 c and d. Shown in Figure 4 is the transition state conformation, in reference to the two stable structures. As can be seen from Figure 4, the potential barrier for the transition is ∼0.57 eV, which is substantially higher than the thermal energy of room temperature. This indicates that the tetrahedral Sc4C2 core cannot rotate freely at room temperature. As can be seen from Figure 4, the transition state conformation involves displacement of the C2 dimer as well, indicating that the rotation is not completely along the C2 axis. This is to be contrasted to the previous calculations that only the path along the potential energy surface for the rotation of the tetrahedral Sc4 around the C2 axis was considered.6 Conclusions In summary, we have studied the level alignment between C80 and the Sc4C2 core. We have demonstrated that the structural
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