Which Do Endohedral Ti2C80 Metallofullerenes Prefer Energetically

Christine M. Beavers , Manuel N. Chaur , Marilyn M. Olmstead , Luis Echegoyen and Alan L. Balch. Journal of the American Chemical Society 2009 131 (32...
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J. Phys. Chem. B 2005, 109, 20251-20255

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Which Do Endohedral Ti2C80 Metallofullerenes Prefer Energetically: Ti2@C80 or Ti2C2@C78? A Theoretical Study Takashi Yumura,*,†,‡ Yuta Sato,† Kazutomo Suenaga,† and Sumio Iijima†,‡ Research Center for AdVanced Carbon Materials, National Institute of AdVanced Industrial Science and Technology (AIST) Tsukuba, 305-8565, Japan, and Department of Materials Science and Engineering, Meijo UniVersity, Tenpaku-ku, Nagoya, 468-8502, Japan ReceiVed: April 16, 2005

Four possible isomers of the Ti2C80 metallofullerene are discussed in detail at the B3LYP DFT level of theory: two isomers in Ti2@C80 formula with two Ti atoms encapsulated inside a C80 cage and the other two in Ti2C2@C78 formula with a Ti2C2 cluster involved inside a C78 cage. In the encaged Ti2C2 cluster, there are end-on and side-on C2 bridging modes into the two Ti atoms. The optimized end-on cluster has a linear Ti-C-C-Ti array, whereas the side-on cluster has a butterfly-like structure where the two Ti atoms and the C2 unit do not lie in a plane. DFT calculations show that the Ti2C2@C78 molecule with the end-on Ti2C2 cluster is energetically most favorable in the four isomers. Stabilities of the Ti2C80 molecules are essentially dominated by Ti binding sites inside fullerene cages. The Ti atoms bind over the hexagon rings in preference to a junction between hexagon and pentagon rings. In the Ti2C2@C78 molecules, orbital interactions between the Ti2C2 cluster and the outer cage play a significant role in determining the C2 bridging modes into the dititanium center and their relative stabilities.

Introduction Endohedral metallofullerenes have fascinated many researchers due to their novel electronic properties.1-3 Higher fullerenes can encage one or more metal ions inside their hollow space.4 Up to now, even metal clusters such as dimetalcarbides5,6 and trimetalnitrides7,8 have been reported to be trapped inside fullerene cages. Electronic properties of endohedral species can be modified, and thus unstable species that have never been observed in themselves can exist inside fullerene cages. For example, a Sc2C2 cluster inside a C84 cage was found from a maximum entropy method (MEM) analysis, although the species cannot exist as a solid scandium carbide.5 DFT calculations indicated that the encaged cluster has a C2 unit coordinating in a side-on fashion into the Sc atoms.6 Also Y2C84 metallofullerenes have an Y2C2 cluster encapsulated inside a C82 cage according to a 13C-nuclear magnetic resonance (NMR) analysis.9 Thus, the ability of fullerene cages to stabilize encapsulated species, especially transition-metal carbides, is of interest. In another metallofullerene involving transition-metal atoms, structural features of the Ti2C80 metallofullerene have been also investigated by several experimental methods.10-13 Its 13C NMR spectrum with eight peaks (δ ) 130-145 ppm) indicated that it is composed of two Ti2@C80 isomers with the D5h and Ih C80 cages.10 However another possible interpretation of the NMR spectrum is that the Ti2C80 metallofullerene has a Ti2C2 cluster incorporated inside a D3h C78 cage. In fact, the Ti2@C80 molecules proposed in ref 10 do not explain the recent highresolution transmission electron microscopy (HR-TEM) images of the Ti2C80 molecules inside a single-walled carbon nanotube (SWNT),13 as shown in Figure S1 (Supporting Information). * To whom all correspondence should be addressed at AIST. E-mail: [email protected]. † AIST. ‡ Meijo University.

Accordingly the proposal that the Ti2C80 metallofullerenes have the Ti2@C80 formula is disputable, and their structural features are still under debate. In the present study we discuss which the endohedral Ti2C80 metallofullerenes prefer energetically Ti2@C80 or Ti2C2@C78 with the aid of quantum chemical DFT calculations that can yield more reliable insights into their conformational preferences.14 Moreover, we will put a special emphasis on orbital interactions of the encapsulated species with the outer cages in order to clarify the role of the outer cages in determining the structures of the encapsulated species. Method of Calculation We carried out quantum chemical calculations on the basis of the hybrid Hartree-Fock/density functional theory (B3LYP) method15,16 using the Gaussian 03 program package.17 The B3LYP method consists of the Slater exchange, the HartreeFock exchange, the exchange functional of Becke,15 the correlation functional of Lee, Yang, and Parr (LYP),16 and the correlation functional of Vosko, Wilk, and Nusair (VWN).18 The basis set we used for the C and Ti atoms is 6-31G*.19,20 We obtained local energy minima and a saddle point of the Ti2C80 molecules with close-shell configurations. Harmonic vibrational frequencies were also calculated by the analytical evaluation of the second derivatives of the energy with respect to nuclear displacement in order to confirm that each optimized geometry corresponds to a local minimum that has only real frequencies or a saddle point that has only one imaginary frequency. Results and Discussion Geometrical Features of Possible Isomers for the Ti2C80 Metallofullerene. On the basis of the NMR study in ref 10, we considered six possible isomers for the endohedral Ti2C80 metallofullerenes; two isomers, 1 and 2, have the Ti2@C80

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Figure 2. Optimized geometries of the Ti2C2@C78 molecules 3 and 4 at the B3LYP DFT level of theory. Bond lengths are in Å. In 3 (4) the C2 unit binds in an end-on (a side-on) fashion around the dititanium center inside a D3h C78 cage. Figure 1. Optimized geometries of the Ti2@C80 molecules 1 and 2 at the B3LYP DFT level of theory. Bond lengths are in Å. 1 has the Ih C80 cage, and 2 has the D5h C80 cage.

formula in which two Ti atoms are encapsulated inside a C80 cage, and the other four isomers, 3, 4, 5, and 6, have the Ti2C2@C78 formula in which a Ti2C2 cluster is incorporated inside a C78 cage. Figure 1 shows that the optimized structures of 1 and 2 have the Ih and D5h C80 cages, respectively. 1 and 2 have been proposed as the Ti2C80 metallofullerene in ref 10, although the empty C80 cages have not been experimentally detected. As seen in Figure 1 each Ti atom21 resides over the center of a hexagon ring through a C2 rotation axis of the Ih C80 cage in 1; the nearest Ti-C contact was calculated to be ∼2.2 Å. In contrast, 2 involves two Ti atoms21 off the C5 rotation axis of the D5h C80 cage; each Ti atom is located over a [5,6] junction, a C-C bond between pentagon and hexagon rings, as shown in Figure 1. The closet Ti-C contact in 2 is ∼2.1 Å. The encapsulations of the Ti atoms in 1 and 2 result in distortions of the C80 cages; in 1 (2) a C-C bond length adjacent to the Ti atoms is increased up to 1.466 (1.479) Å. As other possible isomers for the Ti2C80 metallofullerene, we optimized two isomers, Ti2C2@C78 3 and 4, that have a Ti2C2 cluster involved in the D3h-C78(78:5) cage, as shown in Figure 2. The other two isomers, Ti2C2@C78 5 and 6, with the D3h(78:4) cage were also considered. In the isomers 3 and 4 (5 and 6) with the D3h(78:5) (D3h(78:4)) cage, exactly eight NMR peaks are expected in the range for sp2-hybridized C atoms,22 as experimentally obtained in ref 10. To the best of our knowledge, their structural features, however, have never been investigated. Our DFT calculations show that 5 and 6 are unstable in energy relative to 3 and 4, as shown in Table 1. Thus, we focus our discussions on the two isomers Ti2C2@C78 3 and 4 with the D3h(78:5) cage. In 3 and 4, the C2 units bind in end- and side-on fashions into the two Ti atoms23 inside the C78 cages, respectively, as shown in Chart 1. In the end-on Ti2C2 cluster of 3, the encaged Ti and C atoms lie on a line along the C3 rotation axis. Each Ti atom sits over the center of a hexagon ring through the axis, and the separation between the two Ti atoms is 5.139 Å. In the linear Ti2C2 cluster, the Ti-C and C-C bond lengths are 1.955 and 1.229 Å, respectively. The results indicate that the C78 cage needs to have a large hollow space to accommodate the end-on Ti2C2 cluster with the linear Ti-C-C-Ti array. We see in fact that the C78 cage expands

along the C3 rotation axis (8.236 Å) relative to the empty C78 cage (8.051 Å). In contrast, 4 has the C78 length of ∼7.9 Å along the C3 rotation axis, which is shorter than that in the empty C78 cage. In the small hollow space the C2 unit binds in the side-on fashion into the two Ti atoms23 (3.731 Å apart). The small Ti-Ti separation in 4 is reasonable because each Ti atom is located over a [5,6] junction adjacent to a hexagon ring through the C3 rotation axis. The computed Ti-C and C-C bonds are, respectively, ∼2.0 and 1.340 Å, and therefore the side-on Ti2C2 cluster has a butterfly-like structure where the two Ti atoms and the C2 unit do not lie in a plane. The Ti locations inside the C78 cage are responsible for determining the C2 bridging modes into the dititanium center. The Ti2C2 cluster adopts the end-on (side-on) bridging mode, when the Ti atoms are on (off) the C3 rotation axis. The structures of the Ti2C2@C78 molecules 3 and 4 obtained from the DFT calculations are consistent with those from HR-TEM observations in that the Ti2C2 clusters are encapsulated inside the C78 cage and the Ti atoms have two distinctive binding sites inside the cage,13 as shown in Figure S1. These agreements suggest that the Ti2C80 metallofullerenes have the end- and side-on Ti2C2 clusters inside the C78 cage. This is in a good contrast to the Sc2C2@C84 molecules where only side-on Sc2C2 cluster is involved.5 Relative energies of the four possible isomers 1-4 at B3LYP DFT levels of theory are listed in Table 1. The Ti2C2@C78 molecule with the end-on cluster is energetically most favorable in the four Ti2C80 isomers; 3 is more stable than the Ti2@C80 molecules 1 and 2, and the Ti2C2@C78 molecule 4 by 0.83, 1.43, and 1.66 eV, respectively, at the B3LYP/6-31G* level of theory.24 1 and 3 have the two Ti atoms situated over the center of hexagon rings in the C78 and C80 cages, respectively, whereas unstable species 2 and 4 have the two Ti atoms situated over the [5,6] junctions. These imply that the Ti atoms bind over the hexagon rings in preference to the [5,6] junctions, and the stabilities of the Ti2C80 molecules are essentially dominated by Ti binding sites inside fullerene cages. Here a question arises whether the conversion of the end-on bridging mode25 into the side-on bridging mode takes place in the Ti2C2@C78 molecule, as shown in Scheme 1, because the C78 cage in the most stable species 3 is identical to that in 4. For this purpose, we optimized a transition state for the C2 rotation around the dititanium center inside the C78 cage, as

Endohedral Ti2C80 Metallofullerenes

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TABLE 1: Relative Energies of Possible Isomers for Ti2C80 in eV

a

species

cage symmetry

Ti2@C80 1 Ti2@C80 2 Ti2C2@C78 3 TS (3 f 4) Ti2C2@C78 4 Ti2C2@C78 5 Ti2C2@C78 6

Ih(80:7) D5h(80:5) D3h(78:5) D3h(78:5) D3h(78:5) D3h(78:4) D3h(78:4)

C2 unit bridging modes

B3LYP/3-21G

end-on side-on end-on side-on

2.00 2.57 0.00 2.63 2.12 3.76 3.48

B3LYP/6-31G*+3-21Ga

B3LYP/6-31G*

0.00 2.26 1.72 3.51 3.37

0.83 1.43 0.00 2.11 1.66 3.59 3.49

In the basis set system, the 6-31G* basis set is used for the Ti2C2 cluster, and the 3-21G basis set is used for the C78 cage.

CHART 1

SCHEME 1

shown in Figure 3. This transition state has another C2 bridging mode that is inbetween the end- and side-on bridging modes. With respect to the transition state, the imaginary mode of vibration shows that two Ti-C bonds are newly formed, and hence the transition state correctly connects between the isomers 3 and 4. Scheme 2 depicts a Ti atom migration during the

Figure 3. Energy profile (in eV) for the C2 rotation around the dititanium center inside the C78 cage. Bond lengths are in Å. TS (3 f 4) denotes the transition state for the conversion.

process, where a sumanene-like cap in the C78 cage is presented in blue. In the transition state, a Ti atom migrates to sit over one of the carbon atoms of the hexagon ring through the C3 rotation axis; at the same time the Ti atom is relatively close to other two carbon atoms in the hexagon ring. The Ti-Ti separation is shortened (4.028 Å), and then the C2 unit cannot bind in the end-on fashion around the dititanium center. Thus, the C2 unit rotates around the dititanium center with an activation energy of 2.11 eV relative to the isomer 3. After the rotation, the Ti atom moves completely over the [5,6] junction, and consequently the Ti2C2 cluster inside the C78 cage adopts the side-on C2 bridging mode into the dititanium center. These behaviors are intriguing because the end-on cluster that is energetically unstable for itself26,27 exists favorably inside the C78 cage. As mentioned above, we demonstrate from DFT calculations that the C2 bridging modes into the dititanium center in the Ti2C2@C78 molecules are connected to the Ti binding sites inside the fullerene cage. To clarify the importance of the Ti locations inside the fullerene cage to the stabilities in the Ti2C2@C78 molecules 3 and 4, we discuss the energy difference between 3 and 4 from a viewpoint of orbital interactions. According to orbital interaction concepts, two-orbital twoelectron interactions stabilize systems, whereas two-orbital fourelectron interactions destabilize. A second-order perturbation concept tells us that the mixing between occupied and unoccupied orbitals lying in the frontier orbital region makes an important contribution to the stabilization energy. Thus, we can estimate attractive interactions between the Ti2C2 cluster and the C78 cage from orbital energy differences between the Ti2C2@C78 and C78 molecules near the frontier orbital region. Taking into cognizance of the orbital interaction concepts, we pay attention to the orbital energy changes between the Ti2C2@C78 and C78 molecules. Figure 4 shows orbital energies of the isomers 3, 4, and the C78 molecule in the frontier orbital regions. Here significant molecular orbital correlations between the Ti2C2@C78 and C78 molecules are given by solid lines. Although the orbital energies in the Ti2C2@C78 molecules 3 and 4 are shifted from those in the C78 molecule, the frontier orbitals in 3 and 4 are mainly derived from those in the C78 molecule; there are the 2-fold highest occupied molecular orbitals (the HOMOs), the next HOMO (the HOMO-1), the lowest unoccupied molecular orbital (the LUMO), and the 2-fold next LUMOs (the LUMO+1s) in the empty C78 cage, as shown in Figure 4. The occupied orbitals are antisymmetric with respect to the σh plane, whereas the unoccupied orbitals are symmetric with respect to the σh plane. Because the orbital symmetries of the HOMOs (the LUMO+1s) of the C78 cage are similar to those of an antisymmetric (a symmetric) d-based orbital of the end-on Ti2C2 cluster with respect to the plane (Chart 2), the HOMOs (the LUMO+1s) of the C78 cage can nicely interact with the antisymmetric (symmetric) d-based orbital. We see in fact in Figure 4a significant stabilizations of the HOMOs and

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SCHEME 2

LUMO+1s of the C78 cage in 3 where the Ti atoms are located over the hexagon rings through the C3 rotation axis (the long

CHART 2

axis); the HOMOs and LUMO+1s are pushed down by 0.90 and 2.04 eV, respectively. The state of affairs is a little different in the Ti2C2@C78 molecule 4, in which the Ti atoms are situated over the [5,6] junctions. Figure 4b shows that the LUMO+1s of the C78 cage are also stabilized by the interactions in 4 to push down by 1.67 and 1.39 eV. However, the HOMOs of the C78 cage weakly interact with an antisymmetric d-based orbital of the side-on Ti2C2 cluster (Chart 2), and these orbital energies do not almost change by the encapsulation of the side-on cluster inside the cage. These are reasonable because the HOMOs have small orbital amplitudes at the [5,6] junction of the C78 cage over which the two Ti atoms reside. The weak interactions result in the energy difference between 3 and 4. Since the orbital interaction analyses in the Ti2C2@C78 molecules reveal that the Ti bindings over the hexagon rings are energetically stable relative to those over the [5,6] junctions, the preference for the end-on Ti2C2 cluster over the side-on Ti2C2 cluster is characteristic in such a confined space. Thus, we illuminate from DFT calculations that the orbital interactions between the encaged species and the outer cage are responsible for the relative stabilities of the encaged species. Conclusions

Figure 4. Orbital energies (in eV) in frontier orbital regions of two Ti2C2@C78 molecules 3 and 4, and the C78 molecules at the B3LYP DFT level of theory. In the top panel the red and black dots indicate, respectively, the Ti and C atoms in the Ti2C2 cluster. The symbols s and a denote symmetric and antisymmetric orbital with respect to a plane, and their orbital patterns are displayed in Chart 2.

We have analyzed at the B3LYP DFT level of theory the structures of endohedral Ti2C80 metallofullerenes, and discussed in detail the four isomers that are relatively stable in energy. The two isomers have the Ti2@C80 formula in which two Ti atoms are encapsulated inside the Ih and D5h C80 cages, and the other two have the Ti2C2@C78 formula in which a Ti2C2 cluster is involved inside the D3h-C78(78:5) cage. In Ti2C2@C78 molecules there are two-types of Ti2C2 clusters encaged inside the C78 cage; an end-on cluster with a linear Ti-C-C-Ti array and a side-on cluster with a butterfly structure. We have demonstrated from DFT calculations that the Ti2C2@C78 molecule with the end-on Ti2C2 cluster is the most stable in the four isomers. In the Ti2C80 molecules, Ti bindings over the hexagon ring are energetically preferable relative to those over

Endohedral Ti2C80 Metallofullerenes a junction between hexagon and pentagon rings. The Ti locations are also responsible for determining the C2 bridging modes around the dititanium center inside the C78 cage. When the Ti atoms are on the C3 rotation axis, the Ti2C2 cluster adopts the end-on bridging mode, while the cluster adopts the side-on bridging mode when the Ti atoms are off the axis. The end-on cluster converts into the side-on cluster with an activation energy of 2.11 eV, and Ti migrations inside the cage play a significant role in the process. The structures of the Ti2C2@C78 molecules obtained from the DFT calculations can well explain HR-TEM images of Ti2C80 metallofullerenes inside a SWNT in Figure S1. Thus, we predicted from DFT calculations that the Ti2C80 metallofullerenes have the Ti2C2 clusters inside the C78 cage, in which the C2 units bind in end- and side-on fashions around the dititanium center, depending on the metal binding sites. Acknowledgment. T.Y. thanks the Japan Society for the Promotion of Science for a postdoctral fellowship. Partial support by the NEDO Nano-Carbon Technology project is acknowledged. We thank Profs. Susumu Okada (Tsukuba University), Minoru Otani (University of Tokyo), and Miklos Kertesz (Georgetown University) for fruitful discussions. Supporting Information Available: TEM image of the Ti2C80 metallofullerenes encapulated inside a single-walled carbon nanotube (Figure S1). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Shinohara, H. Rep. Prog. Phys. 2000, 63, 843. (2) Akasaka, T.; Nagase, S. Endofullerenes; A New Family of Carbon Clusters; Kluwer Academic Publisher: Dordrecht, The Netherlands, 2002. (3) Nagase, S.; Kobayashi, T.; Akasaka, T.; Wakahara, T. Fullerenes: Chemistry, Physics and Technology; Kadich, K. M., Ruoff, R. S., Eds.; John Wiley & Sons: New York 2000; Chapter 9, p 395. (4) (a) Inakuma, M.; Yamamoto, E.; Kai, T.; Wang, C.-R.; Tomiyama, T.; Shinohara, H.; Dennis, T. J. S.; Hulman, M.; Krause, M.; Kuzmany, H. J. Phys. Chem. B 2000, 104, 5072. (b) Nishibori, E.; Takata, M.; Sakata, M.; Inakuma, M.; Shinohara, H. Chem. Phys. Lett. 1998, 298, 79. (c) Wang, C. R.; Inakuma, M.; Shinohara, H. Chem. Phys. Lett. 1999, 300, 379. (5) Wang, C.-R.; Kai, T.; Tomiyama, T.; Yoshida, T.; Kobayashi, Y.; Nishibori, E.; Takata, M.; Sakata, M.; Shinohara, H. Angew. Chem., Int. Ed. 2001, 40, 397. (6) Krause, M.; Hulman, M.; Kuzmany, H.; Dubay, O.; Kresse, G.; Vietze, K.; Seifert, G.; Wang, C.; Shinohara, H. Phys. ReV. Lett. 2004, 93, 137403. (7) (a) Olmstead, M. M.; de Bettencourt-Dias, A.; Duchamp, J. C.; Stevenson, S.; Marciu, D.; Dorn, H. C.; Balch, A. L. Angew. Chem., Int. Ed. 2001, 40, 1223. (b) Stevenson, S.; Fowler, P. W.; Heine, T.; Duchamp, J. C.; Rice, G.; Glass, T.; Harich, K.; Hajdu, E.; Bible, R.; Dorn, H. C. Nature, 2000, 408, 427. (c) Olmstead, M. M.; Lee, H. M.; Duchamp, J. C.; Stevenson, S.; Marciu, D.; Dorn, H. C.; Balch, A. L. Angew. Chem., Int. Ed. 2003, 42, 900. (8) Krause, M.; Kuzmany, H.; Georgi, P.; Dunsch, L.; Vietze, K.; Seifert, G. J. Chem. Phys. 2001, 115, 6596. (b) Kobayashi, K.; Sano, Y.; Nagase, S. J. Comput. Chem. 2001, 13, 1353. (c) Campanera, J. M.; Bo, C.; Olmstead, M. M.; Balch, A. L.; Poblet, J. M. J. Phys. Chem. A 2002, 106, 12356.

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