J. Phys. Chem. B 2005, 109, 5267-5272
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On the Structure and Relative Stability of C50 Fullerenes† Xiang Zhao* Department of Chemistry, College of Science, Xi’an Jiaotong UniVersity, Xi’an 710049, People’s Republic of China ReceiVed: October 16, 2004; In Final Form: January 11, 2005
The complete set of 271 classical fullerene isomers of C50 has been studied by full geometry optimizations at the SAM1, PM3, AM1, and MNDO quantum-chemical levels, and their lower energy structures have also been partially computed at the ab initio levels of theory. A D5h species, with the least number of pentagon adjacency, is predicted by all semiempirical methods and the HF/4-31G calculations as the lowest energy structure, but the B3LYP/6-31G* geometry optimizations favor a D3 structure (with the largest HOMOLUMO gap and the second least number of adjacent pentagons) energetically lower (-2 kcal/mol) than the D5h isomer. To clarify the relative stabilities at elevated temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the HF/4-31G level for the first time. The computed relativestability interchanges show that the D3 isomer behaves more thermodynamically stable than the D5h species within a wide temperature interval related to fullerene formation. According to a newly reported experimental observation, the structural/energetic properties and relative stabilities of both critical isomers (D5h and D3) are analyzed along with the experimentally identified decachlorofullerene C50Cl10 of D5h symmetry. Some features of higher symmetry C50 nanotube-type isomers are also discussed.
Introduction Since the discovery1 of C60, along with the macroscopic scale synthesis2 in bulk, there has been a long standing scientific interest focusing not only on the extent of C60, C70, and some higher fullerenes but also on the smaller fullerene system with less than 60 carbon atoms. Compared with intensive progress on syntheses and characterizations of C60 and its larger homologues,3 smaller fullerenes have received rather little attention because of their assumed higher reactivity and lower stability. Owing to the highly strained structures along with some unavoidable adjacent pentagons so that the well-known isolated pentagon rule (IPR)4 is violated, smaller fullerenes are predicted to lead to a high instability and a special difficulty to isolate. However, recent reports on the successful syntheses of C365 and C206 fullerenes have significantly attracted a growing attention7-18 both experimentally and theoretically to their unusual properties and indicated some revision of the conventional views. In fact, Kroto4 pointed out that the fullerenes Cn with the magic number n ) 24, 28, 32, 36, 50, 60, and 70 may possess some enhanced stability linked to the special behaviors in the experimental observations. The fullerenes in the range of 20-50 carbon atoms have been indeed explored19-21 by various experimental techniques. It is reported20 that the fraction of fullerene structures was observed close to 5% for C32, about 25% for C40, and virtually up to 90% for C50 with the gas-phase ion chromatography technique. Some synthetic routes22 toward smaller fullerenes have also been studied. Very recently, Xie et al. reported23 the first synthesis of a decachlorofullerene C50Cl10 related to fullerene C50, which suggested a possible way for the preparation of a pure C50 cage molecule. These observations have indicated fullerene C50 as an interesting system to be * E-mail:
[email protected]. † Dedicated to Professor Eiji Osawa with esteem on the occasion of his 70th birthday.
understood and obviously spurred more efforts of experimental and computational studies to determine the structures, energetics, and stabilities. Although C50 has long been recognized as one of the most stable fullerenes Cn (n < 60) owing to its considerably high abundance1,24-26 in mass spectroscopy, theoretical studies devoted to this system still remain very limited and incomplete. Fullerene C50 allows27 for 271 isomeric cages built from pentagons and hexagons on a definition of the classical fullerenes. So far, a few theoretical studies on some typical C50 isomers have been reported.28-31 In the works of tight-binding molecular dynamics calculation28 and recent density functional study29 on Cn (n ) 50-60), only the D5h isomer of C50 was treated in both cases. After the MNDO geometry optimizations for 30 fullerene cages Cn (20 < n < 540) 30 were carried out with three typical C50 isomers, Slanina et al.31 reported the relative stability of C50 containing three isomers (D5h, D3, and C2V) with the MNDO method and predicted the D3 isomer as the most stable one at high temperatures. A recent work32 based on the HF/3-21G and B3LYP/3-21G computations has also addressed the electronic and equilibrium structures of three C50 isomer candidates (D5h, D3, and D5h) with their hydrogenated derivatives, where one D5h species and the D3 species are predicted as near isoenergetic isomers. Within all 271 isomers available for a C50 cage upon the concept 27 of classical fullerenes, what is the most thermodynamically stable C50 fullerene isomer? To our best knowledge, this question is still treated incompletely and should however be analyzed in detail. In this paper, a comprehensive examination on the C50 isomeric fullerene set using several quantum-chemical procedures has been carried out for the first time. As fullerene production is achieved at rather higher temperatures, the abundance of the fullerene isomers may be governed by the high temperature free energies ∆G of the molecules rather than their potential energies. To evaluate the temperature-dependent
10.1021/jp0452610 CCC: $30.25 © 2005 American Chemical Society Published on Web 02/24/2005
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relative stabilities of the C50 classical fullerene system, the entropy contributions are taken into account on the basis of the Gibbs function under the condition of the interisomeric thermodynamic equilibrium. According to the present results on the consideration of both enthalpy and entropy, the stability issue of the system is discussed in detail to aid further experimental study. Calculations The geometry optimizations of all 271 conventional fullerene cages, generated by a topological procedure, were performed first with several semiempirical quantum-chemical methods (SAM1,33 PM3,34 AM1,35 and MNDO 36), to confirm the essential energetic classifications for the C50 isomeric set. The SAM1 computations were carried out primarily with the AMPAC program package,37 and calculations at the PM3, AM1, and MNDO levels were performed with the updated MOPAC program.38 The geometry optimizations were carried out with no symmetry constraints in Cartesian coordinates and with an analytically constructed energy gradient. Upon the optimized geometries, the harmonic vibrational analyses at the PM3 quantum-chemical level were carried out by a numerical differentiation of the analytical energy gradient and have determined that all the localized stationary points are indeed local energy minima or transition states. Rotational-vibrational partition functions were constructed from the computed structural and vibrational data at the PM3 quantum-chemical level of theory (though, only of the rigid rotator and harmonic oscillator quality and with no frequency scaling). Relative concentrations (mole fractions) wi of m isomers can be expressed through the partition functions qi and the ground-state energies ∆H°0,i by a compact formula:39-41
TABLE 1: Relative Energetics and Band Gaps for Selected C50 Isomersa labelb: sym
PAc
SAM1
PM3
AM1
MNDO
gap
271:D5h 270:D3 266:C2 262:Cs 260:C2 263:C2 264:Cs 268:C1 267:Cs 265:C2 226:C2 261:C2 222:C1 248:C1 225:C1 249:C1 246:C1 221:C1 256:C2V 242:C2V 208:C3 179:C2V 181:D3 258:C3 43:C2V 157:C3V 125:C2V 13:C2V 3:D3h 1:D5h
5 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 8 8 9 9 9 9 11 12 13 14 18 20
0.0 26.5 27.9 29.6 30.2 36.1 39.3 47.8 50.5 52.7 55.9 56.9 58.7 63.7 64.2 66.7 68.9 70.0 82.1 118.1 104.0 130.9 135.6 150.1 178.2 174.6 238.1 277.1 344.3 406.5
0.0 29.9 39.9 26.2 28.3 38.3 38.8 44.7 47.4 49.9 50.1 50.6 54.0 59.3 58.8 60.5 65.9 65.5 72.6 106.0 95.7 119.2 121.5 136.3 157.0 163.9 225.6 244.1 301.6 388.2
0.0 31.9 42.6 29.3 30.5 40.7 40.8 49.1 51.9 54.2 55.5 56.7 59.1 64.5 64.1 65.8 71.1 70.7 80.5 114.5 105.5 131.6 129.1 148.7 172.9 180.5 225.0 265.4 330.1 385.3
0.0 26.9 36.0 27.9 28.2 39.4 45.9 44.7 46.6 48.0 53.5 53.1 55.3 58.9 60.3 59.7 64.6 65.4 74.5 104.1 95.9 116.6 120.5 134.6 162.2 177.9 223.6 262.1 334.2 382.0
0.1031 0.4679 0.2481 0.2095 0.1401 0.3642 0.1591 0.1969 0.2288 0.1927 0.3275 0.2376 0.1844 0.1285 0.1042 0.0439 0.0751 0.0532 0.2396 0.1057 0.2354 0.0315 0.1232 0.0271 0.1044 0.2395 0.0679 0.1320 0.0000 0.0000
a Energy units in kilocalories per mole; band gap calculated at the HMO level, in units of |β|, where β is the Hu¨ckel resonance integral. b Numbering convention of isomers recommended in ref 27. c PA: the number of pentagon adjacency.
Results and Discussion
wi )
qi exp[-∆H°0,i/(RT)] m
(1)
qj exp[-∆H°0,j/(RT)] ∑ j)1 where R is the gas constant and T is the absolute temperature. Clearly enough, the conventional heats of formation at room temperature ∆H°f,298 (resulting from the semiempirical quantumchemical calculations) have to be converted to the heats of formation at the absolute zero temperature ∆H°f,0. Chirality contributions, frequently ignored, must be also considered in eq 1, as its partition function qi is doubled for an enantiomeric pair. In this way, temperature-dependent relative concentrations can finally be evaluated, where the partial thermodynamic equilibrium is described by a set of equilibrium constants so that both enthalpy and entropy terms are considered accordingly. It is necessary to stress that eq 1 is, however, an exact relationship that is derived from the principle of equilibrium statistical thermodynamics, that is, from the standard Gibbs energies of the isomers, and it is strongly temperature-dependent. All the entropy contributions are evaluated through the isomeric partition functions. Only two presumptions are involved: the ideal-gas behavior of reaction components and the existence of the interisomeric thermodynamic equilibrium. The equation does not require the total heats of formation, just the relative energy terms (like ∆∆H°f,0). It is still on progress for applying this approach to isomeric fullerenes;40,41 all the rest of the available calculations are based on potential energy/heats of formation only.
Computations start from topologically generated structures42-44 with correct bond connectivity preoptimized by the MM3 method.45 Like the smaller fullerenes (i.e., C32 and C36),9,43,46 the fullerene cages were generated by the topological program44 based on the generalized Stone-Wales transformations, which has been successfully applied to a comprehensive search of fullerene structures. If the topological search condition was expanded to the quasi-fullerenes (with one square or one heptagon), not only the 271 classical fullerenes but also 2783 quasi-fullerene structures came out. Since all quasi-fullerene geometries are energetically unstable with respect to the classical ones after the prescreening of AM1 calculations, it is certainly reasonable to focus just the 271 conventional cage structures with only pentagons and hexagons. Therefore, only classical fullerene cages are analyzed in the present report. All 271 C50 topologies have first been subjected to the full geometry optimizations with SAM1, PM3, AM1, and MNDO models to produce the primary classifications of energetics and stability. Table 1 surveys the computed energetics of the 18 lowest energy structures and some selected representative symmetrical ones. As one kind of kinetic-stability measure, the calculated HOMOLUMO gaps from the simple Hu¨ckel MO level, which are consistent with the reference values,27 are also presented for comparison in Table 1. As shown in Table 1, all applied semiempirical methods predict a structure of D5h symmetry (FM code,27 271:D5h) with the smallest number of pentagon adjacency as the lowest energy isomer out of the classical C50 fullerene cages. There are only nine kinds of symmetry (C1(195), Cs(25), C2(37), C2V(6), C3(2), C3V(1), D3(2), D3h(1), and D5h(2)) distributively available in the C50 fullerenes, where
Structure and Relative Stability of C50 Fullerenes
J. Phys. Chem. B, Vol. 109, No. 11, 2005 5269 TABLE 2: Calculated Energies and HOMO-LUMO Gapsa for Some C50 Isomers
labelb: sym 271:D5h 270:D3 266:C2 262:Cs 260:C2 263:C2 264:Cs 268:C1 267:Cs 265:C2 226:C2 261:C2 222:C1 248:C1 225:C1 249:C1 246:C1 221:C1 157:C3V 3:D3h 1:D5h
B3LYP/ 6-31G* E
B3LYP/ 6-31G* ∆E
HOMOLUMO
HF/ 4-31G ∆E
-1904.9290 -1904.9322 -1904.9191 -1904.8927 -1904.8956 -1904.9151 -1904.9032
2.0 0.0 8.2 24.8 23.0 10.7 18.2
1.38 2.27 1.77 1.63 1.49 2.09 1.61
-1904.7302 -1904.4462 -1904.3718
126.8 305.0 351.7
1.74 1.19 1.32
0.0 2.4 6.7 6.9 14.4 3.9 11.2 28.4 31.5 29.3 37.0 34.4 47.1 38.3 70.6 50.3 45.0 55.4 153.2 353.0 476.0
a The total energies E in hartrees, the HOMO-LUMO gaps in electronvolts, and the relative energies ∆E in kilocalories per mole fully optimized at the B3LYP/6-31G* level of theory. The last column lists the relative energies computed at the HF/4-31G level of theory. b Numbering convention recommended in ref 27.
Figure 1. B3LYP/6-31G* optimized structures of some important C50 isomers.
nonsymmetry structures are predominantly leading in number. Interestingly enough, the highest energy species in the set is another D5h symmetry structure (FM code, 1:D5h) of the zigzag nanotube style with the maximum number of pentagon adjacency and is located about 406 (SAM1), 388 (PM3), 385 (AM1), and 382 (MNDO) kcal/mol above the lowest energy structure. Moreover, there is a rather higher energy species with D3h point group symmetry (FM code, 3:D3h), which also belongs to a typical smaller armchair nanotube (see Figure 1). Notice that both 1:D5h and 3:D3h structures have a single graphite network with concentrated pentagons at their tube ends and possess the zero band gaps estimated at the HMO level. After energies have been evaluated by several semiempirical quantum-chemical methods for all 271 classical fullerene cages in their respective equilibrium optimized geometries, deviations of up to more than 50 kcal/mol from the 271:D5h species and a general trend of energetic costs are found while the number of the pentagon adjacency (PA) is increasing. Since nonsymmetrical structures in C50 cages are dominant as the PA value is up, for simplicity only, some symmetrical species with PA > 7 are listed in Table 1. In general, semiempirical methods produce considerably good results of equilibrium structures and energetics for fullerenes,41,47 but it has always been advisable to check those results at some higher levels of theory. Hence, further calculations on their separation energetics have been performed at the ab initio Hartree-Fock SCF level with the standard 4-31G basis set, based on the optimized PM3 geometries. Even though the HF/4-31G energetic results generally support the semiempirical conclusions, some isomers with six adjacent pentagons (PA ) 6) are predicted with the smaller energy difference
against the lowest energy species 271:D5h. Therefore, for the sake of higher accuracy on energetics, full geometry optimizations on some critical structures have moreover been performed at the density functional B3LYP/6-31G* level of theory. All ab initio calculations employed the G98 suite of programs.48 Table 2 lists the energies and HOMO-LUMO gaps of some representative C50 isomers computed at the B3LYP/6-31G* level of theory together with the HF/4-31G separation energies. As shown in Table 2, in contrast to energies of all semiempirical MO methods and the HF/4-31G approach, the B3LYP/6-31G* energetic result predicts the 270:D3 species to be the lowest energy isomer (with an energy difference of 2.0 kcal/mol compared to the 271:D5h species), holding the largest HOMOLUMO gap (2.27 eV) in the C50 classical fullerene set. Although two narrow-nanotube-type species (3:D3h and 1:D5h) have also been confirmed with larger separation energies to the lowest energy and rather smaller band gaps at the B3LYP/6-31G* level of theory, it is worthy to mention that the species 3:D3h (PA ) 18) has in its middle a diameter of ∼4.06 Å and 1:D5h (PA ) 20) has one of ∼3.98 Å; both computed measurements correspond quite well to the recent observed value49 of 4 Å. Only the separation energy itself cannot predict relative stabilities in an isomeric system at high temperatures, as stability interchanges induced by the enthalpy-entropy interplay are possible. To obtain further insight into the thermodynamic stability of C50 fullerenes, we have investigated the entropy effects and evaluated the relative concentrations through the Gibbs free energy terms at the HF/4-31G level of theory. Although previous experience for higher fullerenes intimates that in some cases the energy handicap as high as 45 kcal/mol can be overcompensated 50 by a pronounced entropy term, the entropy effects are expected to some extent to be proportional to the system dimension. Hence, it is reasonable to select and focus on only the structures with an optimized separation energy below some 35 kcal/mol in the C50 equilibrium isomeric mixture, and this is the reason that only lower energy isomers (with PA
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Figure 2. HF/4-31G relative concentrations of the lower energy C50 isomers.
< 7) are counted for equilibrium statistical thermodynamic analyses in the present work. It is known that fullerene formation occurs at high temperatures, and thus, the temperature development of the equilibrium concentrations in the C50 system has been evaluated in order to gain a deeper insight into the relative-stability problem. Figure 2 presents the relative concentrations of C50 fullerenes in a wide temperature interval from the HF/4-31G separation energies and the PM3 entropies applied within eq 1. The evaluation exhibits that the interisomeric thermodynamic equilibrium behaves rather selectively. It turns out that even though the 271:D5h structure (as the isomer lowest in potential energy) must of course prevail, its relative fraction rapidly decreases as the temperature increases and its stability order is reversed after ∼300 K. Then, it is surpassed by the 270:D3 structure (with the largest HOMOLUMO gap in the C50 classical fullerene set), and the latter increases its relative fraction to a temperature of ∼400 K with its maximum yield of 48.4% compared to the 271:D5h species with a fraction of 32.6%. Clearly, it is shown that the 270:D3 isomer should be more thermodynamically stable than the 271:D5h structure over a wide range of temperatures with respect to the fullerene formation. However, a third species coded by 263:C2 with a swift increase that eventually overcomes both the 271:D5h species from ∼490 K and the 270:D3 isomer from ∼800 K becomes quite significant at higher temperatures, as shown in Figure 2. This result indicates that the 263:C2 isomer (with the second largest HOMO-LUMO gap) is predicted to have some chemical stability at high temperatures, even though such a HF/4-31G based dominancy within high temperatures is due to a rather small separation energy (∆E ) 3.9 kcal/mol). If the relative concentrations in the C50 set are evaluated from the separation energies of B3LYP/6-31G* geometry optimizations combined with the PM3 entropy contributions, the 270:D3 isomer is overwhelming and most abundant at all temperatures. Historically, the well-known D5h isomer (FM code, 271) is usually regarded as the best candidate for extractable fullerene C50 and its derivatives in the earlier28-30 and recent32,51-52 theoretical studies, mainly owing to its feature of the minimum number of pentagon adjacencies. Since smaller fullerenes (Cn, n < 60) cannot avoid the energetically unfavorable pentagon fusions within their structures, it is certainly considered10 that minimization of the number of pentagon adjacencies may enhance the relative stability. Therefore, according to such an
empirical rule, it is predicted that the lowest energy isomer should be one with the minimum count of pentagon adjacencies (PAs). In contrast to the above idea, our present results on C50 fullerenes give a new revision related to the empirical consideration. Not only the HF/4-31G thermodynamic equilibrium evaluation but also the B3LYP/6-31G* computations indicate that the 270:D3 isomer is more stable than the famous 271:D5h species. Among the C50 isomers with the same pentagon adjacency (PA ) 6), the 270:D3 species is unique in its structural motif where each pentagon adjacency is separate from one another, compared with the rest of the five isomers that include at least one subunit of three-pentagon adjacency. Moreover, to obtain meaningful structural and energetic characteristics, the full geometry optimizations have been carried out at the B3LYP/ 6-31G* level of theory on the singlet and triplet states of two critical isomers (271:D5h and 270:D3). We found that both triplet states are higher in energy than their singlet states, respectively. Interestingly enough, the singlet-triplet splitting energy ∆E(S-T) of 271:D5h is only 4.56 kcal/mol (0.2 eV), implying that the triplet state would be reached very easily. Furthermore, the frontier orbitals (particularly the HOMO) of the 271:D5h species are found to be localized mainly around five subunits of the adjacent pentagon fusion. Even though a very recent experimental report23 on the preparation of a smaller fullerene derivative (C50Cl10) may ignite reasonable interest in producing a pure sample of the bare C50 cage, it appears that it may be unlikely to capture the C50 fullerene (271:D5h) in various isolation processes, due to its high reactivity and instability compared to the distinct chemical stability of C50Cl10 (271:D5h). In fact, it is reported in the experiment23 that such a decachlorofullerene[50] molecule was produced by adding 10 chlorine atoms just to the five most reactive sites (the adjacent pentagon fusions). Our B3LYP/6-31G* investigations further exhibit that the HOMO level of C50Cl10 (271:D5h) is significantly decreased and its LUMO level is reasonably raised, compared to the pure C50 (271:D5h), resulting in a conspicuously enhanced HOMOLUMO gap (3.07 eV for C50Cl10 vs 1.38 eV for C50) which could rival with the Ih-C60 band gap (2.76 eV). A detailed analysis on the stabilization of fullerene C50 and its derivatives is discussed53 elsewhere. We believe that it is hard to form a pristine C50 fullerene by losing the chlorine atoms from C50Cl10, as the C50 (271:D5h) is very reactive and less thermodynamically stable. Overall, it is predicted that the 270:D3
Structure and Relative Stability of C50 Fullerenes isomer should be the best candidate of fullerene C50 found in the experiment if available. Conclusions In this paper, the complete C50 fullerene set has been systematically investigated, for the first time, using various semiempirical quantum-chemical approaches together with the ab initio SCF method and a hybrid density functional theory technique. Even though the well-known D5h isomer (with only five pentagon fusions) was predicted to be the lowest in energy by four semiempirical MO methods and the ab initio HF/431G computations, the B3LYP/6-31G* optimizations indicate a species of D3 symmetry (with six separate pentagon fusions) as the most stable one. The relative stability under the interisomeric thermodynamic equilibrium has been evaluated in terms of the Gibbs function. The HF/4-31G evaluation of entropy effect suggests that the structure (270:D3, PA ) 6) is more thermodynamically stable than the D5h isomer (PA ) 5; FM code, 271) and should be preferentially isolated in the related experiment. Our results also show that C50 belongs to the family of isomeric fullerenes with a substantial role of entropy.54-58 The synthesis of fullerene derivative C50Cl10 (D5h) has been recently reported,23 and thus, it is speculated52 that such a reactive pristine D5h-C50 isomer might be isolated through eliminating the chlorine atoms from the decachlorofullerene[50] molecule C50Cl10 (D5h) with some chemical methods. The presented results demonstrate that there is indeed a correlation between band gaps and chemical reactivity, since small HOMOLUMO gaps are fairly good measures for low energy (triplet) states. The detailed analysis results at the B3LYP/6-31G* level of theory confirm that C50Cl10 (D5h) has an exceptional chemical stability in contrast to an explicit chemical instability of the D5h-C50 isomer, implying that capturing the latter from the former is no doubt an uphill task. Fullerene synthesis is after all unique in various respects by its very high temperature, so that the T∆S°T term of the Gibbs function cannot be negligible. The reported entropy contribution actually gives a reasonable explanation as to why some particular species, which may not be the structures lowest on the potential energy scale, still represent relatively thermodynamically stable isomers and could be preferentially isolated experimentally. In the reported study of C50, the 270:D3 species is such a case even in either semiempirical or HF/4-31G energy scales, and its relative stability has been proven by further analyses based on the B3LYP/6-31G* results. The temperature region where fullerene formation occurs is not yet known, but it should be somewhere in a broad interval between 500 and 3000 K, as it may vary depending on specific experimental arrangements.59-62 Acknowledgment. The author wishes to thank Prof. Z. Slanina for many stimulating and helpful discussions. The reported research was partially supported by the Natural Scientific Grants of Xi’an Jiaotong University (no. Xjj2004001) and the Japan Society for the Promotion of Science (JSPS). The facilities of the Research Center for Science at Xi’an Jiaotong University are gratefully acknowledged, too. References and Notes (1) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (2) Kratschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D. R. Nature 1990, 347, 354. (3) Diederich, F.; Ettl, R.; Rubin, Y.; Whetten, R. L.; Beck, R.; Alvarez, M.; Anz, S.; Sensharma, D.; Wudl, F.; Khemani, K. C.; Koch, A. Science 1991, 252, 548.
J. Phys. Chem. B, Vol. 109, No. 11, 2005 5271 (4) Kroto, H. W. Nature 1987, 329, 529. (5) Piskoti, C.; Yarger, J.; Zettl, A. Nature 1998, 393, 771. (6) Prinzbach, H.; Weiler, A.; Landenberger, P.; Wahl, F.; Worth, J.; Scott, L. T.; Gelmont, M.; Olevano, D.; lssendorff, B. v. Nature 2000, 407, 60. (7) Louie, S. G. Nature 1996, 384, 612. (8) Crossman, J. C.; Cote, M.; Louie, S. G.; Cohen, M. L. Chem. Phys. Lett. 1998, 284, 344. (9) Slanina, Z.; Zhao, X.; Osawa, E. Chem. Phys. Lett. 1998, 290, 311. (10) Fowler, P. W.; Mitchell, D.; Zerbetto, F. J. Am. Chem. Soc. 1999, 121, 3218. (11) Jagadeesh, M. N.; Chandrasekhar, J. Chem. Phys. Lett. 1999, 305, 298. (12) Yuan, L. F.; Yang, J. L.; Deng, K.; Zhu, Q. S. J. Phys. Chem. A 2000, 104, 6666. (13) Slanina, Z.; Uhlik, F.; Zhao, X.; Osawa, E. J. Chem. Phys. 2000, 113, 4933. (14) Gueorguiev, G. K.; Pacheco, J. M. J. Chem. Phys. 2001, 114, 6068. (15) Saito, M.; Miyamoto, Y. Phys. ReV. Lett. 2001, 87, 035503. (16) Paulus, B. Phys. Chem. Chem. Phys. 2003, 5, 3364. (17) Iqbal, Z.; Zhang, Y.; Grebel, H.; Vijayalakashmi, Lahamer, A.; Benedek, G.; Bernasconi, M.; Cariboni, J.; Spagnolatti, I.; Sharma, R.; Owens, F. J.; Kozlov, M. E.; Rao, K. V.; Muhammed, M. Eur. Phys. J. B 2003, 31, 509. (18) Chen, Z.; Heine, T.; Jiao, H.; Hirsch, A.; Thiel, W.; Schleyer, P. v. R. Chem.sEur. J. 2004, 10, 963. (19) Helden, G.; Hsu, M. T.; Kemper, P. R.; Bowers, M. T. J. Chem. Phys. 1991, 95, 3835. (20) Helden, G.; Gotts, N. G.; Bowers, M. T. Nature 1993, 363, 60. (21) Bowers, M. T.; Kemper, P. R.; Helden, G.; Koppen, P. A. M. Science 1993, 260, 1446. (22) Wahl, F.; Worth, J.; Prinzbach, H. Angew. Chem., Int. Ed. 1993, 32, 1722. (23) Xie, S. Y.; Gao, F.; Lu, X.; Huang, R. B.; Wang, C. R.; Zhang, X.; Liu, M. L.; Deng, S. L.; Zheng, L. S. Science 2004, 304, 699. (24) Rohlfing, E. A.; Cox, D. M.; Kaldor, A. J. Chem. Phys. 1984, 81, 3322. (25) Cox, D. M.; Reichmann, K. C.; Kaldor, A. J. Chem. Phys. 1988, 88, 1588. (26) Zimmerman, J. A.; Eyler, J. R.; Bach, S. B.; McElvany, S. W. J. Chem. Phys. 1991, 94, 3556. (27) Fowler, P. W.; Manolopoulos, D. E. An Atlas of Fullerenes; Clarendon Press: Oxford, U.K., 1995. (28) Zhang, B. L.; Wang, C. Z.; Ho, K. M.; Xu, C. H.; Chan, C. T. J. Chem. Phys. 1992, 97, 5007. (29) Diaz-Tendero, S.; Alcami, M.; Martin, F. J. Chem. Phys. 2003, 119, 5545. (30) Bakowies, D.; Thiel, W. J. Am. Chem. Soc. 1991, 113, 3704. (31) Slanina, Z.; Adamowicz, L.; Bakowies, D.; Thiel, W. Thermochim. Acta 1992, 202, 249. (32) Xu, W. G.; Wang, Y.; Li, Q. S. THEOCHEM 2000, 531, 119. (33) Dewar, M. J. S.; Jie, C.; Yu, J. Tetrahedron 1993, 49, 5003. (34) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209. (35) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902. (36) Dewar, M. J. S.; Thiel, W. J. J. Am. Chem. Soc. 1977, 99, 4899. (37) Holder, A. J. AMPAC, version 6.55; Semichem, Inc.: Shavnee, KS, 1997. (38) Stewart, J. J. P. MOPAC 2000, version 1.06; Fujitsu Limited: Tokyo, Japan, 1999. (39) Slanina, Z. Int. ReV. Phys. Chem. 1987, 6, 251. (40) Slanina, Z.; Zhao, X.; Osawa, E. AdVances in Strained and Interesting Organic Molecules; JAI Press Inc.: Stamford, CT, 1999; Vol. 7, p 185. (41) Slanina, Z.; Zhao, X.; Deota, P.; Osawa, E. In Fullerenes: Chemistry, Physics, and Technology; Kadish, K. M., Ruoff, R. S., Eds.; John Wiley & Sons: New York, 2000; p 283. (42) (a) Yoshida, M.; Osawa, E. Bull. Chem. Soc. Jpn. 1995, 68, 2073. (b) Yoshida, M.; Osawa, E. Bull. Chem. Soc. Jpn. 1995, 68, 2083. (43) Zhao, X.; Ueno, H.; Slanina, Z.; Osawa, E. In Recent AdVances in the Chemistry and Physics of Fullerenes and Related Materials; Kadish, K. M., Ruoff, R. S., Eds.; The Electrochemical Society: Pennington, NJ, 1997; Vol. 5, p 155. (44) Osawa, E.; Ueno, H.; Yoshida, M.; Slanina, Z.; Zhao, X.; Nishiyama, M.; Saito, H. J. Chem. Soc., Perkin Trans. 2 1998, 943. (45) Allinger, N. L.; Yuh, Y. H.; Lii, J. H. J. Am. Chem. Soc. 1989, 111, 8551. (46) Zhao, X.; Slanina, Z.; Ozawa, M.; Osawa, E.; Deota, P.; Tanabe, K.; Fullerene Sci. Technol. 2000, 8 (6), 595. (47) Cioslowski, J. Electronic Structure Calculations on Fullerenes and Their DeriVatiVes; Oxford University Press: Oxford, U.K., 1995. (48) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.;
5272 J. Phys. Chem. B, Vol. 109, No. 11, 2005 Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Salvador, P.; Dannenberg, J. J.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian98, revision A.11; Gaussian, Inc.: Pittsburgh, PA, 2001. (49) (a) Qin, L.-C.; Zhao, X.; Hirahara, K.; Miyamoto, Y.; Ando, Y.; Iijima, S. Nature 2000, 408, 50. (b) Wang, N.; Tang, Z. K.; Li, G. D.; Chen, J. S. Nature 2000, 408, 51. (50) Slanina, Z.; Zhao, X.; Lee, S. L.; Osawa, E. Chem. Phys. 1997, 219, 193. (51) Xie, R.; Bryant, G. W.; Cheung, C. F.; Smith, V. H., Jr.; Zhao, J. J. Chem. Phys. 2004, 121, 2849.
Zhao (52) Chen, Z. F. Angew. Chem., Int. Ed. 2004, 43, 4690. (53) Zhao, X.; et al. Manuscript in preparation. (54) Slanina, Z.; Zhao, X.; Deota, P.; Osawa, E. J. Mol. Model. 2000, 6, 312. (55) Zhao, X.; Slanina, Z.; Goto, H.; Osawa, E. J. Chem. Phys. 2003, 118, 10534. (56) Zhao, X.; Slanina, Z.; Goto, H. J. Phys. Chem. A 2004, 108, 4479. (57) Zhao, X.; Slanina, Z. THEOCHEM 2003, 636, 195. (58) Zhao, X.; Goto, H.; Slanina, Z. Chem. Phys. 2004, 306, 93. (59) Wakabayashi, T.; Kikuchi, K.; Suzuki, S.; Shinomaru, H.; Achiba, Y. J. Phys. Chem. 1994, 98, 3090. (60) Wakabayashi, T.; Kasuya, D.; Shinomaru, H.; Suzuki, S.; Kikuchi, K.; Achiba, Y. Z. Phys. D 1997, 40, 414. (61) Mckinnon, J. T.; Bell, W. L.; Barkley, R. M. Combust. Flame 1992, 88, 102. (62) (a) Peters, G.; Jansen, M. Angew. Chem., Int. Ed. 1992, 31, 223. (b) Mittlebach, A.; Honle, W.; von Schnering, H. G.; Carlsen, J.; Janiak, R.; Quast, H. Angew. Chem., Int. Ed. 1992, 31, 1640.
