J. Phys. Chem. C 2007, 111, 17099-17103
17099
Potential High-Capacity Hydrogen Storage Medium: Hydrogenated Silicon Fullerenes Dongju Zhang,* Chen Ma,* and Chengbu Liu Key Lab of Colloid and Interface Chemistry, Ministry of Education, School of Chemistry and Chemical Engineering, Shandong UniVersity, Jinan, 250100, P. R. China ReceiVed: August 4, 2007; In Final Form: September 9, 2007
Searching for hydrogen storage materials suitable for applications has been the focus of extensive research in industry and academia. With the great success in obtaining stable hollow silicon-based nanostructures, one is naturally led to wonder whether silicon-based nanostructures are possible for chemical hydrogen storage. Here a hydrogenated silicon fullerene (HSF), Si60H60, is considered as a prototype of stable silicon-based nanostructures for hydrogen storage. By performing density functional theory calculations we show that the HSF is stable over hydrogen molecule attack and thus qualified for acting as a potential hydrogen storage medium. The interaction between the HSF with hydrogen molecules is found to be essentially via van der Waals force, making the HSF prefer storing hydrogen in molecular form. It is demonstrated that up to 58 hydrogen molecules can be stored into its interior cavity, and together with 60 hydrogen atoms in the exterior surface, total gravimetric density of hydrogen of 58H2@Si60H60 amounts to 9.48%, which is much higher than any reported capacity of hydrogen storage in other media or the target of the Department of Energy (6 wt %). The present results provide valuable guidance for developing practical high-capacity hydrogen storage materials.
Introduction Hydrogen, an ideal alternative for fossil fuels used presently, has great potential as an environmentally harmless energy carrier in the future sustainable energy system. A major hurdle that must be overcome to enable the use of hydrogen as an energy carrier is to create inexpensive hydrogen storage materials with high gravimetric and volumetric density under near-ambient temperatures and pressures.1 In the past years, much effort has been devoted to searching for innovative hydrogen storage materials, including carbon-based materials (such as the nanotubes,2 fullerenes,3 and activated carbons4), metals,5 metal alloys,6 metal-organic framework compounds,7-8 and clathrates.9 None of these materials, however, has yet been established to be appropriate for practical applications since their hydrogen storage temperatures and capacities do not meet the industry standard, which requires the materials to have a gravimetric density of at least 6% at ambient temperature and pressure. Therefore, developing efficient and safe materials for hydrogen storage is still one of the most challenging problems for transportation applications of hydrogen. The overwhelming majority of hydrogen storage materials considered in the literature consists of light elements such as Li, C, B, N, Mg, and Al, and carbon-based materials are among the major candidates due to their abundant natural precursors.10 Recently, several theoretical groups11-13 have predicated that coating metal atoms on the carbon nanotubes and fullerenes is a promising strategy for improving their hydrogen storage capabilities. Zhao11 and Yildrim12 showed that transition-metalcoated carbon nanotubes and fullerenes could store molecular hydrogen with a gravimetric density of about 8%. However, Jena el al.14 found by performing density functional theory (DFT) calculations that transition-metal atoms prefer to cluster * To whom correspondence should be addressed. E-mail: zhangdj@ sdu.edu.cn.
on the surface of fullerenes, making fullerenes no longer effective for storing hydrogen in large quantities. Nevertheless, Sun et al.13 claimed that the cluster behavior can be avoided by substituting transition-metal atoms with Li atoms. Very recently, Mpourmpakis and Froudakis15 reported hydrogen storage in silicon-carbon nanotubes. By performing ab initio calculations and classical Monte Carlo simulations they found that the weight percent of the adsorbed hydrogen in silicon-carbon nanotubes is remarkably larger than that in pure carbon nanotubes. Currently, silicon-based materials are of worldwide interest due to their technological importance. It is well known that hollow silicon nanostructures, such as silicon nanotubes and silicon fullerenes, are unstable due to the unfavorable sp2 hybridization of silicon. Recent research, however, indicates that these structures can be efficiently stabilized via various chemical decorations, including encapsulating a metal atom inside silicon clusters16-17 and coating silica18 or capping19 with hydrogen on silicon clusters. For example, the high stability of hydrogenated silicon nanotubes20 and silica-coated silicon fullerenes18 has been confirmed theoretically, and silica-coated silicon nanotubes have been successfully synthesized via a hydrothermal process.21,22 Moreover, synthesis of silicon clathrates,23 silicon clathrate-like compounds,24 and guest-free crystalline silicon clathrates25 have been reported in the literature. These siliconbased nanostructures possess large inner cavities and are potential candidates for hydrogen storage. To the best of our knowledge, not much is known about their hydrogen storage capability, although a lot of effort has been devoted to stabilizing hollow silicon nanostructures.18,19,26-32 Kumar and Kawazoe19 recently showed the stability of hydrogenated silicon fullerenes SinHn (n ) 16 and 20). This fact has opened up new possibilities for developing their homologues and further finding novel applications of these hydrogenated silicon fullerenes in a range of scientific and technical areas. To explore the desired possibilities, here Si60H60
10.1021/jp076263y CCC: $37.00 © 2007 American Chemical Society Published on Web 10/18/2007
17100 J. Phys. Chem. C, Vol. 111, No. 45, 2007
Zhang et al.
TABLE 1: Calculated and Experimental Structural Parameters (distances (Å) and angles (deg)) and Bond Dissociation Energies (De, eV) for Si2H6 and H2 Si2H6
H2 a
TABLE 2: Calculated Parameters of the Geometry and Energy for the Si60H60 Fullerene
B3LYP/6-31G(d,p)
GGA/DND
expt.
2.349 1.488 110.6 4.003 0.743 4.844
2.342 1.493 110.6 3.988 0.748 4.613
2.327a 1.486a 111.0a 3.855b 0.741c 4.533c
RSi-Si RSi-H ∠HSiSi De (Si2H5-H) RH-H De (H-H) b
c
Reference 38. Reference 39. Reference 40.
cluster is considered as a representative of larger hydrogenated silicon fullerenes. This hydrogenated silicon is also an appropriate prototype of hollow silicon nanostructures. By performing DFT calculations we explore its structural stability and hydrogen storage capability. We are especially interested in the following questions: (1) Whether the hydrogenated silicon fullerene is a suitable medium for hydrogen storage? (2) If yes, does it store atomic or molecular hydrogen? (3) What are the amounts of energy needed to push hydrogen entering or escaping from the cage? (4) How are the largest hydrogen gravimetric densities? We expect to show through the study of the prototype system that hollow silicon-based nanostructures might be qualified to act as high-capacity hydrogen storage materials and thus provide a valuable clue to resolving the most challenging hydrogen storage problem in a new hydrogen economy. Computational Details To address the above-mentioned questions we performed firstprinciples calculations within the framework of DFT using both the Dmol3 code33 and Gaussian 03 program package.34 The Dmol3 calculations were carried out at the all-electron level, and the exchange-correlation contribution to the total energy was treated at the generalized gradient approximation (GGA) level of theory using the PW91 exchange-correlation functional35 combined with a double numeric basis including d-polarzation function (DND),36-37 denoted as GGA/DND. Geometry optimizations were done with the medium geometry convergence criteria and medium scf convergence criteria. To ensure that true minima were found, all geometries were optimized without symmetry constraints in the wavefunction and gradient evaluation. The Gaussian calculations were performed at the B3LYP/ 6-31G(d,p) level but only for the hydrogenated silicon fullerene with a number of H2 molecules encapsulated lower than 20 to reduce computational costs. Prior to presenting the main part of our computational results we investigated the reliability of the methods chosen in the present work by performing benchmark calculations for Si2H6 and H2. The calculated structural parameters and bond dissociation energies are shown in Table 1. It is found that theories yield the structural parameters in good agreement with the experimental values38-40 but slightly overestimated the bond dissociation energies. While this comparison might indicate that the GGA calculations with the numeral functions are just as good as the B3LYP calculations with Gaussian-type functions, we performed most calculations at the GGA/DND level. In the following sections the results quoted are from the GGA/DND calculations unless otherwise specified. Results and Discussion In order to better understand the properties of the hydrogenated silicon fullerene, Si60H60, we first compare its geometry and stability with a hypothetical clean Si60 fullerene, an analog of C60 with In symmetry. All Si-Si distances in Si60H60 and
da (Å) R1b (Å) R2c (Å) Egd (eV) VIPe (eV) VEAf (eV)
B3LYP/6-31G(d,p)
GGA/DND
11.79 2.38 2.37 4.71 7.71 1.47
11.73 2.37 2.36 3.62 7.43 1.86
a Fullerene diameter. b Length of the Si-Si bonds shared by the fiveand six-membered rings. c Length of the Si-Si bonds shared by the six-membered rings. d HOMO-LUMO energy gap. e Vertical ionization potential. f Vertical electron affinity.
Si60 were initially taken as 2.35 Å, the value in the bulk materials. When fully optimized the initial structure of Si60 without visible strain has transformed into an accidental hollow structure, which agrees with the result given by Sun et al.41 The instability of the clean silicon fullerene is attributed to the energetically unfavorable dangling bonds on the surface of the Si60 cage. In contrast, the hydrogenated silicon fullerene maintains the highest possible Ih symmetry. The optimized geometrical parameters at both the GGA/DND and the B3LYP/ 6-31G(d,p) levels are shown in Table 2. The fullerene diameter (the largest Si-Si distance in this structure) is determined to be 11.73 Å at the GGA/DND level. The length of the Si-Si bonds which are shared by the five- and six-membered rings is 2.37 Å, while that of the Si-Si bonds which are shared by the six-membered rings is 2.36 Å. These calculated Si-Si bond lengths are in good agreement with those from the B3LYP calculations and also very close to that in the bulk silicon (2.35 Å). Vibrational analyses for the highly symmetrical fullerene show all frequencies are real, suggesting that it is a dynamically stable structure (true local minima on the potential-energy surfaces). Further, the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) corresponds to 3.62 eV at the GGA/DND level and 4.71 eV at the B3YP/6-31G(d,p) level. The HOMO is highly localized on the Si atoms, and the LUMO has its weight around the inner periphery of the fullerene. We also calculated its vertical ionization potential (VIP) and electron affinity (VEA), as reported in Table 2. These values are comparable with the corresponding experimental values of C60, 7.5842 and 2.6743 eV, respectively, guaranteeing the structural stability of the Si60H60 fullerene, which is substantial for hydrogen storage. Next we studied the possibility of the Si60H60 fullerene serving as a hydrogen storage medium. It should be noted that the hydrogenated silicon fullerene is a fully coordinated structure, so it would interact with molecular hydrogen via van der Waals force. We first studied its interaction with a single H2 molecule. Figure 1a shows the optimized Si60H60 cage with H2 at the exterior of the cage, denoted as H2-Si20H20, and Figure 1b is the case as H2 resides in the interior of the cage, denoted as H2@Si60H60. As seen and expected, the H2 molecule is physically adsorbed on the outer surface of the cage or resides almost at the center of the cage. The distances between the H2 and the Si atoms are large for both cases due to weak interaction between two closed shell molecules. The geometrical parameters for the Si60H60 and H2 units in these two complexes are almost the same as those in the isolated molecules. For example, at the GGA/DND level the H-H bond lengths are 0.751 and 0.753 Å in H2-Si60H60 and H2@Si60H60, respectively, while that in isolated H2 is 0.748 Å. The binding energy, which is defined as the energy difference between the complex and separated H2 and Si60H60, is as small as -0.12 eV for H2-Si60H60 and -0.10 eV for H2@Si60H60.
Hydrogenated Silicon Fullerenes
J. Phys. Chem. C, Vol. 111, No. 45, 2007 17101
Figure 2. Relative energy of Si60H60 with H2 (with respect to isolated H2 and Si60H60) as a function of the distance from the fullerene center to H2 as H2 approaches vertically Si60H60 along the center of a pentagon, calculated at the GGA/DND level.
Figure 1. Optimized geometries at the GGA/DND level for Si60H60 with (a) one H2 at the exterior of the cage, (b) one H2 molecule at the interior of cage, (c) 15 hydrogen molecules encapsulated, (d) 50 hydrogen molecules encapsulated, (e) 58 hydrogen molecules encapsulated, and (f) 65 H2 molecules which were initially encapsulated into the cage and 7 of them escaped after optimization.
It would be interesting to know how H2 enters the cage: through the five- or six-membered ring. To answer this question, potential-energy scans have been performed for two different configurations: H2 vertically enters into the cage through the center of a pentagon and the center of a hexagon, respectively. We calculated the energy of the fullerene with H2 relative to the isolated Si60H60 and H2 as a function of the distance from the center of the fullerene to H2. Figure 2 shows the results for H2 insertion along the hexagon pathway, and that along the pentagon pathway is not given for simplification. The estimated barriers for H2 entering the cage through the hexagon and pentagon are 2.56 and 5.43 eV, while the corresponding ones for H2 escaping the cage are 2.65 and 5.52 eV, respectively. Clearly, H2 entering the cage through a hexagon is energetically much more favorable than through a pentagon. To obtain the weight percentage of hydrogen that can be stored in the hydrogenated fullerene, we gradually add the number of H2 molecules inside the cage and optimize the cage with H2 molecules capsulated. The thus-obtained representative structures are shown in panels c-f of Figure 1. We find that the fullerene cage can store up to 58 H2 molecules. When the number of H2 molecules is further increased into the cage, the added H2 molecules escape from the cage after optimization. For example, when 65 H2 molecules were initially encapsulated into the cage, it was found that 7 H2 molecules run away to the
Figure 3. Bonding energy as a function of the number of H2 capsulated. Circles and triangles represent the calculated data, and the lines are the fitting results.
exterior of cage after optimization. The total gravimetric densities of hydrogen in 58H2@Si60H60 amount to 9.48%, which is much higher than any reported hydrogen storage capacity in other medium. We noted that the fullerene cage framework was not broken throughout the optimizations for all structures considered here, indicating its intrinsic rigidity and stability. In Figure 3 we show the variation of the calculated binding energy (Eb) with the number of H2 molecules (N) capsulated. From Figure 3 it is found that the energy tendency with N from the GGA calculations is in good agreement with that from the B3LYP calculations, although the relative energy values from two methods are different. By performing a polynomial fit we found that the binding energy increases as N2. As expected, the cage volume expands while the H2 molecules stored in the cage slightly shrink with increasing number of H2 molecules capsulated, as indicated by calculated average Si-Si and H-H bond lengths in Figure 4. The Si-Si bond length increases as N2, while the H-H distance decreases linearly with N. The average Si-Si and H-H bond lengths in 58H2@Si60H60 are 2.522 and 0.744 Å, respectively. The former is larger by 6.64% than that (2.365 Å) in the empty cage, and the latter is smaller by 0.53% than that in isolated H2 molecule (0.748 Å). Furthermore, we examined the changes of the HOMO-LUMO energy gap with
17102 J. Phys. Chem. C, Vol. 111, No. 45, 2007
Zhang et al. media. In this sense, our present study provides valuable guidance for finding appropriate high-capacity hydrogen storage media. Concluding Remarks
Figure 4. Variation of the average Si-Si and H-H bond lengths with the number of H2 capsulated. Solid and open circles represent the calculated data at the GGA/DND level, and the lines are the fitting results.
In summary, the energetic stability and hydrogen storage capability of the hydrogenated silicon fullerene have been studied by performing DFT calculations. It was found that up to 58 hydrogen molecules can be stored inside the Si60H60 cage in molecular form. The gravimetric density of hydrogen in 58H2@Si60H60 amounts to 9.48%, which is much higher than any reported capacity of hydrogen storage in other media or the DOE target of 6 wt %. If the synthetic challenge could be mastered successfully in the near future, hydrogenated silicon fullerenes may serve as a high-capacity hydrogen storage media in the future hydrogen economy. Acknowledgment. The work described in this paper is jointly supported by the National Basic Research Program of China (973 Program) (nos. 2007CB936602 and 2004CB719902), the National Science Foundation of China (nos. 20473047 and 20773078), and the Natural Science Foundation of Shandong Province (no. Z2006B03). References and Notes
Figure 5. HOMO-LUMO energy gap as a function of the number of H2 capsulated. Circles and triangles represent the calculated data, and the lines are the fitting results.
N. As shown in Figure 5, the gap decreases as N2 from both the GGA and B3LYP calculations. As commonly accepted, we observed that the GGA calculations significantly underestimated the energy gap. However, the predicated overall trend is in good agreement with that from the B3LYP calculations. Thus, we believe that the present GGA calculation is at least qualitatively acceptable to describe the H2-Si60H60 interaction. Clearly, our DFT calculations show that the hydrogenated silicon fullerene can effectively store hydrogen in molecular form. The high hydrogen capacity of the hydrogenated fullerene is expected to extend its homologues, hydrogenated silicon nanotubes, which have been theoretically predicted to possibly form.44 Although such materials are highly speculative at present, we believe that the synthetic challenge could be mastered successfully in the near future since we are now able to controllably produce desired clusters in size from a small atom to a few nanometers in diameter with various experimental techniques. We can imagine several appropriate pathways for synthesizing hydrogenated silicon fullerenes/nanotubes, for example, direct synthesis via chemical vapor deposition (CVD) or thermal evaporation of silicon and/or silicon oxide in the ambience of hydrogen and indirect synthesis from their structural precursors, silica-coated silicon nanotubes/fullerenes, via etching the silica coat using hydrofluoric acid. Once these techniques become available, there is a real feasibility for using the hydrogenated silicon fullerenes/nanotubes as hydrogen storage
(1) Service, R. F. Science 2004, 305, 958-961. (2) Dillon, A. C.; Jones, K. M.; Bekkedahl, T. A.; Kiang, C. H.; Bethune, D. S.; Heben, M. J. Nature (London) 1997, 386, 377-379. (3) Ahn, C.; Fultz, B.; Vajo, J.; Ye, J.; Zinck, J. Appl. Phys. Lett. 2000, 77, 2171-2173. (4) Stan, G.; Cole, W. M. J. Low Temp. Phys. 1999, 110, 539-544. (5) Griessen, R.; Riesterer, T. Hydrogen in Intermetallic Compounds I; Springer-Verlag: Germany, 1988; p75. (6) Buchener, H.; Povel, R. Int. J. Hydrogen Energy 1982, 7, 259266. (7) Rosi, N. L.; Eckert, J.; Eddaoudi, M.; Vodak, D. T.; Kim, J.; O’Keeffe, M.; Yaghi, O. M. Science 2003, 300, 1127-1129. (8) Krawiec, P.; Kramer, M.; Sabo, M.; Kunschke, R.; Fro¨de, H.; Kaskel, S. AdV. Eng. Mater. 2006, 8, 293-296. (9) Lee, H.; Lee, J. W.; Kim, D. Y.; Park, J.; Seo, Y. T.; Zeng, H.; Moudrakovski, I. L.; Ratcliffe, C. I.; Ripmeester, J. A. Nature 2005, 434, 743-746. (10) Hirscher, M.; Becher, M. J. Nanosci. Nanotechnol. 2003, 3, 3-17. (11) Zhao, Y.; Kim, Y.-H.; Dillon, A. C.; Heben, M. J.; Zhang, S. B. Phys. ReV. Lett. 2005, 94, 155504. (12) Yildrim, T.; Ciraci, S. Phys. ReV. Lett. 2005, 94, 175501. (13) Sun, Q.; Jena, P.; Wang, Q.; Marquez, M. J. Am. Chem. Soc. 2006, 128, 9741-9745. (14) Sun, Q.; Wang, Q.; Jena, P.; Kawazoe, Y. J. Am. Soc. Chem. 2005, 127, 14582-14583. (15) Mpourmpakis, G.; Froudakis, G. E. Nano Lett. 2006, 6, 15811583. (16) Kumar, V.; Kawazoe, Y. Phys. ReV. Lett. 2001, 87, 045503. (17) Khanna, S. N.; Rao, B. K.; Jena, P. Phys. ReV. Lett. 2002, 89, 016803. (18) Zhang, D. J.; Guo, G. L.; Liu, C. B. J. Phys. Chem. B 2006, 110, 14619-14622. (19) Kumar, V.; Kawazoe, Y. Phys. ReV. Lett. 2003, 90, 055502. (20) Ponomarenko, O.; Radny, M. W.; Smith, P. V. Surf. Sci. 2004, 562, 257-268. (21) Chen, Y. W.; Tang, Y. H.; Pei, L. Z.; Guo, C. AdV. Mater. 2005, 17, 564-567. (22) Tang, Y. H.; Pei, L. Z.; Chen, Y. W.; Guo, C. Phys. ReV. Lett. 2005, 95, 116102. (23) Reny, E.; Yamanaka, S.; Cros, C., Pouchard, M. Chem. Commun. 2000, 2505-2506. (24) He, J.; Klug, D. D.; Uehara, K.; Preston, K. F.; Ratcliffe, C. I.; Tse, J. S. J. Phys. Chem. B 2001, 105, 3475-3485. (25) Gryko, J.; McMillan, P. F.; Marzke, R. F.; Ramachandran, G. K.; Patton, D.; Deb, S. K.; Sankey, O. F. Phys. ReV. B 2000, 62, 7707-7710. (26) Harada, M.; Osawa, S.; Osawa, E.; Jemmis, E. D. Chem. Lett. 1994, 1, 1037-1040. (27) Sheka, E. F.; Nikitina, E. A.; Zayets, V. A.; Ginzburg, I. Y. Int. J. Quantum Chem. 2002, 88, 441-448.
Hydrogenated Silicon Fullerenes (28) Sun, Q.; Wang, Q.; Jena, P.; Rao, B. K.; Kawazoe, Y. Phys. ReV. Lett. 2003, 90, 135503. (29) Ponomarenko, O.; Radny, M. W.; Smith, P. V. Surf. Sci. 2004, 562, 257-268. (30) Kang, J. W.; Hwang, H. W. Nanotechnology 2003, 14, 402-408. (31) Sun, Q.; Wang, Q.; Kawazoe, Y.; Jena, J. Eur. Phys. J. D 2004, 29, 231-234. (32) Singh, A. K.; Kumar, V.; Kawazoe, Y. Phys. ReV. B 2005, 71, 115429. (33) DMOL3 Code; Biosym Technologies, Inc.: San Diego, CA, 1999. (34) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.;
J. Phys. Chem. C, Vol. 111, No. 45, 2007 17103 Piskorz, P.; Komaromi, I.; 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.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision D.01; Gaussian, Inc.: Wallingford, CT, 2004. (35) Wang, Y.; Perdew, J. P. Phys. ReV. B 1991, 44, 13298-13307. (36) Delley, B. J. Chem. Phys. 1990, 92, 508-517. (37) Delley, B. J. Chem. Phys. 1991, 94, 7245-7250. (38) Callomon, J. H.; Hirota, E.; Kuchitsu, K.; Lafferty, W. J.; Maki, A. G.; Pote, C. S. Structure Data on Free Polyatomic Molecules; LandoltBornstein, New Series, Group II; Springer-Verlag: Berlin, 1976; Vol. 7. (39) Chatgilialoglu, C.; Guerra, M.; Guerrini, A.; Seconi, G.; Clark, K. B.; Griller, D.; Kanabus-Kaminska, J.; Martinho-Simoes, J. A. J. Org. Chem. 1992, 57, 2427-2433. (40) CRC Handbook of Chemistry and Physics; Lide, D. R., Ed.; CRC Press: New York, 2000. (41) Sun, Q.; Wang, Q.; Rao, B. K.; Kawazoe, Y. Phys. ReV. Lett. 2003, 90, 135503. (42) De Vries, J.; Steger, H.; Kamke, B.; Menzel, C.; Weisser, B.; Kamke, W.; Hertel, I. V. Chem. Phys. Lett. 1992, 188, 159-162. (43) Brink, C.; Andersen, L. H.; Hvelplund, P.; Mathur, D.; Voldstad, J. D. Chem. Phys. Lett 1995, 233, 52-56. (44) Seifert, G.; Ko¨hler, Th.; Urbassek, H. M.; Hernandez, E.; Frauenheim, Th. Phys. ReV. B 2001, 63, 193409.
