Alkali-Metal-Doped B80 as High-Capacity Hydrogen Storage Media

Nov 14, 2008 - We study the feasibility of the alkali-metal (AM = Li, Na, K)-doped B80 fullerenes for hydrogen storage using first-principles calculat...
0 downloads 0 Views 561KB Size
Download PDF
19268

J. Phys. Chem. C 2008, 112, 19268–19271

Alkali-Metal-Doped B80 as High-Capacity Hydrogen Storage Media Yuanchang Li, Gang Zhou,* Jia Li, Bin-Ling Gu, and Wenhui Duan Department of Physics, Tsinghua UniVersity, Beijing 100084, People’s Republic of China ReceiVed: August 11, 2008; ReVised Manuscript ReceiVed: October 20, 2008

We study the feasibility of the alkali-metal (AM ) Li, Na, K)-doped B80 fullerenes for hydrogen storage using first-principles calculations. It is found that the AM atoms are strongly attached at the centers of the pentagons of the B80, forming B80AMm complexes (1 e m e 12). This bonding can be attributed to the charge transfer between the AM atoms and fullerenes, such as the case of the C60AM. The charge redistribution induces an electric field mainly around the positively charged AM atoms, which polarizes the H2 molecules but does not make them dissociate. The B80Na12 and B80K12 can store up to 72 H2 molecules with binding energies of 1.67 and 1.99 kcal/mol, respectively, resulting in gravimetric densities of hydrogen of 11.2% and 9.8%. Moreover, the AM atoms do not cluster on the B80, which facilitates the reversible hydrogen adsorption/ desorption. I. Introduction Nowadays soaring oil prices are driving development of new, renewable energy sources, such as biofuel, hydrogen fuel, solar energy, wind energy, etc. Because of its nonpolluting nature, easysynthesis,andabundantsources(e.g.,waterandhydrocarbons),1,2 hydrogen has received considerable attention as a highly important substitute for fossil fuel. In addition to the preparation of hydrogen, the storage and transport of hydrogen are also very important for the ultimate use, especially for fuel-cell powered vehicles.3-5 Recently, a great deal of effort has been devoted to finding safe and applicable hydrogen storage materials, which must meet the requirements of high gravimetric/volumetric storage density, fast kinetics, favorable thermodynamics, and good reversibility.1,5-7 Previous experiments and simulations have showed that the isolated transition metal (TM)8,9 and alkali metal (AM) atoms or ions10 could bind a certain number of hydrogens in molecular form. After releasing hydrogen, however, the isolated metal atoms or ions would cluster together easily,11,12 which is unfavorable for reversible hydrogen storage. A few theoretical studies have suggested that capping the metal atoms onto some carbon (C) nanostructures (e.g., nanotubes and fullerenes) might resolve this problem.10,13-15 On one hand, due to their large surface area, the nanostructures as the substrates have enough sites to attach the metal atoms separately and, hence, provide enough space to store hydrogen. Typically, the theoretical maximum retrievable H2 storage density of the TM-decorated C60 is 9 wt %,13 higher than the target of the U.S. Department of Energy (6 wt % by the year 2010).16 On the other hand, the large binding energy between the nanostructure and the attached metal might prevent clustering of dopants and be advantageous to reversible hydrogen sorption accordingly. For instance, the AM atoms, including lithium (Li), sodium (Na), and potassium (K), were predicted to adsorb individually on the C60 fullerene, and the resulting C60AM complexes may act as high-capacity hydrogen storage materials accordingly.10,15 Boron (B) nanostructures, including nanotubes and fullerenes, have received considerable attention due to their same merit as carbon nanostructures: light mass. Like C nanotubes, B nano* E-mail: [email protected]

tubes are also used as a substrate for TM atom doping (e.g., metal diboride nanotubes)17 in hydrogen storage applications. TM-doped, B-based organometallic nanostructures may be another promising hydrogen storage material because clustering of the doped TM atoms, which generally occurs in TM-doped C60 complexes, is effectively prevented.18 On the other hand, the B80 fullerene was theoretically demonstrated to be the most stable B cage.19 Structurally, it is similar to the well-known C60 fullerene except for an additional B atom at each hexagon center. It is expected that numerous pentagons or hexagons of the B80 would provide enough adsorption sites for metal atoms. As compared to doped TM, doped AM atoms are lightweight and can bind more H2 molecules, which can help to achieve a higher gravimetric density of hydrogen.10 Taking into account these merits, in this paper, we propose that the B80 fullerene doped with the AM atoms can be used as an efficient hydrogen storage media. We first focused on the binding mechanism between the AM atoms and B80. Next, in terms of the charge redistribution and polarization induced, we discussed the hydrogen storage mechanism of the AM-doped B80. Finally, from the electric fields around the coated fullerenes, we evaluated the hydrogen storage capabilities of AM-doped B80 complexes. II. Methodological Details All calculations were performed within the framework of density functional theory (DFT) using the DMol3 package.20 The PW91 functional21 based on the generalized gradient approximation was employed to describe the exchange and correlation effects of electrons. The basis set consists of the double numerical atomic orbitals augmented by polarization functions. Geometry optimizations without any symmetry constraint were carried out until the energy, gradient, and displacement converged to 10-5, 10-3, and 10-3 au, respectively. In addition, the linear/quadratic synchronous transit method22 was adopted to calculate the diffusion barrier of the AM atom on the B80 fullerene. The energy difference between the reactants (AM atom, H2 molecule, and host fullerene) and the complex products was defined as the binding energy of the complexes. With the calculation parameters mentioned above, we achieved a HOMO-LUMO gap of 1.0 eV and a cohesive energy of the

10.1021/jp807156g CCC: $40.75  2008 American Chemical Society Published on Web 11/14/2008

AM-Doped B80 as High-Capacity H2 Storage Media

J. Phys. Chem. C, Vol. 112, No. 49, 2008 19269 TABLE 1: Calculated B-AM Bond Lengths, AM Binding Energies, and Mulliken Charges for the B80AM Complexes system B80Li B80Na

Figure 1. Several representative initial AM adsorption sites on the B80 cage. Green (red) shows positive (negative) atomic charges. The brighter green corresponds to more positive charge and smaller dihedral angle. Symbols H and P denote the center sites of the hexagon and pentagon, respectively. Symbols T1 and T2 denote the center sites of the two different triangles of the hexagon. Symbols B1, B2, and B3 denote three different bridge sites between B atoms.

B80 fullerene of 5.79 eV/atom, which are in agreement with the previous results of Szwacki et al. using the Gaussian03 package.19 Furthermore, it is recognized that the time-consuming second-order Møller-Plesset perturbation theory (MP2)23 is usually more accurate to describe the weak van der Waals interaction than the conventional DFT.24,25 Using the MP2 method,26 we have checked the binding of H2 in similar wellknown systems of Li-, Na-, and K-doped cyclopentadiene rings (Cp ) C5H5) and found that the H2 binding energies are 3.89, 1.73, and 1.31 kcal/mol, respectively, which are comparable to the values of 3.39, 1.91, and 1.52 kcal/mol obtained by the DMol3 package. This indicates that the DMol3 package may provide a reasonably reliable description of the weak binding of H2 to AM-doped fullerenes. III. Results and Discussion Different coordination numbers and bonding characteristics of two types of constituent B atoms lead to a charge redistribution of the B80 fullerene. As shown in Figure 1, the B atoms located at the centers of the 20 hexagons can be regarded as “cations”, and all the other 60 B atoms located at the C60-like framework can be regarded as “anions”. According to the unique geometry of the B80 fullerene,27 we consider numerous sites as the initial sites for the AM adsorption. Figure 1 shows seven representative initial sites, including the center of the hexagon (H site), the center of the pentagon (P site), the centers of the two different triangles of the hexagon (T1 and T2 sites), and three bridge sites between B atoms (B1, B2, and B3 sites). Our full structural relaxations reveal two stable adsorption sites: the negatively charged P site and the positively charged H site. As compared to the H site, the negatively charged P site is more favorable for AM-doping (see Table 1). Since the electron affinity of the B80 fullerene is much higher than those of the AM atoms, the AM atom attached to the B atom is found to be positively charged, similar to the case in the C60AM. Our calculations further show that in the B80AM complexes, the induced positive charge of the AM atoms increases in the order of Li, Na, and K, which is very compatible with their reactivities, but not quite consistent with the order of their binding energies (see Table 1). Such a discrepancy between the charge transfer and the binding energy has also been observed in the C60AM.10 In what follows, we elucidate the reason for the above discrepancy from the electronic structures.

B80K B80Na2 B80Na5 B80Na12 B80K12

site P H P H P H P P P P

B-AM bond binding charge on length, (Å) energy, (kcal/mol) the AM atom, (e) 2.26 2.29-2.55 2.70 2.68-2.98 3.10 3.08-3.29 2.68 2.66 2.62 2.98

61.21 48.81 43.60 36.96 53.12 49.40 42.19 41.84 37.78 39.74

0.08 0.29 0.59 0.62 0.78 0.79 0.56 0.51 0.41 0.58

Figure 2. LDOS of AM and B atoms at the host P site for AM-doped B80 complexes: (a) B80Li, (b) B80Na, and (c) B80K.

Obviously, the discrepancy is reflected in the fact that among Li, Na, and K, the Li atom has the highest binding energy to the B80 (see Table 1) but with a relatively smaller charge transfer. This means that the bonding between the Li atom and the fullerene is not simply ionic, distinctly different from the ionic bonding in Na- and K-doped B80 fullerenes. Figure 2 shows the local density of states (LDOS) of B80AM complexes. As expected, in the Na-doped/K-doped fullerenes, the bonding originates from the mixing of the 3s (4s) orbital of Na/K and 2p orbital of B, and simultaneously, there exists a charge transfer from the 3s (4s) orbital of Na (K) to the 2p orbital of B (as showed in parts b and c of Figure 2). Unlike Na and K, Li p orbitals participate in the bonding as the Li atom is attached to the fullerene, which results in a significant difference in the bonding mechanism. In detail, from Figure 2a, we can see that the attached Li first donates the s electrons to the B80 fullerene, leading to partially filled B p orbitals. Meanwhile, the empty p orbitals of the Li split under the strong ligand field generated by the B80, and thus, the B80 back-donates some electrons to the low-lying Li p orbitals, leading to a strong hybridization between the B 2p and Li 2p orbitals and partial occupancy of Li 2p orbital (as revealed in Figure 2a). Consequently, the net charge transfer between the Li and B80 is quite small. On the other hand, the p-p hybridization is stronger than the s-p hybridization, so the binding energy of the Li on the B80 is larger than those of Na- and K-doped B80 fullerenes. The contribution of Li 2p states to the binding has also been confirmed in Li-ethylene complexes.28 Furthermore, we find that the calculated binding energies of the AM on the B80 fullerene [61.21 kcal/mol (P site) and 48.81 kcal/mol (H site) for Li, 43.60 kcal/

19270 J. Phys. Chem. C, Vol. 112, No. 49, 2008

Li et al.

TABLE 2: Calculated AM-H Distances, H2 Binding Energies, Mulliken Charges, and H-H Bond Lengths of H2 Molecules for the B80AMm(H2)n Complexes

system

AM-H, (Å)

binding energy, (kcal/mol)

B80LiH2 B80NaH2 B80KH2 B80Li(H2)2 B80Na(H2)6 B80K(H2)8 B80Na2(H2)12 B80Na5(H2)30 B80Na12(H2)72 B80K12(H2)72

2.06-2.11 2.49-2.58 2.96 2.15-2.25 2.66-2.87 3.14-3.40 2.70-2.96 2.70-3.14 2.65-3.25 2.86-3.18

3.39 2.24 1.71 2.54 1.76 1.51 1.73 1.65 1.67 1.99

charge on the AM atom, (e)

H-H

0.03 0.54 0.75 0.01 0.33 0.61 0.33 0.31-0.33 0.27-0.30 0.50

0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75-0.76

mol (P site) and 36.96 kcal/mol (H site) for Na, and 53.12 kcal/ mol (P site) and 49.40 kcal/mol (H site) for K] are higher than those of C60AM [41.51 kcal/mol for Li, 31.59 kcal/mol (P site) and 32.28 kcal/mol (H site) eV/atom for Na, and 45.19 kcal/ mol (P site) and 46.12 kcal/mol (H site) eV/atom for K]. Apparently, the B80 is a more suitable substrate,19 superior to the C60, at least for the AM doping. This finding could be important for developing hydrogen storage materials. Previous studies have showed that the AM cations10 or positively/negatively charged C fullerenes29 have potential to store hydrogen in the molecular form. According to the above calculations and analysis, we can anticipate that B80AM should exhibit similar hydrogen adsorption properties. That is, as one H2 molecule approaches the attached AM atom, a weak “bond” is formed between them due to the polarization. Meanwhile, there exists a very small charge transfer from the bonding σ orbital of the bound H2 to the s orbital of the attached AM atom (i.e., 0.05 e for Li and Na, 0.03 e for K). As a consequence, the H-H bond length slightly expands from 0.74 Å (the value of the free molecular state) to 0.75 Å, but H2 does not dissociate. The distances between the AM atom and H2 are presented in Table 2. In addition, the calculated binding energies of H2 to Li-, Na-, and K-doped B80 fullerenes are 3.39, 2.24, and 1.71 kcal/mol, respectively, which are comparable to those to C60AM.10,15 These results, indicating a good reversibility of hydrogen adsorption and desorption at lower than room temperature, are very important for practical applications. The underlying binding mechanism of H2 to B80AM complexes is in essence the same as that of H2 on C60AM, which is closely related to the high electric field near the AM atoms, generated by the substantial charge redistribution upon AM doping. As an example, the electrostatics potential of B80Na fullerene is illustrated in Figure 3a, and Figure 3b shows the radial component of the electric field from the center of the B80 cage to the attached AM atom of B80AM complexes. Our calculations indicate that the optimum distances between the hydrogen and the host AM are 2.1, 2.5, and 3.0 Å for the Li-, Na- and K-doped B80 fullerenes, respectively. At such optimum hydrogen distances, the associated electric fields are 1.9 × 1010, 1.5 × 1010, and 1.1 × 1010 V/m, respectively, which are very compatible with their H2 binding energies (see Table 2). The above electric fields are comparable to that of C60Ca,30 which is considered to be high enough to significantly polarize the H2 molecules. In practice, the optimum distance is an important parameter for estimating the hydrogen storage capacity of any material. It determines a finite-scale region for storing more H2 molecules around the attached atom (known from a and b of Figure 3). In

Figure 3. (a) The electrostatic potential of the B80Na complex. (b) The radial component of the electric field as a function of the distance from the center of the B80AM cage. The vertical dashed, dotted, and dotted-dashed lines denote the positions of the attached Li, Na, and K atoms, respectively. The electric fields at the positions of the adsorbed H2 molecules are also given (i.e., -1.9, -1.5, and -1.1 × 1010 V/m for B80Li, B80Na, and B80K, respectively). (c) Adsorption configurations of B80Li(H2)2, B80Na(H2)6, and B80K(H2)8.

this region, the H2 molecules adsorbed successively on one hand are attracted by the host AM and, on the other hand, are repulsed by the previously adsorbed H2 molecules. So a large optimum distance is advantageous to reduce the repulsion between the adsorbed H2 molecules, but with little effect on the attraction between the host AM and H2 molecules. In general, the larger the optimum distance is, the larger the hydrogen adsorption region is, and the higher the hydrogen storage capacity may be. Typically, our calculation indicates that one Li atom can adsorb up to only two H2 molecules in the B80Li, whereas in B80Na and B80K, the maximum numbers of H2 molecules adsorbed are, respectively, six and eight on one AM atom. The associated configurations of B80AM(H2)n are illustrated in Figure 3c. To estimate the gravimetric density of hydrogen for the AMdoped B80, we first study the dependence of the stability of B80(AM)m on the number of the attached AM atoms, m. The Li-doped B80 complex is not taken into account any further, since it adsorbs fewer H2 molecules. Herein, the B80Na is taken as an example because it has the appropriate hydrogen binding strength and storage capacity. From Table 1, we can see that with increasing m (the number of the attached Na atoms), the binding energy monotonically decreases. However, even when all 12 pentagons of the B80 are covered by Na atoms, the system (i.e., B80Na12) is still stable, with a binding energy of 37.78 kcal/ mol. Note that the decrease in binding energy with increasing m is very compatible with the decrease in the positive charge on each AM atom. Similar phenomena have been observed in a previous study of C60Nam.10 Next, we study the case that every AM atom of the B80AM12 binds the maximum number of H2 molecules. It is found that all attached Na(H2)6 clusters on the B80Na12 are still stable, like that on the B80Na, and the only change is that the difference between the shortest and longest Na-H bond lengths slightly increases, whereas the original K(H2)8 clusters on the B80K12 are not stable any more due to large repulsion between the neighboring attached K(H2)8 clusters (note: the distance between the K and the H2 molecule is the largest), and then the B80K12 can adsorb up to 72 H2 molecules (i.e., each K atom adsorbs 6 H2 molecules). The larger the optimum distance is, the more uniformly the adsorbed H2 molecules might distribute (corresponding to a smaller fluctuation of the distances between the AM and the H2 molecules). For instance, as revealed in Table 2, the distribution of H2 molecules on the B80K12 is more uniform than that in the

AM-Doped B80 as High-Capacity H2 Storage Media

J. Phys. Chem. C, Vol. 112, No. 49, 2008 19271 and 2006CB0L0601) and the National Natural Science Foundation of China. References and Notes

Figure 4. Optimized configurations of (a) B80Na12(H2)72 and (b) B80K12(H2)72. They correspond to the gravimetric densities of hydrogen of 11.2 and 9.8 wt %, respectively.

B80Na12. Importantly, both B80Na12 and B80K12 can store 72 H2 molecules (as shown in parts a and b of Figure 4), corresponding to the gravimetric densities of hydrogen of 11.2 and 9.8 wt %, respectively, which are larger than the estimated values for the C60Na8 (9.5 wt %)10 and Li12C60 (9 wt %).15 For practical applications of AM-doped fullerenes as hydrogen storage materials, the clustering of metal dopants on the host substrate is an important issue to be addressed, which directly determines the reversibility of hydrogen adsorption and desorption. Our calculations show that the binding energies of the AM atoms to the B80 are not only larger than those of C60AM complexes, where the AM atoms are expected not to cluster,15 but also higher than the cohesive energies of the AM bulks. Moreover, our calculations also demonstrate that the adsorption of separated AM atoms is more favorable in energy than that of AM12 icosahedron cluster on the B80, such as the cases of C60AM complexes.15 This clearly indicates that the clustering of AM atoms hardly occurs in the B80AMm fullerenes. We further calculate the diffusion barrier of the AM atom on the B80 from the H site to the P site. All the B and AM atoms are relaxed in search of the transition state. The found transition state is the AM on top of the bridge site between the H and P sites. The small barrier obtained (0.07 eV for Na and 0.13 eV for K) implies that Na and K atoms can easily move on the B80 at room temperature, which facilitates the ultimate formation of AM-fully decorated B80 fullerenes as feasible hydrogen storage materials. IV. Conclusion We propose a high-capacity hydrogen storage material, AMdoped B80 complexes, through first-principles calculations. Due to the charge transfer from the AM atoms to the fullerenes, the AM atoms are strongly attached to the centers of 12 pentagons of the B80 fullerenes. The electric field induced around the positively charged AM atom polarizes the H2 molecules, and the resulting binding is strong enough for potential applications but does not dissociate H2. The hydrogen storage capacities of the B80Na12 and B80K12 are 11.2 and 9.8 wt %, respectively, which exceed the target of the U.S. Department of Energy (9 wt % by the year 2015).16 The Na and K atoms do not cluster on the B80 fullerene, which facilitates reversible hydrogen adsorption/desorption, whereas the B80Li is not advantageous to hydrogen storage because the attached Li atom adsorbs fewer H2 molecules. In addition, the small binding energy of H2 reveals the B80AM12 could be used only at temperatures lower than room temperature. Acknowledgment. This work was supported by the Ministry of Science and Technology of China (Grant Nos. 2006CB605105

(1) Schlapbach, L.; Zu¨ttel, A. Nature 2001, 414, 353. (2) Cortright, R. D.; Davada, R. R.; Dumesic, J. A. Nature 2002, 418, 964. (3) Zu¨ttel, A. Mater. Today 2003, 9, 24. (4) Alper, J. Science 2003, 299, 1686. (5) Bogdanovic, B.; Felderhoff, M.; Kaskel, S.; Pommerin, A.; Schlichte, K.; Schu¨th, F. AdV. Mater. 2003, 15, 1012. (6) Chen, P.; Xiang, Z.; Luo, J. Z.; Tan, K. L. Nature 2002, 420, 302. (7) Rosi, N. L.; Eckert, J.; Eddaoudi, M.; Vodak, D. T.; Kim, J.; O’Keefe, M.; Yaghi, O. M. Science 2003, 300, 1127. (8) Wang, X. F.; Andrews, L. J. Am. Chem. Soc. 2002, 124, 5636. (9) Bowers, M. T. Acc. Chem. Res. 1994, 27, 324. (10) Chandrakumar, K. R. S.; Ghosh, S. K. Nano Lett. 2008, 8, 13. (11) Niu, J.; Rao, B. K.; Jena, P. Phys. ReV. Lett. 1992, 68, 2277. (12) Gagliardi, L.; Pyykko, P. K. J. Am. Chem. Soc. 2004, 126, 15014. (13) Zhao, Y. F.; Kim, Y.-H.; Dillon, A. C.; Heben, M. J.; Zhang, S. B. Phys. ReV. Lett. 2005, 94, 155504. (14) Yildirim, T.; I´n˜iguez, J.; Ciraci, S. Phys. ReV. B 2005, 72, 153403. (15) Sun, Q.; Jena, P.; Wang, Q.; Marquez, M. J. Am. Chem. Soc. 2006, 128, 9741. (16) See U.S. DOE website, http://www.eere.energy.gov. (17) Meng, S.; Kaxiras, E.; Zhang, Z. Y. Nano Lett. 2007, 7, 663. (18) Zhao, Y. F.; Lusk, M. T.; Dillon, A. C.; Heben, M. J.; Zhang, S. B. Nano Lett. 2008, 8, 157. (19) Szwacki, N. G.; Sadrzadeh, A.; Yakobson, B. I. Phys. ReV. Lett. 2007, 98, 166804. (20) Delley, B. J. Chem. Phys. 1990, 92, 508. 2000, 113, 7756. DMol3 is available from Accelrys. (21) Wang, Y.; Perdew, J. P. Phys. ReV. B 1991, 44, 13298. (22) (a) Govind, N.; Petersen, M.; Fitzgerald, G.; King-Smith, D.; Andzelm, J. Comput. Mater. Sci. 2003, 28, 250. (b) Halgren, T. A.; Lipscomb, W. N. Chem. Phys. Lett. 1977, 49, 225. (23) Zaremba, E.; Kohn, W. Phys. ReV. B 1976, 13, 2270. (24) Okamoto, Y.; Miyamoto, Y. J. Phys. Chem. B 2001, 105, 3470. (25) Kim, Y.-H.; Zhao, Y. F.; Williamson, A.; Heben, M. J.; Zhang, S. B. Phys. ReV. Lett. 2006, 96, 016102. (26) In the MP2 calculations, we applied the basis set AUG-CC-PVDZ for C, H, Li, Na, and 6-311+G(2d) for K, as implemented in the Gaussian03 code.31 (27) Our calculations show that B80 is highly stable at the fullerene structure with Th symmetry. Previous calculations revealed a number of local minima isomers of B80 with slightly different geometry and close energies. Szwacki, N. G.; Sadrzadeh, A.; Yakobson, B. I. Phys. ReV. Lett. 2008, 100, 159901. Although the symmetries of these isomers (Ih, Th, or C1) are different, their bonding to the AM atoms are basically the same, and consequently, all of them exhibit almost the same hydrogen storage capacity. (28) Zhou, W.; Yildirim, T.; Durgun, E.; Ciraci, S. Phys. ReV. B 2007, 76, 085434. (29) Yoon, M.; Yang, S.; Wang, E.; Zhang, Z. Y. Nano Lett. 2007, 7, 2578. (30) Yoon, M.; Yang, S.; Hicke, C.; Wang, E.; Geohegan, D.; Zhang, Z. Y. Phys. ReV. Lett. 2008, 100, 206806. (31) Frisch, M. J. ; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mnnucci, 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, O.; Kitao, H.; 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.; 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 C.02; Gaussian, Inc.: Wallingford, CT, 2004.

JP807156G