Hydrogen Storage in Lithium-Functionalized 3-D Covalent-Organic

Nov 24, 2009 - Jiang , J.-X.; Su , F.; Trewin , A.; Wood , C. D.; Niu , H.; Jones , J. T. A.; Khimyak , Y. Z.; Cooper , A I. J. Am. Chem. Soc., 2008, ...
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J. Phys. Chem. C 2009, 113, 21253–21257

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Hydrogen Storage in Lithium-Functionalized 3-D Covalent-Organic Framework Materials Emmanouel Klontzas,† Emmanuel Tylianakis,‡ and George E. Froudakis*,† Department of Chemistry, UniVersity of Crete, P.O. Box 2208, 71003 Heraklion, Crete, Greece, and Materials Science and Technology Department, UniVersity of Crete, P.O. Box 2208, 71409 Heraklion, Crete, Greece ReceiVed: July 29, 2009; ReVised Manuscript ReceiVed: October 16, 2009

To enhance the hydrogen storage ability of covalent-organic framework materials (COFs), we have studied the insertion of lithium alkoxide groups in these materials. First-principles calculations predicted the structure of the lithium alkoxide group in the material and its interaction with multiple hydrogen molecules. Grand Canonical Monte Carlo simulations have shown enhanced gravimetric and volumetric hydrogen uptake both at 77 and 300 K and pressures up to 100 bar for the new materials. Lithium alkoxide COF reached 22 wt % and 51 g/L at 77K and 100 bar, while at room temperature overpasses the Department of Energy target for gravimetric uptake (6 wt %). Introduction In the past years a lot of effort has been focused on the quest of appropriate materials for hydrogen storage applications in order to achieve the targets that have been established by Department of Energy (DOE).1 Among them, framework materials such as metal-organic frameworks (MOFs) have attracted a lot of interest for the specific application, and there have been a lot of publications for the sorption capabilities of these materials. A drawback of these materials, relative to the established DOE targets, has been the incorporation of heavy metal atoms that prevent the increase of the gravimetric storage percentage. Low-density organic microporous materials such as hypercrosslinked polymers (HCPs),2-9 polymers of intrinsic microporosity (PIMs),10-13 and conjugated microporous polymers (CMPs)14-21 have been proposed also as hydrogen storage materials. Other materials with the same property that contain heteroatoms such as Si-containing element-organic materials (EOFs),22 N-containing crystalline triazine-organic frameworks (CTFs),23 and covalent-organic framework materials (COFs)24-37 that contain B and O atoms were also proposed and investigated. Most of the above-mentioned low-density materials present a relatively high surface area and high microporosity, but they do not form crystalline solids. So far, the exceptions in this category are CTF materials that form a 2D porous crystal structure and COF materials that can form either 2D or 3D porous crystalline structures. The discovery of the 3D COF materials27 has attracted a lot of attention since they are constructed of strong covalent bonds and they exhibit high surface areas (4210 m2 per gram for COF-103) and extremely low densities (0.17 g per cubic centimeters for COF-108). These characteristics have made them ideal materials for hydrogen storage. 3D COFs have been already investigated for hydrogen storage by performing Grand Canonical Monte Carlo (GCMC) simulations and by multiscale theoretical approaches that combine both accurate quantum mechanic calculations with GCMC simulations.28,38,39 As expected, the simulation results showed that these materials are very good candidates for hydrogen storage, where the total gravi* To whom correspondence should be addressed. Phone: +30-2810545055. Fax: +30-2810545001. E-mail: [email protected]. † Department of Chemistry, University of Crete. ‡ Materials Science and Technology Department, University of Crete.

metric uptake has reached the value of 21 wt % at 77 K and 100 bar and the very promising value of 4.5 wt % at room temperature and 100 bar in the case of COF-108.28 The gravimetric uptake in 3D COFs exceeded the corresponding value for IRMOFs whereas the volumetric uptake did not differ substantially with respect to IRMOFs. It has been concluded that the major reason for this elevated hydrogen uptake must be attributed to the special characteristics of the materials such as low density, high surface area, pore size, and framework topology rather than the existence of increased interaction strengths between the hydrogen and the pore surface. A further step to achieve improved storage capacities in these materials would be the introduction of charged species on the pore surface. This strategy has been used successfully in the past, both in carbon-based materials and MOFs to improve their storage capabilities.40-43 This improvement can be achieved through the introduction of lithium atoms in the material. Hydrogen interacts with the lithium atom through chargeinduced dipole with quadrupole moment contributions. On top of this a lithium cation can interact simultaneously with multiple hydrogen molecules with interaction energies up to 6 kcal · mol-1.44 From the literature, lithium intercalation in the case of MOF has been achieved either by interaction of the Li with the p system of the organic linkers or by forming ionic bonds between lithium and functional groups of the organic linker. In this case, neutral lithium atoms interact with multiple hydrogen molecules with somewhat decreased interaction energies. GCMC simulations on these lithium doped molecular structures showed a great enhancement of the total hydrogen uptake. In this study we intend to apply this strategy to improve the storage capacity of 3D-COFs by introducing into the 3D-COF structures lithium alkoxide groups as we have done previously with IRMOF materials.42 There is some experimental evidence lately for the formation of lithium alkoxide groups in MOF45-47 and MIL48 materials. Recently, two theoretical studies have been published for Li doped 3D COFs by Cao et al.49 and Choi et al.,50 where Cao et al. found that Li-doped COF-105 and COF108 can reach gravimetric adsorption capacities of 6.84 and 6.73 wt%, respectively, at room temperature and P ) 100 bar. Nevertheless Li doping strategy has severe experimental difficulties.

10.1021/jp907241y CCC: $40.75  2009 American Chemical Society Published on Web 11/24/2009

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Figure 1. Optimized molecular model of the lithium alkoxide modified HHTP building unit; carbon, silicon, oxygen, boron, hydrogen, and lithium atoms are shown as gray, yellow, red, pink, white, and purple colors, respectively.

We have selected the best performed 3D-COF for hydrogen storage, i.e., COF-105, for our study. To examine it, we used a multiscale theoretical approach as has been done in previous studies.28,38,42 First, ab initio calculations at the density functional level of theory (DFT, RI-PBE/def2-TZVPP) were employed to relax the geometries of the functionalized linkers and to obtain the hydrogen binding sites for multiple hydrogen molecules and the corresponding interaction energies. Second, GCMC simulations, based on the ab initio results, were carried out to obtain the hydrogen uptake of these modified materials under different thermodynamic conditions. Computational Details COF-105 crystal structure was synthesized by the reaction of the rigid molecular building blocks of triangular hexahydroxytriphenylene (HHTP) with the tetrahedral tetra(4-dihydroxyborylphenyl)silane (TBPS).28 Because of the large size of their crystal structures, the model system must be decreased in size, in order not to end up to prohibitively large computations during the performance of the quantum calculations. The reduction of the size can be achieved by reducing the structure to smaller molecular models that would lead to an accurately description of the local geometry that we investigate. We have selected to introduce three lithium alkoxide groups on the HHTP building unit, where the molecular model that we have used is bigger than a HHTP unit, to include the effect of the surrounding C2O2B rings. We let the model to be fully optimized (Figure 1), and then we studied the interaction of multiple hydrogen molecules (n ) 1-5 H2 molecules) with the one lithium alkoxide group of a slightly smaller model to get the corresponding geometries (Figure 2) and interaction energies. We followed this procedure since we were mainly interested in the effect of the lithium containing group of our model with hydrogen molecules and the results can be extended for the other two lithium alkoxide groups. All calculated distances between hydrogen molecules and interaction sites were measured with respect to the center of mass of each hydrogen molecule and are presented on Table 1. DFT in the resolution of identity (RI) approximation51 is applied to our calculations. The PBE exchange-correlation

Klontzas et al. functional52 along with the def2-TZVPP basis set together with the corresponding auxiliary basis set for the RI approximation was used. All structures are optimized without any symmetry constraints and the optimized minimum-energy structures were verified as stationary points on the potential energy surface by performing numerical harmonic vibrational frequency calculations. The SCF (self-consistent field Hartree-Fock) convergence criteria were set at 10-8 au. DFT has been known to underestimate the interaction energies of weakly bonding systems. The validity of the DFT method that we used in this study was tested in comparison with high accurate MP2 calculations in a previous study43 and showed good agreement with the calculated binding energies. All calculations were performed with the TURBOMOLE program.53 On top of this, all binding energies are corrected for the basis set superposition error (BSSE) with the counterpoise (CP) method as proposed by Boys and Bernardi.54 These corrections have been proven essential since the BSSE may become critical for non bonding interactions. GCMC (constant chemical potential, µ, cell volume, V, and temperature, T) simulations were conducted both at 77 K and room temperature for various pressures for lithium alkoxide COFs. Periodic boundary conditions were applied to all three dimensions. For each state point, GCMC simulation consisted of 10 × 106 steps to guarantee equilibration followed by 10 × 106 steps to sample the desired thermodynamic properties. Nonbonded interactions were treated using the Lennard-Jones (LJ) potential. The LJ parameters for the hydrogen interaction with the framework atoms were taken from the Dreiding force field.55 Lorentz-Berthelot mixing rules were employed to calculate the cross parameters between framework atoms and hydrogen molecules. The parameters for the hydrogen interaction with the oxygen and lithium atoms of the alkoxide group were derived by fitting the LJ potential to our ab initio calculated potential energy surface. In this way these parameters were calculated to be σH2-O ) 0.243 nm, εH2-O ) 1.7 kcal/mol, σH2-Li ) 0.18 nm, and εH2-Li ) 2.98 kcal/mol, respectively, for oxygen and Lithium atoms of the alkoxide group. Quantum effects were taken into consideration through Feynman Hibbs effective potential since these corrections have been proven to be of significant importance especially at low temperatures. The framework was assumed to be rigid for all simulations. A cutoff radius of 15 Å was applied to the LJ interactions. Calculations were carried out assuming 77 K and room temperature at various pressures, ranging from 1 to 100 bar for Li alkoxide COFs. Results and Discussion As a first step, we optimized the molecular model that can be seen in Figure 1 without any geometrical constrains by using quantum mechanical calculations, as we have described in the previous section. The optimization procedure led to the structure that can be seen in Figure 1. Lithium atom preferred to be located in a position between the two neighboring oxygen atoms. The bond lengths of Li-Oalkoxide and Li-OC2O2B are 1.76 Å and 1.93 Å, respectively, and the angle between Li-Oalkoxide-Calkoxide was 106.9°. The position of the lithium atom is in the same plane with HHTP building block. The molecular model of the HHTP unit can be seen in Figure 2 was also optimized and led to the same geometrical characteristics as for the model in Figure 1. In the next step of our investigation we studied the interaction of multiple hydrogen molecules with lithium alkoxide group. We added several hydrogen atoms toward lithium atom and every time we let the system to be optimized. The optimization

Lithium-Functionalized 3-D COFs

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Figure 2. The optimized geometries of the interaction of multiple H2 (n ) 1-5) with the lithium alkoxide group. Carbon, silicon, oxygen, boron, hydrogen, and lithium atoms are shown as gray, yellow, red, pink, white, and purple colors, respectively.

TABLE 1: Interaction Energies (IE) and Average Interaction Distances for H2 from Li Atom over Lithium Alkoxide Groupa 1H2 2H2 3H2 4H2 5H2

IE (kcal · mol-1)

Distance from H2 center of mass (Å)

-2,95 -5,15 -6,25 -7,0 -8,04

2,075 2,109 2,287 2,123 (3,521) 2,155 (3,634)

a All energy values have been BSSE corrected and are in kcal · mol-1. Distance values are in Å. Values in parentheses refer to distances of H2 from the lithium atom for the H2 that are closer to the oxygen atom of the alkoxide.

procedure led to molecular interaction geometries that we located to be stationary points. The optimized molecular configurations (nH2 ) 1-5) can be seen in Figure 2. The first hydrogen molecule formed a T-shaped geometrical configuration upon the interaction with the Li atom. This configuration has been reported in many studies where hydrogen interacted with Li and has been attributed to the charge quadrupole contributions between Li and hydrogen. The distance between Li and the center of mass of the H2 was 2.075 Å, and the position of the

H2 was in the same plane with HHTP unit. The bond length of H2 was found slightly larger than a free H2 at 0.756 Å, where the interaction energy of H2 calculated at -2.95 kcal · mol-1. The addition of the second H2 led to a different configuration, where the two molecules stayed above and below the plane of the HHTP unit, while they kept the T-shape configuration with respect to lithium. The average interaction distance between H2 and Li was 2.109 Å, and the bond lengths of them were 0.756 Å. The interaction energy for the 2 H2 calculated at -5.15 kcal · mol-1. When a third H2 was added, the bond lengths of H2 were 0.755 Å, and the average interaction distance between H2 and Li was 2.287 Å. The total interaction energy upon the addition of the third H2 was calculated at -6.25 kcal · mol-1. After the addition of a fourth H2, we found a different molecular configuration around lithium alkoxide group. In this case, the first 2 H2 were closer to lithium atom having a T-shape configuration, while the other two were near the oxygen atom of the alkoxide with a perpendicular configuration of their axis toward oxygen atom. The H-H bond lengths of the first and second group of H2 molecules were 0.756 Å and 0.754 Å, respectively, and the total binding energy was calculated at -7 kcal · mol-1. For the 2 H2 that were nearest to Li, the interaction distance with Li was 2.12 Å, where for the other pair the average

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Figure 3. Total gravimetric and volumetric adsorption isotherms for hydrogen adsorption at 77 and 300 K for original (red triangles) and OLi group modified (green circles) COF 105.

distances between them with Li and O atom were 3.525 Å and 3.022 Å, respectively. The addition of a fifth molecule did not lead to significant changes in the molecular configuration around lithium alkoxide group. The total interaction energy was calculated at -8.04 kcal · mol-1, and the average H-H bond length was 0.754 Å. In summary, the average interaction energy decreased as we added H2 molecules in the molecular system, where the average interaction distance increased. The first three H2 molecules interacted directly with lithium having a T-shape molecular configuration, where there was a contribution to the interaction of the next molecules from the polarized oxygen atom of the alkoxide group. (Please see Table 1 for details.) The hydrogen storage capacities of the modified COF were studied by performing GCMC simulations at 77 and 300 K for pressures up to 100 bar. We simulated both the total gravimetric and volumetric adsorption isotherms for H2 adsorption in these materials. The corresponding isotherms can be seen in Figure 3. From these figures it can clearly be seen that the proposed structure modification leads to significant improvement of hydrogen uptake in both gravimetric and volumetric terms. Nevertheless the improvement is more pronounced for the volumetric uptake than the gravimetric. The reason for this is that the proposed modification with the OLi group increases the weight of the material, since a single hydrogen molecule is substituted by a group of considerably larger weight. This is not the case for the volumetric uptake since in that case the system volume does not change upon the structure modification. In addition the improvement of the uptake is more important for the low loading range, i.e., at high temperatures. This improvement leads to the material to meet the DOE goal for gravimetric uptake (6 wt %) even at room temperature.

Conclusions We have tried to improve hydrogen storage characteristics of 3D-COF materials through the introduction of lithium alkoxide groups into the structure of COF-105. We added three lithium alkoxide groups per HHTP building unit, and we performed a multiscale theoretical study to evaluate the hydrogen storage characteristics of the modified COF-105. DFT calculations showed that up to five H2 can interact directly with the lithium alkoxide group. The first H2 interact with Li, and the interaction energy was calculated at 2.95 kcal · mol-1, a value that is almost three times larger than the interaction of H2 with the unmodified material. H2 capacity of the modified COF-105 was studied by performing GCMC simulations at 77 and 300 K for pressures up to 100 bar. We found that the proposed structure modification lead to significant improvement of hydrogen uptake in both gravimetric and volumetric terms. The improvement is more pronounced for the volumetric uptake than the gravimetric. The reason for this is that the proposed modification with the OLi group increases the weight of the material, since a single hydrogen molecule is substituted by a group of considerably larger weight. This is not the case for the volumetric uptake where the system volume does not change upon the structural modification. In addition the improvement of the uptake is more important for the low loading range, where the modified COF-105 reaches the DOE target for gravimetric uptake (6 wt %) even at room temperature. Acknowledgment. The present research study has been cofinanced by E.U.-European Social Fund (75%) and the Greek Ministry of Development-GSRT (25%) (IIENE∆ 2003-03E∆ 548). Partial funding by the European Commission DG RTD

Lithium-Functionalized 3-D COFs (FP6 Integrated Project NESSHY, Contract SES6-518271) and Interreg IIIA Gr-Cy K2301.004 is gratefully acknowledged. References and Notes (1) US DOE website, http://www.eere.energy.gov. (2) Weder, C. Angew. Chem., Int. Ed. 2007, 46, 2. (3) Lee, J. Y.; Wood, C. D.; Bradshaw, D.; Rosseinsky, M. J.; Cooper, A. I. Chem. Commun. 2006, 25, 2670. (4) Wood, C. D.; Tan, B.; Trewin, A.; Niu, H. J.; Bradshaw, D.; Rosseinsky, M. J.; Khimyak, Y. Z.; Campbell, N. L.; Kirk, R.; Stockel, E.; Cooper, A. I. Chem. Mater. 2007, 19, 2034. (5) Germain, J.; Hradil, J.; Frechet, J. M. J.; Svec, F. Chem. Mater. 2006, 18, 4430. (6) Spoto, G.; Vitillo, J. G.; Cocina, D.; Damin, A.; Bonino, F.; Zecchina, A. Phys. Chem. Chem. Phys. 2007, 9, 4992. (7) Germain, J.; Frechet, J. M. J.; Svec, F. J. Mater. Chem. 2007, 17, 4989. (8) Germain, J.; Svec, F.; Frechet, J. M. J. Chem. Mater. 2008, 20, 7069. (9) Germain, J.; Frechet, J. M. J.; Svec, F. Chem. Commun. 2009, 2009, 1526. (10) McKeown, N. B.; Gahnem, B.; Msayib, K. J.; Budd, P. M.; Tattershall, C. E.; Mahmood, K.; Tan, S.; Book, D.; Langmi, H. W.; Walton, A. Angew. Chem., Int. Ed. 2006, 45, 1804. (11) Gahnem, B. S.; Msayib, K. J.; McKeown, N. B.; Harris, K. M. D.; Pan, Z.; Budd, P. M.; Butler, A.; Selbie, J.; Book, D.; Walton, A. Chem. Commun. 2007, 2007, 67. (12) Weber, J.; Antonietti, M.; Thomas, A. Macromolecules 2008, 41, 2880. (13) Weber, J.; Thomas, A. J. Am. Chem. Soc. 2008, 130, 6334. (14) Jiang, J.-X.; Su, F.; Trewin, A.; Wood, C. D.; Campbell, N. L.; Niu, H.; Dickinson, C.; Ganin, A. Y.; Rosseinsky, M. J.; Khimyak, Y. Z.; Cooper, A. I. Angew. Chem., Int. Ed. 2007, 46, 8574. (15) Kobayashi, N.; Kijima, M. J. Mater. Chem. 2007, 17, 4289. (16) Jiang, J.-X.; Su, F.; Trewin, A.; Wood, C. D.; Niu, H.; Jones, J. T. A.; Khimyak, Y. Z.; Cooper, A I. J. Am. Chem. Soc., 2008, 130, 7710. (17) Trewin, A.; Willock, D. J.; Cooper, A. I. J. Phys. Chem. C 2008, 112, 20549. (18) Stockel, E.; Wu, X.; Trewin, A.; Wood, C. D.; Clowes, R.; Campbell, N. L.; Jones, J. T. A.; Khimyak, Y. Z.; Adams, D. J.; Cooper, A. I. Chem. Commun. 2009, 2009, 212. (19) Trewin, A.; Darling, G. R.; Cooper, A I. New J. Chem. 2008, 32, 17. (20) Jiang, J. X.; Su, F.; Niu, H.; Wood, C. D.; Campbell, N. L.; Khimyak, Y. Z.; Cooper, A. I. Chem. Commun. 2008, 2008, 486. (21) Jiang, J.-X.; Trewin, A.; Su, F.; Wood, C. D.; Niu, H.; Jones, J. T. A.; Khimyak, Y. Z.; Cooper, A. I. Macromolecules 2009, 42, 2658. (22) Rose, M.; Bohlmann, W.; Sabo, M.; Kaskel, S. Chem. Commun. 2008, 2008, 2462. (23) Kuhn, P.; Antonietti, M.; Thomas, A. Angew. Chem., Int. Ed. 2008, 47, 1. (24) Maly, K. E. J. Mater. Chem. 2009, 19, 1781. (25) Mastalerz, M. Angew. Chem., Int. Ed. 2007, 46, 2.

J. Phys. Chem. C, Vol. 113, No. 50, 2009 21257 (26) Uribe-Romo, F. J.; Hunt, J. R.; Furukawa, H.; Klock, C.; O’Keeffe, M.; Yaghi, O. M. J. Am. Chem. Soc. 2009, 131, 4570. (27) Campbell, N. L.; Clowes, R.; Ritchie, L. K.; Cooper, A. I. Chem. Mater. 2009, 21, 204. (28) El-Kaderi, H. M.; Hunt, J. R.; Mendoza-Cortes, J. L.; Cote, A. P.; Taylor, R. E.; O’Keeffe, M.; Yaghi, O. M. Science, 2007, 316, 268. (29) Klontzas, E.; Tylianakis, E.; Froudakis, G. E. J. Phys. Chem. C 2008, 112, 9095. (30) Hunt, J. R.; Doonan, C. J.; LeVangie, J. D.; Cote, A. P.; Yaghi, O. M. J. Am. Chem. Soc. 2008, 130, 11872. (31) Cote, A. P.; Benin, A. I.; Ockwig, N. W.; O’Keeffe, M.; Matzger, A. J.; Yaghi, O. M. Science 2005, 310, 1166. (32) Cote, A. P.; El-Kaderi, H. M.; Furukawa, H.; Hunt, J. R.; Yaghi, O. M. J. Am. Chem. Soc. 2007, 129, 12914. (33) Tilford, R. W.; Gemmill, W. R.; zur Loye, H.-C.; Lavigne, J. J. Chem. Mater. 2006, 18, 5296. (34) Tilford, R. W.; Mugavero, S. J., III; Pellechia, P. J.; Lavigne, J. J. AdV. Mater. 2008, 20, 2741. (35) Srepusharawoot, P.; Scheicher, R. H.; Araujo, C. M.; Blomqvist, A.; Pinsook, U.; Ahuja, R. J. Phys. Chem. C 2009, 113, 8498. (36) Yang, Q.; Zhong, C. Langmuir 2009, 25, 2302. (37) Garberoglio, G.; Vallauri, R. Microporous Mesoporous Mater. 2008, 116, 540. (38) Garberoglio, G. Langmuir 2007, 23, 12154. (39) Han, S. S.; Furukawa, H.; Yaghi, O. M.; Goddard, W. A., III J. Am. Chem. Soc. 2008, 130, 11580. (40) Mavrandonakis, A.; Tylianakis, E.; Stubos, A. K.; Froudakis, G. E. J. Phys. Chem. C 2008, 112, 7290. (41) Blomqvist, A.; Moyses Araujo, C.; Srepusharawoot, P.; Ahuja, R. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 20173. (42) Han, S. S.; Goddard, W. A. J. Am. Chem. Soc. 2007, 129, 8422. (43) Klontzas, E.; Mavrandonakis, A.; Tylianakis, E.; Froudakis, G. E. Nano Lett. 2008, 8, 1572. (44) Lochan, R. C.; Head-Gordon, M. Phys. Chem. Chem. Phys. 2006, 8, 1357. (45) Mulfort, K. L.; Hupp, J. T. Inorg. Chem. 2008, 47, 7936. (46) Mulfort, K. L.; Farha, O. K.; Stern, S. L.; Sarjeant, A. A.; Hupp, J. T. J. Am. Chem. Soc. 2009, 131, 3866. (47) Mulfort, K. L.; Hupp, J. T. J. Am. Chem. Soc. 2007, 129, 9604. (48) Himsl, D.; Wallacher, D.; Hartmann, M. Angew. Chem., Int. Ed. 2009, 48, 1. (49) Cao, D.; Lan, J.; Wang, W.; Smit, B. Angew. Chem., Int. Ed. 2009, 48, 1. (50) Choi, Y. J.; Lee, J. W.; Choi, J. H.; Kang, J. K. Appl. Phys. Lett. 2008, 92, 173102. (51) Weigend, F.; Haser, M.; Patzelt, H.; Ahlrichs, R. Chem. Phys. Lett. 1998, 294, 143. (52) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (53) Version 5.9 http://www.turbomole.com. (54) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (55) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. J. Phys. Chem. 1990, 94, 8897.

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