J. Phys. Chem. C 2008, 112, 17465–17470
17465
Dynamics of Hydrogen Spillover on Carbon-Based Materials Xianwei Sha, M. Todd Knippenberg,† Alan C. Cooper, Guido P. Pez, and Hansong Cheng* Air Products and Chemicals, Inc., 7201 Hamilton BouleVard, Allentown, PennsylVania 18195-1501 ReceiVed: April 22, 2008; ReVised Manuscript ReceiVed: July 9, 2008
We investigate the dynamics of physisorbed atomic hydrogen on several carbon based materials (various fullerenes and a graphene sheet) using first principles molecular dynamics simulations. The physisorbed H atoms, generated upon H2 dissociative chemisorption on metal catalysts and interaction with carbonized “bridge” materials and substrates (Chen, L.; et al. J. Phys. Chem. C 2007, 111, 18995), can diffuse freely on carbon surfaces with high mobility. Our results indicate that physisorption of H atoms is a metastable state and the atoms will readily recombine to form H2 molecules, which can be recycled to generate more H atoms, or attack the substrates to form C-H bonds. The strength of the resulting C-H bonds exhibits a strong dependency on the carbon material surface curvature. The implication of C-H bond strength on the dehydrogenation of hydrogenated carbon materials to form molecular H2 is discussed. I. Introduction Carbon-based materials (graphite, graphite nanofibers, carbon nanotubes, fullerenes, etc.) have drawn considerable research interest as potential hydrogen storage media for proton exchange membrane (PEM) fuel cell applications. Recent experiments have shown that the hydrogen storage capacity could be significantly improved via hydrogen spillover, in which molecular hydrogen undergoes dissociative chemisorption on metal catalysts and H atoms migrate onto the surface and into the bulk of various carbon-based materials.1-4 The underlying mechanisms of hydrogen spillover in these materials have remained a subject of extensive studies. Hydrogen spillover phenomena have been observed and well-documented in experimental studies with materials such as MoO3 and WO3. Mechanistically, the observed hydrogen spillover in metal oxides is attributed to the favorable thermodynamics and the small energy barriers of H-migration from catalysts to substrates and the subsequent proton diffusion in bulk lattice derived from the massive H-bonding network intrinsic to these materials.5,6 However, a mechanism that invokes high proton mobility cannot account for spillover in carbon-based materials because a similar H-bonding environment does not exist. In a recent publication, we showed that H-migration from a fully saturated Pt subnano cluster to graphitic carbon materials is facile, with a small energy barrier, but subsequent H-diffusion would be energetically difficult if the H atoms are chemisorbed because H-diffusion leads to C-H bond breaking.7 We concluded that hydrogen spillover in graphitic carbon-based materials is only possible if physisorption of H atoms also occurs simultaneously upon H-migration from catalysts to the substrates and proposed that physisorbed H atoms might be generated via the following process: (1) H2 molecules undergo dissociative chemisorption on a Pt catalyst particle located on the carbon surface or a “bridge” material made of carbonized sugar. (2) Upon full H atom saturation of the surfaces of the Pt catalyst, the H atoms migrate from the catalyst to the “bridge” with relatively small energy barriers. (3) The migrated H atoms may hydrogenate * Corresponding author. E-mail:
[email protected]. † Present address: Department of Chemistry, United States Naval Academy, Annapolis, MD 21403.
the graphitic substrates to form C-H bonds if they are sufficiently “hot” (high kinetic energy), in which case further diffusion of H was found to be energetically impractical and thus spillover is effectively terminated. (4) The migrated H atoms may exist in a transient physisorption state if they are sufficiently “cold” (low kinetic energy), which would allow H atoms to diffuse to the substrate sites far from the active catalytic centers. Our current study is focused on determining the feasibility of steps 3 and 4 at a temperature (300 K) that is relevant to the published experimental reports of hydrogen spillover. Therefore, our MD simulations model the carbon materials in the presence of atomic hydrogen at C-H distances that would be consistent with transfer of H atoms from an engaged catalyst particle on the carbon material surface. We note here that the physisorption of H atoms on graphitic materials has been observed in several published experimental studies. The vibrational spectrum of H and D atoms on the (0001) surface of graphite was reported by Ghio and coworkers.8 Recently, Ye and Chiu reported that atomic hydrogen is mobile on graphite at room temperature on the basis of their observation in the experiment of graphite-mediated reduction of azoaromatic compounds with elementary iron in lialysis cells.9 The physisorbed H atoms are weakly bound to the graphitic carbon materials via a van der Waals interaction and are free to diffuse over the graphite surface because the physisorption energy is essentially site-independent.8-10 In understanding the stability of these physisorbed H atoms, the key questions are how fast and to what extent the H atoms will remain highly mobile free radicals or recombine to form molecular hydrogen or form C-H bonds with the substrates. An additional issue is whether the substrate structures influence the spillover efficiencies. In this paper, we report a first-principles molecular dynamics (MD) simulation study based on density functional theory (DFT) to understand the dynamics of physisorbed H atoms on a graphene sheet and C60 and examine the bond energy differences of C-H bonds formed by H spillover as a function of graphitic carbon curvature using various fullerenes. We show that physisorbed H atoms will be quickly “quenched” by forming either H2 molecules or C-H bonds with the substrates and that the hydrogenation capacity of a series of fullerenes increases with the local carbon curvature.
10.1021/jp803495y CCC: $40.75 2008 American Chemical Society Published on Web 09/06/2008
17466 J. Phys. Chem. C, Vol. 112, No. 44, 2008
Sha et al.
Figure 1. Energy profile as an H atom approaches the graphene sheet and fullerene molecules C60 and C20. All the geometric parameters were allowed to fully relax at each given C-H distance.
II. Computational Method All MD calculations were performed with the Vienna ab initio simulation package (VASP).11,12 The Kohn-Sham equation is solved iteratively using a plane wave basis set to represent the valence electrons and nonlocal optimized ultrasoft pseudopotentials to describe the ionic cores.13 The exchange-correlation effects are incorporated in the generalized gradient approximation (GGA) using the Perdew-Wang (PW91) functional.14 We sampled the Brillouin zone within a 2 × 2 × 1 Monkhorst-Pack15 k point mesh for graphene and Gamma point for C60, and used the Methfessel-Paxton technique16 for electron smearing with a width of σ ) 0.2 eV. We used an energy cutoff of 350 eV to make sure the total energy is well converged. A constant-volume canonical ensemble was simulated using the Nose´ thermostat17 with the initial temperature of 300 K. We utilized the Verlet algorithm to integrate the Newton’s equations of motion with a time step of 1 fs. Calculations of the hydrogenation of fullerenes were performed without a periodic boundary condition using DFT/GGA with PW91 functional as implemented in DMol3 package.18,19 We employed a double numerical basis set augmented with polarization functions to describe both core and valence atomic orbitals. All structures were fully optimized. To understand the relative reactivity of fullerenes toward C-H bond formation via attack of H atoms and the energetics of H desorption from hydrogenated carbon materials, we calculated the energies required to partially hydrogenate the selected fullerenes, which, upon normalization with the number of H atoms, gives an average C-H bond energy defined by
1 Ebond ) [E(Cm) + nE(H) - E(CmHn)] n
(1)
where E(Cm), E(H) and E(CmHn) are the total energies for the fullerene Cm, atomic hydrogen, and hydrogenated fullerene CmHn, respectively (where m and n are the numbers of C and H in the unit cell). III. Results and Discussions Prior to MD simulations, we first calculated the energy profile of an H atom approaching selected fullerene molecules and graphene (Figure 1). The calculation with graphene shows that there is a barrier of approximately 0.2 eV at a C-H distance of
Figure 2. Initial configuration for the molecular dynamics simulations of H adsorbed on a graphene sheet. The unit cell is shown by the dashed-line box, and the hydrogen and carbon atoms are represented as white and green spheres, respectively. The distance between the inner H layer and graphene sheet, dC-H, was varied from 2.5 to 3.0 Å, and the layer distance between H, dH-H, was set to be 4.0 Å.
ca. 2.5 Å before forming a C-H bond on the substrate as the C atom changes its hybridization from sp2 to sp3. In the calculation involving C60, there is a very small barrier of 0.02 eV for the approach of the H atom coupled with a substantially larger well-depth of 2.08 eV, indicating that a H atom in proximity to the C60 molecule can readily form a C-H bond with C60. For smaller fullerenes (e.g., C20), the energy barrier for approach of the H atom vanishes completely and the corresponding well depth for formation of a C-H bond increases. Obviously, a small barrier for approach of the H atom allows the carbon substrate to be hydrogenated more easily and a large well-depth makes H desorption from the hydrogenated carbon material more difficult. We also note that the recombination of 2 H atoms to form a H2 molecule is a highly exothermic process with a heat of reaction of approximately -4.7 eV, which is significantly lower than the reaction energy required to form a C-H bond with most fullerenes and with a graphene sheet. Therefore, H2 recombination presents a more energetically competitive process than the hydrogenation of these carbon materials. We next performed MD simulations of an assembly of H atoms in a sufficiently large rectangular box containing a single graphene sheet. The unit cell contains 50 C atoms within the graphene sheet, which was sandwiched by four layers of H atoms, two above and two below, as shown in Figure 2. Each H layer includes 9 H atoms. To avoid interactions between graphene sheets due to the periodic boundary condition imposed in the MD simulation, the vacuum spacing that separates the sheets was set to be 25 Å. The H atoms were placed at least 4.0 Å apart from each other to prevent the atoms from very rapid recombination to form H2 molecules. With the distance
Hydrogen Spillover on Carbon-Based Materials
J. Phys. Chem. C, Vol. 112, No. 44, 2008 17467 TABLE 1: Distributions of H Atoms on Graphite and C60 from MD Simulationsa substrate NH
DC-H time chemisorbed physisorbed molecular (Å) (ps) state state state
graphite
2.5
36
2.75 3.0 C60
50
3.2
0.25 1 4 0.25 0.25 1 0.1 1 1.5
15 10 10 4 1 1 1 4 6
7 8 2 6 7 3 23 24 8
14 18 24 26 28 32 26 22 36
a
NH is the number of initial H atoms, and DC-H is the nearest initial C-H distance.
Figure 3. Molecular dynamics simulation snapshots for H atoms on a graphene sheet, at (a) 0.25 and (b) 4 ps for initial configuration with nearest C-H layer distance at 2.5 Å, and at 0.25 ps for an initial distance at 2.75 (c) and 3.0 (d) Å.
of the entrance barrier for H chemisorption on the substrate in mind,10,20 we set the initial positions of the inner H layers to 2.5, 2.75 and 3.0 Å from the substrate, respectively, and the outer H layers 4 Å from the inner H layers. These initial structural arrangements are, of course, rather arbitrary; however, other physisorption configurations are not expected to differ significantly in total potential energies because moving H atoms around in the physisorption region does not give rise to significant energy variations. Nevertheless, reactive events (e.g., H atom recombination) may vary depending on the relative positions of atoms in the unit cell. In addition, MD simulations on such a small unit cell are not statistically significant. Our primary interest here is to investigate qualitatively whether an assembly of physisorbed H atoms is capable of interacting with the substrate to form C-H bonds at a near-ambient temperature. Our MD simulation results indicate that for the inner H-layers initially located 2.5 Å from the substrate, a strong attraction between the H atoms and the substrate causes most of the H atoms in the inner layers to immediately move toward the graphene and become chemisorbed after 0.25 ps (Figure 3a). The substrate undergoes substantial structural changes upon C-H bond formation as the interacting C atoms pucker out of the plane to form C-H bonds with a bond length of ap-
proximately 1.15 Å, consistent with the previous DFT study.10,21 In parallel, most of the H atoms on the outer layers rapidly form H2 molecules, which subsequently are weakly attracted to the graphene sheet and show high mobility along the graphene surface. For the chemisorbed H atoms, no further movement, including diffusion to other chemisorption sites, was observed during the 4 ps simulation time. However, Eley-Rideal recombination,22,24 in which a gas-phase H atom strikes the C-H bond to form an H2 molecule, was observed, indicating that the surface C-H bonds are rather weak compared with the C-H bonds in organic molecules. We found that the Eley-Rideal recombination on the graphene sheet is a significant process that results in depletion of the chemisorbed H atoms from the substrate. Indeed, at 4 ps, the result is that the number of the chemisorbed H atoms is reduced compared with the number present at 0.25 ps (Figure 3b). Over the course of the MD simulation, C-H bonds formed upon continued attack of H atoms on the graphene were not ordered with respect to existing C-H bond sites, despite the fact that the structural configuration with alternating C-H bonds on graphene (i.e., one C-H bond above the plane is adjacent to another C-H bond below the plane) is thermodynamically more favorable than the structure with randomly distributed isolated C-H bonds.23 This suggests that the chemisorption process is kinetically controlled. In subsequent simulations, the initial configurations of the layers of H atoms were moved away from the graphene sheet by an additional 0.25 and 0.5 Å, resulting in initial C-H distances of 2.75 and 3 Å, respectively. Now all the H atoms are blocked by the energy barrier that separates the physisorption and chemisorption states. As expected, the MD simulation yielded a drastically smaller number of chemisorbed H atoms on the graphene sheet largely due to fact that there is an energy barrier in the entrance channel and, more importantly, the recombination of H atoms to form H2 molecules is barrierless and thus an thermochemically and kinetically more favorable process. The calculated numbers of events are summarized in Table 1. At 0.25 ps, four H atoms were found to form C-H bonds with the substrate for the MD simulation with the inner H atom layers initially located at 2.75 Å from the surface (Figure 3c). Only 1 H atom was chemisorbed during the simulation with the inner H atom layers initially located at 3.0 Å (Figure 3d). No H desorption/diffusion from the chemisorbed H atoms or Eley-Rideal recombination was observed in the entire simulation time in both cases. An additional simulation with an increase of the initial inner H layer distance to 3.2 Å away from the graphene sheet resulted in no hydrogen chemisorption during the course of the simulation. The hydrogenation kinetics are obviously sensitive to the relative distance between H atoms and C atoms at the beginning of the MD simulation as a short
17468 J. Phys. Chem. C, Vol. 112, No. 44, 2008
Sha et al.
Figure 4. Molecular dynamics simulation snapshots for H atoms on C60 at (a) 0, (b) 0.1, (c) 1, and (d) 1.5 ps.
hydrogen is confined with the catalyst/substrate mixture, H2 molecules formed via H recombination could again interact with the metal catalyst to regenerate H atoms.
Figure 5. Calculated average C-H bond energy as a function of hydrogenation percentage in several selected fullerene molecules.
distance increases the probability for an H atom to strike the substrate to form a C-H bond and a longer distance gives rise to a higher probability for H2 recombination reaction. Morisset et al. examined the formation of the H2 molecule through two initially physisorbed atoms on a graphite surface via quantum wave packet method and reported that the reaction occurs with a significant probability,25,26 which is consistent with what is observed in our MD simulations. Despite the lack of statistical significance of the current method due to a small number of atoms used in the theoretical model and the relatively short simulation time, it can be qualitatively concluded that the transition from physically adsorbed H atoms to formation of C-H bonds with a graphene sheet can be a significant event at a near-ambient temperature. In a closed system where gaseous
To deepen our understanding of the effects on H spillover of varying the types of graphitic substrates, we performed a MD simulation at 300 K for an assembly of H atoms on C60 confined in a sufficiently large box. The cell parameters were set to 27.34 Å, and the number of H atoms in the box was set to 50. Initially, the H atoms were placed 4.0 Å apart from each other and the distance between H atoms and C60 was set to be at least 3.2 Å. Similar to the simulations involving graphene, all of the H atoms exhibited high mobility during the MD runs, suggesting that H diffusion in the physisorption state is facile. However, both H chemisorption leading to the formation of C-H bonds and H recombination to form H2 take place quickly and simultaneously. Of the 50 H atoms in the box, 6 of the H atoms become chemisorbed and the remainder form H2 molecules (Table 1). Figure 4 displays several snapshots of the MD trajectories. The chemisorption of hydrogen on C60 appears to be more facile than for graphene, as evidenced by the fact that more H atoms form C-H bonds on C60. This observation appears to be due to the nearly barrierless approach of the H atoms and the more favorable thermochemical energy of C-H bond formation resulting from the higher carbon surface curvature.27,28 The MD studies of H spillover dynamics on graphene and C60 qualitatively indicate that physisorption of H atoms facilitates H diffusion and ultimately leads to either H chemisorption or H2 formation as time evolves. Our MD simulations indicate that the efficiency of hydrogen spillover in graphitic materials can be enhanced by using carbon materials with curved surfaces. To gain additional understanding of this “curvature effect”, we examined the hydrogenation energies of fullerenes with various sizes where all hydrogenation takes place at the exohedral sites (external surface of the fullerene).
Hydrogen Spillover on Carbon-Based Materials
J. Phys. Chem. C, Vol. 112, No. 44, 2008 17469
Figure 6. Optimized configurations for nine fully hydrogenated fullerenes, C20H20, C28H28, C32H32, C36H36, C40H40, C44H44, C48H48, C60H60, and C70H70.
TABLE 2: Calculated and the Available Experimental HOMO-LUMO Gaps of Nine Selected Fullerene Molecules molecule C20 C28 C32 C36 C40 C44 C48 C60 C70
HOMO-LUMO gap (eV) (cal) 0.37 0.78 1.43 0.45 0.88 0.85 0.73 1.67 1.72
HOMO-LUMO gap (eV) (exp)
1.30 0.80 0.70 0.80
TABLE 3: Calculated Average Desorption Energies for Several Selected Hydrogenated Fullerene Molecules at Different Hydrogenation Percentage hydrogenation percentage molecules
20%
40%
60%
80%
100%
C20 C32 C44 C60 C70
2.34 1.58 0.86 0.12 0.02
2.96 1.3 0.56 0.32 0.2
1.98 1.1 0.44 0.06 -0.04
2.3 1.3 0.8 0.3 0.18
2.68 1.6 1.06 0.46 0.26
1.60
Hydrogenation of C60 has been a subject of extensive theoretical29,30 and experimental31-34 studies, and full hydrogenation of C60 has not been successfully achieved in experiments. To date, C60H36, which contains 4.76 wt % H2, is the most highly hydrogenated derivative of C60.34 In contrast, for some smaller fullerenes, such as C20, full hydrogenation (∼7.7 wt % of H2) has been accomplished.35 To understand the energetics required to partially or fully hydrogenate fullerenes, we calculated the average C-H bond energies at various H loadings with results shown in Figure 5. The optimized fully hydrogenated fullerene structures are shown in Figure 6. In all cases, upon hydrogenation, the C-C bond distances of fullerenes increase slightly as the hybridization of the C atoms changes from sp2 to sp3 whereas the C-H bond lengths (1.095 Å) are consistent for all the nine fully hydrogenated fullerenes. In probing the C-H bond energy for examples where there is only one C-H bond, we find that the C-H bond energy generally decreases with fullerene size, reflecting the strong influence of carbon material curvature on the C-H bond strength. The only exception is for C32, on which the C-H bond is in fact weaker than on C44. A detailed analysis indicates that
the surprisingly weaker C-H bond in C32 arises from the exceptionally stable electronic structure of C32. C32 has been known to be much more stable than other small fullerene molecules except C60.36,37 Ultraviolet photoelectron spectroscopy of C32 and C60 exhibits unusually large HOMO-LUMO gaps of 1.3 and 1.6 eV, respectively.38 In contrast, the HOMO-LUMO gaps of other fullerene molecules are much smaller, ranging from 0.70 to 0.80 eV. The calculated HOMO-LUMO gaps of the selected fullerenes, shown in Table 2, compare well with the experimentally measured values. We also note that the C-H bond energy in C20 is substantially larger than those in other fullerenes, resulting from the highly acute C-C-C bond angles, resulting in C atoms that behave like carbon radicals. The results of our calculations of higher levels of hydrogenation for the set of fullerenes show that the calculated C-H bond energies decrease monotonically with the fullerene size. For larger fullerenes, the average C-H bond energy varies in a relatively small range, roughly within 0.4 eV, with respect to hydrogenation percentage; considerably larger variation of C-H bond energies vs hydrogenation percentage for smaller fullerenes, particularly C20, was found because these fullerenes exhibit higher reactivity. Compared with the typical C-H bond energy in organic molecules (∼4.3 eV), the average C-H bond energies
17470 J. Phys. Chem. C, Vol. 112, No. 44, 2008
Sha et al.
in fullerenes, except C20, are much smaller. Nevertheless, our results suggest that hydrogenation of fullerenes by physisorbed H atoms is a highly exothermic process. As the fullerene size decreases, the well-depth of C-H bond formation increases. It is therefore anticipated that as the size of the fullerene decreases, the hydrogenated fullerenes will become increasingly stable and dehydrogenation will be increasingly more difficult. Table 3 displays the calculated average desorption energy to form H2 molecules from the breaking of C-H bonds in selected hydrogenated fullerenes (CnHm) at a given capacity, defined by
∆Edes )
2 m E(Cn) + E(H2) - E(CnHm) m 2
[
]
(2)
In all cases, the hydrogen desorption is an endothermic process and, as expected, the desorption energy decreases with increasing fullerene size. In particular, at 80% to full hydrogen saturation, the required hydrogen desorption energy for C60 and C70 appear to be quite small. Therefore, it appears that the key challenge to making these materials useful for hydrogen storage is to find a catalytic process that allows the C-H bonds to be broken with suitable activation energies for near-ambient temperature operation. IV. Summary It has been proposed that hydrogen spillover in carbon nanostructured materials will only occur if the H atoms generated via dissociation by metal catalysts remain physisorbed.7 To gain a more complete understanding of hydrogen spillover mechanisms, it is essential to understand the dynamic behavior of these physisorbed H atoms. In the present study, we conducted extensive theoretical calculations using DFT by first mapping out the energy profile of hydrogenating one C atom on selected carbon materials and subsequently performing ab initio molecular dynamics simulations on an assembly of physisorbed H atoms on graphene and C60 at room temperature. We finally explored the influence of substrate type on hydrogen spillover capacity and on dehydrogenation by evaluating the average C-H bond strength. Our results indicate that the energetic well-depth of the C-H bond formation increases as the size of fullerenes decreases and kinetically this reactive process is essentially barrierless. Hydrogenation of graphene requires approximately 0.2 eV activation energy and the corresponding well-depth is 0.76 eV. Hydrogenation of these carbon materials presents an energetically competitive process to H recombination to form H2. Our ab initio MD simulations suggest that both processes will occur simultaneously. In particular, our study indicates that the physisorbed H atoms in the selected carbon environments are only metastable and ultimately will either react with the carbon substrates to form C-H bonds or recombine to form H2 molecules. The recombined H2 molecule can of course interact again with the metal catalysts to regenerate H atoms in a cyclic hydrogen/physorbed H atom/recombined hydrogen process. It appears that the H physisorption process provides a means for H atoms to diffuse from the sites near the metal catalyst particles to distant sites, which is a necessary component of the H spillover phenomenon. The present study suggests that the degree of inherent curvature of the external surfaces of fullerenes and the resulting effects of the bond angle distortions of the carbon atoms in the fullerenes has a profound influence on the thermodynamics of C-H bond formation. The calculated reaction energies of
forming H2 molecules from the hydrogenated fullerene molecules as well as for graphene appear to be favorable. However, on the basis of the calculated average C-H bond energies, we believe that it will be kinetically challenging to break the moderately strong C-H bonds and a carefully designed catalytic process would be necessary to facilitate the hydrogen desorption process. Acknowledgment. We gratefully acknowledge funding for this work provided by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy via the Hydrogen Sorption Center of Excellence (contract DE-FC-05GO15074). References and Notes (1) Li, Y. W.; Yang, R. T. J. Phys. Chem. B 2006, 110, 17175. (2) Li, Y. W.; Yang, R. T. J. Am. Chem. Soc. 2006, 128, 8136. (3) Lachawiec, A. J.; Qi, G. S.; Yang, R. T. Langmuir 2005, 21, 11418. (4) Yang, F. H.; Lachawiec, A. J.; Yang, R. T. J. Phys. Chem. B 2006, 110, 6236. (5) Chen, L.; Cooper, A. C.; Pez, G. P.; Cheng, H. J. Phys. Chem. C 2008, 112, 1755. (6) Chen, L.; Pez, G.; Cooper, A. C.; Cheng, H. J. Phys.-Condens. Matter 2008, 20, 064223. (7) Chen, L.; Cooper, A. C.; Pez, G. P.; Cheng, H. J. Phys. Chem. C 2007, 111, 18995. (8) Ghio, E.; Mattera, L.; Salvo, C.; Tommasini, F.; Valbusa, U. J. Chem. Phys. 1980, 73, 556. (9) Ye, J.; Chiu, P. EnViron. Sci. Technol. 2006, 40, 3959. (10) Sha, X. W.; Jackson, B. Surf. Sci. 2002, 496, 318. (11) Kresse, G.; Furthmuller, J. Phys. ReV. B 1996, 54, 11169. (12) Kresse, G.; Furthmuller, J. Comput. Mater. Sci. 1996, 6, 15. (13) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892. (14) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (15) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (16) Methfessel, M.; Paxton, A. T. Phys. ReV. B 1989, 40, 3616. (17) Nose, S. Mol. Phys. 1984, 52, 255. (18) Delley, B. J. Chem. Phys. 1990, 92, 508. (19) Delley, B. J. Chem. Phys. 2000, 113, 7756. (20) Sha, X. W.; Jackson, B.; Lemoine, D.; Lepetit, B. J. Chem. Phys. 2005, 122, 014709. (21) Jeloaica, L.; Sidis, V. Chem. Phys. Lett. 1999, 300, 157. (22) Sha, X. W.; Jackson, B.; Lemoine, D. J. Chem. Phys. 2002, 116, 7158. (23) Zecho, T.; Guttler, A.; Sha, X. W.; Lemoine, D.; Jackson, B.; Kuppers, J. Chem. Phys. Lett. 2002, 366, 188. (24) Hornekaer, L.; Rauls, E.; Xu, W.; Sljivancanin, Z.; Otero, R.; Stensgaard, I.; Laegsgaard, E.; Hammer, B.; Besenbacher, F. Phys. ReV. Lett. 2006, 97, 186102. (25) Morisset, S.; Aguillon, F.; Sizun, M.; Sidis, V. J. Chem. Phys. 2005, 122, 194702. (26) Morisset, S.; Aguillon, F.; Sizun, M.; Sidis, V. J. Chem. Phys. 2004, 121, 6493. (27) Ruffieux, P.; Groning, O.; Bielmann, M.; Mauron, P.; Schlapbach, L.; Groning, P. Phys. ReV. B 2002, 66, 245416. (28) Ruffieux, P.; Groning, O.; Bielmann, M.; Groning, P. Appl. Phys. A-Mater. Sci. Process. 2004, 78, 975. (29) Okamoto, Y. J. Phys. Chem. A 2001, 105, 7634. (30) Yoshida, Z. I.; Dogane, I.; Ikehira, H.; Endo, T. Chem. Phys. Lett. 1993, 201, 481. (31) Bruhwiler, P. A.; Andersson, S.; Dippel, M.; Martensson, N.; Demirev, P. A.; Sundqvist, B. U. R. Chem. Phys. Lett. 1993, 214, 45. (32) Nozu, R.; Matsumoto, O. J. Electrochem. Soc. 1996, 143, 1919. (33) Ballenweg, S.; Gleiter, R.; Kratschmer, W. Tetrahedron Lett. 1993, 34, 3737. (34) Talyzin, A. V.; Klyamkin, S. Chem. Phys. Lett. 2004, 397, 77. (35) Ternansky, R. J.; Balogh, D. W.; Paquette, L. A. J. Am. Ceram. Soc. 1982, 104, 4503. (36) Kietzmann, H.; Rochow, R.; Gantefor, G.; Eberhardt, W.; Vietze, K.; Seifert, G.; Fowler, P. W. Phys. ReV. Lett. 1998, 81, 5378. (37) Chang, Y. F.; Jalbout, A. F.; Zhang, J. P.; Su, Z. M.; Wang, R. S. Chem. Phys. Lett. 2006, 428, 148. (38) Golden, M. S.; Knupfer, M.; Fink, J.; Armbruster, J. F.; Cummins, T. R.; Romberg, H. A.; Roth, M.; Sing, M.; Schmidt, M.; Sohmen, E. J. Phys.-Condens. Matter 1995, 7, 8219.
JP803495Y
