Adsorption and Dissociation of Molecular Hydrogen on Palladium

Article pubs.acs.org/JPCC

Adsorption and Dissociation of Molecular Hydrogen on Palladium Clusters Supported on Graphene I. Cabria,*,† M. J. López,† S. Fraile,‡ and J. A. Alonso† Departamento de Física Teórica, Atómica y Ó ptica and ‡Departamento de Física Aplicada-LATUV, Universidad de Valladolid, 47011 Valladolid, Spain

†

S Supporting Information *

ABSTRACT: Doping of porous carbon materials with metallic atoms, clusters and nanoparticles is viewed as a way to enhance the hydrogen storage in those materials. Transition metals are dopants of interest. For this reason we present a theoretical study of the interaction of molecular hydrogen with small palladium clusters (Pdn, n = 1−6) supported on a graphene layer. The adsorption of H2 on those supported Pd clusters leads to two types of adsorption states. The simplest one is an activated state of the hydrogen molecule, with the H−H distance stretched and the H−H bond weakened, but not broken. Adsorption in the activated states occurs with no barriers and the binding energies are in a range of values of interest for achieving a favorable reversible hydrogen storage in the doped material. The second type is a dissociated and chemisorbed state, with the separated hydrogen atoms attached to the Pd cluster. The dissociative chemisorption states are more stable than the activated states. However, starting with Pd4, there are barriers for the dissociative chemisorption of H2, and the heights of those energy barriers are a few tenths of an electronvolt.

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INTRODUCTION One of the main issues remaining to be solved in hydrogen car technology is the on-board hydrogen storage. The storage should be reversible at room temperature. Different materials able to store hydrogen have been studied. One active research line is the storage in nanoporous carbon materials.1,2 Pure porous carbons do not store enough hydrogen to serve as ideal containers. According to recent calculations, transition metal atoms,3−8 alkali metal atoms,9−11 and alkaline-earth atoms12,13 stabilized on graphene, nanotubes, fullerenes, and other carbon materials can bind one or more hydrogen molecules with binding energies of 0.2−1.0 eV per molecule. Those energies are intermediate between physisorption and chemisorption energies. Thermodynamic estimations14 indicate that adsorption energies of 0.3−0.4 eV per molecule are required to get reversible hydrogen storage at room temperature and moderate pressures. Therefore, doping with these metals seems to be a way to enhance hydrogen storage in carbonaceous materials. The bonding mechanism involved in the interaction between a H2 molecule and a transition metal (TM) atom is called Kubas bonding.15 This bonding is based on molecular polarization and multiple σ-bonding between the H2 molecule and the d orbitals of the transition metal atoms. This type of bonding has been observed in H2-TM complexes. It has also been observed in nickel nanoparticles dispersed on the surface of multiwalled carbon nanotubes,16,17 in Ti metal−ethylene complexes,18 in mesoporous Ti oxides,19 and in isolated Pd atoms dispersed on porous carbon.20 Experiments and simulations on carbon surfaces showed that TM-doped carbons suffer from metal oxidation, segregation and clustering. These effects can decrease the storage capacities of the doped © 2012 American Chemical Society

materials. A recent paper has stressed the oxidation problem: the O2 molecules block the adsorption of H2 on a metal−doped graphene surface, occupying adsorption sites that the hydrogen molecules cannot use, except for Ni, Pd, and Pt dopants.21 Many of these metal atoms tend to form clusters22−24 because the TM-TM bonds are stronger than the TM-carbon bonds. In spite of those effects, the experiments indicate that carbon materials doped with highly dispersed nanoparticles of some transition metals (Pt,25,26 V,27 Pd,20,27−33 and Ni26,32,34 among others) have larger hydrogen storage capacities than the pure carbon materials. For instance, in the case of a graphite oxidelike carbon foam doped with Pd/Hg nanoparticles, Psofogiannakis and co-workers31 measured a promising reversible gravimetric storage capacity of 3 wt % at room temperature and 2 MPa, halfway to the target of 5.5 wt % for 201535 issued by the U.S. Department of Energy. The enhanced storage in this and the other cited works was ascribed, in part, to the socalled spillover mechanism. Conner and Falconer36 defined the concept of spillover as the transport of a molecule adsorbed on a first surface onto a second surface that does not adsorb the molecule under the same conditions. On the other hand, there is extensive literature on hydrogen adsorption on Pd surfaces, mostly related to catalysis and a smaller part to hydrogen storage. Experiments and simulations indicate that the H2 molecule dissociates easily on Pd surfaces, but subsurface bonding is energetically less favorable.37−40 Different hydrogen sorption sites at Pd surfaces have been Received: June 8, 2012 Revised: September 7, 2012 Published: September 8, 2012 21179

dx.doi.org/10.1021/jp305635w | J. Phys. Chem. C 2012, 116, 21179−21189

The Journal of Physical Chemistry C

Article

0.0001 eV. Optimization of geometries was run until the forces on the atoms were less than 0.05 eV/Å. The optimization of the geometry of pure graphene yielded a C−C distance of 1.422 Å. The geometries of the materials studied in this paper have been plotted with the xcrysden43 and xmakemol programs.

identified that could exist also on Pd clusters supported on graphene. Hydrogen storage on Pd bulk and films is based on the molecular dissociation and insertion of the H atoms on the bulk interstitial sites. In this case, a large volumetric hydrogen storage capacity is obtained, but with very small gravimetric storage capacity and very low storage reversibility at room temperature due to the strong H binding. The important technological and scientific reasons to study hydrogen spillover on Pd clusters supported on carbon surfaces are thus evident. The details involved in the different steps of this process, adsorption of hydrogen on the metallic nanoparticle, migration through the nanoparticle, and spilling over the carbon surface, are not well-known. In particular, one may ask if hydrogen is adsorbed and transported in molecular form or dissociated, and what is the state and the location of hydrogen after spilling into the carbon surface. Besides, the spillover depends also on the characteristics of the support: surface area, acidity/basicity, redox properties and support− metal interactions. In particular, for a carbonaceous support, which is the case of interest here, spillover will depend on the size of the metal particle, the structure of the carbon support (degree of graphitization, defects, etc.), and the amount of hydrogen already present. Graphene is the simplest carbon surface, and doped graphene is a reasonable starting point to model the hydrogen spillover on doped carbon materials. In a former paper24 we studied the formation of Pd clusters on graphene. The purpose of the present paper is to study the interaction of hydrogen molecules with Pd clusters supported on graphene, which represents the first step in the spillover mechanism. We do not treat other steps of the process here. The size of the cluster is relevant due to the high cost of palladium. It is then important to understand the effect of cluster size on the adsorption of hydrogen. The computational method is presented in section II. We present in section III the results for Pd clusters supported on graphene. The interaction of H2 with free Pd clusters is studied in section IV, and the adsorption of hydrogen on Pd clusters supported on graphene in section V. Finally, the conclusions of the work are given in section VI.

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PD CLUSTERS SUPPORTED ON GRAPHENE Small isolated Pdn clusters with sizes n = 1−5 have been studied in a previous paper.24 Here we summarize and update the results, adding results for Pd6. The cohesive energies of these clusters, defined Ec = nE(Pd) − E(Pd n)

(1)

where E(Pd) and E(Pdn) are the total energies of the free Pd atom and Pdn cluster respectively, are given in Table 1. The Table 1. Structure and Total Cohesive Energies (in eV) of Free Pdn Clusters, n = 2-6 cluster Pd2 Pd3 Pd4 Pd4 Pd4 Pd5 Pd5 Pd6 Pd6 Pd6 Pd6

rhombus square tetrahedron square pyramid trigonal bipyramid octahedron incomplete pentagonal bipyramid capped square pyramid tent with rhombic base

Ec 1.30 3.75 5.84 5.88 6.68 9.00 9.05 11.74 11.46 11.23 11.20

lowest energy structure of Pd3 is an equilateral triangle. Pd4 is a tetrahedron and Pd6 is an octahedron. Two structures are practically degenerate in energy in Pd5. The ground state of all these Pd clusters is a spin triplet (magnetic moment M = 2 μB), in agreement with the calculations of Rogan et al.44 There are also singlet states (M = 0) with the same geometry and close energies. The results for Pdn clusters supported on graphene are given in Table 2. This table updates and enlarges the information given in our previous paper.24 In some cases we have considered different orientations of a given isomer: for instance, parallel or perpendicular to the graphene plane in the cases of Pd2 and Pd3, or different orientations of the Pd4 tetrahedron and the Pd6 octahedron on the surface. The incomplete pentagonal bipyramid structure of Pd6 transforms into the octahedral structure upon deposition on the graphene layer. The adsorption energy of the cluster is defined

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METHOD Density functional theory (DFT) calculations have been performed using the supercell method, a plane wave basis set, and ultrasoft pseudopotentials, as implemented in the DACAPO code.41 The pseudopotential for Pd uses a Kr-like core. The generalized gradient approximation (GGA) of Perdew and Wang, PW91,42 has been used to treat electronic exchange and correlation effects. Spin−polarized calculations have been performed in all cases. The supporting graphene layer was simulated as a periodically repeated unit cell consisting of 32 carbon atoms in the (x, y) plane, forming the well-known honeycomb structure. This size was adequate for most adsorption cases studied, but for the Pd6 cluster on graphene we used a larger cell consisting of 50 carbon atoms. To minimize interactions between cells, the cell parameter c in the z direction perpendicular to the graphene plane was 12 Å. An energy cutoff of 350 eV was taken for the plane wave expansion of the wave functions, and a cutoff of 1000 eV for the density. The Monkhorst−Pack k-point set was [4, 4, 1]. The value of c, the cutoffs, and the Monkhorst−Pack set were chosen to deliver adsorption energies with a numerical precision of 0.005 eV. The calculations were done selfconsistently with a total energy convergence tolerance of

Ead = E(graphene) + E(Pd n) − E(Pd n on graphene)

(2)

where E(graphene) is the energy of the graphene layer, E(Pdn) is the energy of the isolated cluster isomer, and E(Pdn on graphene) is the energy of the system formed by graphene with that cluster isomer adsorbed. The absolute binding energy of the system, that is, the binding energy with respect to graphene and n free Pd atoms, is the sum of Ead and Ec of Table 1. dPd−plane is the distance between atoms of the cluster and the graphene plane. Consequently, two distances are given in the case of Pd2, Pd3, and so on. dPd−C is the average Pd−C distance, considering only the closest Pd atoms to the plane, and dPd−Pd is the average nearest-neighbor Pd−Pd distance. 21180



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Table 2. Optimized Structures, Adsorption Energies Ead (in eV), Distances (in Å), and Total Magnetic Moment M (in μB) of Pdn Clusters Supported on Graphenea n

structure

Ead

1 1 1 2 2 3 3 4 4 4 4 5 5 6 6

Pd on C Pd on C−C Pd on hexagon horizontal vertical on hexagon horizontal vertical horizontal rhombus vertical square tetrahedron on face tetrahedron on edge pyramid on base bipyramid on edge octahedron on face capped square pyramid tent with rhombus base

1.04 1.09 0.91 1.26 0.64 0.57 0.76 0.40 0.86 0.66 0.84 0.68 0.49 1.14 0.99

2.16 2.16 2.04 2.15 2.13, 2.17 2.23, 2.27 2.25, 2.31, 2.24, 2.26, 2.27, 2.27, 2.24,

1.19

2.29, 4.56

6

dPd−plane

4.10 4.49 4.79 4.44 4.22 4.14 3.04, 4.54 4.49 4.07, 4.16

dPd−C

Table 3. Structural Parameters (Representative Distances d and Angles θ), and Binding Energies Eb of Isolated PdH2 and Pd(H2)2a

dPd−Pd

M

geometry

dH2−Pd

dH−H

dPd−H

θH−Pd−H

Eb

2.14 2.22 2.47 2.26 2.24 2.29 2.34 2.39 2.36 2.43 2.35 2.43 2.38 2.34 2.32

2.75 2.63 2.77 2.62 2.72 2.54 2.67 2.65 2.69 2.69 2.71 2.72

0 0 0 0 0 0 2 2 0 2 2 0 2 2 2

linear Pd−H−H López-Corral et al.52 isosceles triangle López-Corral et al.52 Contescu et al.20 H2PdH2 Contescu et al.20

2.14 2.15 1.62 1.63 1.58 1.69

0.79 0.80 0.90 0.90 0.92 0.85 0.85

1.75 1.75 1.68 1.69 1.65 1.74 1.73

0 0 31 31 32 28

0.46 0.41 1.12 0.94 1.11 1.02 1.04

2.38

2.67

2

a

Distances in Å, angles in deg, and binding energies Eb in eV/ molecule.

distance of free H2, dH−H = 0.754 Å (experimental dH−H = 0.76 Å), is nearly preserved in the linear Pd−H−H isomer, which has dH−H = 0.79 Å. On the other hand, the H−H distance in the isosceles triangle is 0.90 Å. In this stretched state, the hydrogen molecule is activated as a result of the Kubas interaction, although not yet dissociated. The binding energy E b = E(Pd) + E(H 2) − E(Pd+H 2)

a

Several isomers and orientations with respect to the graphene plane are considered. The meaning of the distances is explained in the text.

(3)

of the isosceles triangle isomer, that is, the binding energy of the hydrogen molecule to the Pd atom, is 1.1 eV/molecule, a strength midway between the physisorption and chemisorption regimes. These results for the activated state of adsorbed H2 are robust, as we will see later in the context of the adsorption of H2 on Pd clusters supported on graphene. Figure 1 shows the

Table 2 shows that different isomers of a given Pdn cluster have different adsorption energies. Usually, the most stable isomer of the free cluster leads to the lowest total energy for the adsorbed system (largest Ec + Ead). The exception occurs for Pd5. The free trigonal bipyramid is slightly more stable than the square pyramid. However, the adsorption energy of the square pyramid, 0.68 eV, is higher than the adsorption energy of the bipyramid, 0.49 eV, and the total energy of the system formed by the square pyramid adsorbed on graphene is lower. The most stable structure of the adsorbed Pd clusters preserves the magnetic moment M = 2 μB of the corresponding free cluster for Pd3, Pd4, and Pd6 and changes the magnetic moment to zero for Pd2 and Pd5. It is possible, in careful laboratory experiments, to control with good precision the size of the metallic clusters deposited on a graphene surface.45 When porous carbons are doped with the focus on hydrogen storage studies, the methods of doping do not permit a similar degree of size control of the metallic clusters. Recent experiments by Contescu et al.20 showed that 18% of the metal in Pd-doped porous carbons is in atomic form and the rest is in the form of clusters.

Figure 1. Interaction energy between H2 and Pd (lower panel), and H−H distance (upper panel) vs the Pd−H2 distance. The interaction energy is Eint = E(Pd+H2) − E(Pd) − E(H2). The H−H distance is optimized for each Pd−H2 separation.

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INTERACTION OF H2 WITH A FREE PALLADIUM ATOM AND A PALLADIUM DIMER Before studying the interaction of H2 with supported Pd clusters it is convenient to analyze the interaction with free Pd atoms or clusters, because some features of the Pd−H2 interaction appear to be independent of the environment. The interaction of Pd atoms and clusters with H2 has also been studied by other groups.20,46−52 We found two stable isomers of PdH2, a linear Pd−H−H, and an isosceles triangle, which is the ground state. The results for binding energies and structural features are given in Table 3. The total magnetic moment is zero in all cases. A linear H−Pd−H isomer is unstable against fragmentation into Pd and H2. The comparison of our results with the density functional GGA calculations of López-Corral et al.52 and with other papers20,46,49 is satisfactory. The H−H

results for the interaction between H2 and the Pd atom. There is no barrier for the formation of the isosceles triangle. It can be also seen that the linear H−Pd−H isomer is unstable. In addition, an isomer with quasi-equilateral structure reported in some papers, which in our calculations corresponds to dH2−Pd = 1.30 Å (dH2−Pd is the distance between the Pd atom and the mass center of H2) and dPd−H = 1.55 Å, is not stable and relaxes to the isosceles triangle. For Pd(H2)2 we found that the most stable geometry has the two H2 molecules on opposite sides of the atom, similar to the geometry reported by Contescu et al.20 The relevant geometric parameters and the binding energy per H2 molecule, E b = (E(Pd) + 2E(H 2) − E(Pd+2H 2))/2 21181

(4)



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Table 4. Optimized Geometries (Figure 2), Relevant Distances (in Å), Magnetic Moments M (in μB), and Binding Energies Eb (in eV) of Several Isomers of Free Pd2H2a dH−H

geometry (a) linear (b) H2 perpendicular to Pd2 (c) trapezoid (d) distorted trapezoid (e) rhomboid a

0.77 0.83 1.05 1.12 2.03

(0.79) (0.87) (1.03) (1.94)

dPd−H

dPd−Pd

1.99, 2.76 1.80, 4.31 1.61, 1.61 1.58, 1.66 1.69 (1.67)

2.54 2.54 2.61 2.66 2.71

M

(2.77) (2.78) (2.65) (2.73)

2 2 0 0 0

Eb 0.18 0.59 1.33 1.35 2.21

(0.21) (0.71) (1.29) (2.07)

DFT results of Efremenko et al.46 are shown in parentheses.

to a spin uncoupling caused by strong chemical interaction with H2. We have also found a triplet (M = 2 μB) to singlet (M = 0 μ B ) lowering for Pd 2 H 2 in the case of dissociative chemisorption of the H2 molecule, whereas there is no spin change in the activated state. In fact, this spin uncoupling is a well-known feature of the chemical interaction of transition metal atoms at the right side of the periodic table and molecular hydrogen.53 Calculations for PdxH2 (x = 1−4) by Efremenko et al.46 and by Moc et al.47 also predict singlet states and similar Pd−H distances.

given in Table 3, are very similar to those reported by that group. The two H2 molecules are activated. The results for several optimized geometries of Pd2H2 are given in Table 4 and Figure 2. We find good agreement with

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INTERACTION OF H2 WITH A SINGLE PD ATOM DEPOSITED ON GRAPHENE In a recent work on the storage of hydrogen in porous carbon doped with palladium, Contescu et al.20 reported that 18% of the palladium was in the form of adsorbed single atoms. The study of the interaction of H2 with a Pd atom adsorbed on graphene is then a topic of high interest. In our simulations, the H2 molecule was initially placed at Pd−H2 distances in the range 3.0−3.5 Å. We tested different orientations for the molecular axis. As H2 approaches the supported Pd atom, activation of the molecule occurs without barrier, elongating the H−H distance, but not breaking the H−H bond. This can be seen in a movie of the relaxation process provided as Supporting Information. Figure 3 shows the initial and final snapshots of that simulation. The relevant distances d(H−H), d(Pd−H2), and d(Pd−H) are given in Table 5. The binding energy

Figure 2. Geometries of several isomers of the free Pd2H2 molecule found in the present calculations. The H2 molecule is dissociated in panels c−e.

the DFT calculations of Efremenko et al.,46 who used the B3LYP approximation. The H2 molecule is physisorbed in the linear isomer (panel a), activated in the isomer with the H2 axis perpendicular to that of Pd2 (panel b), and dissociated in the other isomers. In the dissociated state, the H−H distances are 1.05 Å or larger, the binding energies E b = E(Pd 2) + E(H 2) − E(Pd 2+H 2)

(5)

are 1.33 eV or larger, and the magnetic moment of the system is zero. In contrast, the magnetic moment is 2 μB when the H2 molecule is activated or physisorbed, the binding energies are below 0.6 eV, and the H−H distances are in the range typical of the activated or physisorbed states. The ground state corresponds to the rhomboidal isomer of panel d. Free Pd2, and more generally Pdn clusters with n = 2−7 have a triplet ground state,24,44 M = 2 μB. Former papers47,50,51 have reported a lowering of the spin multiplicity of Pd clusters due

E b = E(Pd on graphene) + E(H 2) − E(H 2+Pd on graphene)

(6)

Figure 3. Initial and final geometries (left and right panels, respectively) of the H2 molecule interacting with one Pd atom supported on graphene. In the final snapshot, the molecule is activated, with d(H−H) = 0.86 Å. 21182



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reported average binding energies of 0.96, 0.59, 0.53, and 0.41 eV/molecule for one, two, three, and four H2 molecules, respectively, adsorbed on a Pd atom supported on graphene. The adsorption energy of H2 to a Pd atom supported on graphene, 0.96 eV, is very similar to the adsorption energy, 0.93 eV, of the PdH2 complex to the graphene layer. That is, it costs nearly the same energy to desorb the whole PdH2 complex from graphene than to desorb the H2 molecule from the adsorbed Pd. The adsorption energy of a complex of general formula Pdn(H2)m to graphene is defined

Table 5. Optimized Interatomic Distances (in Å), H−Pd−H Angles (in deg), and Adsorption Binding Energies (in eV/ molecule) for the Adsorption of One and Two Hydrogen Molecules on a Pd Atom Supported on Graphene system

dH2−Pd

dH−H

dPd−H

θH−Pd−H

Eb

isosceles PdH2 on graphene Pd(H2)2 on graphene

1.68 1.72

0.86 0.85

1.74 1.77

28.6 27.8

0.96 0.60

is 0.96 eV. The calculated geometry and binding energy of the activated state are in good agreement with those reported in other works.20,52 The simulations for the interaction of two H2 molecules with a single supported Pd atom were started from different initial positions and orientations of the molecules, and we found the final arrangement, with the H2 molecules activated, plotted in Figure 4. The relevant interatomic distances d(H−H), d(Pd−

E = E(graphene) + E(Pd n(H 2)m ) − E(Pd n(H 2)m on graphene)

(8)

The adsorption energy of the complex Pd(H2)2 to graphene is 0.25 eV. Then, the desorption of the whole complex competes with the desorption of only one hydrogen molecule, which costs almost the same energy, 0.24 eV. Therefore, desorption of PdH2 or Pd(H2)2 complexes may limit the contribution of the Pd adatoms to the reversible hydrogen storage capacity of Pd doped porous carbons. Of course, this problem does not exist for Pd atoms occupying substitutional positions at vacancies in graphene.

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INTERACTION OF H2 WITH PDN CLUSTERS DEPOSITED ON GRAPHENE The investigation of the interaction of H2 with Pd2 supported on graphene yielded molecular adsorption (activation) and molecular dissociation states, shown in Figure 5. The magnetic moment of the system is zero in all cases, just like for Pd2 on graphene. The geometrical parameters and binding energies of the activated and dissociated states are reported in Table 6. Labels a−d in that table refer to the corresponding panels in Figure 5. The molecular activation occurs with no barrier. The structures found on graphene are similar to the isomers of free Pd2H2 shown in Figure 2. We have found different distorted trapezoidal configurations, and this is the reason for the range of d(H−H) and d(Pd−Pd) distances in Table 6. In some simulations, the adsorption of the hydrogen molecule displaced the Pd dimer from its initial location on the supporting graphene. That displacement is rooted on the fact that the Pd−H interaction is as strong as the Pd−C interaction

Figure 4. Geometry of Pd(H2)2 supported on graphene. The two molecules are activated.

H2), and d(Pd−H), given in Table 5, are the same for the two molecules. The binding energy E b = E(Pd on graphene) + 2E(H 2) − E(2H 2+Pd on graphene)

(7)

is 1.20 eV, or 0.60 eV/molecule. Hence, the binding energy per molecule decreases from 0.96 to 0.60 eV/molecule when two molecules are absorbed by a Pd atom on graphene. The second hydrogen molecule attaches to the PdH2 complex adsorbed on graphene with an adsorption energy of 0.24 eV, much lower than the adsorption energy (0.96 eV) of the first hydrogen molecule. The geometries and binding energies are in good agreement with the results by Contescu et al.20 These authors

Figure 5. (a)−(c) activated states of the H2 molecule adsorbed on Pd2 supported on graphene. (d) shows the dissociated state of the H2 molecule. 21183



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Table 6. Optimized Interatomic Distances (in Å) and Adsorption Binding Energies (in eV/molecule) for H2 Interacting with a Pd2 Cluster Supported on Graphenea

Table 7. Optimized Interatomic Distances (in Å) and Adsorption Binding Energies (in eV/molecule) of H2 Interacting with Pd3 Supported on Graphenea

structure

dH−H

dPd−H

dPd−Pd

Eb

system

dH−H

dPd−H

dPd−Pd

Eb

(a) perfect trapezoid (b) distorted trapezoid (c) distorted rhomboid parallel to graphene (d) rhomboid perpendicular to graphene

0.95 0.89−0.97 1.04

1.71 1.71 1.81

2.63 2.72−2.74 2.69

0.91 1.01−1.06 1.00

2.04

1.70

2.72

1.66 (2.28)

(a) activated H2 (b) dissociated H2 (c) dissociated H2 (d) dissociated H2 (e) dissociated H2

0.88 1.23 1.93 1.90 2.13

1.71 1.61 1.71 1.84 1.76

2.62 2.70 2.77 2.72 2.77

0.53 0.84 (1.03) 1.28 1.86 1.95

a The configurations are shown in Figure 6. Binding energies are measured with respect to a reference with Pd3 perpendicular to the graphene layer. In Eb, the value in parentheses is the binding energy with respect to Pd3 parallel to the layer.

The configurations are shown in Figure 5. In (d), the first value of Eb is calculated with respect to a reference with Pd2 parallel to the layer, and the value in parentheses with respect to vertical Pd2. a

cases, panels b and e, the simulations started with an horizontal orientation of Pd3. In the simulation leading to the state in panel e, the Pd3 cluster spontaneously changed its orientation to a perpendicular one. Table 7 is sorted from the smallest to the largest binding energy. The largest binding energies occur when the two H atoms are not on the same face of the Pd3 triangle. The Pd−H distances in that table are averages of the smallest Pd−H distances of the relaxed geometries. In all the dissociated cases shown, dissociation of the hydrogen molecule occurs with no barrier. B3LYP calculations for free Pd3H2 by Cui et al.55 showed that the hydrogen molecule also dissociates on free Pd3 with no barrier. The magnetic moment of Pd3 vertical on graphene is 2 μB. Adsorption of the hydrogen molecule, in both the activated and dissociated cases, gives a zero magnetic moment for the system, similar to the case of activated and dissociated states of H2 on Pd and Pd2 supported on graphene. The most stable configuration of Pd4 supported on graphene is a tetrahedron lying on an edge in contact with the graphene layer (see Table 2). Similar to the adsorption of H2 on smaller supported Pd clusters, the simulations led to activated and dissociated states of the molecule. The geometrical parameters and the adsorption binding energies of the most stable activated and dissociated states are shown in Table 8. Labels a and b in that table refer to the corresponding panels in Figure 7. The magnetic moment of the system with the hydrogen molecule in the activated states is 2 μB, and zero for the dissociated states. To investigate the possible barriers to dissociative chemisorption, we have considered dissociation paths starting with the H2 molecule placed on top a Pd atom and with the molecule on top of the upper Pd−Pd bond of the tetramer. In both cases the molecule was initially oriented parallel to the graphene plane. As an example, starting with the activated state of the molecule shown in panel a of Figure 7, we have used the nudged elastic band (NEB) method56 to calculate the minimum energy path between the activated and the dissociated states. This minimum energy path is shown in Figure 8. We have plotted in that figure the geometries of some configurations along the dissociation path. There is a barrier of about 0.7 eV between the activated state of the molecule and the dissociated state. The H−H distances along the path are plotted in the upper panel of the figure. The spin magnetic moment is 2 μB for the activated molecule, close to 0 μB when climbing the transition state barrier, and exactly 0 μB for the rest of the configurations. We did not find activated states for the second case, the molecule on top of the upper Pd−Pd bond, but we found a barrier of about 0.4 eV for the dissociation of the molecule. Moc et al.47 found that the dissociation of H2 on

(displacements of the Pd atoms due to their interaction with H2 also occur for larger Pd clusters). The H−H distances in the trapezoidal geometries are about 18−28% larger than in the free H2 molecule, and the adsorption binding energies are between 0.9 and 1.1 eV per molecule. The adsorption binding energy is defined E b = E(Pd n on graphene) + E(H 2) − E(H 2+Pd n on graphene)

(9)

In this case n = 2, but eq 9 is valid for other values of n to be treated later. These H−H distances and binding energies indicate molecular adsorption (activation) of H2. In structure d of Figure 5, Pd2H2 forms a rhomboid perpendicular to the graphene plane. This structure was obtained from simulations starting with Pd2 perpendicular to the graphene layer, which led to the dissociation of the hydrogen molecule with no barrier. Hence, the Pd dimer is the smallest adsorbed Pd cluster that dissociates the hydrogen molecule. B3LYP and CASPT2 (complete active space with second-order perturbation theory) calculations for free Pd2H2 by Cui et al.54 showed that the free Pd dimer dissociates the hydrogen molecule with no barrier. The comparison between the adsorption binding energies in Tables 4 and 6 indicates that the strength of the interaction between H2 and Pd2 decreases for the supported Pd dimer. The adsorption energies of the Pd2H2 complexes to graphene are 0.84, 0.97, and 0.71 eV for the structures shown in panels a, b, and d of Figure 5, respectively. Those energies have been calculated from eq 8, taking the free complexes in the same isomeric structures than the adsorbed ones. The adsorption energies of the Pd2H2 complexes are smaller than the adsorption energies of hydrogen to the supported Pd2 cluster. This indicates that the desorption of the whole Pd2H2 complex will be preferred to the desorption of the hydrogen molecule, and this will reduce the contribution of supported Pd2 clusters to the reversible hydrogen storage of nanoporous carbon materials. The interaction of a hydrogen molecule with a Pd trimer supported on graphene produces activated and dissociated states of the molecule. The geometrical parameters and the adsorption binding energies of the most relevant states are reported in Table 7. Labels a−e correspond to the structures shown in Figure 6. Structure a corresponds to an activated molecule and the other structures to dissociated states. The vertical orientation of Pd3 is the reference taken to evaluate the binding energies from eq 9. Most of the simulations of the adsorption of the H2 molecule, panels a, c, and d of Figure 6, started with a Pd3 cluster in the vertical orientation. But in a few 21184



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Figure 6. (a) Activated state of H2 adsorbed on Pd3 supported on graphene. (b)−(e) show dissociated states of the molecule.

Table 8. Optimized Interatomic Distances (in Å) and Adsorption Binding Energies (in eV/molecule) of H2 Interacting with the Pd4 Cluster Supported on Graphene system

dH−H

dPd−H

dPd−Pd

Eb

(a) activated H2 (b) dissociated H2

0.83 2.28

1.80 1.80

2.67 2.78

0.42 1.47

free Pd4 occurs with a barrier of 0.46 eV. In a more recent study, Barone et al.51 have analyzed pathways for the dissociation of H2 on isolated tetrahedral Pd4, obtaining barriers of 0.49 and 0.62 eV. All these previous results are close to the barriers we have obtained for the dissociation of H2 on Pd4 supported on graphene. Finally, the calculated zero point energy of the free H2 molecule is 0.26 eV, in agreement with experiment and other theoretical results. This value is smaller than the height of the dissociation barriers, and therefore, the barriers are high enough to keep the molecule in activated states up to a certain temperature. The most stable configuration of Pd5 supported on graphene is a square pyramid with the base in contact with the graphene layer, as indicated in Table 2, and this was the starting configuration in the simulations of the interaction of H2 with

Figure 8. Nudged elastic band calculation of the minimum energy path (in eV) between the activated state of the H2 molecule and the dissociated state for adsorption on tetrahedral Pd4 supported on graphene. Energies are measured with respect to the Pd4 cluster supported on graphene and a free H2 molecule. The geometries of configurations 2, 5, 6, and 9 are also shown. The upper panel gives the variation of the H−H distance along the dissociation path.

supported Pd5. We found activated and dissociated states of the hydrogen molecule, some of them shown in Figure 9. The

Figure 7. Activated and dissociated states of H2 on Pd4 supported on graphene. 21185



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Figure 9. Activated and dissociated states of H2 on Pd5 supported on graphene.

corresponding binding energies and geometric parameters are shown in Table 9. Labels a−c refer to the corresponding panels Table 9. Optimized Interatomic Distances (in Å) and Adsorption Binding Energies (in eV/molecule) of H2 Interacting with a Pd5 Cluster Supported on Graphenea

a

system

dH−H

dPd−H

dPd−Pd

Eb

(a) activated H2 (b) dissociated H2 (c) dissociated H2

0.88 2.65 2.28

1.74 1.69 1.79

2.74 2.79 2.80

0.69 1.07 1.24

The configurations are shown in Figure 9. Figure 10. Nudged elastic band calculation of the minimum energy path (in eV) between the activated state of the H2 molecule and the dissociated state for adsorption on Pd5 supported on graphene. The geometries of configurations 1, 4, and 8 are shown. Energies are measured with respect to the Pd5 cluster supported on graphene and a free H2 molecule.

in Figure 9. In the case of the activated state of H2, the structure of the Pd5 cluster has changed from the original squarepyramidal form to a trigonal bipyramid with a triangular face in contact with the graphene plane. This is not too surprising, because the total energy of the system formed by a Pd5 bipyramid supported on graphene is only 0.2 eV higher than that of a supported square pyramid. On the other hand, Pd5 remains in its square-pyramidal form when the H2 molecule dissociates. The difference between panels b and c of Figure 9 is that the H atoms are on the edges of the pyramid in (b), and on the triangular faces of the pyramid in (c). The adsorption binding energies in the dissociated states are smaller than the binding energies on supported Pd3 and Pd4. The dissociation barrier between the activated state and the dissociated state, (a) and (c) in Figure 9, respectively, has been calculated using the NEB method. The minimum energy path is given in Figure 10. The process involves not only the dissociation of H2 but also the transformation of the Pd5 trigonal bipyramid into a square pyramid. The barrier height read from the figure is 0.26 eV. The magnetic moment of the activated states is 2 μB, whereas the magnetic moment of the dissociated states is zero. The most stable structure of supported Pd6 is an octahedron with a triangular face in contact with the graphene layer. Simulations of the interaction of H2 with this supported cluster led to activated and dissociated states. Some of these states are shown in Figure 11, and the corresponding adsorption binding energies and relevant interatomic distances are given in Table 10. The spin magnetic moment of the system is M = 2 μB in the cases of the activated molecule, panels a and b of Figure 11, and M = 0 μB in the dissociated cases, panels c−e.

Summarizing, the general magnetic behavior found for hydrogen adsorption on supported Pdn clusters with n = 1−6 is as follows: (a) The spin magnetic moment of the system is M = 0 μB when the hydrogen molecule is dissociated. (b) When the molecule is activated, the spin magnetic moment of the system is the same as the magnetic moment before hydrogen adsorption; the spin magnetic moment is zero on supported Pd1 and Pd2, and M = 2 μB on Pdn clusters with n = 4−6. The only exception is supported Pd3, in which the adsorption of hydrogen in the activated state quenches the magnetic moment of the system from 2 μB to 0 μB. Molecular adsorption leading to the activated states, (a) and (b), of Figure 11 occurs with no barrier as the molecule approaches the Pd6 cluster; this is the same behavior found for adsorption on smaller Pd clusters. To study the dissociation of the adsorbed molecule, we have simulated the minimum energy path between the activated state (a) and the dissociated state (d) using as reaction coordinate the H−H distance. That is, at each step along this path the positions of the H and Pd atoms are relaxed, keeping fixed the value of d(H−H). The energies of the system along this dissociation path are shown in Figure 12. The two curves in the figure correspond to spin magnetic moments of the system equal to 2 μB and 0 μB, respectively. The curves cross at the transition state, labeled (t) in the figure. 21186



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Figure 11. Geometries of activated states, (a) and (b), and dissociated states, (c)−(e), of H2 interacting with Pd6 supported on graphene.

al.57 After passing the barrier, the system falls into the dissociated configuration (c). This is, however, a local minimum, which is separated from the absolute energy minimum configuration (d) by a very small energy barrier of 0.14 eV. The adsorption energy of the whole Pd6H2 complex to graphene is 1.0 and 1.13 eV for the activated (a) and dissociated (d) states, respectively. These energies are calculated from eq 8 considering the same isomer for the free and the adsorbed complex. The adsorption energies of the complex are larger than the adsorption energies of hydrogen on the supported Pd6 cluster. This indicates that the desorption of molecular hydrogen is preferred to the desorption of the complex and, therefore, this cluster size is a good candidate to enhance the reversible storage capacity of nanoporous carbons.

Table 10. Optimized Interatomic Distances (in Å) and Adsorption Binding Energies (in eV/molecule) of One H2 Molecule Interacting with a Pd6 Cluster Supported on Graphene system

dH−H

dPd−H

dPd−Pd

Eb

(a) activated H2 (b) activated H2 (c) dissociated H2 (d) dissociated H2 (e) internal H

0.85 0.85 1.80 3.00 2.46

1.77 1.76 1.76 1.77 1.77

2.72 2.71 2.80 2.80 2.85

0.56 0.50 0.89 1.19 0.78

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CONCLUSIONS Simulations of the interaction of a hydrogen molecule with Pd clusters supported on graphene show that the result of that interaction can be (a) the adsorption of the hydrogen molecule in an activated state or (b) the dissociation of the molecule and the chemisorption of the two hydrogen atoms. In the activated state, the H2 bond length is slightly stretched but the bond is not broken. Adsorption of H2 on a supported Pd atom leads to activation of the hydrogen molecule. Adsorption on supported Pdn n = 2−6 clusters produces activated and dissociated states, depending on the initial conditions, that is, on the location of the hydrogen molecule and its orientation with respect to the Pd cluster. The activated states are metastable, and the lowest energy configurations correspond to dissociated states. An activation barrier has to be surpassed to achieve the dissociation of the H2 molecule on Pd4, Pd5, and Pd6, whereas there is no barrier on Pd2 and Pd3. The distances d(Pd−H) are similar for the activated and the dissociated states despite the stronger H− Pd interaction in the dissociated state of the molecule. d(Pd− H) ranges between 1.71 and 1.80 Å in the case of activated states, and between 1.61 and 1.84 Å for dissociated states.

Figure 12. Interaction energy (in eV) of H2 with Pd6 supported on graphene vs the H−H distance (in Å). The molecule was originally adsorbed in the activated state on top of a Pd atom (label a). The blue and red curves correspond to spin magnetic moments 2 μB and 0 μB, respectively. The configurations corresponding to labels a, c, and d are shown in Figure 11. Label t indicates the transition state.

At this point, the spin magnetic moment of the system changes from 2 μB to 0, and the dissociation proceeds with zero magnetic moment. The barrier between the activated state and the transition state amounts to 0.3 eV. This value has to be considered as an upper limit for the dissociation barrier, because not all possible dissociation paths have been explored, and it is in reasonable agreement with the value of 0.47 eV of the dissociation barrier of H2 on free Pd6 calculated by Wang et 21187



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The enhancement of the hydrogen storage capacities in Pddoped carbon materials could come from two sources. One is the spillover effect, a complex process of which only the initial steps have been studied here. The second arises from the activated H2 molecules adsorbed on Pd atoms and clusters. Our simulations predict the formation of activated states of H2 on supported Pd atoms and clusters, and it is reasonable to expect that a sizable amount of the hydrogen stored on Pd-doped carbon materials is in the form of activated molecules. The binding energies of the activated hydrogen molecules are between 0.4 and 1 eV/molecule, and these values decrease when additional molecules are adsorbed. Those energies are close to the estimated energies required to obtain reversible storage at room temperature and moderate pressures, 0.3−0.4 eV/molecule.14

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ASSOCIATED CONTENT

S Supporting Information *

Movies of the relaxation process from different perspectives (top and lateral views). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by MEC of Spain and the European Regional Development Fund (Grants MAT2008-06483-C03-01 and MAT2011-22781) and by Junta de Castilla y León (Grants GR23 and VA158A11-2).

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Adsorption and Dissociation of Molecular Hydrogen on Palladium

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