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Manipulating the Magnetic Moment of Palladium Clusters by Adsorption and Dissociation of Molecular Hydrogen Maria J. Lopez, Maria Blanco-Rey, Joseba Inaki Juaristi, Maite Alducin, and Julio A. Alonso J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b03996 • Publication Date (Web): 04 Sep 2017 Downloaded from http://pubs.acs.org on September 5, 2017

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The Journal of Physical Chemistry

Manipulating the Magnetic Moment of Palladium Clusters by Adsorption and Dissociation of Molecular Hydrogen María J. López,∗,† María Blanco-Rey,‡,¶ J. Iñaki Juaristi,§,¶ Maite Alducin,§,‡,¶ and Julio A. Alonso†,¶ Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47011 Valladolid, Spain, Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), Paseo Manuel de Lardizabal 5, 20018 Donostia-San Sebastián, Spain, Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain, and Departamento de Física de Materiales, Facultad de Químicas UPV/EHU, Apartado 1072, 20080 Donostia-San Sebastián, Spain E-mail: [email protected]

∗

To whom correspondence should be addressed Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47011 Valladolid, Spain ‡ Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), Paseo Manuel de Lardizabal 5, 20018 Donostia-San Sebastián, Spain ¶ Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain § Departamento de Física de Materiales, Facultad de Químicas UPV/EHU, Apartado 1072, 20080 Donostia-San Sebastián, Spain †

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Abstract There is a sizable probability for the dissociation of H2 deposited at low energy on palladium clusters supported on graphene. This is accompanied by a total or partial quenching of the magnetic moment of the cluster, and we have investigated the interplay between these two processes, magnetization change and molecular dissociation. For this purpose, the density functional formalism has been used, in the form of ab initio molecular dynamics simulations and static calculations. Two different cluster sizes have been investigated, Pd6 and Pd13 , and the conclusion is that the size of the Pd cluster has a strong influence on the sequence of these two processes. The effect of H2 dissociation is to reduce the magnetic moments of both clusters by about 2µB , resulting in unpolarized Pd6 on the one hand, and Pd13 with magnetic moment of 2µB on the other hand. In the case of Pd6 , the quenching of the magnetic moment occurs immediately after the dissociation of the H2 molecule. In contrast, the quenching of the magnetic moment in Pd13 is induced by the arrival of the H2 molecule at its preferred adsorption sites on specific Pd atoms. Once settled in those positions, dissociation takes place almost spontaneously, with a very small activation barrier and no further change of the magnetization. In this way, adsorption and dissociation of H2 can be viewed as an effective tool to manipulate the magnetic state of clusters and nanoparticles supported on carbonaceous substrates, which could lead to interesting applications in devices.


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Introduction The dissociation of molecular hydrogen in two hydrogen atoms is a topic of interest in different areas of physics and chemistry. Collision-induced dissociation of H2 is an important process in the interstellar medium, where the collision partners are H, He, or other H2 molecules. 1 Dissociation of H2 is also relevant for promising technologies using hydrogen, instead of gasoline, as a fuel in cars. 2,3 Those cars use an electric motor based on a hydrogen fuel cell. 4 The hydrogen gas coming from the storage tank reacts in the cell with atmospheric oxygen producing an electric current, and the only emission from the reaction is pure water. An important step in the operation of the fuel cell is the dissociation of molecular hydrogen in the anode of the cell. Dissociating free H2 has an energy cost of 4.52 eV per molecule, and catalytic transition metal nanoparticles embedded in the anode are used to facilitate the dissociation. 5,6 Another crucial ingredient is the storage of the hydrogen needed to feed the cell 7 . Storage in porous materials, in particular porous carbons, is a field of intense activity. 8 Pure carbon materials do not store enough hydrogen, 9 and doping the porous materials with metal nanoparticles has been proposed as a way to enhance hydrogen storage. 10,11 Although the reasons for that enhancement are under debate, it appears that the dissociation of molecular hydrogen is likely to be involved. The dissociation of molecular hydrogen catalyzed by transition metal nanoparticles, mainly palladium and platinum nanoparticles, is then a phenomenon occurring both in the process of storing hydrogen and also in the step of using the hydrogen in the fuel cell. The dissociation of H2 on palladium and platinum atoms and nanoparticles supported on carbonaceous substrates has been recently studied in the context of hydrogen storage by using theoretical techniques based on the density functional formalism. Both static calculations 12–14

and ab initio molecular dynamics simulations 15 have been performed. An interesting

observation from those works is a reduction of the spin magnetic moment of the metal cluster associated to the dissociation of the hydrogen molecule. Apart from the applications mentioned above, the possibility of changing the magnetic moment of supported transition 3 ACS Paragon Plus Environment


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metal nanoparticles by adsorbing hydrogen is interesting in itself and might lead to other applications. Here we focus attention on the change of the spin magnetic moment of the supported Pd clusters associated to the H2 dissociation. Because the interatomic H-H bond distance varies in the process of dissociation from its equilibrium value in the molecule to a larger final value, the following questions can be asked: How is the precise relation between the two physical processes? Do the cluster spin changes take place in a single step or in various stages during the H2 dissociation? Does the spin change precede or follow molecular dissociation? In this paper we investigate these questions by scrutinizing the time evolution of the relevant physical quantities in ab initio molecular dynamics simulations (AIMD) for palladium clusters of different sizes. After a brief account of the theoretical method used in the calculations, we report and discuss the results, ending with the conclusions. It is worth to stress that our aim in this work is not to dig into the materials science aspects of hydrogen storage. We just want to focus on the dynamics of the cluster spin changes associated to the H2 adsorption and dissociation.

Theoretical framework and details of the simulations The computational details of the spin-polarized density functional theory (DFT) calculations aimed to characterize the dynamics of H2 on Pd clusters supported on graphene were described in a previous work analyzing the spillover effect 15 and, hence, those details are briefly summarized here. All (microcanonical) AIMD simulations are carried out with the plane-wave DFT code vasp 16,17 using the generalized gradient approximation PW91 exchange-correlation functional 18 and allowing for spin polarization of the system. The interaction between valence electrons and the atomic cores is treated in the projector augmented wave (PAW) approximation with the PAW potentials supplied with the vasp package. 19 The electronic wave


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functions are expanded in a basis of plane waves, with an energy cut-off of 400 eV, and the Brillouin zone integration is performed with a Γ–centered 2 × 2 × 1 Monkhorst-Pack grid of special k-points. 20 Fractional occupancies are determined through the first order MethfesselPaxton broadening scheme, using a width of 0.1 eV. 21 Periodic boundary conditions are used with large enough supercell sizes. A height of 14 Å is chosen, and 6 × 6 and 5 × 5 graphene unit cells are used for Pd13 and Pd6 , respectively. To get a better understanding of the dynamical simulations we have performed additional static calculations of the dissociation barriers with the DFT-based Dacapo code, 22 which uses Vanderbilt ultrasoft pseudopotentials. 23 The electronic wave functions and densities are expanded in plane wave basis sets with cutoff values of 500 eV and 1000 eV, respectively. The same exchange-correlation functional as in the AIMD calculations, PW91, is used. In both sets of calculations (AIMD and static), periodic boundary conditions are used with the same large supercells that mimic the low coverage limit. The most stable structure of free Pd6 is an octahedron. When Pd6 is supported on graphene this structure is preserved. In this case, one of the triangular faces of the octahedron rests on the graphene surface. 24 As a consequence, the supported Pd6 cluster can be viewed as composed by two parallel triangular layers, with the bottom one in contact with the graphene layer. The ground state structure of both the free and the supported Pd13 nanoparticles consists in two (111) f cc planes with seven and six atoms, respectively. For the supported Pd13 cluster, it is the face with seven atoms the one that rests on the graphene layer. 15 In the AIMD simulations the initial translational and vibrational energies of the H2 molecules are Ei = 0.125 eV and Evib (ν = 0, j = 0) = 0.27 eV, respectively. All the simulations of the deposition of H2 on the Pd clusters supported on graphene are carried out at normal incidence with the molecule initially located at a height of Z = 9 Å above the graphene layer. Before starting the dynamical simulations the substrate is relaxed until the Pd and C atoms reach their equilibrium positions (for each atom the forces are below 0.01 eV/Å). Along the dynamics, all the atoms are allowed to move according to the adiabatic



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forces acting on them, and consequently all the interatomic distances are allowed to change. Although the Pd atoms are displaced from their equilibrium positions upon interaction with the incident molecule, the Pd nanoparticles suffer minor deformations only upon H2 dissociation, keeping their original structure nearly intact. 15 Using a total simulation time of 1 ps and a time-integration step of 0.5 fs, three distinct types of events were identified and conveniently analyzed in Ref. 15, namely, (i) dissociative adsorption of the H2 molecule, (ii) non-dissociative molecular adsorption, and (iii) reflection (non-reactive scattering). The present work is focused on the H2 dissociative adsorption mechanism, for which a substantial change in the spin state of the whole system is observed that depends on the size of the Pd cluster, as discussed in the next section. Remarkably, such a change is at variance with the constant spin magnetic moment that characterizes the molecular adsorption and reflection processes.

Results and discussion The important question that we want to address is whether the change of magnetization takes place before or after the dissociation of the molecule, and whether it depends on the size of the Pd cluster. With this aim, we show in Figures 1 and 2 the results of AIMD simulations for the time evolution of the H-H internuclear distance and the system magnetic moment when a H2 molecule dissociates on supported Pd6 and Pd13 clusters, respectively. In the case of the Pd6 cluster the molecule dissociates in only three of the 60 performed simulations. 15 Figure 1 corresponds to one of those three trajectories, which is representative of all of them. In the case of the Pd13 nanoparticle, for which 20 out of 60 simulations led to dissociation, 15 we distinguish two types of trajectories according to the time spent until dissociation occurs. In the first group, which can be characterised as fast dissociation, the molecule dissociates rapidly after interacting with the nanoparticle, at around 100 fs from the start of the simulations, which is the time needed by the approaching


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H2 molecule to reach a height Z = 5 − 6 Å (measured with respect to the graphene plane). In all the simulations leading to fast dissociation, the falling hydrogen molecule impacts directly on the nanoparticle. In contrast, in the second group, formed by the simulations leading to slow dissociation after 300-400 fs, the impinging molecule interacts briefly with the graphene surface nearby the Pd atoms, approaches the nanoparticle lateral regions and remains wandering before it dissociates. Figure 2 shows the results for one trajectory of each kind. These figures reveal that the evolution of the magnetization of the system during the dissociation process is very different in the two studied nanoparticles. In the case of the Pd6 nanoparticle the magnetic moment of the system is initially 2 µB and it remains nearly constant until the H-H interatomic distance is around 2 Å, i.e., until the molecule is effectively dissociated. At this instant, the magnetic moment of the system is drastically reduced down to zero. In other words, the change in the magnetization of the Pd6 cluster upon dissociative hydrogen adsorption takes place after the dissociation of the molecule. The situation is completely different in the larger Pd13 nanoparticle supported on graphene. In this case, the initial magnetic moment of the cluster is 3.5 µB and it is reduced to 2 µB in the final dissociated state. However, at variance with the Pd6 case, the change of magnetization precedes the dissociation of the molecule, as shown in Figure 2. This occurs for the molecules that dissociate rapidly after the impact with the cluster (Figure 2(a)) and also for those moving around the cluster during long times (Figure 2(b)). In both cases, once the change in the spin magnetic moment of the system takes place the molecule dissociates rapidly. Interestingly, such a reduction of the spin magnetic moment of the system that occurs while the H2 molecule is still bound is observed in all the dissociating trajectories, but not on those giving rise to reflection or molecular adsorption. This result suggests that the configurational space leading to H2 dissociation on Pd13 is associated to a reduction in the spin state of the system. In order to explain the different behavior observed in the two clusters, we have investi-



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gated the change in magnetic moment along minimum energy paths (MEP) for the dissociative adsorption of hydrogen on Pd6 and Pd13 . The respective calculated MEPs are shown in Figures 3 and 4. In both cases, the MEP begins with the hydrogen molecule far from the palladium cluster, then goes through an intermediate stage in which the H2 molecule is adsorbed on top of a Pd atom and ends with the hydrogen dissociatively chemisorbed on the palladium cluster. Two different reaction coordinates are considered along the path: (i) in the first part of the MEP (until the molecular adsorption of the hydrogen molecule takes place), the reaction coordinate is the distance between the center of mass of the hydrogen molecule and the Pd atom where the H2 adsorbs. (ii) In the second part of the MEP, leading to the dissociative chemisorption of hydrogen, the reaction coordinate is the distance between the two hydrogen atoms. Let us first focus on the Pd6 case. The magnetic moment of the clean (without hydrogen adsorbed) supported cluster is 2 µB . As the hydrogen molecule approaches the cluster, the magnetic moment remains constant equal to 2 µB . The molecule adsorbs on top of a Pd atom without changing the magnetic moment of the cluster. Then, the H-H distance increases and the molecule begins to dissociate. The magnetic moment maintains its value until the molecule reaches the top of the dissociation barrier. At that point the magnetic moment drops to zero and the dissociative chemisorption of hydrogen takes place with zero magnetic moment. This means that the magnetization of the system does not change until the hydrogen molecule is essentially dissociated (on the other side of the dissociation barrier), which explains the results obtained in the dynamical simulations. This behavior is in contrast with the case of Pd13 . The magnetic moment of the clean supported Pd13 cluster is 4 µB in our static calculations. Note that in the dynamical calculations the initial magnetic moment was 3.5 µB . The reason is that, as we show below, the energy difference between these two magnetic configurations is very small and, consequently, the slightly different magnetic ground state found in the two calculations can be attributed to the different computational settings (pseudopotential, cutoff energies, etc.). As we will see below, this difference barely affects the dissociation energetics. The triangular upper layer of


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Pd13 exhibits two distinct adsorption sites for molecular hydrogen: (i) the Pd atoms at the corners of the triangle and (ii) the Pd atoms at the middle of the edges of the triangle. When the hydrogen molecule adsorbs at the cluster in its molecular form (that is, non dissociated), two different spin states occur in the system depending on the adsorption site. Adsorption at the corners of the triangle leads to the high spin state (µ = 4µB ), whereas adsorption at the mid-edges leads to the low spin state (µ = 2µB ). The latter is the most stable configuration but the energy difference between the two configurations amounts to 0.087 eV only. As the hydrogen molecule approaches to Pd13 in the direction of a mid-edge Pd atom, the high spin configuration (4 µB ) of the clean Pd13 becomes unstable and the magnetic moment of the system drops to a value of 2 µB before H2 reaches the molecular adsorption site on top of that Pd atom (see Figure 4). Then, from this configuration, the dissociation of the hydrogen molecule takes place in this lower spin configuration almost spontaneously, that is, with a very small activation barrier of 0.03 eV. On the other hand, if the hydrogen molecule adsorbs in the high spin configuration on top of one of the corner Pd atoms, it can migrate to the mid-edge site finding an energy barrier of 0.27 eV between the two positions. Along with the diffusion of hydrogen on the surface of the palladium cluster, the system experiences a drop in the magnetic moment from µ = 4µB to µ = 2µB at approximately mid-path between the two adsorption sites. The MEP for the diffusion process, calculated using the nudged elastic band method, 25 together with the magnetic moments along the path, are shown in Figure 5. These static results are consistent with the results of the dynamical simulations. For the dissociation of H2 to occur it is necessary that the magnetic moment of the system changes from its initial value of 4 µB to the value that allows dissociation, 2 µB , which explains why in this case the change of magnetization precedes dissociation. Moreover, because in the case of molecular adsorption the most favorable magnetic state depends on the position and orientation of the molecule, the dissociation process can be fast (Figure 2(a)) or slow (Figure 2(b)), depending on the time required for the molecule to arrive at the configuration in which the low magnetic state is favorable.



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In Figure 6, the relation between the change of magnetization of the system and the dissociation process for H2 interacting with the Pd13 nanoparticle is displayed. The figure shows the potential energy of the system in the dynamical (AIMD) simulation run as a function of time (the continuous curve) compared to the potential energy for different magnetic states calculated at each point in the trajectory at the same configurations of the dynamical run. The constrained magnetic moments values considered are 4 µB (the high magnetic state in the static calculations), 3.5 µB (the high magnetic state in the dynamical calculations) and 2 µB (the low magnetic state), and the corresponding curves are the three dashed curves plotted in different colors. First of all, we observe that at times when the molecule is in nondissociated configurations the difference between the potential energies for magnetic moments 4 µB and 3.5 µB is very minor, which confirms that both the static and dynamical calculations give essentially the same description of the magnetism of the system in this initial regime. More important, we see that both for fast and slow dissociation processes the high magnetic state is slightly more favorable than the low magnetic state in the initial part of the trajectory (left side in the figures). Note that in this part of the trajectories the molecule is already adsorbed on the cluster but in positions and orientations for which the low magnetic state (2 µB ) has a higher energy. Then, at a certain time, the nondissociated H2 molecule arrives at a specific location of the cluster where the low magnetic state of the system is more favorable and, as a consequence, the magnetic moment of the system is reduced to 2 µB . After the system reaches this low magnetic state the molecule dissociates with no further change in its magnetic moment. The time to reach the low magnetic state is higher in the case of slow dissociation. Also, both panels of the Figure reveal that the dissociation of the H2 molecule occurs in a short time, about 10 fs after the magnetic transition. Another relevant question concerns the spatial distribution of the magnetic moments in the graphene-palladium-hydrogen systems. The local distribution of the magnetic moment is given by the difference between the electronic density with spin up (the majority spin), ρup ,


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and the electronic density with spin down (the minority spin), ρdown . Figures 7 and 8 show ρup − ρdown for the Pd6 and Pd13 systems, respectively. In the case of free palladium clusters, the magnetic moment is almost evenly distributed among all the atoms and there are no regions with an excess of electrons with the minority spin, which indicates a ferromagnetic type of behavior. Some structure, however, is apparent in the case of Pd6 where the electronic density around the two apex atoms of the octahedron is less spin-polarized than around the atoms of the square base (Figure 7(a)). When the clusters are supported on graphene, the magnetic moment remains localized in the palladium clusters whereas the graphene layer is almost perfectly spin compensated. In the case of Pd6 , the free and the supported clusters have the same magnetic moment and all the Pd atoms of the supported cluster present similar spin polarizations. In contrast, the magnetic moment of the supported Pd13 (4 µB ) is smaller than that of the free cluster (6 µB ). This drop in the magnetic moment is due to the reduction in the spin polarization of the Pd atoms in direct contact with the graphene layer, as Figure 8(b) shows. The molecular adsorption of hydrogen induces a reduction of the spin polarization at the adsorption site whereas the adsorbed hydrogen molecule remains perfectly spin compensated. In the case of Pd6 the local reduction of the spin polarization at the adsorption site is compensated by the other Pd atoms and the total magnetic moment of the system remains unchanged upon the molecular adsorption of hydrogen. However, in the case of Pd13 there is a further reduction of the spin polarization of the Pd atoms in direct contact with the graphene layer and, as a result, the magnetic moment drops from 4 to 2 µB upon the molecular adsorption of hydrogen. On the other hand, the dissociative chemisorption of hydrogen induces a reduction of the magnetic moment of Pd6 from 2 to 0 µB , i.e., the system becomes perfectly spin compensated. In contrast, the dissociative chemisorption of hydrogen does not change the magnetic moment of Pd13 (2 µB ), which remains the same as in the case of hydrogen adsorbed as a molecule. There is, however, a reduction of the spin polarization of the Pd atoms around the H adsorption sites with respect to the Pd cluster without hydrogen and the chemisorbed H atoms remain perfectly



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spin compensated. One interesting observation from the dynamical simulations presented above is that molecular adsorption of H2 on supported Pd6 leaves the magnetic moment of the cluster unchanged, and the ensuing H2 dissociation has to overcome an activation energy barrier of 0.3 eV. On the other hand, adsorption of H2 on supported Pd13 lowers the magnetic moment of the cluster, and the ensuing dissociation is practically barrier-less. The question arises if this behavior is general. Table 1 presents a compilation of results 15,24 from static calculations for supported Pd3 , Pd4 , Pd5 , Pd6 and Pd13 , showing the magnetic moment in different situations: 1) for Pdn deposited on graphene, 2) when hydrogen is adsorbed in molecular form, and 3) after dissociation of the adsorbed hydrogen molecule. Two groups can be clearly distinguished. The first one is formed by Pd4 , Pd5 and Pd6 . In this group, adsorption of molecular hydrogen does not change the magnetic moment of the cluster, and dissociation of the adsorbed molecule needs to surmount an activation energy barrier of 0.3 - 0.5 eV. Note that in this group dissociation induces the lowering of the magnetic moment. The second group is formed by Pd3 and Pd13 . Adsorption of molecular hydrogen induces a change of the magnetic moment of the cluster, and dissociation occurs with barriers of negligible magnitude and no further change of the cluster magnetic moment. Then, the behavior appears to be general. In short, when molecular adsorption induces a lowering of the cluster magnetic moment, the dissociation barrier then practically vanishes. The two clusters Pd6 and Pd1 3, for which the dissociative adsorption dynamics of H2 has been investigated in detail in this work, are, therefore, representative of the two groups in Table 1.

Conclusions Using DFT-molecular dynamics simulations and calculated minimum energy paths (MEP) we have investigated the interplay between magnetization and reactivity during H2 dissociation on Pd6 and Pd13 clusters supported on graphene. The effect of the H2 dissociation is to


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reduce the magnetic moments of both clusters by about 2µB , resulting in a spin-unpolarized Pd6 cluster, and a Pd13 cluster with a magnetic moment of 2µB . The main result is that spin quenching occurs at different stages of the reaction depending on the cluster size: Pd6 is demagnetized approximately 10 fs after the H-H bond breaking, whereas the Pd13 magnetization is lowered immediately before the molecule splits up. This shows that the relation between the dissociation process and the magnetization lowering depends on the cluster size, showing that the nature of the dissociation process is also different, and displaying well the main characteristic of the non–scalable regime of clusters, in which each atom counts. A close inspection of the reaction steps in the static and dynamic calculations reveals that in both systems dissociation proceeds from a molecular adsorption configuration where H2 stands upright on top of a Pd atom of the top layer of the cluster. In the Pd13 cluster this precursor configuration, which has the reduced magnetic moment of 2µB , occurs for H2 on a Pd atom in the middle position of the edges of the top cluster layer. The time spent by the molecule in arriving at this "bottleneck" configuration determines whether the dissociation of H2 on Pd13 is fast and direct, or slow and indirect. Unlike graphene-supported Pd6 , supported Pd13 shows a spatially inhomogeneous spin density, with lower spin densities on the Pd atoms at the Pd-C interface. For both clusters the effect of the molecular precusor state is to slighlty demagnetize the Pd atom bound to the hydrogen molecule, i.e. there is a ligand effect. This local perturbation is weaker and almost quenched in the Pd6 cluster, and the net magnetization does not change. On the contrary, Pd13 , because of its larger size, can sustain the additional inhomogenity caused by the molecule and the overall result is a reduction of the total magnetization. In summary, we have found that the mechanism leading to a lowering of the magnetic moment in graphene-supported palladium clusters promoted by H2 dissociative adsorption is dependent on the size of the clusters and it is correlated with the spin polarization of the molecularly adsorbed precursor state. One can think on the adsorption and dissociation of



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hydrogen as a practical tool to manipulate the magnetic state of clusters and nanoparticles supported on carbonaceous substrates, which could lead to interesting applications in devices.

Acknowledgement M. B. R., J. I. J. and M. A. acknowledge support by Basque Departamento de Educación, Universidades e Investigación, the University of the Basque Country UPV/EHU (Grant No. IT-756-13). J. A. A. and M. J. L. acknowledge support by Junta de Castilla y León (Grant No. VA050U14). The Spanish MINECO is acknowledged for Grants FIS2013-48286-C2-2-P (M. B. R., J. I. J. and M. A.), FIS2016-76471-P (J. I. J. and M. A.), FIS2016-75862-P (M. B. R.), and MAT2014-54378-R (J. A. A. and M. J. L.). The authors thankfully acknowledge the computer resources provided by the DIPC computing center, and also the facilities provided by Centro de Proceso de Datos - Parque Científico of the University of Valladolid.


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References (1) Martin, P. G.; Keogh, W. J.; Mandy, M. E. Collision-induced Dissociation of Molecular Hydrogen at Low Densities. Astrophys. J. 1998, 499, 793. (2) Ogden, J. M. Hydrogen: The Fuel of the Future? Phys. Today 2002, 55:4, 69–75. (3) Cabria, I.; López, M. J.; Alonso, J. A. In Handbook of Nanophysics, Vol. 5 (Functional Materials); Sattler, K., Ed.; CRC Press: Boca Ratón, FL, 2010; p 41.1. (4) Fuel Cell Handbook, 7th ed.; EG&G Technical Services, Inc., US DOE: Morgantown, West Virginia, 2004. (5) Antolini, E. Palladium in Fuel Cell Catalysis. Energy Environ. Sci. 2009, 2, 915–931. (6) Adams, B. D.; Chen, A. The Role of Palladium in a Hydrogen Economy. Mater. Today 2011, 14, 282 – 289. (7) Züttel, A. Materials for Hydrogen Storage. Mater. Today 2003, 6, 24 – 33. (8) Alonso, J. A.; Cabria, I.; López, M. J. Simulation of Hydrogen Storage in Porous Carbons. J. Mater. Res. 2013, 28, 589–604. (9) Gogotsi, Y.; Dash, R. K.; Yushin, G.; Yildirim, T.; Laudisio, G.; Fischer, J. E. Tailoring of Nanoscale Porosity in Carbide-Derived Carbons for Hydrogen Storage. J. Am. Chem. Soc. 2005, 127, 16006–16007, PMID: 16287270. (10) Contescu, C. I.; Brown, C. M.; Liu, Y.; Bhat, V. V.; Gallego, N. C. Detection of Hydrogen Spillover in Palladium-Modified Activated Carbon Fibers during Hydrogen Adsorption. J. Phys. Chem. C 2009, 113, 5886–5890. (11) Bhat, V. V.; Contescu, C. I.; Gallego, N. C.; Baker, F. S. Atypical Hydrogen Uptake on Chemically-Activated, Ultramicroporous Carbon. Carbon 2010, 48, 1331 – 1340.



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(12) Granja, A.; Alonso, J. A.; Cabria, I.; Lopez, M. J. Competition Between Molecular and Dissociative Adsorption of Hydrogen on Palladium Clusters Deposited on Defective Graphene. RSC Adv. 2015, 5, 47945–47953. (13) López-Corral, I.; Germán, E.; Juan, A.; Volpe, M. A.; Brizuela, G. P. DFT Study of Hydrogen Adsorption on Palladium Decorated Graphene. J. Phys. Chem. C 2011, 115, 4315–4323. (14) López-Corral, I.; Piriz, S.; Faccio, R.; Juan, A.; Avena, M. A Van der Waals DFT Study of PtH2 Systems Absorbed on Pristine and Defective Graphene. Appl. Surf. Sci. 2016, 382, 80–87. (15) Blanco-Rey, M.; Juaristi, J. I.; Alducin, M.; López, M. J.; Alonso, J. A. Is Spillover Relevant for Hydrogen Adsorption and Storage in Porous Carbons Doped with Palladium Nanoparticles? J. Phys. Chem. C 2016, 120, 17357–17364. (16) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15 – 50. (17) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558–561. (18) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Phys. Rev. B 1992, 46, 6671–6687. (19) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector AugmentedWave Method. Phys. Rev. B 1999, 59, 1758–1775.


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(20) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188–5192. (21) Methfessel, M.; Paxton, A. T. High-Precision Sampling for Brillouin-Zone Integration in Metals. Phys. Rev. B 1989, 40, 3616–3621. (22) Dacapo, See https://wiki.fysik.dtu.dk/dacapo for a description of the total energy code, based on the density functional theory. 2009. (23) Vanderbilt, D. Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism. Phys. Rev. B 1990, 41, R7892. (24) Cabria, I.; López, M. J.; Fraile, S.; Alonso, J. A. Adsorption and Dissociation of Molecular Hydrogen on Palladium Clusters Supported on Graphene. J. Phys. Chem. C 2012, 116, 21179–21189. (25) Henkelman, G.; Jóhannesson, G.; Jónsson, H. In Progress on Theoretical Chemistry and Physics; Swartz, S. D., Ed.; Kluwer Academic, 2000; Chapter 10. Methods for Finding Saddle Points and Minimum Energy Paths.



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Table 1: Magnetic moment (in units of µB ) in different situations: Pd cluster adsorbed on graphene (Pdn @G), with molecular hydrogen adsorbed (H2 ads), and with dissociated hydrogen (H+H ads). The dissociation energy barrier (Edis ) is also given. Pd3

Pd4

Pd5

Pd6

Pd13

µ [Pdn @G] µ [H2 ads] µ [H+H ads]

2 0 0

2 2 0

2 2 0

2 2 0

4 2 2

Edis (eV)

0

0.7

0.26

0.3

0. 03


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Figure 1: Time-evolution of the total magnetic moment of the system (left axis, black) and hydrogen molecule bond length (right axis, red) in an AIMD dissociation trajectory on graphene-supported Pd6 .



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Figure 2: Time-evolution of the total magnetic moment of the system (left axis, black) and the hydrogen molecule bond length (right axis, red) for two individual AIMD trajectories representative of the fast and slow H2 dissociation processes on graphene-supported Pd13 .


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 =2 B  =0 B

Figure 3: Minimum Energy Path, MEP, for the adsorption and dissociation of a hydrogen molecule on Pd6 supported on a graphene layer. The left panel shows the path for molecular adsorption (in the lowest-energy configuration), starting with the hydrogen molecule far from the palladium cluster and ending with the molecule adsorbed on top of a Pd atom, as a function of the distance between that Pd atom and the center of mass of the hydrogen molecule. The right panel shows the path for the dissociative chemisorption of hydrogen, starting from the molecule adsorbed on the Pd6 cluster, as a function of the H-H distance. The zero of energy is set for the configuration with the hydrogen molecule far from the supported Pd6 cluster. Blue and red curves correspond to the energies of the high-spin configurations (µ = 2µB ) and the low-spin configurations (µ = 0µB ), respectively. The crossing between the two curves on the right panel shows that the drop of the magnetic moment from 2 to 0 µB occurs when the hydrogen molecule has overcome the barrier for dissociation, that is, when it is already dissociated. Some configurations along the path are also shown as insets in the figure.



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 =4 B  =2 B

Figure 4: Minimum Energy Path, MEP, for the adsorption and dissociation of a hydrogen molecule on Pd13 supported on a graphene layer. The left panel shows the path for molecular adsorption (in the lowest-energy configuration), starting with the hydrogen molecule far from the palladium cluster and ending with the molecule adsorbed on top of a mid-edge Pd atom of the triangular upper layer, as a function of the distance between that Pd atom and the center of mass of the hydrogen molecule. The right panel shows the path for the dissociative chemisorption of hydrogen, starting from the molecule adsorbed on the Pd13 cluster, as a function of the H-H distance. The zero of energy is set for the configuration with the hydrogen molecule far from the supported Pd13 cluster. Blue and red curves correspond to the energies of the high-spin configurations (µ = 4µB ) and the low-spin configurations (µ = 2µB ), respectively. The crossing between the two curves on the left panel shows that the drop of the magnetic moment from 4 to 2 µB occurs before the molecule begins to dissociate. Some configurations along the path are shown as insets in the figure.


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 =4 B  =2 B

Figure 5: Minimum Energy Path, MEP, for the diffusion of a hydrogen molecule on Pd13 supported on graphene, calculated using the nudged elastic band technique. The extreme configurations of the path are: (i) molecular hydrogen adsorbed on top of a Pd atom at the corner of the triangular upper layer of Pd13 (high-spin configuration) and (ii) molecular hydrogen adsorbed on top of a Pd atom at the mid-edge of the triangular upper layer of Pd13 (low-spin configuration). The latter structure is the most stable configuration for molecular adsorption. Blue and red curves correspond to the energies of the high-spin configurations (µ = 4µB ) and the low-spin configurations (µ = 2µB ), respectively.



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Figure 6: Potential energies (left axis, solid black) and H-H interatomic distance (right axis, solid red) sampled during two AIMD trajectories representative of the fast and slow dissociation processes on Pd13 supported on graphene. The dashed curves correspond to the potential energies of the visited geometries calculated with various constrained values of the total magnetic moment µ.


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a)

b)

2 B

c)

2 B

d) 2 B

0 B

Figure 7: Spin density difference (ρup − ρdown ) of free Pd6 (a), Pd6 supported on a graphene layer (b) and hydrogen adsorbed on the supported palladium cluster in the molecular (c) and dissociative (d) forms. The green isosurfaces correspond to excess of spin up electrons (positive spin density difference = 0.007 e/au3 ) and the orange isosurfaces correspond to excess of spin down electrons (negative spin density difference = −0.007e/au3 ). The absence of contours in (d) shows perfect spin compensation in the whole system. The total magnetic moments are indicated in the figure. Grey, blue and yellow balls represent C, Pd and H atoms, respectively.



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a)

b)

6 B

c)

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4 B

d) 2 B

2 B

Figure 8: Spin density difference (ρup −ρdown ) of free Pd13 (a), Pd13 supported on a graphene layer (b) and hydrogen adsorbed on the supported palladium cluster in the molecular (c) and dissociative (d) forms. The green isosurfaces correspond to excess of spin up electrons (positive spin density difference = 0.007e/au3 ) and the orange isosurfaces correspond to excess of spin down electrons (negative spin density difference = −0.007e/au3 ). The total magnetic moments are indicated in the figure. Grey, blue and yellow balls represent C, Pd and H atoms, respectively.


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TOC Graphic

2 B

2 B

0 B

Magnetization along the dissociation path 4 B

2 B

2 B



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ACS Paragon Plus Environment

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 =2 B  =0 B


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 =4 B  =2 B



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a)

b)

2 B

c)

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2 B

d) 2 B


0 B

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a)


b)

6 B

c)

4 B

d) 2 B


2 B


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2 B

2 B

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0 B

Magnetization along the dissociation path 4 B

2 B


2 B

Manipulating the Magnetic Moment of Palladium ... - ACS Publications

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