Extended atomic hydrogen dimer configurations on

THE JOURNAL OF CHEMICAL PHYSICS 131, 084706 共2009兲

Extended atomic hydrogen dimer configurations on the graphite„0001… surface Ž. Šljivančanin, E. Rauls,a兲 L. Hornekær, W. Xu, F. Besenbacher, and B. Hammerb兲 Interdisciplinary Nanoscience Center (iNANO) and Department of Physics and Astronomy, University of Aarhus, DK 8000 Aarhus C, Denmark

共Received 19 February 2009; accepted 2 July 2009; published online 25 August 2009兲 We present density functional theory calculations and scanning tunneling microscopy experiments investigating the structures and kinetics of extended hydrogen dimer configurations on the graphite 共0001兲 surface. We identify several hydrogen dimer structures where surface mediated interactions between the two hydrogen atoms lead to increased binding energy even at interatom separations as large as 7 Å. By modeling the formation of dimers as sequential adsorption of hydrogen atoms, we find that these dimer configurations exhibit decreased barriers to sticking for the second H atom, compared to the sticking barrier of an H atom on the clean surface. According to our calculations, the activation energies for desorption of a single H atom from any of the experimentally observed extended dimers are higher than the barriers for diffusion to the paradimer configuration. Consequently, molecular hydrogen formation out of the extended dimer structures takes place via diffusion over the paradimer configuration. © 2009 American Institute of Physics. 关DOI: 10.1063/1.3187941兴 I. INTRODUCTION

Adsorbate structures and kinetics of atomic hydrogen on the graphite共0001兲 surface has been studied extensively due to both its fundamental interest and its relevance in connection with interstellar molecular hydrogen formation, hydrogen storage, and plasma fusion devices. The existence of a chemisorbed state of hydrogen on graphite has been demonstrated both experimentally and theoretically.1–4 Calculations show that a hydrogen atom can bind on top of a carbon atom with a binding energy of ⬃0.7 eV. The carbon atom on which the hydrogen atom binds puckers out of the surface by ⬃0.3 Å. Due to the puckering a barrier of 0.2 eV exists to enter into the chemisorbed state.2,3 Ultraviolet photon spectroscopy1 and scanning tunneling microscopy 共STM兲共Ref. 5兲 experiments demonstrated the existence of chemisorbed hydrogen atoms on the graphite surface, while high resolution electron energy loss spectroscopy experiments4 corroborate the theoretical predictions regarding the energetics of the binding states of individual hydrogen atoms. Formation of molecular hydrogen from chemisorbed atomic hydrogen on graphite has been observed in temperature programmed desorption 共TPD兲 measurements4 and via Eley–Rideal processes.6 The Eley–Rideal abstraction process between an adsorbed hydrogen atom and an incoming gas phase hydrogen atom has been the subject of intense theoretical studies, involving both abstraction from physisorbed7 and chemisorbed7–9 states. Eley–Rideal reactions involving chemisorbed hydrogen atoms have been observed to occur with a large cross section in experiments6 and the internal a兲

Present address: Physics Department, Faculty of Natural Sciences, University of Paderborn, D-33098 Paderborn, Germany. b兲 Author to whom correspondence should be addressed. Electronic mail: [email protected]. FAX: ⫹45 8612 0740. 0021-9606/2009/131共8兲/084706/6/$25.00

state distribution of hydrogen molecules formed on the graphite surface via Eley–Rideal or hot atom mechanisms has been measured.10 TPD measurements show molecular hydrogen formation from chemisorbed hydrogen atoms at temperatures of 400–600 K.4 The formed hydrogen molecules immediately desorb exhibiting a hyperthermal kinetic energy distribution.11 The TPD spectra exhibit several interesting features such as a first order desorption behavior and several desorption peaks. The first order desorption behavior indicates that the H2 formation process is not a standard diffusion mediated Langmuir–Hinshelwood mechanism. This is further corroborated by the theoretical finding that the diffusion barrier of an isolated H atom on the graphite surface is higher than 1 eV and thereby exceeds the binding energy of the H atom in the chemisorbed state making diffusion unlikely.12,13 An explanation of the first order desorption behavior in the TPD spectra is offered by the experimental finding that hydrogen atoms preferentially stick into hydrogen dimer 共or larger兲 structures on the graphite surface.13–15 Density functional theory 共DFT兲 calculations substantiate this finding by showing that the barriers to hydrogen atom sticking on graphite are reduced and in some cases even vanishing in the vicinity of already chemisorbed H atoms.13,16 Kinetic Monte Carlo simulations show how this can result in prepairing of hydrogen atoms on the graphite surface.17 This results in an H2 formation process, which is governed by the energetics and kinetics of these preformed hydrogen atom dimer or cluster structures. Hence the first order behavior observed in the TPD spectra is governed by the barriers to H2 formation from these preformed dimer and cluster structures and the multiple peaks observed in TPD are caused by the existence of different dimer and cluster structures on the surface with varying barriers to H2 formation.18

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O

M

P

MO

OP

MP

MM

OPO

POM

POP

FIG. 1. Hydrogen atom dimer configurations on the graphene surface.

Numerous theoretical attempts have been made to determine which hydrogen dimer structures are the most stable on the graphite surface. These attempts focused on dimer structures with a small separation between the two H atoms in the dimer, most notably on the ortho-共nearest neighbor兲 dimer, the meta-共next nearest neighbor兲 dimer, and the paradimer 共two H atoms on opposite sides of a carbon hexagon兲, see Fig. 1. Several calculations have shown that the binding energy of the orthodimer exceeds the binding energy of two separately adsorbed H atoms by roughly 1 eV.13,16,18–20 These calculations also show that the binding energy of the metadimer is comparable to the binding energy of two separately adsorbed H atoms. Calculations furthermore show that the paradimer has a binding energy, which is comparable to the binding energy of the orthodimer.13,16,18 By comparison between STM images and simulated images based on DFT calculations both the para- and the orthodimer have been identified experimentally and have been observed to be the most numerous hydrogen dimer structures on graphite.18 However, other authors reported STM experiments where the most numerous dimer structures were determined to be the paradimer and some dimer structures with even larger H atom separation.14 In these experiments no comparison between STM images and simulated images were made, mak-

ing the identification of the dimer structures rather uncertain. Furthermore, in these experiments the samples were exposed to air following the H atom deposition but prior to the STM measurements. This procedure is in contrast with the procedure followed in Ref. 18 where H atom deposition and STM experiments were performed in the same ultrahigh vacuum 共UHV兲 chamber. The possible effect of air exposure to H atom adsorbate structures on graphite is unknown. These conflicting findings point to the need of investigating in greater detail the energetics and kinetics of hydrogen dimer structures on the graphite surface and to include in these investigations dimer structures with a larger interatom separation than in previous studies. In the following we present DFT calculations investigating the binding energies and adsorption barriers for such extended hydrogen atom dimer structures on the graphite surface and contrast these findings to the experimental evidence found in STM measurements. We show that for some configurations surface mediated interactions between the two hydrogen atoms in a dimer configuration cause increased binding energies even at interatom separations as large as 7 Å. STM experiments reveal that a wide range of different hydrogen dimer configurations exists on the graphite surface, but that some specific dimer states are the most abundant. In accord with earlier findings18 we identify these states as the paradimer and orthodimer states. Due to the energetics and kinetics, specific dimer states will have increased probability for formation and increased stability against diffusion, recombination, and desorption and will therefore dominate in numbers. Based on DFT calculations we identify the most stable dimer states as the para- and orthodimer states. The calculations also reveal that four other, more extended, dimer states, while not quite as stable as the ortho- and paradimer states, have increased formation probability and binding energy compared to isolated chemisorbed H atoms. II. THEORETICAL AND EXPERIMENTAL METHODS

The DFT calculations were performed with the plane wave based DACAPO program package,21,22 applying ultrasoft pseudopotentials23,24 to describe electron-ion interactions and the Perdew–Wang functional 共PW91兲 for the electronic exchange correlation effects. The electron wave functions and augmented electron density were expanded in plane waves with cutoff energies of 25 and 140 Ry, respectively. The graphite surface was modeled by periodically repeated rhombohedral super cells containing one graphite sheet. The sheets were separated by 15 Å of vacuum. These supercells equally well model graphene and are henceforth referred to as such. The binding energy of the H monomer and dimer configurations to the graphene was carefully tested with respect to the simulation cell size using up to 98 carbon atoms per cell and with respect to the number of k-points for which the Chadi–Cohen scheme25 was used. The number of special points used to sample the entire surface Brillouin zone are given in Tables I and II. All atoms were relaxed using the Broyden–Fletcher– Goldfarb–Shanno algorithm.26 The potential energy curves for adsorption of H atoms on graphite surfaces were calcu-


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Extended hydrogen dimers on graphite共0001兲

TABLE I. Binding energies 共in eV兲 of hydrogen monomers adsorbed on graphene as a function of the simulation cell size and the number of k-points used to sample the Brillouin zone. No. of k-points Cell size 2⫻2 3⫻3 4⫻4 5⫻5 6⫻6 7⫻7

共8 C atoms兲共18 C atoms兲共32 C atoms兲共50 C atoms兲共72 C atoms兲共98 C atoms兲

6

18

54

162

0.38 0.63 0.67 0.73 0.77 0.78

0.80 0.80 0.80 0.80 0.81 0.82

0.82 0.81 0.81

0.83

lated applying the nudged elastic band method.27 These calculations were done using spin-polarized DFT. Simulated STM images were constructed as topographs of constant local density of states, ␳共x , y , z , ␧兲 = ␳0.28 All experiments were performed in an UHV system 共base pressure of 3 ⫻ 10−10 Torr兲 equipped with a home built Aarhus STM.29 Highly ordered pyrolytic graphite 共HOPG兲 samples were cleaved in air immediately prior to being inserted into the UHV chamber. In vacuum the samples were annealed to 1300 K by electron bombardment of the backside of the sample to desorb any hydrogen or oxygen species bound at the surface and at step edges or defects. Atomic hydrogen/deuterium dosing was performed using a hot 共1600–2200 K兲 hydrogen atom beam source 共Either HABS 40 from MBE Komponenten or a similar Jülich type source30兲. In the majority of the experiments, deuterium atoms were used to obtain a better signal to background ratio in thermal desorption spectroscopy 共TDS兲 experiments. III. THEORETICAL RESULTS

Our calculated binding energies of the monomeric hydrogen atom adsorbed on the graphene sheet are shown in Table I. From the table, it is seen that as long as the Brillouin TABLE II. Binding energies 共in eV兲 of different configurations of hydrogen dimers, as a function of the simulation cell size and number of k-points used to sample the Brillouin zone. The last column is to be considered the most accurate. The binding energies are given relative to the energy of two H atoms in the gas phase. Extended dimer configurations identified experimentally in Fig. 5 have their formation energies underlined.

Config.

6 ⫻ 6 cell

7 ⫻ 7 cell

No. of k-points

No. of k-points

6 O M P MO OP MP MM OPO POM POP

2.73 1.58 2.68 1.72 1.52 2.07 1.57 1.84 1.55 2.09

18 2.76 1.65 2.72 1.78 1.58 2.13 1.65 1.88 1.62 2.17

6 2.73 1.60 2.70 1.74 1.56 2.10 1.59 1.91 1.56 2.04

18 2.75 1.65 2.72 1.81 1.61 2.14 1.65 1.96 1.62 2.08

zone is sampled with a sufficient number of k-points there is essentially no influence of the cell size on the calculated binding energies. The converged binding energy is about 0.8 eV per hydrogen atom relative to the hydrogen atom in the gas phase. The hydrogen dimer configurations on the graphene surface considered in this work are displayed in Fig. 1. Binding energies have already been reported for some of these configurations in several recent publications.31–34 Yet, due to different methods and the computational setups used in these studies, the calculated results vary significantly. Hence, one of the main aims of the present investigation is to clarify the influence of the unit cell size and the number of k-points on the calculated binding energies of H dimers chemisorbed on graphene and to produce relatively well converged values. Our results are presented in Table II for two different cell sizes and two different number of k-points. The binding energies in the table are given with respect to the energy of two H atoms in the gas phase whereby binding energies exceeding ⬃1.6 eV 共=2 ⫻ 0.8 eV, cf. Table I兲 reflect stronger bonding than for two isolated chemisorbed H atoms. The notation adopted for different configurations is inspired by vector algebra. Using the orthodimer, O, the paradimer, P, and the metastable configuration in between, M, as the “basis,” all other dimer configurations are represented as their linear combinations 共e.g., MO= M + O, POP= P + O + P, etc.兲 The para- and orthodimer are observed to be the two dimer configurations with highest binding energy. However, three other dimer configurations with increased interatomic separations also show markedly increased binding energies. These are the POP, MP, and OPO dimer configurations. Furthermore, the MO dimer configuration displays a slightly increased binding energy of ⬃0.2 eV compared to two isolated chemisorbed H atoms. In agreement with the results of Refs. 33 and 34 the ferromagnetic configuration is observed for the M, OP, MM, and POM dimer structures. The others are nonmagnetic. In order to understand the strong bonding found for several hydrogen dimers, we examined two main effects of the interaction: 共i兲 the deformation of the graphite surface due to hydrogen adsorption and 共ii兲 the adsorbate induced changes in the electronic structure. The surface deformation energies are obtained by removing the adsorbates from the surface and comparing total energies of the surface prior to and after the full geometry optimization. The results, given in Table III, show that the deformation energy per adsorbed H atom varies less than 0.2 eV. Thus, it cannot account for the large variation in binding energies among the different dimer structures. We therefore focused on changes in the electronic structure of the surface upon hydrogen adsorption and their effect on the stability of the dimer structures that will be formed. Adsorption of a single H atom on graphene changes the electronic properties of the surfaces considerably, with a pronounced effect on the reactivity of the surface. This is demonstrated in Fig. 2, which shows a contribution to the local density of states of the H monomer on the graphene surface, resulting from the states in the vicinity of the Fermi energy. In contrast with the clean graphene surface, where the electronic properties of all C atoms are identical, at the


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TABLE III. The graphene surface deformation energies Edef. 共in eV per H atom兲 calculated for the hydrogen monomer and all dimer structures shown in Fig. 1. Conf. Edef. 共eV/H兲

Mono

O

M

P

MO

OP

MP

MM

OPO

POM

POP

1.0

1.14

1.01

1.05

0.99

0.96

1.04

0.98

1.01

0.98

1.03

surface with a preadsorbed H atom the local density of states varies significantly. This gives rise to different interactions with the 1s orbitals of the second H atom deposited on the surfaces, enabling formation of several favorable dimer structures. The most stable ortho- and parastructures are indeed formed when the second H atom is adsorbed at the C sites with the highest local density of states. Other favorable structures 共the POP, MP, and OPO兲 are also observed for C atoms with enhanced local density of states. An increase in the stability of the dimer structures due to hydrogen induced changes in the graphene electronic properties has already been suggested by Casolo et al.34 They correlated the H dimers binding energies with the local magnetization of the relevant C atoms. Similar conclusions were drawn by Ferro et al.33 Casolo et al.34 found that the dimer structures where both H atoms are adsorbed on the C atoms belonging to the same graphite sublattice are magnetic, which is confirmed in the present study. The gain in the total energy due to spinpolarization effects is given in Table IV for four ferromagnetic dimer configurations. The spin-polarization effects are rather small 共0.12 eV or less兲 compared to the total H binding energies. In addition, these dimer structures are less favorable than those where hydrogens adsorb on the C atoms from different graphite sublattices. Only such H dimers are experimentally observed and all of them are nonmagnetic. Therefore, we conclude that the spin-polarization effects are not essential for the correct reproduction of the trends in the stability of the hydrogen dimers on the graphite/graphene. In Fig. 3 the potential energy curves for H adsorption on graphene are given. For H adsorbing on the bare surface, and forming the monomer, we find a barrier of ⬃0.25 eV. For H

O POP MP

OPO

P

adsorbing on a graphene surface already containing one H atom 共thereby forming H dimers兲, we find barriers in the range from 0 eV 共paradimer兲 to 0.2 eV 共OPO dimer兲. Hence, all dimer configurations considered exhibit reduced barriers to sticking, compared to the value calculated for the isolated H atom. Similar results for O and P dimers were already reported by Rougeau et al.16 They also discussed the role of the spin configuration on the produced potential energy curves. For all five paths in Fig. 3 related to the H sticking on the graphene surface with preadsorbed H atom, we found that the most favorable spin configuration is antiferromagnetic, as long as the approaching H atom has not formed a strong chemical bond to the surface. When such a bond forms near the final states on the sticking curves, the electronic ground state becomes nonmagnetic since the hybridization of the H 1s and the C 2p states quenches the magnetism. Based on sticking probabilities, the paradimer is expected to be the one most likely to form on the surface followed by the ortho-POP and MP dimers. Of course any imaginable dimer configuration is expected to be able to form on the surface due to the finite probability for a hydrogen atom to stick on top of any carbon atom on the graphite surface. In our previous study18 it was shown that the paradimer exhibits the lowest barrier, 1.4 eV, for recombination. The direct recombination from the orthodimer to the H2 molecule is unlikely due to the high energy barrier of 2.5 eV. Instead, the orthodimer diffuses over the metadimer to the paradimer and then recombines. To investigate the stability of the different dimer configurations with respect to diffusion and molecular hydrogen formation, we calculated reaction paths for H2 formation from several stable dimer structures. The results are shown in Fig. 4. It is assumed that only diffusion events where one hydrogen atom moves to a neighbor carbon atom are allowed 共i.e., diffusion across carbon hexagons and diffusion involving simultaneous movement of two H atoms are not allowed兲. Furthermore, we assume that molecular hydrogen formation will only occur via the paradimer configuTABLE IV. The gain in the dimer binding energies 共in eV兲 due to the spin-polarization effects calculated for the ferromagnetic dimers. The results are given as a function of the simulation cell size and number of k-points used to sample the Brillouin zone.

Config. FIG. 2. Isosurface plot of the local density of states for a system composed of an H atom adsorbed on a graphene surface. The local density of states has been integrated over an energy interval around the Fermi level, EF ⫾ 0.1 eV. The blue sphere marks the position of the H atom and the arrows indicate the dimer configurations formed when a second H atom is adsorbed on the surface.

M OP MM POM

6 ⫻ 6 cell

7 ⫻ 7 cell

No. of k-points

No. of k-points

6 0.11 0.12 0.06 0.05

18 0.10 0.12 0.06 0.04

6 0.08 0.09 0.02 0.02

18 0.07 0.09 0.02 0.01


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Extended hydrogen dimers on graphite共0001兲

0,5 monomer

O

POP

P

MP

OPO

(a)

(b)

(c)

(d)

(e)

(f)

Energy (eV)

0 -0,5 -1

AMP

APOP AO

-1,5

AOPO

AP

5Å

-2 Reaction coordinate (arb. units)

FIG. 3. Potential energy curves for sticking of one hydrogen atom on the graphene surface. The first curve shows sticking on a pristine graphene surface. The following curves show sticking on surfaces already containing one H, thereby forming the ortho-共O兲, para-共P兲, and three extended dimer configurations: POP, MP, and OPO. All calculations are done with the 共6 ⫻ 6兲 unit cell and six k-points. The offset, A, of the energy of the final dimer state from the dashed line represents the dimer formation energy relative to two isolated adsorbed monomers. We have AO = 1.19 eV, A P = 1.14 eV, A POP = 0.55 eV, A MP = 0.53 eV, and AOPO = 0.30 eV.

ration as described in Ref. 18, since this is the only identified configuration where H2 formation has a lower barrier than diffusion into other dimer configurations. For the POP and MP dimmers, we find barriers to desorption of a single hydrogen atom of ⬃1.5 eV and the barriers to diffusion out of the dimer configuration of ⬃1.3 eV. For the OPO dimer we find a desorption barrier for one hydrogen atom of 1.25 eV and a barrier to diffusion of 1.2 eV. Since for all extended dimers with increased binding energy we find diffusion pathways ending in the paradimer configuration with diffusion barriers lower than the 1.4 eV, we conclude that they also recombine from the paradimer configuration, as shown in Fig. 4.

a) 1.26

POM

POP

0.32

1.30 OP

0.65

1.40

MP

P

b) 1.20

H 2 (g)

1.40

OPO P

H 2 (g)

0.50

c) M 1.63 O

1.40 P

5Å

FIG. 5. Comparison between simulated images and STM images of dimer structures on the graphite surface. 共a兲 MP dimer, 共b兲 OPO dimer, and 共c兲 POP dimer. 共d兲–共f兲 STM images of hydrogen adsorbate configurations on the graphite 共0001兲 surface. Imaging parameters: 共d兲 It = −0.58 nA, Vt = −312 mV, 共e兲 It = −0.45 nA, Vt = −1250 mV, 共f兲 It = −0.43 nA, and Vt = −1250 mV.

IV. EXPERIMENTAL RESULTS

In Fig. 5 simulated STM images of the three extended dimer configurations with increased binding energy are compared to STM images of experimentally observed extended dimers. Figures 5共a兲–5共c兲 show simulated STM images of the MP, OPO, and POP dimer configurations. Figures 5共d兲–5共f兲 show experimentally observed STM images of extended dimers on the HOPG共0001兲 surface after a 1 min dose of D atoms at 2200 K onto a room temperature HOPG sample. In accord with earlier observations, the bright protrusions are ascribed to chemisorbed deuterium atoms, as they only appear after D dosing and their presence correlates with the D2 desorption peaks observed in the TDS spectra.18 The deuterium atoms are not observed to diffuse at room temperature. Based on comparison with the simulated STM images we present the observed dimers in Figs. 5共d兲–5共f兲 as candidates for the MP, OPO, and POP dimer configurations. A wide range of dimer and cluster configurations of H共D兲 atoms are observed, in good agreement with the observation that H共D兲 atoms have a finite probability to stick into any position on the surface. However, the paradimer configuration 共characterized by high binding energy and no sticking barrier兲 is observed to be the dominant structure. V. CONCLUSION

0.32

OP

5Å

H 2 (g)

FIG. 4. Potential energy diagram showing the recombination mechanisms of various dimer configurations: 关共a兲 and 共b兲兴 extended dimers POP, MP, and OPO identified in this work. 共c兲 The corresponding results for short dimers O, M, and P from Ref. 18. All energies are in eV.

We identified a number of extended hydrogen dimer configurations on the graphite 共0001兲 surface with increased binding energy compared to the binding energy of two isolated adsorbed hydrogen atoms. The DFT calculations reveal that for all these extended dimer configurations the second H atom experiences reduced barriers to adsorption relative to the sticking of an H atom on the pristine surface. None of these extended dimers show binding energies as high as the previously identified ortho- and paradimer configurations. The extended dimers experience energy barriers for reconfiguration via H atom diffusion in the range 1.2–1.3 eV. The kinetic stability of the extended dimers is thus smaller than that of the ortho- and paradimers, as the barrier for the diffusion causing the orthodimer to evolve into the paradimer is 1.6 eV and as the barrier for the H2 formation and desorption from the paradimer is 1.4 eV. The small barriers found for the H diffusion causing the extended dimers to transform


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into the paradimer configuration indicate that for all dimer configurations, molecular hydrogen formation will take place via diffusion over the paradimer configuration. ACKNOWLEDGMENTS

This work was supported by the Danish Ministry of Science, Technology, and Innovation through the iNANO center, the Danish Research Councils, and the Danish Center for Scientific Computing. 1

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