The Reactivity of Substrate-Supported Graphene: A Case Study of

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The Reactivity of Substrate-Supported Graphene: A Case Study of Hydrogenation Himadri R. Soni, Julian Gebhardt, and Andreas Gorling J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11220 • Publication Date (Web): 21 Dec 2017 Downloaded from http://pubs.acs.org on December 22, 2017

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The Journal of Physical Chemistry

The Reactivity of Substrate-Supported Graphene: A Case Study of Hydrogenation Himadri R. Soni,∗,† Julian Gebhardt,‡ and Andreas Görling† †Chair of Theoretical Chemistry, Friedrich-Alexander University of Erlangen-Nuremberg, Egerlandstrasse 3, D-91058 Erlangen, Germany. ‡Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, United States E-mail: [email protected] Phone: +49 9131 85 27347. Fax: +49 9131 85 27736 Abstract Using density-functional theory, we study the adsorption and reaction of hydrogen and single-sided graphene. This is a graphene sheet that is accessible for chemical reaction from only one side, whereas the other side is occupied by a substrate. Motivated by our earlier study on the hydrogenation and dehydrogenation of graphene on Ni(111), we choose graphene on Ni(111) as well as a system intercalated by gold, as representative models for strongly and weakly interacting surfaces and compare it with the free-standing reference case. We demonstrate that the structural alignment of graphene on a substrate and the substrate itself, both play a major role on the reactivity of metal supported graphene, drastically changing the obtained reaction patterns and expected maximal coverages. Specific substrates can stabilize reaction patterns that would otherwise lead to unfavorable spin structures. We present a systematic way of studying the reactivity of such single-sided graphene,

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which is not limited to hydrogenation on the selected substrates, but should also be applicable to predict the reactivity of graphene supported by other substrates and towards other reagents.

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Introduction Graphene is an outstanding material, possessing a variety of interesting and unique properties, both from an academic and a technological point of view. 1 However, after more than a decade of intensive research on graphene (most of the times graphene supported by a substrate, rather than free-standing graphene) under mostly physical aspects, it seems that it is time to also discover this exceptional material from a traditional chemical point of view, i.e., the reactivity of graphene towards other compounds. Of course, with the structural doping, 2–6 the deposition of physisorbed compounds, 7–10 and even the investigation of the interplay between graphene and a substrate, 11,12 steps into this direction have already been taken in the past. However, the covalent functionalization of graphene seems to be still in its infancy, and many interesting effects of it on graphene’s electronic, magnetic, optical, and chemical properties can be envisioned. 13 Furthermore, chemical effects such as the enhancement of hydrogen and CO2 capture by carbon vacancies are possible. 14,15 The most straight-forward element to react with a carbon compound is hydrogen and it is, therefore, no surprise that already a number of studies addressed the hydrogenation of graphene as a first example for covalent functionalization. 16 A hydrogen atom being covalently bound to a graphene network changes the hybridization of the carbon atom it is bound to formally from sp2 to sp3 , which is accompanied by an out-of-plane bending of the hydrogenated carbon atom with respect to the graphene sheet. 17 In the hypothetical case of free-standing graphene, further hydrogenation occurs in an alternating pattern from both sides of the two-dimensional graphene sheet (trans-reactivity), forming socalled graphane at the maximal coverage of one monolayer. Here and in the following, a monolayer is defined as a coverage of two hydrogen atoms per graphene unit cell, i.e., one hydrogen atom per carbon atom of graphene. 17,18 The geometrical changes upon hydrogenation are accompanied by a change of the electronic structure; a transition from the band-gap-less semiconductor graphene 19 towards the insulating graphane, with a band

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gap of 3.5 eV, 18 is observed. Considering more practical experiments, the first step for a covalent functionalization of graphene is its fabrication. Although methods exist that create free-standing graphene membranes 20 or dissolved graphene sheets in solution, 21 it is still most likely to find graphene adsorbed on top of some substrate. Especially metal substrates have been used for that purpose in the past, showing excellent chemical-vapor deposition growth of high quality graphene. 22,23 However, such a situation, i.e., graphene on a substrate, is likely to behave different from the above free-standing graphene, as one side of the graphene sheet is occupied by the substrate. Of course, the accessibility of the side of the graphene sheet that is oriented towards the substrate depends on the strength of the graphene-substrate interactions, and examples exists where these interactions are weak. In such a case, e.g., if a layer of gold atoms is intercalated between graphene and a Ni(111) support, 5,24 a reactant, added afterwards, can indeed interact with (and gain access to) the graphene surface that is oriented towards the substrate side. Nevertheless, there has to be a distinct driving force for such a reaction, because i) the graphene-substrate interactions have to be overcome and ii) their might be reactions competing with the reactivity of the substrate side of graphene that are energetically more favorable, such as the recombination of atomic to molecular hydrogen in the case of hydrogenation. 25 The latter point is emphasized by the observed hydrogen intercalation of graphene and h-BN on Pt(111) when dosing the metal supported monolayers with molecular instead of atomic hydrogen. 26 For the hydrogenation on only one graphene surface (cis-reactivity), several alternative structures were proposed and investigated. Hydrogenation by 0.5 ML was first proposed in an alternating fashion, hydrogenating only carbon atoms of the same sublattice. 27,28 It was shown 29,30 that such a material, denoted ”graphone”, is thermodynamically not stable for free-standing graphene compared to mixed hydrogenation on both carbon sublattices due to the (infinite) large magnetic moment of free-standing graphone. 25 On a Ni(111) surface, however, we showed that graphone is stabilized by substrate effects and that it can be fabricated with hydrogen coverages up to 0.5 ML. 25 In recent studies, 31,32 4


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this concept was applied to CO adsorption on nickel supporting graphene, showing that Ni(111) as substrate enhances the reactivity of graphene due to charge hybridization. This already shows that substrates can have a severe effect on the graphene reactivity, beyond the mere blocking of one side of the graphene surface. This becomes even more evident by the reported hydrogenation of gold intercalated graphene/Ni(111). 16 After intercalation, the maximally achieved hydrogen coverage is only half (0.25 ML) compared to what can be reached before gold intercalation, and a different hydrogen arrangement was proposed. 16 The above examples show that substrates play an important role for the graphene reactivity. Even more, one substrate is likely to be different from another, i.e., every case has to be treated with special care and individually. In this report we address this by investigating the reactivity of one-sided, substrate supported graphene, proposing a systematical approach in order to determine the most likely adsorption patterns for different substrates. Hydrogen serves as exemplary chemical probe. Starting from the low coverage regime, we first identify the thermodynamically most stable adsorption site. Next, we compare the different possibilities that a second hydrogen atom has for adsorption. There, one may distinguish reactions with respect to the carbon sublattices that are functionalized (two possibilities) or the relative position to the first hydrogenation site (three possibilities within the same carbon hexagon). We further show, that in our examples, adsorption patterns for subsequent functionalization can be derived from the behavior of this first pair, i.e., structural arrangements in the high coverage regime are in line with, and the consequence of, observations made at low coverages. As substrates, we chose vacuum, Ni(111), and Au/Ni(111) respectively for a strongly and a weakly interacting substrate, as well as the free-standing model case. For Ni(111), we show that even the alignment of the graphene sheet with respect to the surface has a severe effect on the resulting functionalization pattern. The gold intercalated system behaves completely different, giving a possible explanation for the experimentally found reduced maximal coverage.

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Computational Details We applied spin-polarized density-functional theory (DFT) as implemented in the Vienna Ab initio Simulation Package, 33 which employs a plane-wave basis set and the projector augmented-wave method. 34 The applied Perdew-Burke-Ernzerhof exchange-correlation functional 35 was supplemented by the D3 van der Waals correction 36 (including BeckeJohnson damping) 37 to take dispersive forces into account. An energy cutoff of 415 eV was used in conjunction with a Methfessel Paxton smearing 38 of order one with 0.01 eV half-width. Vacuum layers of 15 ˚ A decouple periodic images from each other along the z direction. The Brillouin zone (BZ) was sampled by 5 × 5 × 1 Monkhorst-Pack k-point grids 39 for hexagonal (4 × 4) unit cells and 5 × 7 × 1 grids for rectangular (4 × 2) unit cells. Both unit cells contain 32 carbon atoms and, therefore, hydrogen coverages are directly comparable. Electronic structures and geometries were converged below 1 × 10−6 eV and 0.01 eV˚ A−1 with respect to total energies and forces acting on ions, respectively. For the hydrogenation of free-standing graphene, we performed two sets of calculations, one where the cell was allowed to relax, keeping only the cell volume constant and another set, where we have used the unit cell dimensions obtained from pristine free-standing graphene for all hydrogen coverages. For graphene on Ni(111) (referred to as graphene/Ni(111) hereafter) we have considered three layers of the nickel substrate, keeping the bottom most two layers at their bulk position. This setup was shown to provide good results in our previous work. 25 A dipole correction was employed along z in order to correct for the finite size of the slabs. For graphene/Ni(111) intercalated by gold atoms (graphene/Au/Ni(111)), we have used a unit cell that contains 0.75 ML of gold atoms with respect to the nickel substrate on top of the previously described nickel slab. 11 Hydrogenation energies Ehyd per hydrogen atom are calculated according to

Ehyd = [EnH (S) − Eprist (S) − n · EH ]/n

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(1)

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throughout the text. Here, Eprist (S) and EnH (S) are the energies per considered unit cell of pristine graphene and graphene functionalized by n hydrogen atoms per considered unit cell, with S denoting the substrate S = vacuum, Ni(111), or Au/Ni(111). As reference, we chose the energy EH of a single hydrogen atom in vacuum. Sometimes effects become clearer when considering not the averaged effect of all adsorbed hydrogen atoms per unit cell as in eq. (1) but the effect of stepwise functionalization instead. For that purpose, we compute stepwise hydrogenation energies according to

step = [EnH (S) − E(n−m)H (S) − m · EH ]/m , Ehyd

(2)

with m usually being one. Analogously, H2 desorption energies are computed according to

Edes = E(n−2)H (S) + EH2 − EnH (S) ,

(3)

with the energy (EH2 ) of an H2 molecule in vacuum. Charge-density differences (CDD) are calculated by

%CDD = %nH (S) − %−nH (S) − %nH ,

(4)

i.e., subtracting the charge densities of the (supported) graphene sheet after removal of the hydrogen atoms (%−nH(s) ) and of the isolated hydrogen atoms in vacuum (%nH ) from the density of the combined system (%nH (S)). Reported magnetic moments always refer to the (hydrogenated) graphene sheets. In the free-standing case, this is the total magnetic moment. In the substrate adsorbed cases, these were determined by Bader analysis 40 of the magnetization density (%α − %β ).

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Results and Discussion Free-standing Graphene We begin with the simplest case of free-standing graphene. As a bipartite lattice with two interpenetrating and chemically identical sublattices, every adsorption site of graphene is identical for the first functionalization step and an inequality of the two sublattices occurs after this initial functionalization. As mentioned in the introduction, a hydrogen atom is known to form a C-H bond (bond length of 1.13 ˚ A) with a hydrogenation energy of -0.85 eV. This also changes the structure of the carbon lattice, since the hybridization of the hydrogenated carbon atom changes from sp2 to sp3 , in line with an out-of-plane shifting of the respective carbon atom (0.46 ˚ A with respect to the averaged z position of the unhydrogenated carbon atoms in the graphene sheet) and a changed C-C-C dihedral angle of 115◦ (compared to 120◦ in pristine graphene). Since the carbon atom contributes with its pz electron to the newly formed C-H bond, the π conjugation is broken and a change in the C-C bond length compared to pristine graphene can be observed: the three C-C bonds that contain the functionalized carbon atom are elongated from 1.43 ˚ A (pristine graphene) to 1.50 ˚ A, which is close to the bond length of an isolated C-C single bond (1.53 ˚ A). For comparison, we calculated C=C and C-C bond lengths for our computational setup from isolated ethene and ethane. Both values are with 1.33 and 1.53 ˚ A, respectively, in good agreement with reference data. 41,42 The adjacent graphene C-C bonds are slightly shortened (1.41 ˚ A), approaching the bond length of a localized C=C double bond, whereas changes to all other graphene C-C bonds are negligible (±0.01 ˚ A compared to the delocalized graphene C-C bond). According to a Bader charge analysis, the averaged valence charge per carbon atom remains to be four electrons and one electron is attributed to the hydrogen atom, i.e., no significant charge transfer (or bond polarization) is observed. The broken π bond results in an unpaired electron, which is localized on the functionalized carbon sublattice, leading to a magnetic moment of 1 µB . Besides chemical intuition, this

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also follows Lieb’s theorem, 43 which states that the inequality between two sublattices introduces a net magnetic moment. Induced magnetic properties are universal and independent of the adsorbate considered, e.g., the same effect can be observed by deploying adatoms on graphene. 44 Thus, this is also expected to occur for other reactants, as it was already shown for flourinated graphene. 45 In order to explain the arising magnetic structure in detail, we have calculated total and spin resolved charge-density differences for the first hydrogenation step in Figure 1. β spin-density of the double bonds contributes to the C-H bond, pairing with the α density of the hydrogen atom. α density of the former double bonds is accumulated on the neighboring carbon atoms leading to the observed magnetic structure. These changes can be followed in Figure 1, showing charge redistribution from β to α charge density on the neighboring unhydrogenated carbon sublattice. This effect is most pronounced on the three direct neighbors of the hydrogenated carbon atom but delocalized to some extend. The charge flow that is responsible for the C-H bond is also observed, with β charge density accumulation at the hydrogenated carbon atom. The combined effects of these charge rearrangements upon C-H bond formation are visible in the CDD and the magnetization density. Overall, charge is accumulated at the C-H bond as well as the three neighboring carbon atoms, in line with the newly formed covalent bond as well as the unpaired α density on the carbon neighbors. The magnetization density shows the resulting magnetic structure, i.e., the unpaired α density. Although the charge rearrangements are much more pronounced in the direct vicinity of the formed C-H bond, the resulting magnetic structure is delocalized over the full (unhydrogenated) carbon sublattice.

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Figure 1: Spin-resolved charge-density difference upon adsorption of a single hydrogen atom on free-standing graphene. The adsorbed hydrogen atom is displayed in green, carbon sublattices A and B are represented by black and gray spheres, respectively. Positive (bright colors, charge accumulation) and negative (dark colors, charge depletion) α (red) and β (blue) densities are shown for isodensity values of ± 0.02 e/˚ A3 . Charge is transferred from β towards α for the carbon atoms surrounding the hydrogenated carbon atom and from α towards β in the region of the C-H bond, respectively. This results in a magnetization on the unhydrogenated carbon sublattice (α - β, red 0.02 e/˚ A3 ) and charge rearrangements due to the C-H bond formation (CDD, red 0.02 e/˚ A3 , blue -0.02 e/˚ A3 ).

For the second hydrogen adsorption, we can distinguish between functionalization on the same (AA) and on opposing carbon sublattices (AB). Adsorption on the opposing sublattice allows for recombination of the two unpaired electrons and, hence, a nonmagnetic structure. This quenching of the magnetic moment can either be explained by a reordering of electrons to form a chinoide, non-magnetic π system or as an antiferromagnetic coupling of the two spins. In any case, such a structure is known to be thermodynamically more stable than adsorption of the second reactant on the same carbon sublattice, since this results in a magnetic structure of 2 µB . This is because a reordering of electrons and, hence, a quenching of the spin. We can analyze this in detail analogously to Figure 1, see Figures S1 to S3 in the supporting information (SI). The results are summarized as a model in Figure 2.

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Figure 2: Model for spin arrangement during hydrogen adsorption on free standing graphene for the four elementary cases: hydrogenation of the first hydrogen atom (1H), and hydrogenation of a second hydrogen atom in the same carbon hexagon in ortho, meta, and para position. Electrons are colored indicating the observed quenching via spin flip (ortho, para) or lack thereof (meta) (this is of course only a pictographic model, since electrons are indistinguishable).

For AB hydrogenation, we distinguish two cases (ortho and para) analogously to our previous work, 25 i.e., a total of three different hydrogenation patterns exists in one carbon hexagon, denoted ortho, meta, and para as shown in Figure 3.

Figure 3: (a) Ortho (o), meta (m), and para (p) functionalization patterns shown for a second hydrogenation with respect to a first hydrogen atom at the position marked by a green circle in a hexagonal (4 × 4) unit cell (cyan, orange unit cell vectors a1 and a2 ). (b) shows the analogous rectangular (4×2) unit cell used for ortho functionalization patterns.

In all three cases, C-H bond formation of the second hydrogen atom proceeds analogously to the first hydrogenation step, indicated by a charge redistribution from α11



towards β-spin at the hydrogenated carbon atoms. This is in line with a diminished double bond character, accumulating β charge for the C-H bond, leaving α charge density on the surrounding carbon atoms, whereas these charges were evenly distributed before hydrogenation. Adsorption energies and total magnetic moments for these structures are compared in Table 1. For AB patterns, the effect on the neighbors is a stronger localization of the double bonds, indicated by an increase of charge in the CDD (see Figure S1 and Figure S3). In the para case, this effect is more pronounced on the two double bonds between the para arranged hydrogen atoms, in line with a chinoid double bond pattern. No magnetism is observed in the magnetization density for the AB patterns, because of spin pairing on neighboring carbon atoms (see Figure 2). AA hydrogenation, i.e., the meta arrangement, behaves differently. There, besides the C-H formation, charge redistribution is also observed at the carbon atoms of the unhydrogenated carbon sublattice (see Figure S2), indicating β charge flow (to contribute in the C-H bond formation) to α charge density that was distributed evenly prior to hydrogenation. Effectively, this is observed as an increase of α charge density on the unhydrogenated carbon sublattice, which results in a positive magnetization density on those carbon atoms, since the spins have no opportunity to recombine (see Figure 2). As a result of the induced magnetism, meta (A-A sublattice functionalization) is energetically unfavorable, whereas ortho and para (A-B sublattice functionalization) have almost identical adsorption energies, being stabilized by 0.55 eV/H compared to meta (see Table 1). Next, we compare functionalization in close vicinity of the initial functionalization to situations where the two adatoms are separated. We find that it is always energetically favorable (by 0.03 and 0.16 eV/H comparing separated AA/BB to meta hydrogenation and separated AB to ortho/para hydrogenation, respectively) if adsorptions occur close to each other, i.e., functionalization of the same carbon hexagon twice is favorable over spatially separated adsorptions (see Table S1 and Figure S4).

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Table 1: Averaged hydrogenation energies and total magnetic moments for one to four hydrogen atoms in a (4 × 4) unit cell of free-standing graphene comparing separated (denoted AA and AB) and close distance (denoted ortho, meta, and para) patterns for AB and AA functionalization, respectively. See Figure 3 and Figure S4 for the adsorption geometries. In the case of ortho functionalization, values in parenthesis are for a hexagonal cell, whereas the other values are obtained in a favorable rectangular cell (Figure 3b). nH Structure Ehyd /H/eV µ/µB 1H -0.85 1.0 2H ortho -1.41 (-1.40) 0.0 (0.0) para -1.40 0.0 AB -1.24 0.0 meta -0.84 2.0 AA -0.81 2.0 3H ortho -1.42 (-1.40) 1.0 (1.0) AB -1.24 1.0 para -1.35 1.0 AB’ -1.23 1.0 meta -0.78 3.0 AA -0.81 3.0 AA’ -0.83 3.0 4H ortho -1.60 (-1.53) 0.0 (0.0) AB -1.31 0.0 para -1.50 0.0 AB’ -1.36 0.0 meta -0.79 4.0 AA -0.79 4.0 Upon further addition of hydrogen, we recheck whether functionalization prefers spatial proximity over spatial separation for a total of three and four hydrogen atoms per unit cell, respectively. For AB functionalization this is, indeed, the case with a stabilizing effect of at least 0.12 eV/H. In the case of AA functionalization this is somewhat different: even for the first pair, the energy difference was not as distinct as for the AB patterns. For increasing coverages it shows that isolated and close functionalization are energetically almost identical, with a small preference for isolated hydrogen pairs. From these results, we are able to identify the most stable functionalization pattern for each adsorption arrangement by computing structures up to a maximal coverage of 0.5 ML. We chose this maximum, as covalent functionalization is always accompanied by a structural bending of graphene. This results in structures that can be related to an 13



armchair or bathtub cyclohexene, i.e., further cis-functionalization of the remaining half of unreacted carbon atoms is highly unlikely and would induce large strain into the carbon network. This means, further functionalization would always occur on the other side of the graphene sheet, leading to graphane. Since we want to address one-sided graphene as a model for substrate supported graphene here, we limit ourselves to the natural limit of cis-functionalization, i.e., 0.5 ML. Structural data, hydrogenation energies, and magnetic moments for all coverages are compared in Table S1. In the case of ortho structures, we find that hydrogenation prefers to occur along an armchair rather than a zig-zag direction of the graphene structure, i.e. along a2 rather than along a1 (see Figure 3b). In order to allow for such a direction, we alternatively chose a rectangular (4×2) unit cell (see Figure 3b). No stabilization of meta and para patterns in this alternative cell was found. Ortho hydrogenation along an armchair direction is completed at a coverage of 0.25 ML (see Figure 4). For further increasing the coverage, the next neighbors of each functionalized carbon atoms are skipped, as functionalization at those sites would correspond to unfavorable and unreasonably strained structures. Consequently, further functionalization occurs along a second armchair line, skipping one armchair row of unhydrogenated carbon atoms in between. The unhydrogenated carbon atoms are bending downwards, leading to a battlement shaped structure for the maximally coverage of 0.5 ML (Figure 4b). This armchair arrangement has an adsorption energy of -1.63 eV/H, which is favored over an alternative “stirrup” arrangement 29 obtained from hydrogenation along zig-zag lines by 0.11 eV/H. A comparison of adsorption energies between rectangular and hexagonal unit cells can be found in Figure S5. In the case of para functionalization, it turns out that most stable structures are obtained when closing a ring around a carbon hexagon, yielding a structure of 0.25 ML (Figure 4c and Table 1). Further functionalization in para orientation is no longer possible, however, we can still add hydrogen in a varying A-B sublattice fashion, forming an alternative 0.5 ML structure, which was denoted “boat” before. With -1.57 eV/H this is slightly less stable compared to the armchair ortho structure. 14


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For completeness we also consider meta arrangements for larger coverages. Here, subsequent functionalization in isolated pairs is slightly more stable than close proximity functionalization, however, the energy difference is negligible (demonstrated by three possible structures for 0.25 ML, see Figure S6).

Figure 4: Top and side views on the ortho 0.25 ML, ortho 0.5 ML (armchair), para 0.25 ML (closed ring), boat (0.5 ML, ortho/para), and graphone (0.5 ML, meta) arrangements. Carbon and hydrogen atoms are black and green spheres, respectively. In (d) orange spheres represent further hydrogen atoms in AB position after the maximal AA para pattern is reached at 0.25 ML.

For a more detailed analysis, we plotted the data for the hydrogenation energies with increasing coverage from 0.03 to 0.5 ML for the most stable arrangements of ortho, meta, and para patterns in Figure 5 (see also Table S1).

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prist. graphene

0.25 ML

−0.7 E hyd /eV

0.5 ML

ortho para/ortho meta orthofc para/orthofc

−0.9 −1.1 −1.3 −1.5 −1.7 −1.9

(a)

0

E des /eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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−1 −2 −3 (b) 0

8 Number of hydrogen atoms

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Figure 5: (a) Averaged hydrogenation energies and (b) H2 desorption energies for the most stable hydrogenation patterns on free-standing graphene for varying hydrogen coverages. In (a), we additionally show energies for hydrogenation within a unit cell fixed to the pristine graphene unit cell (subscript fc). After the first functionalization, the three different possible patterns differ. As discussed above, meta functionalization is not favorable, showing a slowly decreasing adsorption energy per hydrogen atom, ranging from -0.85 to -0.66 eV for the first and the last hydrogen atom in order to form graphone, respectively. This is due to the increasing magnetic moment, reaching a maximum of 16 µB /unit cell in graphone, see Table S1. Besides chemical intuition, this can again be correlated to Lieb’s theorem and our discussion above. To that end, we denote the number of pz electrons of each sublattice as NA and NB . Upon each functionalization by a hydrogen atom, one pz electron contributes to the formation of a C-H bond, i.e., one electron is removed from the graphene π system. Functionalization then leads to a magnetic moment of µB = |NA − NB |. Thus, upon subsequent functionalization of the same carbon sublattice, the magnetic moment is increased in every functionalization step by one. 16


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In contrast to that, alternating functionalization on the two different carbon sublattices is stabilized compared to the first adsorbed hydrogen atom. Despite small differences, the two different possibilities of ortho and para arrangements are similar in energy. Overall, functionalization by an odd number of hydrogen atoms is always slightly destabilizing, whereas even numbers of hydrogen atoms lead to an increase in the hydrogenation energy. This effect is more pronounced when looking at the stepwise adsorption energies (Figure S7), but yields a zig-zag behavior also in the averaged adsorption energies displayed in Figure 5. This is again in line with the magnetic moment of 1 µB that is necessarily introduced for an odd number of defects (|NA − NB | = 1), which is quenched by the next functionalization (even number of hydrogen atoms) step (|NA − NB | = 0). This effect is more pronounced in the para compared to the ortho arrangements. For coverages beyond two hydrogen atoms, ortho functionalization is slightly more stable than para up to coverages around 0.25 ML. Beyond, the thermodynamic stability is very similar for both AB functionalization patterns as differences in the stepwise adsorption are averaging out to a large extend. The spin resolved CDDs for the stable structures at a coverage of 0.25 ML are shown in Figures S8 to S10 and the results are in line with the discussion at lower coverages, explaining the obtained total magnetic moments. For the medium coverage of 0.25 ML we observe the most stable arrangements for AB functionalizations, with a maximal adsorption energy of -1.86 eV/H in case of the ortho arrangement. The increased stability for this coverage is best visualized by the desorption energies plotted in Figure 5b. Together with the fact, that H2 desorption for low coverages is hindered kinetically, since in that case diffusion of isolated hydrogen atoms was shown to be the rate determining step, 25 this indicates that coverages around 0.25 ML are especially favorable to be formed experimentally for substrates on which graphene behaves as on free-standing graphene. For free-standing graphene, the adsorption strength of the next hydrogen (beyond a coverage of 0.25 ML) is dramatically weakened, with stepwise adsorption energies that are reduced by as much as 2.41 and 2.15 eV for ortho and para functionalization, respectively (see Table S1). Nevertheless, the averaged adsorption 17



energies remain lower than that of the first pair of adsorbed hydrogen atoms. Thus, from a thermodynamical point of view, hydrogenation of free-standing graphene (involving both carbon sublattices) should be possible up to coverages of 0.5 ML (always keeping in mind, however, that atomic hydrogen has to be offered, because molecularly adsorbed hydrogen is thermodynamically more favorable 25 ). However, an intermediate coverage of 0.25 ML seems to be especially stable and afterwards, H2 desorption becomes more likely. During the stepwise increase of the hydrogen coverage up to 0.5 ML, we observed changes in the unit cell area, i.e., the graphene sheet dimensions, compared to pristine graphene (see Table S1) if we allow the relaxation of the graphene sheet dimensions. However such relaxation are mainly suppressed by a substrate (see section S1.1 for an in depth discussion). All things considered, a coverage of 0.25 ML exhibits stabilizing structural properties that lead to a thermodynamical stabilization for ortho and para patterns considering further hydrogenation. In case of ortho, a bending of the unhydrogenated parts of the graphene sheet becomes necessary to release the strain induced upon hydrogenation for this intermediate coverage. Any further hydrogenation reduces the possibility to release this stress significantly, and thus reduces the tendency for hydrogenation and increases the probability of dehydrogenation of additional hydrogen atoms. Similarly, for para arrangements, unhydrogenated carbon hexagons are buckled down in the closed ring structure at 0.25 ML. Structural strain is again introduced with any new hydrogenation in an ortho position. In addition, here electronic effects may play a role, since the enclosed ring shows an increase of localized electron density (see Figure S8). These effects are mostly absent in case of meta hydrogenation. There, growth proceeds (thermodynamically) without specific order in isolated meta arranged hydrogen pairs and, thus, hydrogenation energies are decreasing monotonic up to 0.5 ML.

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Graphene/Ni(111) After closely examining free-standing graphene as model case, we now turn to a strongly interacting substrate, namely the Ni(111) surface. In a previous work, 25 we already discussed the energetically most stable hydrogenation patterns, identifying the experimentally found coverages of 0.5 ML by the formation of graphone on top-fcc oriented graphene/Ni(111). Herein, we briefly reiterate our results, focusing on the differences that occur by taking into account the second stable adsorption geometry of graphene on Ni(111), namely the bridge-top adsorption site. 3,46 Both structures of graphene/Ni(111) in bridge-top as well as in top-fcc geometries are shown in Figure 6. In the case of the top-fcc geometry, carbon atoms are located either on top of nickel surface atoms (A=top) or on fcc-hollow sites (B=fccH). The bridge-top geometry is obtained by shifting the graphene √ layer against the Ni(111) surface by 1/4a1 + 3/12a2 . In the resulting structure, the two carbon adsorption sites are more alike, bridging either a top and an fcc-hollow site (A=top-fccH) or a top and an hcp-hollow site (B=top-hcpH) of the underlying Ni(111) surface.

Figure 6: Structures of graphene/Ni(111) in (a) top-fcc and (b) bridge-top geometries. Atoms are represented by gray (nickel) and black (carbon) spheres, respectively. As we have reported before, 25 hydrogen adsorption is favorable on the fccH (-2.29 eV/H) over the top site (-1.74 eV/H) by 0.55 eV/H in the case of the top-fcc geometry, see Table 2. In the case of the bridge-top structure, the adsorption energy difference of one hydrogen is almost negligible between the two different sites, with adsorption energies of -2.11 and -2.07 eV for the top-fccH and the top-hcpH sites, respectively. Thus, hydrogen adsorption is slightly less favorable for the bridge-top compared to the top-fcc geometry. Overall, the Ni(111) substrate enhances the hydrogen adsorption energy compared 19



to free-standing graphene by ∼1.4 eV. Table 2: Averaged hydrogenation energies and total magnetic moments of carbon atoms for different structures and coverages in a (4 × 4) unit cell of graphene on Ni(111). the magnetic moments (µC ) of the hydrogenated graphene sheets are considered, see computational details. nH 1H 2H

16H

Ehyd /H/eV µC /µB top-fcc bridge-top top-fcc bridge-top -1.74 -2.07 0.3 0.1 -2.29 -2.11 0.2 0.1 -2.05 -2.15 0.3 0.1 -2.04 -2.10 0.2 0.0 -2.27 -2.17 0.1 0.1 -2.06 -2.12 -0.4 -0.5 -2.08 -2.10 -0.3 -0.4 -2.11 -2.02 -0.6 -0.5

Structure A B ortho para meta stirrup boat graphone

For all 1H cases, the magnetic moment of the graphene sheet is largely quenched compared to the free-standing case (Table 2). In order to analyze this in detail, we have plotted spin resolved CDDs for the adsorption of a single hydrogen atom on top-fcc graphene/Ni(111), analogous to our analysis above (see Figure 7). Similar to free-standing graphene, β spin-density contributes to the C-H bond formation (for hydrogenation at the A site) and α spin-density is accumulated on B sublattice carbon atoms. However, nickel atoms of the top-most layer loose charge (in addition, some smaller rearrangements between nickel α and β densities are observed), which is accumulated in the β channel of the unhydrogenated carbon atoms (B sublattice carbon atoms) of the graphene layer. This charge rearrangement towards the unhydrogenated carbon atoms largely balances the charge of the graphene layer (see Table S2). As a result, no magnetization is observed on the B site carbon atoms in Figure 7 (in fact, a small magnetization arises on the A site instead, which is mostly balanced by the nickel substrate). In total, these effects are visible as a charge transfer from the top-most nickel layer to the graphene sheet and the intermediate region in the CDD.

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Figure 7: Spin resolved charge-density differences upon adsorption of a single hydrogen atom on a top-fcc site of graphene/Ni(111). The adsorbed hydrogen atom is displayed in green, carbon sublattices A and B are represented by black and gray spheres, respectively. Positive (bright colors, charge accumulation) and negative (dark colors, charge depletion) α (red) and β (blue) densities are shown for isodensity values of ± 0.005 e/˚ A3 . The third 3 column shows the magnetization density (α - β, red 0.007 e/˚ A ) CDD (red 0.007 e/˚ A3 , blue -0.007 e/˚ A3 ) respectively.

Similar to free-standing graphene, the formation of the C-H bond is accompanied by a hybridization change and, therefore, a changed C-C-C angle. However, this change is more pronounced, with C-C-C angles around the hydrogenated carbon atom of 110-111◦ in the four possible structures of a single hydrogen atom on graphene/Ni(111). This is accompanied by the out of plane shifting of the hydrogenated carbon atom, which is in line with the shift observed on free-standing graphene (0.46 ˚ A). For graphene on Ni(111), the C-C bond length is 1.44 ˚ A, which is 0.01 ˚ A larger than in pristine graphene. Upon hydrogenation, the three C-C bonds containing hydrogenated carbon atoms are elongated from 1.44 to 1.51 ˚ A. The adjacent C-C bond length remain at 1.44 ˚ A. As in the free-standing case, one electron is attributed to the hydrogen atom by a Bader analysis. The structural changes upon functionalization favor C-H formation in a way that the functionalized carbon atom is located over hollow sites, since in such a structure, the nearest neighboring 21



carbon atoms are at top sites, which allows them to buckle downwards, accompanied by a strengthening of carbon-substrate bonds. In case of the top-fcc geometry, this results in a preference for hydrogenation of the fccH compared to the top site. In case of the bridge-top geometry, one can attribute the preference of the top-fccH over the top-hcpH sites to this effect as well, since in the former case, the unhydrogenated carbon atoms are closer to the surface because they are bridging an hcp-hollow instead of an fcc-hollow site. The bonding of the substrate also heavily affects the adsorption of the second hydrogen atom. While the adsorption of the second hydrogen atom on the same carbon sublattice is more stable in free-standing graphene, with AB (ortho/para) being favorable over AA (meta) patterns, the site preference of fccH adsorption in the top-fcc geometry changes this behavior. Here meta is 0.22-0.23 eV favorable over AB functionalization (see Table 2). Besides the geometrical/energetic effect from the hydrogen adsorption site preference, the relative stabilization of meta adsorption compared to ortho/para adsorption can be explained by the quenching of the magnetic moment as shown for the 1H case. As shown in Table 2, this effect is observed for AA hydrogenation (meta) and odd numbers of hydrogen atoms alike. For the 2H meta case, nickel atoms of the top-most layer transfer charge to carbon atoms on the top site (B sublattice), resulting in no magnetization density on the B sublattice and negligible overall magnetic moment in the hydrogenated graphene sheet. The same effects also apply for a maximal coverage of 0.50 ML, which is shown in the charge analysis in Figure S12. Consequently, the charge transfer from the nickel atoms to the hydrogenated graphene sheet increases with the number of adsorbed hydrogen atoms (Table S2). The two possible adsorption sites of the bridge-top geometry are quite similar and energetically almost identical for adsorption of the first hydrogen atom. In particular, they are less stable compared to fccH adsorption, indicating a weaker interaction with the nickel substrate. As a result, AA adsorption is not as stabilized as in the case of the top-fcc geometry and AB (ortho/para) functionalization becomes energetically favorable, analogously to free-standing graphene. These changes with respect to free-standing 22


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graphene as for the changes in the top-fcc arrangement, can be explained by the magnetism of the nickel substrate. The resulting total magnetic moment for ortho and meta adsorption geometries are identical, i.e., the meta arrangement is not affected by the unstable antiferromagnetic state of 2 µB . In summary, the findings of hydrogenating graphene/Ni(111) at low coverages suggest: i) In the case of the top-fcc geometry, subsequent meta adsorption, up to graphone for a coverage of 0.5 ML, should be preferable, due to the preference of adsorbing in the fccH site and the effective quenching of the magnetic moment due to the nickel substrate. ii) In the case of the bridge-top geometry, possible 1H adsorption sites are isoenergetic but at the same time AA site hydrogenation is not penalized due to unstable magnetic structures. The preference of ortho patterns over para structures found for 2H and at higher coverages suggests a preference of ortho > para, with meta arrangements that are close in energy. To study these hypothesis, we again consider the increase of the hydrogen coverage up to a maximum of 0.5 ML. Rechecking various structural alternatives showed that the energetically favorable hydrogenation sequences are the same as we have identified for free-standing graphene for meta (isolated pairs) and para (ring closure) arrangements (see Figure 4). In contrast, ortho functionalization is more stable in a hexagonal unit cell along zig-zag lines (see Figure S13), whereas hydrogenation along armchair directions was preferred for free-standing graphene. Adsorption energies with respect to varying coverages are summarized in Figure 8 (see also Table S3) and the stepwise adsorption energies are shown in Figure S14.

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prist. graphene/Ni(111)

0.25 ML

ortho-bt ortho-tf

para-bt para-tf

0.5 ML meta-bt meta-tf

E hyd /eV

−2

−2.2 (a)

0 E des /eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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−0.5

(b) 0


16

Figure 8: (a) Averaged hydrogenation energies and (b) desorption energy of one H2 molecule for the most stable hydrogenation patterns on a (4×4) unit cell of graphene on Ni(111) in top-fcc and bridge-top geometry for varying hydrogen coverages.

As outlined in our previous study, top-fcc arranged graphone/Ni(111) is the most likely obtained structure for hydrogenated graphene/Ni(111). Nevertheless, beyond the specially stable 0.25 ML arrangements in the case of AB functionalization, the resulting hydrogenated graphene sheets in bridge-top arrangements are as stable or sometimes even slightly more stable than the top-fcc AA arrangements. From this data, and the fact that it is highly unlikely that a graphene sheet changes its geometry between top-fcc and bridge-top on a large scale after production of the initial graphene/Ni(111) material, we predict that one either obtains graphone or stirrup patches, depending on the initial relative alignment of graphene and Ni(111). This demonstrates the striking influence that subtle changes of a substrate may have on graphene reactivity. Comparable to free-standing graphene, the thermodynamically favorable ortho structures on the bridge-top geometry have a maximum adsorption energy at a hydrogen coverage of 0.25 ML, which does not show for the meta structures which are stable in

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the top-fcc case. This is in line with the structural stabilizing factors for this coverage in both AB patterns (see section S1.1). Therefore, a coverage of ∼0.25 ML is likely to be the experimental limit for bridge-top graphene/Ni(111), with H2 desorption preventing the observation of larger coverages.

Graphene/Au/Ni(111) Finally, we discuss the influence of a weakly interacting substrate. For this purpose we chose the graphene/Au/Ni(111) interface, see Figure 9. In such a system, graphene is known to be physisorbed similar to graphene on Au(111). 11,24 Therefore, the respective graphene sheet is often referred to as “quasi-free-standing” graphene. Although this substrate has a doping effect on the graphene sheet, 11 the band structure is restored and graphene is expected to behave similarly to free-standing graphene. In the structural arrangement we chose, there are four different sites for functionalization that can be distinguished A=topAu , B=fccHAu , C=topNi , and D=fccHNi (Figure 9).

Figure 9: (a) Top view of different sites for graphene functionalization in the top-fcc graphene arrangements on Au/Ni(111) and (b) side view showing the layer distance between graphene and gold (hC-Au ) and graphene and the top most nickel sheet hC-Ni . Atoms are represented by gray (nickel), yellow (gold), and black (carbon) spheres.

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Table 3: Averaged hydrogenation energies and magnetic moments of carbon atoms for different structures and coverages in a (4×4) unit cell of graphene on Au/Ni(111). For ortho functionalization, again a rectangular (4 × 2) cell allowed for more stable hydrogenation patterns. Values for the hexagonal cell are given in parenthesis. The magnetic moments µC of the hydrogenated graphene sheets are considered, see computational details. nH 1H

2H (ortho) 2H (para) 2H (meta)

Structure topAu (A) fccHAu (B) topNi (C) fccHNi (D) fccHNi -topAu fccHNi -topNi fccHNi -fccHNi fccHNi -fccHAu fccHNi -fccHNi

Ehyd /H/eV µC /µB -0.96 -0.5 -0.91 0.8 -0.98 0.8 -1.05 -0.2 -1.43 (-1.43) 0.0 (0.0) -1.48 (-1.45) 0.0 (0.0) -1.44 0.0 -0.94 1.6 -1.13 0.3

hC-Au /˚ A 3.17 3.19 3.19 3.19 3.13 3.12 3.14 3.09 2.64

hC-Ni /˚ A 5.43 5.46 5.46 5.43 5.39 5.39 5.41 5.36 4.76

Of course, other arrangements of graphene/Au/Ni(111) are possible, such as geometries resulting from intercalation of bridge-top graphene/Ni(111). However, comparison of the intercalated systems resulting from top-fcc and bridge-top geometries showed almost identical energies (see Table S4). Therefore, and since different adsorption geometries are likely to be energetically comparable for weakly interacting metals, we focus on the chosen top-fcc geometry in the following. This is further justified by comparing the hydrogenation of free-standing graphene with the hydrogenation on Au/Ni(111), which overall behaves very similar (see Figure 10), confirming that graphene on weakly interacting metals (physisorbed cases) behaves in good approximation as free-standing. Thus, the meta arrangements (AA functionalization) is greatly destabilized compared to ortho/para arrangements (AB functionalization) and ortho is most stable along an armchair direction. However, on close inspection, there are some differences.

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prist. graphene/Au/Ni(111) 0.25 ML ortho orthofc

0.5 ML para parafc

meta

E hyd /eV

−1

−1.5 (a) 0

E des /eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


−1

−2 (b) 0


16

Figure 10: (a) Averaged hydrogenation energies and (b) desorption energy of one H2 molecule for the most stable hydrogenation patterns on a graphene/Au/Ni(111) for varying hydrogen coverages. For comparison, we show the free-standing case obtained in a fixed unit cell.

Isolated hydrogenation on top of the four different possible sites is energetically different, although all obtained adsorption energies differ by not more than 0.14 eV. As for top-fcc graphene/Ni(111), adsorption at the fccH site is most stable. However, here, the energy difference is only 0.07 eV compared to the top site, whereas the difference was as much as 0.55 eV before gold intercalation. Comparing adsorption sites with (A and B) and without (C and D) gold atoms underneath the functionalized carbon atom shows that the former are destabilized, i.e., having a gold atom underneath a hydrogenated carbon atom is energetically unfavorable. As in the case of Ni(111), the resulting magnetic moment is quenched, although the effect is less pronounced after gold intercalation, indicating a situation that closer resembles the model case of free-standing graphene compared to the Ni(111) substrate. This is also in line with a weakened hydrogenation energy of maximally -1.05 eV for the first 27



hydrogen adsorption, which is in between the values obtained for graphene/Ni(111) (2.29 eV) and free-standing graphene (-0.85 eV), considerably closer to the latter. Again, the formation of the C-H bond (1.13 ˚ A) also influences the carbon lattice. The C-C bond lengths containing the functionalized carbon atom changes similarly to other substrates from 1.42 ˚ A to 1.51 ˚ A. The C-C-C angle around the functionalized carbon atom changes again from 120◦ to 115◦ , i.e., by the same amount as in free-standing graphene and, thus, slightly less than for graphene/Ni(111). The adjacent C-C bond length remain at 1.42 ˚ A. The results obtained so far suggest that results comparable to those on free-standing graphene also can be expected for larger coverages. According to our approach followed so far, we proceed by adding a second hydrogen atom in the same carbon hexagon as the first hydrogen atom at the most stable fccH adsorption site. As for free-standing graphene, AB (ortho/para) adsorption is energetically favorable over AA (meta) functionalization by 0.32-0.33 eV. This corresponds to a difference roughly half to what we observe for free-standing graphene. This is interesting, since the magnetic moment is almost completely quenched in the case of the most stable meta functionalization. We can explain this by the observed difference in graphene adsorption distance. Effective quenching of the magnetic moment in the meta arrangements requires a movement of the hydrogenated graphene layer towards the surface in order to allow for the charge density distribution (Table 3). This is evident by comparing to a meta structure without effective quenching. The resulting graphene/gold distance is 0.5 ˚ A smaller than the optimal adsorption distance, leading to a destabilization of the structure compared to the AB hydrogenation patterns. This means there is a trade off between quenching and a too small adsorption distance. In order to analyze the underlying mechanism of the magnetic spin quenching, we again calculated spin resolved CDDs upon adsorption of a single hydrogen atom (in the most stable fccH site) on graphene/Au/Ni(111) (Figure 11). Once again α density accumulates on the C-H bond and the B-type carbon atoms. For quenching of this excess α density on the unhydrogenated carbon sublattice, β charge is depleted from the top-most Ni atoms 28


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and Au atoms underneath the neighboring carbon atoms. As for graphene/Ni(111), no magnetization arises on the unhydrogenated carbon atoms, but a small magnetization of the hydrogenated carbon sublattice instead. The CDD shows charge accumulation on this carbon sublattice, which is mostly depleted from the substrate. A Bader analysis of the magnetic moments confirms the above charge distribution (see Table 4). Carbon atoms of the graphene layer are mostly demagnetized in stable structures, due to a quenching with Au and Ni layer magnetic moments.

Figure 11: Spin resolved charge-density differences upon adsorption of a single hydrogen atom on a top-fcc site of graphene/Au/Ni(111). The adsorbed hydrogen atom is displayed in green, carbon sublattices A and B are represented by black and gray spheres, respectively. Positive (bright colors, charge accumulation) and negative (dark colors, charge depletion) α (red) and β (blue) densities are shown for isodensity values of ± 0.005 e/˚ A3 . 3 The third column shows the magnetization density (α - β, red 0.007 e/˚ A ) and CDD (red 3 3 0.007 e/˚ A , blue -0.007 e/˚ A ) respectively

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Table 4: Bader analysis of the magnetization density for hydrogen adsorbed on a (4 × 4) unit cell of graphene on Au/Ni(111). nH 1H

2H (ortho) 2H (para) 2H (meta)

Structure pristine topAu (A) fccHAu (B) topNi (C) fccHNi (D) fccHNi -topAu fccHNi -topNi fccHNi -fccHNi fccHNi -fccHAu fccHNi -fccHNi

µH /µB -0.04 0.06 0.06 -0.02 0.00 0.00 0.00 0.13 0.02

µC /µB 0.02 -0.44 0.73 0.73 -0.17 0.02 0.02 0.01 1.37 0.27

µAu /µB 0.07 0.07 0.09 0.09 0.06 0.08 0.08 0.06 0.08 0.05

µNi /µB 9.65 9.64 9.65 9.65 9.63 9.65 9.64 9.61 9.63 9.55

Despite the fundamentally different underlying mechanisms, adsorption energies of two hydrogen atoms on graphene/Au/Ni(111) are comparable to free-standing graphene, because of the discussed opposing effects of quenching the magnetic moment and the adsorption distance. We proceed by adding hydrogen atoms according to the patterns identified for free-standing graphene, which were also shown to be energetically most stable on graphene/Ni(111). However, care has to be taken, here, in order to avoid the unstable Au-top/fccH sites, as it is evident from the considerations of the adsorption of the first hydrogen atom but was also confirmed on further tests (see Table 3 and Figure S15). The resulting most stable hydrogenation energies for increasing coverage are summarized up to 0.5 ML in Figure 10 and Table S3. Interestingly, para AB arrangements are stabilized compared to ortho arrangements in comparison to the results obtained for free-standing graphene. In part, this can be explained by the unit cell, which is fixed by the substrate, i.e., is not able to relax upon functionalization (neither in our calculations, nor in experiments). However, even by taking this effect into account in our free-standing calculations (compare Figure 5), the preference of para arrangements in the case of graphene/Au/Ni(111) remains distinct. Thus, there has to be an additional effect for this difference. This is the amount of unfavorable top/fccHAu sites that have to be taken into account in the case of the ortho 30


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arrangements. For a hydrogen coverage of 0.25 ML, hydrogenation at two sites with a gold atom underneath is inevitable, whereas this is avoided in the para case. From the energy differences in Table 3, this easily makes up for the obtained destabilization of the ortho arrangement. This is also true for larger coverages. At a maximal coverage of 0.50 ML, four unfavorable hydrogenation sites over gold atoms are present in the armchair structure, wheres there is not a single unfavorable hydrogenation site above gold atoms in the boat arrangement. In summary, the larger induced strain and the amount of unfavorable gold atoms beneath hydrogenated carbon atoms destabilizes ortho versus para structures. This difference is increased together with the hydrogen coverage, up to a maximum difference of 0.18 eV/H in the case of 0.25 ML. Further increasing the coverage, the ortho/para adsorption energy difference fluctuates between 0.10 and 0.17 eV/H. As a consequence, para arranged structures are the thermodynamical minimum and most likely to be found in experiments, whereas predictions from free-standing graphene would predict ortho structures. This is in line with the CH4 structure proposed in Ref. 16 for a coverage of 0.25 ML and would yield a boat structure if a coverage of 0.5 ML would be reached. Note however that this effect is small and will depend on the exact arrangement of the intercalated gold atoms in experiments, thus, ortho arrangement might still be accessible. The question remains, however, whether or not coverages up to 0.5 ML can be reached for a graphene/Au/Ni(111) system. For this, we again plotted the desorption energies in Figure 10b) and stepwise adsorption energies in Figure S16. As for free-standing graphene, it is clearly seen that a coverage of 0.25 ML, i.e., the largest possible coverage for pure para adsorption, is a considerable stable conformation. Up to the maximum coverage, i.e., the boat structure for 0.5 ML, all intermediate structures have a thermodynamical higher driving force for H2 desorption rather then consecutive adsorption. Thus, although a maximal coverage of 0.5 ML is again a very stable structure with respect to H2 desorption, it is likely that this point is not reached under experimental conditions.

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Conclusions We studied the reactivity of free-standing graphene, graphene/Ni(111), and graphene/Au/Ni(111) with respect to one-sided functionalization by atomic hydrogen. These substrates are model cases for graphene chemisorbed and physisorbed on metal substrates, respectively. We show that the effects that influence the relative stability of different patterns are i) whether or not unfavorable magnetism is induced and ii) structural rumplings, where the magnetic effect dominates. We show how strongly interacting surfaces can quench occurring magnetic moments, leading to a change of the favorable reaction pattern that depends on the substrate and the particular graphene/substrate alignment. In contrast, physisorbed graphene on weakly interacting surfaces behaves mostly like the free-standing model case. This is even the case on a magnetic substrate like Au/Ni, which is able to quench the system’s overall magnetic moment to a large extend. In this case, the similarity to free-standing graphene is a result of the interplay of the two opposing effects, namely the distance dependence of the quenching mechanism. Comparing physisorbed and chemisorbed cases, the different stabilized hydrogenation patterns lead to a maximal coverage twice as high in the chemisorbed case. Furthermore, comparing the desorption energies for the Au/Ni(111) and the Ni(111) substrates, the stronger hydrogen bonding in the latter case leads to much smaller desorption energies. A value of about -0.5 eV, the desorption energy of the stable 0.25 ML structure of the Au/Ni(111) case that has been observed as maximal coverage experimentally, is reached only for very high coverages close to 0.5 ML in the case of the Ni(111) substrate. Thus, besides the fact that the different substrates invoke different hydrogenation patterns and that the AB-patterns show a particular stability at a coverage of 0.25 ML, the reduced maximal coverage in this case is also in line with the overall reduced bonding strength on the weakly interacting substrate. Although we only discussed results for three substrates, we expect that our results are universally applicable also to other substrates. For example structures with Moiré patterns

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should behave as a mixture of the here presented cases, depending on the distance and relative alignment towards the substrate. Furthermore, since the unfavorable magnetism arises from unpaired electrons that emerge from the change towards sp3 hybridized carbon atoms, these effects are not limited to hydrogen as chemical probe. The reactivity of graphene, and its dependence on the specific surface and the structural alignment, will also occur for other reagents. One example is the halogenation of substrate supported graphene, which is currently under investigation. Thus, the substrate enables a precise control of the functionalization pattern of graphene.

Supporting Information Supporting information contains following sections: Free-standing graphene Structural changes upon hydrogenation Graphene/Ni(111) Graphene/Au/Ni(111)

Contact Information Corresponding author: Dr. Himadri R. Soni Chair of Theoretical Chemistry Friedrich-Alexander University of Erlangen-Nuremberg Egerlandstrasse 3, D-91058 Erlangen, Germany. Email: [email protected] Telephone: +49 (0) 9131 85 27347 Fax: +49 (0) 9131 85 27736

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Acknowledgments The authors gratefully acknowledge the funding of the German Research Council (DFG) by the Collaborative Research Center 953. Infrastructural contributions by the Erlangen Cluster of Excellence ”Engineering of Advanced Materials” are also gratefully acknowledged. J.G. thanks the German Research Foundation for support from Research Fellowship GE 2827/1-1.

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The Reactivity of Substrate-Supported Graphene: A Case Study of

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