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J. Phys. Chem. C 2010, 114, 10240–10248
Cooperativity in Surface Bonding and Hydrogen Bonding of Water and Hydroxyl at Metal Surfaces T. Schiros† Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, and FYSIKUM, Stockholm UniVersity, AlbaNoVa UniVersity Center, S-10691 Stockholm, Sweden
H. Ogasawara and L.-Å. Na¨slund Stanford Synchrotron Radiation Lightsource, P.O. Box 20450, Stanford, California 94309
K. J. Andersson Center for IndiVidual Nanoparticle Functionality (CINF), Department of Physics, Technical UniVersity of Denmark, FysikVej 312, DK-2800 Kgs. Lyngby, Denmark
J. Ren‡ and Sh. Meng§ Department of Physics and School of Engineering and Applied Sciences, HarVard UniVersity, Cambridge, Massachusetts 02138
G. S. Karlberg Competence Centre for Catalysis, Department of Applied Physics, Chalmers UniVersity of Technology, SE-41296 Go¨teborg, Sweden
M. Odelius FYSIKUM, Stockholm UniVersity, AlbaNoVa UniVersity Center, S-10691 Stockholm, Sweden
A. Nilsson Stanford Synchrotron Radiation Lightsource and Stanford Institute of Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, and FYSIKUM, Stockholm UniVersity, AlbaNoVa UniVersity Center, S-10691 Stockholm, Sweden
L. G. M. Pettersson* FYSIKUM, Stockholm UniVersity, AlbaNoVa UniVersity Center, S-10691 Stockholm, Sweden, and Institute of Physics, Chinese Academy of Sciences, 100190 Beijing, China ReceiVed: March 1, 2010; ReVised Manuscript ReceiVed: April 17, 2010
We examine the balance of surface bonding and hydrogen bonding in the mixed OH + H2O overlayer on Pt(111), Cu(111), and Cu(110) via density functional theory calculations. We find that there is a cooperativity effect between surface bonding and hydrogen bonding that underlies the stability of the mixed phase at metal surfaces. The surface bonding can be considered to be similar to accepting a hydrogen bond, and we can thereby apply general cooperativity rules developed for hydrogen-bonded systems. This provides a simple understanding of why water molecules become more strongly bonded to the surface upon hydrogen bonding to OH and why the OH surface bonding is instead weakened through hydrogen bonding to water. We extend the application of this simple model to other observed cooperativity effects for pure water adsorption systems and H3O+ on metal surfaces. I. Introduction The interaction of water and its constituentssoxygen, hydrogen, and hydroxylswith metal surfaces has long been a * Corresponding author. E-mail:
[email protected]. † Current Address: Columbia University, Energy Frontier Research Center (EFRC), 530 West 120th Street, New York, NY 10027. ‡ Institut des Mate´riaux, E´cole Polytechnique Fede´rale de Lausanne, CH1015 Lausanne, Switzerland. § Beijing National Laboratory for Condensed Matter Physics.
subject of interest because of its relevance to a number of important reactions in heterogeneous catalysis and electrochemistry.1–3 In natural and industrial chemical processes, water adsorption always occurs in the presence of other molecules coadsorbed on the substrate. The OH + H2O mixed layer, in particular, has been identified as an important and very stable intermediate in the hydrogen oxidation reaction on Pt.4–6 Because very stable adsorbed reactants can hinder proton and electron transfer, the large metal-hydroxyl (M-OH) adsorption energy
10.1021/jp101855v 2010 American Chemical Society Published on Web 05/14/2010
Bonding of Water and Hydroxyl at Metal Surfaces has been cited as the major cause of the overpotential in the oxygen reduction reaction (ORR) in fuel cell catalysis.4 It is thus of particular importance to understand the interplay between surface bonding (S-bonding) and hydrogen bonding (H-bonding) in such mixed adlayers because that can influence the overall stability of these important intermediates and, as such, is key to tuning adsorption and bond energies to increase the reaction rate. It has been established that the hydrogen bond of water to OH- in solution is much stronger, observed as a shorter distance, than that between two water molecules,7 but the question is if the interaction with the surface can change this balance and if there are some general cooperativity trends that can be established. In H-bonded clusters or pure water clusters, a cooperativity rule has been developed over the years8–15 where the maximum H-bond strength is obtained when there is a balance between donor and acceptor bonds (i.e., when the number of donor and acceptor bonds is equal). This is clearly seen in the difference in the H-bond distance and energy when comparing the water dimer with small cyclic clusters (of three to six water molecules), which reveals a systematic contraction of the nearest O-O separation with increasing cluster size.10,11,16–18 The driving force to maintain a balance between acceptor and donor H-bonds can, however, change dramatically if the H-bonded system is no longer composed of only neutral water molecules. For instance, the hydroxyl ion (OH-) in water favors acceptor bonds more than donating bonds7 because the negative charge on the oxygen atom increases its ability to form strong accepting H-bonds. In addition, the negative charge spills over onto the hydrogen atom, making it less positive and thereby weakening its ability to make donating H-bonds. The reverse is the case for the Eigen form (H3O+) of protonated water, which makes strong donating H-bonds with surrounding water molecules because the hydrogens in H3O+ are more positive and the oxygen is less negative than in neutral water.19,20 It was recently shown from theoretical calculations of hexamers on hexagonally close-packed metal surfaces that there also exists an important balance between a water molecule’s ability to form S-bonds and H-bonds on surfaces.21 As for most metal surfaces explored in that study, it was seen that a hexamer on Cu(111) is buckled with alternating strong acceptor H-bonds and S-bonds indicative of a cooperativity effect similar to what is observed in other H-bonded systems. Here we use density functional theory (DFT) calculations to obtain bond distances, charge rearrangements, and orbital populations to examine the balance of S-bonding and H-bonding for the important OH + H2O adlayer at metal surfaces. We demonstrate how a synergistic interplay between S-bonding and H-bonding drives the stability of the OH + H2O adlayer at metal surfaces (i.e., a cooperativity effect that is more than the simple sum of the individual H2O-OH H-bonding and H2O-M and M-OH S-bonding channels). The OH + H2O adlayers on isoelectronic Cu(110) and Cu(111) and isostructural Pt(111) and Cu(111) surfaces are compared to illuminate general features of the cooperativity effect as well as the role of geometric and electronic structure effects in the balance between S- and H-bonding. We then proceed to discuss such effects for pure water adsorption systems on metal surfaces and show how the rules developed for H-bonded systems can be applied to generate a simple picture of the cooperativity effects in adsorbed H-bonding systems involving water, OH-, and H3O+. II. Methods First-principles calculations were performed with the Vienna ab initio simulation program (VASP),22–24 in a DFT framework,
J. Phys. Chem. C, Vol. 114, No. 22, 2010 10241 using the projector augmented waves (PAW) method.25 Computational details for Cu(110)26,27 and Pt(111)28,29 have been published previously; for Cu(111), the same computational procedure as in ref 30 was applied. Briefly, for Cu(110) the PBE (Perdew-Burke-Ernzerhof) exchange-correlation functional31 was used, which has been shown to reliably describe hydrogen bonds32 as well as surface properties involving water,33 and the Perdew-Wang 91 (PW91)34 exchange-correlation functional was used for the (111) surfaces. We have checked that PW91 and PBE yield very similar bonding structures and energies so that employing PW91/PBE functionals for different surfaces should not introduce significant errors especially for the atomic structure, which is the input for further X-ray spectroscopic analysis. For instance, for the mixed OH and H2O overlayer on Cu(110), Cu-O and O-O bond lengths produced by the two functionals generally differed by 0.001 Å with a maximum difference of 0.006 Å. Likewise, the bonding energy in PW91 is only 0.05 eV higher than that in PBE, and the relative energy difference is systematic. The calculations employed a plane wave cutoff of 400 eV. Two different surface unit cells with five metal layers were used for the (111) surfaces, (3 × 3)R30° and (3 × 3), with 6 × 6 × 1 and 3 × 3 × 1 k-point meshes, respectively; for Cu(110), six layers were used in combination with a c(2 × 2) unit cell and a 2 × 2 × 1 k-point mesh.26,27 We have performed extensive convergence tests on the planewave energy cutoff as well as the number of k points with the criterion that the total energy be converged to ∼0.02 eV/atom or better. As a specific example, for H2O/Cu(110) we found that increasing the number of k points from 2 × 2 × 1 to 6 × 6 × 1 gives a change of only 0.02 eV/atom, making the 2 × 2 × 1 k-point mesh a satisfactory level at a reasonable computational expense; using a single k-point led to a difference of 0.24 eV/atom compared to the 6 × 6 × 1 k-point mesh. The adsorbates were in all cases attached to only one side of the slab, and a dipole correction scheme canceling the resulting field across the slab was used throughout.35 The structure used for the OH- ion in solution is a representative charge-neutral cluster model, including the second hydration sphere, cut from the trajectory of a Car-Parrinello molecular dynamics (CPMD) simulation of a 1 M NaOH(aq) solution.36 To obtain a spectroscopically relevant decomposition of the wave function or density of states, we compute X-ray emission (XES) spectra (i.e., the decay of a valence electron to fill an empty core level with emission from an X-ray photon). The XES spectra were computed within the dipole approximation of the transition between the O 1s core hole and the occupied valence states using the ground-state orbitals for both the initial and final states as discussed in previous work.37–41 Because of the dipole selection rule, the X-ray emission process for an initial O 1s core hole projects local 2p character onto the spatially localized core orbital, making it a useful tool for population analysis of the 2p orbitals of water, which includes the O lone pair, lp (2pz), orbital.37,39,42 By integrating each computed p-component (px, py, pz) spectrum and comparing to the corresponding intensity for the free water molecule or OH- ion in solution, we can derive how water and hydroxyl, respectively, change their orbital occupation upon interaction with the metal surface. Calculations of XES spectra and charge density differences (CDD) were performed using gradient-corrected43,44 DFT within the StoBe-deMon code45 for cluster models, shown in Figure 1, cut from the periodic structures described above. To ensure stability and avoid artifacts due to finite cluster size and edge
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Schiros et al.
Figure 1. Top and side views of cluster models cut from low-energy structures for 1 ML OH + H2O coadsorbed on (a) Pt(111), (b) Cu(111), and (c) Cu(110) in a 1:1 ratio of H2O and OH. Oxygen belonging to H2O and OH groups is indicated in red (darker) and blue (lighter), respectively.
TABLE 1: Bond Lengths (Å) and Total Interaction Energy, Eint, (eV) for (A) the H-Down Monolayer and (B) OH + H2Oa Adsorbed on Pt(111), Cu(111), and Cu(110) Compared to (C) Metal-OH (M-OH) Distances for the Pure (Flat-Lying) Atop-Adsorbed OH Layers (1/3 ML Coverage) at These Surfacesb Pt(111) d(Å), E(eV) d(H2O-H2O) d(OH,H2O) d(H2O,OH) d(OH,OH) d(H2O-M) d(M-OH) Eint
A 2.77
acc
Cu(111) B
2.88
C
don
A
-1.30
C
2.59 3.02 2.66
2.35
B
Cu(110)
2.2 2.1 -1.68
A 2.69
acc
2.76 2.57 3.36 1.99
-1.15
2.06 1.99 -1.90
2.44 1.87
-1.34
B 2.82
don
2.76 2.96 2.53 2.83 2.76 2.01 1.93 -2.05
C
1.82
a Shown in Figure 1. b Values in bold are emphasized to show the shortening (lengthening) of the H2O-M (M-OH) distance in the coadsorbed phase (B). Energy values were obtained as described in the text, and structural details for the pure water layers (A) are provided in ref 65 (Pt) and refs 56 and 64 (Cu).
effects, clusters were kept as large as possible. The calculations were repeated for a range of cluster model sizes to determine the minimal number of atoms needed for convergence of the computed values, ensuring stable energetics (Eint, Table 1) and avoiding artifacts in computed XES spectra from which the orbital occupations are derived (Table 2). For instance, for the central oxygen-bonded water molecule in an H-down layer on Cu(111), the interaction energy, Eint, defined in the following, was nearly identical for three-layer clusters of 37 Cu atoms (used here) and 59 Cu atoms: -1.18 eV (37 Cu atoms) and -1.14 eV (59 Cu). We finally point out that the surface chemical bond was previously shown to be quite local and that stable chemisorption energies can also be computed for rather small clusters.46–49 This is due to the fact that a finite cluster has a discrete set of electronic states, which implies that an excitation with finite energy may be required on certain clusters to reach the bonding state. By using the proper excited state on the bare cluster as reference this energy offset may be compensated for yielding energetics similar to excitations around a Fermi level;48,49 this was, however, not an issue in the present study.
Similar criteria (convergence of energy values and computed spectra) were used to determine that four water molecules, a central O-bonded water molecule fully coordinated by three H-down molecules, provides a sufficient representation of the water monolayers on the metal clusters. Thus, the (111) surfaces were modeled with 37 metal atoms in 3 layers, with 19 atoms in the first layer, 12 in the second, and 6 in the third, and the adlayer included 7 H2O and 6 OH molecules. For Cu(110), 64 Cu atoms arranged in 4 layers and 8 H2O and 8 OH model the system. Four water molecules, a central O-bonded water molecule fully coordinated by three H-down molecules, were sufficient to represent the pure water monolayers on the metal clusters. The metal atoms in the first layer of Cu(111) and the first two layers of the Cu(110) cluster were described at the allelectron level using the DZVP2 DFT optimized basis set of ref 50, and a one-electron effective core potential (ECP)51 provided a sufficient description of subsequent layers. The Pt atoms were described using a 16-electron relativistic ECP developed by Wahlgren52 that also included the 5s2 electrons in the ECP
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TABLE 2: Oxygen Charge Occupancy (Electrons) for Each of the 2p Components (px, py, and pz) of the O-Bonded Water Molecule and OH in Different Environments, Obtained by Integration of the XES Spectra Projected along Different Bond Directionsa O 2p population:
px
py
pz
H2O gas phase H2O/Pt(111) H2O* + OH/Pt(111) H2O/Cu(111) H2O* + OH/Cu(111) H2O/Cu(110) H2O* + OH/Cu(110) OH gas phaseb OH- in solution OH/Pt(111) OH* + H2O/Pt(111) OH/Cu(111) OH* + H2O/Cu(111) OH/Cu(110) OH* + H2O/Cu(110)
1.46 1.73 1.74 1.68 1.74 1.74 1.76 2.26 1.80 1.81 1.85 1.83 1.80 1.78 1.76
1.54 1.54 1.53 1.51 1.58 1.54 1.54 1.6 1.39 1.48 1.53 1.49 1.55 1.41 1.52
2.0 1.75 1.72 1.90 1.73 1.77 1.74 2.13 1.81 1.43 1.53 1.55 1.62 1.64 1.66
a px is oriented through the plane of H2O or OH, py describes the H2O-H2O or OH-H2O bond, and pz corresponds to the O lp perpendicular to the surface. The numerical 2p orbital populations are normalized to O 2pz ) 2 electrons for the free water monomer. For mixed OH + H2O layers, the * indicates whether the orbital occupation corresponds to that of OH or H2O. To facilitate direct comparison, OH/metal systems were modeled with OH parallel to the surface. b The high value is due to more contracted 2p orbitals compared to the reference water monomer.
operator; the form of the ECP follows that of Huzinaga,53 and the size of the core represents a compromise between a large (including 5s and 5p) and small (5s and 5p as valence) core, avoiding difficulties with the large 5d-5p exchange interactions.54,55 Parameters and orbital basis set for the Pt ECP have been given as Supplementary Material in ref 56. Hydrogen and oxygen were described by triple-ζ plus polarization basis sets. Hydrogen has the (5s) basis of Huzinaga57 contracted to 3s and with one p function added. The oxygen of the central water or hydroxyl molecule in the cluster models was described using the IGLO-III all-electron basis set of Kutzelnigg et al.,58 and all other oxygen atoms were described using an ECP.59 We note that in the StoBe-deMon calculations an auxiliary Gaussian basis set is used to expand the Coulomb potential and also that, during the iterations to reach self-consistency, an additional auxiliary basis is used to represent the exchangecorrelation potential over the numerical grid to allow the use of a coarser grid to speed up the iterations; at convergence, the grid is tightened and the exchange-correlation contribution is obtained by numerical integration without the auxiliary basis. Using the nomenclature ((NC(s), NC(spd); NXC(s), NXC(spd)) to indicate the number of s (inner part) and spd-type (valence region, using the same exponents for s, p, and d) Gaussian functions used to fit and expand the Coulomb and exchangecorrelation potentials, respectively, the auxiliary basis sets used were O (5, 2; 5, 2), H (3, 1; 3, 1), Cu (5, 5; 5, 5), and Pt (5, 5; 5, 5). We point out that alternative OH + H2O structures were also considered in the VASP geometry optimizations but were found to be less stable. On Cu(110), for example, short bridge sites were 0.33 eV per cell less stable, or 0.08 eV per H2O favoring top sites. That is, coadsorbed water molecules in the top and bridge site structures have adsorption energies of 0.63 and 0.55 eV, respectively. Top site adsorption was further confirmed by the large difference in computed XPS binding energy for OH
and H2O at bridging sites on Cu(110) compared to experiment60 and by a much better overall XPS agreement for the top site model presented here. On Pt(111), the OH + H2O adlayer has been shown by a combination of experimental and theoretical techniques to consist of both (3 × 3)R30° and (3 × 3) phases.61 For the sake of simplicity, only the (3 × 3) phase, which is slightly lower in energy, is discussed here; our calculations show that the salient features in the chemical bonding are quite similar for the two systems. Recently, novel mixed OH + H2O structures were obtained on metal surfaces by path integral ab initio molecular dynamics simulations.62 In those structures, proton delocalization leads to either distinct H3O2 complexes or symmetrical delocalization around each O atom, depending on the metal surface lattice constant. In both cases, the O atoms in the layers are all, to a large extent, chemically equivalent. This differs significantly from our OH + H2O structures that have distinct OH and H2O species. However, XPS results can clearly distinguish between the situations of equivalent or nonequivalent oxygens in the mixed layers. Because of the attosecond timescale ionization in XPS, nuclear motion is negligible during the ionization process. Equivalent oxygens will result in a single O 1s XPS peak whereas inequivalent oxygens will give rise to two peaks that are chemically shifted with respect to each another. Experimentally, two distinct and well-separated O 1s XPS peaks are observed for mixed OH + H2O layers on the metal surfaces discussed here.61,63 Furthermore, theoretical spectrum calculations of XPS and XAS spectra and comparison with experiments were also fully consistent with the existence of well-defined OH and water molecular units on the Pt(111) surface.61 This shows that the structural models that we use are on average more realistic than structures with equivalent oxygens. Regarding our water monolayer structures, consistent with nonwetting behavior, the optimized (H-down) structure for water on Cu(111) deviates from the wetting structures on Cu(110) and Pt(111) with a large Cu-O distance of 3.36 Å for the O-bonded water molecules, which sit 0.13 Å further from the surface than their H-down neighbors. In fact, the nature of the O-O buckling (vertical displacement between O atoms) on Cu(111) is opposite to that on hydrophilic Pt(111) and Cu(110) where the H2O-M interaction is optimized and the O-bonded molecules sit ∼0.4 Å closer to the surface than their H-down counterparts. To facilitate a direct comparison of orbital interactions for the two copper surfaces, in the cluster model the water layer on Cu(111) was pushed to the optimal O-Cu distance of 2.44 Å obtained for Cu(110).64 To avoid the unphysical situation of very short metal-H-down water (M-H2O) bonds at this distance, the O-O buckling was altered to mimic that of the Pt and Cu(110) surfaces, with distances obtained by scaling the water layer for the (111) surface of Pt65 by the Cu/Pt lattice constant ratio. To enable comparison with adsorbed OH in the OH + H2O structures, the orbital occupation analysis for a single OH adsorbate was performed for OH at atop sites with its O-H axis rearranged to be lying parallel to the metal surfaces in all cases after optimization. This approach is reasonable because (1) only a weak dependence of the interaction potential on the OH tilt angle with respect to the surface, as on Cu(111),66 is anticipated and (2) although single OH adsorbates prefer higher coordination sites,30,67 the dominant S-bonding mechanism for the OH monomer is the same at different sites.66 III. Results and Discussion A. Bond Length. We begin by considering the geometric structure that characterizes mixed OH + H2O-metal coadsor-
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bate systems. Table 1 compares structural parameters for the pure water layer (A), the mixed OH + H2O structures shown in Figure 1 (B), and the pure OH phase (C) on Pt(111), Cu(111), and Cu(110). Interaction energies (Eint) for the different adsorbate systems are also given in Table 1, where we define Eint as the energy difference between the optimized overlayer and the overlayer in the same geometry but with the central water moved to an infinite distance. In this case, the central water is simply used as a probe of the electronic interactions in the site that it occupies. Some background on the structure of the water monolayer adsorbed at metal surfaces will facilitate the discussion. The water monolayer adsorbs at a metal surface with an inner flatlying, O-bonded layer and an outer layer in which water molecules donate one hydrogen bond to complete the monolayer whereas the other hydrogen either bonds to the metal surface (H down)64,65,68 or is directed toward the vacuum (H up).64,69 The degree of O-O buckling between the different types of water molecules in the first monolayer is significantly larger for the H-up configuration than for the more flat, fully coordinated H-down structure.65,68,70 Similar to the H-down water layer, the mixed OH + H2O layer forms a fully coordinated, nearly planar layer at metal surfaces (Table 1). However, the flatness of the OH + H2O layer arises from a decrease in the H2O-M distance and an increase in the M-OH distance compared to those of pure H2O or OH layers (Table 1), in accord with findings for other metals and alloys.71,72 Despite the shorter water-metal distance in the mixed layer compared to that in the pure water adlayer, which increases Pauli repulsion, the relaxed interaction energy (Eint) is larger (more negative). This is most apparent on Cu(111), which is hydrophobic21,56,63 but for which ambient-pressure XPS measurements60,63 show that the wetting property can be tuned by preadsorbed oxygen;63 the resulting OH pins water to the surface via strong H-bonds.60,63,64,73–75 This shows that OH stabilizes water at metal surfaces, in agreement with the current understanding.6,28,60,61,63,76 Although hydrated OH is quite stable on Pt(111), a pure, highcoverage OH phase cannot be prepared experimentally on this surface,73 in contrast to the open surfaces of Ni(110), Cu(110), Ag(110), and Pt(110).77–81 This suggests that water also stabilizes OH on the close-packed (111) surface.30 In addition, both water and hydroxyl occupy top sites in the mixed layer on metal surfaces, indicative of directed dative bonding. This is expected as the preferred site for H2O in the pure water monolayer56 but is different from the adsorption geometry of pure, non-Hbonding OH layers. For instance, the interaction of OH with metal surfaces is generally characterized by ionic bonding at higher coordination sites,30,66,67 such as the three-fold hollow site predicted for Cu(111)66 or short-bridge sites on Cu(110).26,27 Furthermore, our calculations predict an upright geometry as favored for pure OH adsorbed at metal surfaces, which is reasonable given the energetic drive to minimize orbital overlap between the O lp and metal d states. In the mixed OH + H2O layer, however, all OH groups are oriented parallel to the surface and are engaged in H-bonding. This is necessary for the completion of the intermolecular H-bond network, which is favored by the twice-as-strong donating H-bonds from water to chemisorbed OH compared to water-water H-bonds.28 The stronger H-bonds result from the effective negative charge on the OH, which makes it a strong H-bond acceptor (short HOH-OH H-bonds) but a weak H-bond donor (long OH-OH2 H-bonds).61 This results in an asymmetry in O-O distances as observed in Table 1, which our DFT
Schiros et al. geometry optimizations show to be a general phenomenon for the water/hydroxyl (H2O + OH) layer at a large number of metal surfaces;30,70 this is similar to, but less pronounced than, the case of OH- ions in solution.7 Thus, geometric (and energetic) considerations show that strong H-bonds in the mixed water/hydroxyl adlayer (i) stabilize OH on metal surfaces; (ii) compensate for the less favorable OH adsorption geometry (flat, top site; see Figure 1); and (iii) facilitate stronger S-bonds with a shorter H2O-M distance (Table 1). The interplay between S- and H-bonding signals that a cooperativity effect between bonding channels drives the structure and stability of the mixed water/hydroxyl overlayer at metal surfaces. B. Orbital Charge Occupation and Distribution. Details of the interplay between S-bonding and H-bonding in the layer are illuminated by electronic structure considerations. Because water-metal and OH-metal S-bonding primarily involve the lone pair orbitals, which are also implicated in accepting intermolecular H-bonds, the charge occupancy of this orbital is useful in analyzing the interaction in the different bonding channels and at the different surfaces. The O 2p charge occupations obtained using computed XES and projected along the different bond directions (px, py, and pz) for OH and H2O in different bonding environments, including the Pt(111), Cu(111), and Cu(110) surfaces, are given in Table 2, with the bond directions defined in the Table 2 caption. By comparison to the corresponding intensity for the free water molecule or OH- ion in solution, we can derive how water and hydroxyl, respectively, change their orbital occupation upon S- and H-bonding in the mixed water/hydroxyl adlayer at metal surfaces. The charge rearrangement along different bond directions can be visualized using charge density difference (CDD) plots of the calculated densities as shown in Figure 2. To isolate the changes in S-bonding due to the H-bond network, the CDD is taken as the charge density of the fully relaxed system (F(relaxed)) minus that of the system with the central O-bonded H2O separated at a long distance (F(H2O separated)): CDD ) F(total) - F(H2O separated) - F(H2O). Consequently, the CDD plots (Figure 2) contain contributions from both the region of overlapping densities (Pauli exclusion) and from adsorptioninduced charge rearrangements where the latter dominate as seen from the orbital-like character of the CDDs. The CDD plots thus reflect the rearrangement of charge when the central O-bonded water is brought in from an “infinite” distance to bond with surrounding OH and H2O and the metal surface, for which the orbitals have been relaxed with the central water removed. As such, charge movement within the neighboring adsorbate species or metal atoms is induced solely through interaction with the central water molecule. Let us first briefly review the nature of the charge redistribution accompanying water-water (H-) and water-metal (S-) bonding. In both cases, bonding is facilitated by a redistribution of charge that minimizes the Pauli repulsion. H-bonding involves a loss of charge in the lone pair (lp) of the acceptor molecule and a gain (loss) of charge on the O (H) of the water that donates a hydrogen.42 When the molecule is involved in both donor and acceptor bonding, we can view the loss of charge in the O lp as being transferred to the internally OH bonding 1b2 orbital O 2p population. The polarization of charge in the internal OH bond toward the oxygen makes the hydrogen atoms more positive. This has been seen in CDD plots of tetrahedrally H-bonded water as a depletion of charge in the O lp and an increase in charge on the O atom in the HOH plane.42 These rearrangements
Bonding of Water and Hydroxyl at Metal Surfaces
Figure 2. Charge density difference (CDD) plots (see the text) upon water adsorption for the (1) OH + H2O mixed adlayer and (2) water monolayer (H-down) on Pt(111) and Cu(111), plotted along (A) the molecular axis of the central water molecule (px), (B) the OH-H2O bond on the acceptor side of the center water molecule (py), and (C) the O-H bond on the donor side of the central water molecule. Red (dashed lines) indicates the loss of charge, and blue (full line) indicates the gain of charge, where increasing color intensity indicates an increasing loss/gain (in electrons/Å3). (Inset) Schematic illustration of the bonding environment and the density planes for A-C. (D) Schematic of the conduit of charge rearrangement accommodated by the fully coordinated OH + H2O layer at metal surfaces underlying the cooperativity effect; arrows indicate the direction of electron density movement.
minimize the Pauli repulsion, allowing for the relatively short H-bond length, which increases the electrostatic attraction. Upon S-bonding, charge also redistributes along the watermetal bond axis to minimize Pauli repulsion. For flat-lying, O-bonded water molecules, this appears as a depopulation of the O lp and a movement of d electrons from the axial to the equatorial plane of the transition-metal atom.56,65 This is accompanied by a similar outward movement of charge in the metal s states away from the water-metal (S-) bond axis to
J. Phys. Chem. C, Vol. 114, No. 22, 2010 10245 expose the charge of the positive metal core and open up for electrostatic dative bonding.56 In the OH + H2O adlayer, the enhanced water-metal interaction at the shorter H2O-M distance requires that more O lp electron density polarize away from the region between the metal atom and O in H2O.61 This is reflected in a lower O lp population (pz) for all surfaces considered (Table 2), which is especially significant for Cu(111), and a greater redistribution of charge along the water-metal bond axis of water in the mixed layer compared to that in the pure water layer, most clearly seen in the CDD plot for Cu(111) (Figure 2A, right). The influence of the electronic structure of the substrate on water-metal bonding56 is also reflected in the O lp population.61 The unfilled d band of Pt(111) provides a mechanism for major charge rearrangement along the H2O S-bond in both the pure water and mixed water/hydroxyl layers; the degree of charge rearrangement along the planar H-bonds is comparatively minor (Figure 2C, left). The rehybridization of the Pt 5d shell, polarization of the metal s electrons away from the bonded metal atom, and rehybridization of the water orbitals from O lp to the internal 1b2 and 3a1 orbitals reduce the Pauli repulsion56,65 and allow the O lp to polarize toward the positive metal atom, resulting in a dative bond.56 We note that the mechanism for metal s-electron polarization is different from the atomic s to d demotion discussed earlier by Harris and Andersson.82 Both the O lp polarization and in particular the rehybridization of the water molecule to minimize the Pauli repulsion with the Pt 5d orbitals lead to the observed depopulation of the O lp. For isostructural Cu(111), however, the d-shell rehybridization mechanism is not available. The filled d band of the noble metal limits the ability of the 3d shell to rehybridize charge away from the H2O S-bond axis to open up for a dative bond,56 which is reflected in the higher O lp population for Cu(111) than for Pt(111) (Table 2). Consequently, the H-bond network compensates and lateral charge rearrangement dominates in the pure water and mixed OH + H2O layers on Cu(111); this is particularly evident in the mixed layer along the H-bond that water donates to hydroxyl on Cu(111) (Figure 2C, right). Conversely, because there is a greater electrostatic attraction and reduced Pauli repulsion of the OH + H2O layer at the open (110) surface of Cu as a result of the loss of electron density on the (110) ridges (Smoluchowski effect83), this demands less of the H-bond network in terms of stabilizing the interaction and the charge redistribution along the H-bond is less dramatic on Cu(110) (not shown) and more similar to that on Pt(111). Thus, the H-bond matrix in the OH + H2O layer has a very special character; it is rigid enough to stabilize water at the surface and induce long-range order in the adlayer but flexible enough to accommodate the necessary hybridization for bonding to the surface. We now turn our attention to OH S-bonding. We show that coadsorbed hydroxyl contributes more to the overall stability of the OH + H2O layer than just the ability to act as a strong acceptor of H-bonds from H2O and the strong M-OH adsorption energy. On the contrary, we see that the OH S-bond weakens (the bond lengthens) in the mixed OH + H2O layer compared to that in the pure OH phase (Table 1). This is likely due in part to the stronger H-bond network formed in planar geometry in which the H2O-M interaction would be too repulsive at the nominal M-OH distance, leading to M-OH bond lengthening instead. Furthermore, when hydroxyl adsorbs (OHad) alone at a metal surface, charge contracts along its O-H bond away from the hydrogen so that more charge is concentrated on the oxygen for OHad than for OH- in solution;7,61 this
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appears as an increase in py in Table 2. When coadsorbed with H2O, the contraction of charge toward the O of OHad is enhanced; this is seen in the additional increase in py (Table 2) as well as in the CDD plane cut along the H-bond that OH donates to H2O (Figure 2B). (We note that this effect is more pronounced in the CDD plot for Cu compared to Pt, which is partially due to the shorter OH-H2O distance for Cu in the structures considered.) As a result, OHad is a slightly less weak donor of H-bonds than OH- in solution.7,61 The degree of charge spillover to the hydrogen atom that OH donates to water is further reduced by depopulation of the OH lp (pz) along the M-OH bond (Figure 2B). This is also reflected in the lower O lp population (pz) for OH adsorbed alone or in the mixed OH + H2O layer compared to that in solution (Table 2). However, compared to OHad alone, we observe a net increase in the O lp (pz) population of OHad that is H-bonded to H2O at metal surfaces (Table 2). This indicates that the net decrease in the O lp charge of OHad in the mixed layer compared to that in solution reflects a balance of changes in electronic structure due to H2O-OH H-bonding, M-OH, and H2O-M S-bonding interactions. The charge redistribution along the M-OH axis for OH donation (Figure 2B) or accepting (Figure 2C) an H-bond in water further illuminates the details of the cooperativity effect between bonding channels. We observe that the OH lp orbital (pz) loses charge along the surface bond when OH acts as a donor (Figure 2B) and gains charge when it acts as an acceptor (Figure 2C). The latter, along with the stronger H-bond that H2O donates to OH, enables a greater depopulation of the O lp of water and a shorter H2O-M distance, where OHad provides a conduit for charge transfer from the metal atom that binds H2O over to its neighbor that binds OHad. The excess charge accumulates along the M-OH bond and in the OH lp, which may contribute to the longer M-OH bond length in the mixed OH + H2O layer. This is clearly seen in the charge rearrangement in the vertical slice cut along the strong H-bond that water donates to OH in Figure 2C, especially for Cu(111). From these observations, we can summarize the cooperativity between S-bonding and H-bonding (i.e., the details of the circuit that the bonding channels complete (Figure 2), as (i) a contraction of charge along the O-H bond of hydroxyl, which, along with the shorter OH-H2O bond length, suggests that surface-adsorbed OH is a stronger donor than OH- in solution, (ii) a gain of charge in the plane of the water molecules perpendicular to the H2O-M bond axis, which aids both the depopulation of the O lp of water and H-bonding in the layer, (iii) depopulation of the O lp of water to reduce the Pauli repulsion with metal d orbitals, facilitated by (iv) a loss of charge along the M-OH bond when OH donates an H-bond to water and (v) a gain of charge along the M-OH bond when OH accepts an H-bond from water. The ability to accumulate charge along both M-OH and H2O-OH bonds (Figure 2C) leads to reduced Pauli repulsion for H2O due to the loss of charge on O lp; the opposite is true for OHad. This explains the shorter (longer) H2O-M (M-OH) bond distance in the mixed phase compared to that in the pure phases (Table 1). It also shows that it is insufficient to attribute the enhanced stability of water, and general stability, in the OH + H2O adlayer to just the stronger H-bond network and the large M-OH binding energy; the latter is actually sacrificed to enhance the water-metal interaction. Instead, a cooperative effect between the H- and S-bonding channels drives the stability of the mixed water/hydroxyl phase at metal surfaces, facilitated
Schiros et al. by a bonding geometry that forms a closed circuit of efficient charge redistribution, as shown schematically in Figure 2D. C. Cooperativity between S-Bonding and H-Bonding: A Simple Rule. Here we show that the common features of H-bonding and S-bonding identified in this work make it possible to derive a simple picture of cooperativity effects in water/hydroxyl coadsorbate systems in terms of a surfacemediated balance of donor and acceptor bonds. Ultimately, the charge rearrangement and orbital occupation redistributions accompanying both H- and S-bonding are driven by an effort to reduce Pauli repulsion and enhance electrostatic attraction. In particular, the H-bonds between water molecules have been described in terms of electrostatic interactions and a rearrangement of the molecular orbital structure in order to reduce the Pauli repulsion.13,14,42 The changes in the electronic structure of water upon H-bond formation can be described as a depopulation of the lp orbital and an increase in the O content in the 1b2 orbital as charge is polarized toward the interior of the internal OH bond within the HOH plane on the oxygen atom. Similar changes in electronic structure accompany S-bonding. In particular, we see a reduction of oxygen population in the lp and an increase in the 1b2 orbital indicating similar rearrangements as for H-bonding (Table 2 and Figure 2). Common to water and OH adsorption is the formation of a positive metal ion core. This is due to dative bonding in the case of water56 and more ionic bonding in the case of OH. In both S-bonding and H-bonding, the bond is therefore related to electrostatic attraction between the oxygen lp and, respectively, the positive metal ion core or hydrogen atom. Because the internal orbital rehybridization upon both Hbonding and S-bonding results in a slightly increased electron density on the oxygen atom42 (which can be seen by summing the oxygen contributions in Table 2) with an accompanying depletion of electron density on the hydrogen atoms (Figure 2), there is a cooperative effect if both hydrogen and oxygen atoms can participate in electrostatic bonding. If, however, there is more than one bond on each side, then the H-bond will be weakened as seen by the fact that the maximum H-bond strength per bond is obtained for water chains and rings with only one accepting and donating H-bond.10,84 Because both H-bonding and S-bonding occur through similar channels in terms of orbital rearrangements, we propose that we can regard the S-bonding to a positive metal atom core as providing a similar electrostatic interaction with the O atom as the positive H atom in H-bonding. For the O-bonding water with the HOH plane parallel to the surface or for OH with its molecular axis parallel to the surface, the S-bond can then be regarded as accepting an H-bond. Let us test this hypothesis against the observed trends regarding changes between pure overlayers of H2O and OH and the mixed OH + H2O system. We observe that water interacts more strongly with the surface upon OH coadsorption in comparison to when it is only H-bonding parallel to the surface with other water molecules. This is observed in terms of both a shorter surface bond distance and a slightly larger depopulation of the lp. The reverse is seen for the OH species because in this case the OH surface bond becomes longer and the OH lp is less depopulated when coadsorbed with water. We can understand these observations directly on the basis of cooperative effects between S-bonding and H-bonding. In the case of the water monolayer on both Pt and Cu, each flat-lying molecule bonding through the oxygen lp donates two and accepts one H-bond involving neighboring molecules; in addition, it accepts one S-bond from the surface. In this case, we have a balanced situation with two donor and
Bonding of Water and Hydroxyl at Metal Surfaces two acceptor bonds if we treat H-bonds and S-bonds on an equal footing. When we instead coadsorb water with OH, the donor bonds from the water become stronger because the OH unit is more negative. To maintain the balance in terms of equal strength of donor and acceptor bonds for the water molecule, the acceptor bonds also need to strengthen. This leads to substantially stronger S-bonds in order to keep the balance of donor and acceptor bonds, which is exactly what is observed. Furthermore, the water becoming a better acceptor can also explain why OH donates a relatively short H-bond to surrounding water in the coadsorbed overlayer61 in comparison to OHin solutions.7 In the case of the OH species, the balance between donor and acceptor bonds is broken by the negative charge. OH makes stronger acceptor bonds; therefore, the bond distance to the surface for isolated OH is very short. When OH also accepts an H-bond from the neighboring water molecules, the hydrogen atoms will screen part of the electrostatic interaction resulting in a weaker S-bond. This will lead to a longer S-bond as well as less depopulation of the lp on the OH species. If we look only at pure water adsorbed on surfaces, we can also observe a cooperativity effect between S-bonding and H-bonding. If we assume equal bond strengths, S-bonding of ∼0.1-0.4 eV and H-bonding of ∼0.25-0.30 eV,70,76,85 and that each water molecule strives to have the same number of accepting and donating bonds, then we can explain many observations. In the case of the water dimer on surfaces, it is seen on the basis of theoretical calculations that there is a major difference in S-bonding between the donating and accepting water molecules.70,86–89 For the donating molecule, the bonding situation is balanced because we have one accepting S-bond and one donating H-bond. This is the optimum bonding situation, and the bond length to the surface is therefore even shorter than for the monomer. The reverse is seen for the accepting molecule that accepts two bondssone S-bond and one H-bondsmaking for a strongly unbalanced situation because donor bonds are missing. This leads to a weak S-bond and thereby a longer surface distance for the accepting molecule in the dimer in comparison to that for the donating molecule. To take this bonding asymmetry even further, if a water molecule goes on to accept two H-bonds in combination with a S-bond, then it will no longer bind to the surface via its oxygen but directs its HOH plane perpendicular to the surface and bonds very weakly to the surface through one of its hydrogens.90 However, the interaction of hydrogen with the surface is not insignificant. In fact, it leads to a strongly related type of cooperativity effect for the H-down, but not H-up, monolayer on Pt(111).91 In the water monolayer, the non-H-bonded OH group acts as a molecular switch, which in the H-down case closes a circuit involving the two water molecules and two Pt atoms. Similar to the mixed OH + H2O adlayer, the circuit closed by the H-down switch provides a conduit for additional charge depletion of the O-bonded lp to minimize the Pauli repulsion between the lp and Pt 5d compared to that in the H-up case; additional charge can be removed from the O-bonded Pt over to the H-down-coordinated Pt as well as that accepted by the H-down OH σ*. This results in a shorter O-Pt distance (stronger S-bond) in the H-down layer, which is offset by a slightly longer acceptor (2.76 vs 2.71 Å) and stronger donor bonds (2.86 vs 2.91 Å) between water molecules compared to those in the H-up layer in accordance with the cooperativity rules.65,91 Furthermore, the cooperativity between S- and Hbonding also has consequences for the interaction of the
J. Phys. Chem. C, Vol. 114, No. 22, 2010 10247 monolayer with subsequent water layers. We have previously observed that the stronger S-bond severely limits the ability of the O-bonded water to accept an H-bond from a second-layer water molecule in the H-down compared to H-up layer on Pt(111).91 We can readily understand this in the context of a bonding mechanism in which S-bonds can be regarded as accepting H-bonds, consequently producing a simple cooperativity effect that seeks to balance acceptor and donor bonds. On the basis of similar reasoning, we can explain the nature of the buckling of water hexamers on metal surfaces where H-bond and S-bond distances were obtained on the basis of DFT geometry optimization.21 When a molecule in the hexamer accepts a short H-bond, it results in a longer S-bond in order to keep the balance between accepting and donating bonds, and the reverse is seen when a strong donated H-bond is balanced by a stronger accepting S-bond. Extending the discussion to the adsorption of H3O+ at metal surfaces, its very poor H-bond acceptor capability should, according to our chemical bonding picture, lead to a very weak S-bond. Indeed, the expected physisorption of H3O+ is confirmed by Pt-O distances as long as 4.5 ( 0.2 Å as extracted from structures in ref 92 for adsorbed, flat-lying H3O+ in DFToptimized overlayers. Our chemical bonding picture predicts nearly identical results for flat-lying (i.e., not H-down) H3O+ on other metal surfaces. We thus establish a simple rule for cooperativity between S-bonding and H-bonding in water/hydroxyl-metal and water-metal adsorbate systems. We can simply insert the S-bond as an accepting bond and use the general rules regarding cooperativity seen in H-bonding. This can explain most of the balance of various interactions between water-OH and water-water in terms of cooperativity effects. We expect this to be general and applicable to most S-bonding situations on metal surfaces with respect to H-bonding. V. Conclusions We have demonstrated that we can use a simple rule regarding cooperativity effects to describe the balance between surface (S-) and hydrogen (H-) bonding in H2O + OH coadsorbed overlayers. The surface bonding for OH and H2O via oxygen takes place through the formation of a positive metal ion core. We can therefore relate the electrostatic bonding of the negative oxygen atom to the positive metal atom in a similar manner as for bonding to the positive hydrogen atom in the H-bond, whereby the surface bonding becomes similar to an accepted H-bond for the surface-coordinated water molecule or OH species. The rearrangement of the orbital structure within the water molecule leads to an advantage in terms of interaction energies if a balance between donating or accepting H- and S-bonds can be achieved. In the case of adsorbed OH, the negative charge on the oxygen atom leads to an enhancement of accepted H- or S-bonds. If the balance between accepted and donated bonds is broken, then there will be electrostatic screening resulting in a weakening of the bonds. The optimal balance for water in terms of bond strength occurs when for each H- or S-bond accepted (donated) one H- or S-bond is also donated (accepted). The general trends in terms of bond length and charge rearrangements for pure water adsorption systems and mixed OH + H2O overlayers, and thereby the stability of the OH + H2O oxygen reduction reaction intermediate, can be explained through these simple cooperativity rules. Acknowledgment. This work was supported by the Office of Basic Energy Sciences, U.S. Department of Energy under
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the auspices of the President’s Hydrogen Fuel Initiative and through the Stanford Synchrotron Radiation Lightsource, the Advanced Light Source, and the Swedish Research Council. Generous grants of computer time at the Swedish National Supercomputer Center and the Center for Parallel Computing are gratefully acknowledged. K.J.A. acknowledges the WennerGren Foundations for financial support. References and Notes (1) Henderson, M. A. Surf. Sci. Rep. 2002, 46, 1. (2) Thiel, P. A.; Madey, T. E. Surf. Sci. Rep. 1987, 7, 211. (3) Hodgson, A.; Haq, S. Surf. Sci. Rep. 2009, 64, 381. (4) Rossmeisl, J.; Nørskov, J. K.; Taylor, C. D.; Janik, M. J.; Neurock, M. J. Phys. Chem. B 2006, 110, 21833. (5) Vo¨lkening, S.; Bedu¨rftig, K.; Jacobi, K.; Wintterlin, J.; Ertl, G. Phys. ReV. Lett. 1999, 83, 2672. (6) Michaelides, A.; Hu, P. J. Chem. Phys. 2001, 114, 513. (7) Botti, A.; Bruni, F.; Imberti, S.; Ricci, M. A.; Soper, A. K. J. Chem. Phys. 2004, 120, 10154–10162. (8) Gregory, J. K.; Clary, D. C.; Liu, K.; Brown, M. G.; Saykally, R. J. Science 1997, 275, 814. (9) Silvestrelli, P. L.; Parrinello, M. Phys. ReV. Lett. 1999, 82, 3308. (10) Ojama¨e, L.; Hermansson, K. J. Phys. Chem. 1994, 98, 4271. (11) Xantheas, S. S.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 99, 8774. (12) Xantheas, S. S. Chem. Phys. 2000, 258, 225. (13) King, B. F.; Weinhold, F. J. Chem. Phys. 1995, 103, 333. (14) Weinhold, F. J. Mol. Struct. 1997, 398-399, 181. (15) Ludwig, R. Angew. Chem., Int. Ed. 2001, 40, 1808–1827. (16) Xantheas, S. S. J. Chem. Phys. 1994, 100, 7523. (17) Xantheas, S. S. J. Chem. Phys. 1995, 102, 4505. (18) Xantheas, S. S. J. Chem. Phys. 1996, 104, 8821. (19) Ojama¨e, L.; Shavitt, I.; Singer, S. J. J. Chem. Phys. 1998, 109, 5547. (20) Cavalleri, M.; Na¨slund, L.-Å.; Edwards, D. C.; Wernet, Ph.; Ogasawara, H.; Myneni, S.; Ojama¨e, L.; Odelius, M.; Nilsson, A.; Pettersson, L. G. M. J. Chem. Phys. 2006, 124, 194508. (21) Michaelides, A.; Morgenstern, K. Nat. Mater. 2007, 6, 597. (22) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (23) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 48, 13115. (24) Kresse, G.; Hafner, J. Phys. ReV. B 1994, 49, 14251. (25) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953. (26) Ren, J.; Meng, S. J. Am. Chem. Soc. 2006, 128, 9282. (27) Ren, J.; Meng, S. Phys. ReV. B 2008, 77, 054110. (28) Karlberg, G. S.; Wahnstro¨m, G. J. Chem. Phys. 2005, 122, 194705. (29) Karlberg, G. S.; Olsson, F. E.; Persson, M.; Wahnstro¨m, G. J. Chem. Phys. 2003, 119, 1. (30) Karlberg, G. S. Phys. ReV. B 2006, 74, 153414. (31) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865–3868. (32) Hamann, R. Phys. ReV. B 1997, 55, R10157. (33) Kurth, S.; Perdew, J. P.; Blaha, P. Int. J. Quantum Chem. 1999, 75, 889. (34) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (35) Bengtsson, L. Phys. ReV. B 1999, 59, 12301. (36) Chen, B.; Park, J. M.; Ivanov, I.; Tabacchi, G.; Klein, M. L.; Parrinello, M. J. Am. Chem. Soc. 2002, 124, 8534. (37) Nilsson, A.; Pettersson, L. G. M. Surf. Sci. Rep. 2004, 55, 49–167. (38) Nilsson, A.; Hasselstro¨m, J.; Fo¨hlisch, A.; Karis, O.; Pettersson, L. G. M.; Nyberg, M.; Triguero, L. J. Electron Spectrosc. Relat. Phenom. 2000, 110/111, 15. (39) Fo¨hlisch, A.; Bennich, P.; Hasselstro¨m, J.; Karis, O.; Nilsson, A.; Triguero, L.; Nyberg, M.; Pettersson, L. G. M. Phys. ReV. B 2000, 61, 16229. (40) Nilsson, A.; Wassdahl, N.; Weinelt, M.; Karis, O.; Wiell, T.; Bennich, P.; Hasselstro¨m, J.; Fo¨hlisch, A.; Sto¨hr, J.; Samant, M. Appl. Phys. A 1997, 65, 147. (41) Carravetta, V.; Pettersson, L. G. M.; Vahtras, O.; Ågren, H. Surf. Sci. 1996, 369, 146. (42) Nilsson, A.; Ogasawara, H.; Cavalleri, M.; Nordlund, D.; Nyberg, M.; Wernet, Ph.; Pettersson, L. G. M. J. Chem. Phys. 2005, 122, 154505. (43) Becke, A. Phys. ReV. A 1988, 38, 3098. (44) Perdew, J. P. Phys. ReV. B 1986, 33, 8822. (45) Hermann, K.; Pettersson, L. G. M.; Casida, M. E.; Daul, C.; Goursot, A.; Koester, A.; Proynov, E.; St-Amant, A.; Salahub, D. R.; Carravetta, V.; Duarte, A.; Godbout, N.; Guan, J.; Jamorski, C.; Leboeuf, M.; Leetmaa, M.; Nyberg, M. Pedocchi, L.; Sim, F.; Triguero, L.; Vela, A. deMon software, version 5.3;Stockholm, 2005. (46) Siegbahn, P. E. M.; Pettersson, L. G. M.; Wahlgren, U. J. Chem. Phys. 1991, 94, 4024. (47) Pettersson, L. G. M.; Faxe´n, T. Theor. Chim. Acta 1993, 85, 345.
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