J. Phys. Chem. C 2008, 112, 10889–10898
10889
Density-Functional Analysis of Hydrogen on Pt(111): Electric Field, Solvent, and Coverage Effects Ikutaro Hamada†,‡ and Yoshitada Morikawa*,†,‡,§ The Institute of Scientific and Industrial Research (ISIR), Osaka UniVersity, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan, CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan, and Research Institute for Computational Sciences (RICS), National Institute of AdVanced Industrial Science and Technology (AIST), Umezono 1-1-1, Tsukuba, Ibaraki 305-8568, Japan ReceiVed: April 3, 2008; ReVised Manuscript ReceiVed: May 8, 2008
Density-functional theory is utilized to study the energetics and vibrational properties of hydrogen on the Pt(111) surface in order to clarify the adsorption state of hydrogen on a Pt electrode in an electrochemical condition. Particular attention is paid to the Pt-H stretching frequency (νPt-H) of hydrogen on the atop site, which is often referred to as overpotentially deposited hydrogen and considered to be the reaction intermediate of the hydrogen evolution reaction. We investigate the origin of the large potential dependence of νPt-H observed in the electrochemical experiments by taking into account the effects of electric field, solvent, and hydrogen coverage to simulate water/metal electrode interfaces realistically. The electric field effect on νPt-H without water solvent, the Stark tuning rate, is less than 20 cm-1 · V-1. Although it is increased by a factor of 2.5 by taking into account the solvent effect, the electric field effect alone cannot account for the experimentally observed large potential-dependent frequency shift. It is found that the coverage effect on νPt-H is significant indicating that the electric field, solvent, and hydrogen coverage effects should be taken into account to explain fully the experimentally observed large frequency dependence on the electrode potential. The large hydrogen coverage effect on the vibration frequency shift is attributed to the shift of the d-band center due to the hybridization between the hydrogen s state and the substrate d-band. Introduction The catalytic reaction of hydrogen on electrode surfaces is one of the simplest and most fundamental issues and has been studied extensively for many years. Among them, the hydrogen evolution reaction (HER) on Pt electrode is one of the most fundamental and important reactions in electrochemistry. The HER is also important because of its close relationship with the fuel cell technology. However, despite the apparent simplicity of the reaction, the mechanism is not fully understood. The elucidation of the mechanism of the hydrogen evolution at the atomistic level is thus needed. The HER is considered to proceed through the initial adsorption of protons from solution (Volmer step) and the associative desorption of the hydrogen molecule via the recombination of the adsorbed hydrogen (Tafel step) or via an electrochemical reaction of the adsorbed hydrogen and the proton in solution (Heyrovky step). Understanding the adsorption state of hydrogen on the electrode surface serves as a basis for clarifying the microscopic mechanism of the HER. Hydrogen atoms adsorbed on Pt electrode surfaces are categorized into two types: one is the adsorbed species at potentials positive to the thermodynamic reversible potential of HER, the so-called underpotentially deposited (UPD) hydrogen, and the other is called overpotentially deposited (OPD) hydrogen. The OPD hydrogen is considered to be the reaction intermediate of the HER. To characterize these hydrogen species on the electrode, vibrational spectroscopy techniques are usefully * Corresponding author: E-mail:
[email protected]. Tel: +81-6-6879-8535. Fax: +81-6-6879-8539. † Osaka University. ‡ Japan Science and Technology Agency. § National Institute of Advanced Industrial Science and Technology.
applied. However, the consensus is not yet reached on them. By in situ infrared adsorption spectroscopy (IRAS) on polycrytalline Pt and Pt(111) electrodes in acid solution, Nichols and Bewick1 first observed the band at 2090 cm-1, which was assigned to the vibration of OPD hydrogen on the atop site. They concluded that the atop hydrogen is the intermediate of HER. Ogasawara and Ito2 carried out in situ IRAS measurements and observed bands at ∼2010 cm-1 on the Pt(100) and Pt(11 1 1) electrodes and at ∼2080 cm-1 on the Pt(110) electrode that they assigned to the vibration of hydrogen on the atop site. On the well-oriented Pt(111), however, no vibrational band due to the adsorbed hydrogen was observed, and on the incompletely oriented step-rich Pt(111) surface, they observed the vibrational band from the hydrogen. They suggested that the terminal (atop) hydrogen adsorption is sensitive to the surface crystallographic orientation. Sum frequency generation (SFG) experiments were carried out by Tadjeddine and Peremans3,4 on polycrystalline and low-index Pt surfaces. They observed bands at 1890-2050 cm-1, which were assigned to the vibration of UPD hydrogen adsorbed on the atop site (Hatop). In addition, the band at 1770 cm-1 was observed in the overpotential region, which they concluded to correspond to the vibration of the hydride complex of the form H2Pt-R. By using Fourier transform infrared adsorption spectra (FT-IRAS), Nanbu et al.5 also observed a band at ∼1800, ∼2100, and ∼2070 cm-1; however, they suggest that the bands at ∼1800 and ∼2100 cm-1 are due to CO adsorbed on the bridge and atop sites, respectively, and at ∼2070 cm-1, to hydrogen on the atop site. Raman spectroscopy was used by Ren et al.6 and Xu et al.,7 and they observed the band at 2088 cm-1 due to the hydrogen on the atop site. They found that the frequency shifts by changing the electrode potential at the rate of dν/dE ≈ 60 cm-1 · V-1, where ν is the frequency
10.1021/jp8028787 CCC: $40.75 2008 American Chemical Society Published on Web 07/01/2008
10890 J. Phys. Chem. C, Vol. 112, No. 29, 2008 and E is the electrode potential. By using the quantum chemistry calculations, they suggested that the frequency shift originated from the work function shift with the change of electrode potential. In very recent studies using the surface-enhanced infrared reflection absorption spectroscopy (SEIRAS), Kunimatsu et al.8–10 reexamined the HER and the hydrogen oxidation reaction (HOR) and observed a weak vibration at around 2090 cm-1 below 0.1 V (RHE) and assigned this band to the Pt-H stretching mode of hydrogen adsorbed on the atop site. They found a large potential-dependent frequency shift of 130 cm-1 · V-1 for the Pt-H stretching mode. The observed potential dependence of the Pt-H stretching frequency (νPt-H) is remarkably large compared with other adsorbed systems, for example, CO on the Pt surface. The observed frequency shift is 30 cm-1 · V-1 for νC-O11and -10 cm-1 · V-1 for νPt-CO.12 The shift of νC-O was explained in terms of the electric field at the electrode surface (vibrational Stark effect).13 However, Xu et al.7 and Kunimatsu et al.9,10 suggested that the Stark effect is small on the frequency shift of hydrogen on the Pt electrode. On the theoretical side, the electronic structure method based on the density-functional theory (DFT)14,15 can be a useful tool to clarify the atomic geometries and electronic properties of surfaces and interfaces. Vibrational properties can be accurately predicted by DFT and the direct comparison with experiment is possible. By carefully analyzing and comparing theoretical and experimental results, it will be possible to clarify the atomistic origin of the frequency shift and to gain insights into the adsorption state of hydrogen on the electrode. Several theoretical studies on hydrogen on Pt surface in ultrahigh vacuum (UHV) are available in the literature.16–26 Recently it is becoming possible to simulate hydrogen at a realistic water/ electrode interface including the effect of the electrode potential by DFT using a periodic slab27–31 or a finite cluster.32 Recent work by Tomonari and Sugino33 demonstrates the importance of the solvent effect on the vibrational frequency of hydrogen on the Pt surface. They carried out quantum chemistry calculations on the basis of DFT for a Pt13 cluster with an H atom adsorbed on an atop site under external electric fields to investigate the origin of the frequency shift. They included the solvent effect by embedding the cluster in a cavity surrounded by a uniform dielectric medium, the so-called conductorlike screening model (COSMO), and found that the solvent effect significantly enhances the field effect on νPt-H, leading to the shift of 21 cm-1 · V-1nm. Regarding the field effect, it should be noted that there is a comparative DFT study by Wasileski et al.34 They carried out DFT calculations and gave the detailed analyses on energetics and vibrational frequencies of adsorbates on metal surfaces, including hydrogen. In this work, we study hydrogen adsorption on a Pt(111) surface by means of the periodic DFT, which is superior in describing the metal surfaces. We take into account not only the electric field but also the solvent and the hydrogen coverage effects to model the water/electrode interface realistically. The effect of the electrochemical environment on νPt-H of hydrogen on the atop site is systematically examined and analyzed, and the origin of the large potential dependence of Pt-H vibrational frequency is investigated. Computational Details All calculations in this work were carried out by using density-functional theory as implemented in the STATE (simulation tool for atom technology) code, which has been successfully applied to semiconductor as well as metal surfaces.35,36 The electron-ion interaction is described by pseudopotentials37,38
Hamada and Morikawa
Figure 1. Surface unit cells of (a) (1 × 1), (b) (3 × 3), (c) (2 × 2), and (d) (3 × 3) of Pt(111). Pt and H atoms are indicated by gray and white balls, respectively. High-symmetry adsorption sites are also indicated.
and wave functions and the augmentation charge were expanded by a plane wave basis set with the cutoff energies of 25 and 225 Ry, respectively. The Perdew-Burke-Ernzerhof39 generalized gradient approximation (GGA) was used for the exchangecorrelation energy functional. Pt surfaces were represented by three- or five-layer slabs, separated by a vacuum equivalent to a six-layer slab (1.5958 nm). A GGA-optimized lattice constant of 0.3949 nm, which is 0.7% larger than the experimental value of 0.392 nm, was used to construct the slabs. The corresponding interlayer spacing is 0.2280 nm. Hydrogen coverages (ΘH) of 1/12 monolayer (ML) to 2 ML were considered and (1 × 1), (3 × 3), (2 × 2), and (3 × 23) surfaces were employed, depending on the hydrogen coverage. The unit cells used in this work are shown in Figure 1. The surface Brillouin zone was sampled with (12 × 12), (8 × 8), and (6 × 6) unshifted k-point meshes for (1 × 1), (3 × 3), and (2 × 2) surface, respectively, and a (2 × 2) shifted k-point mesh was used for the (3 × 23) surface. The first-order Methfessel-Paxton scheme40 was used to deal with the Fermi level. The smearing width was set to 0.054 eV. The solvent effect was modeled by introducing a water bilayer in a (3 × 3) surface unit cell. The water bilayer model was successfully applied in other theoretical studies of electrochemical interfaces.28–30,41 Adsorbates (hydrogen atoms and water molecules) were introduced on one side of the slab, and the adsorbates and the top two layers were allowed to relax. The work function difference between the two surfaces was not corrected when only hydrogen species were adsorbed on a neutral surface because the induced dipole moment of a hydrogen atom is so small that it does not affect the energetics and vibrational frequencies very much. In the case of the water/Pt and the water/hydrogen/Pt interfaces, the effective screening medium method (ESM)42 was utilized to treat efficiently slabs whose work functions are different on both sides. Electric fields were introduced also by the ESM, with which finite electric fields can be applied on only one side of the Pt slab where hydrogen and water molecules are adsorbed, whereas the other side is exposed to a vacuum with zero electric field. In this condition, excess or deficit charge is accommodated on one side of a slab, and the image charge is automatically induced in the medium (conductor), whereby the electric field is generated at the surface or the interface. It should be noted that within the ESM the compensating uniform background charge is not necessary, and the spurious interaction between electrons and the background charge does not exist. To prevent
Density-Functional Analysis of Hydrogen on Pt(111)
J. Phys. Chem. C, Vol. 112, No. 29, 2008 10891 system, and εi is the eigenvalue of the adsorbed system. Sˆ is the overlap operator,38 which is necessary when the ultrasoft pseudopotentials are used, otherwise identity. Following ref 44, ˜m defined as we used a truncated atomic orbital γ
γ ˜m )
φ ˜m 1 + exp[(r - rc) ⁄ d]
where φ ˜m is the pseudo atomic orbital obtained in the course of the pseudopotential generation, and rc and d are the cutoff radius and the width, respectively. γ ˜m is normalized so as to satisfy 〈γ ˜m|Sˆ|γ ˜m〉 ) 1. For a better understanding of the bonding nature of hydrogen, we carried out a generalized Mulliken population analysis outlined in refs 45 and 46, which is applicable to a plane wave basis set. Wave functions of the adsorbed system ψi is expanded in terms of the wave functions of the separated adsorbate χAm and the substrate χSm as NA
ψi )
∑ m
Figure 2. Typical setting of the biased interface used in this work. (a) Side view of a water/H/Pt slab (shown is a three-layer Pt(111)(3 × 3) slab), (b) electrostatic potentials, (c) difference electrostatic potentials, and (d) induced charge densities.
electron leakage from the surface when accumulating the excess electrons on the surface, we introduced a barrier potential43 in the region of z > ze
( (
))
z - ze π Ve sin min , 1 2 d
where Ve, ze, and d are set to 8 eV, 0.529 nm, and 0.159 nm, respectively. Electrostatic potentials, difference electrostatic potentials, and induced charge densities on the water/hydrogen/ Pt interface are shown in Figure 2 to illustrate the typical setup of the interface model used in this work. Because we are interested in hydrogen on a cathode, only negatively charged states are considered in this work. Excess electrons were accumulated up to 0.05 |e| per surface Pt atom. Note that 0.05 e- per surface Pt atom corresponds to the surface charge of -11.9 µC · cm-2. The strength of the electric field in the vacuum region induced by the surface excess charge is estimated by Gauss’s law, F ) σ/ε0, where σ is the excess charge per unit area and ε0 is the vacuum permittivity. Vibrational frequencies were obtained by diagonalizing the dynamical matrices. The matrices were constructed by taking finite differences of the atomic forces with displacements of (5.29 × 10-4 nm. For these displacements, forces are in the linear regime. Because of the larger atomic mass of Pt compared with hydrogen and oxygen, displacement of Pt was neglected. By including the displacements of surface Pt atoms, the change in νPt-H was less than 5 cm-1. To discuss the field and coverage effects on the electronic structure of hydrogen on the surface, we calculated the projected densities of states (PDOSs) onto the atomic orbitals m defined by
Dm(ε) )
∑ |〈γ˜m|Sˆ|ψi〉|2δ(ε - εi) i
where i is the composite index of the band and the wave vector, ψi is the wave function of the hydrogen-adsorbed Pt(111)
NS
A A cim χm +
∑ cS χSm n
im
where NA and NS are the number of molecular and substrate orbitals used, respectively. χmAand χmS are calculated by using the same unit cell, cutoff energy, and k-points as those for ψi so that all these wave functions are expanded by the same set of plane waves. The expansion coefficients cAim and cSim are obtained by inverting the overlap matrix Smn ) 〈χm|Sˆ|χn〉 , where Sˆ is the overlap operator, as described above. The energy-dependent crystal orbital overlap population (COOP) between the molecular orbital χAm and the substrate orbitals is then calculated as NA NS
A pm (ε) )
∑ ∑ ∑ (cimA*SmncinS + c.c.) δ(ε - εi) i
m
n
Smn ) 〈χmA|Sˆ|χSn 〉 where c.c. denotes the complex conjugate. Here, it should be noted that the calculation of the overlap matrix must be carried out with great care. When we calculate the overlap matrix within the ultrasoft pseudopotential scheme, the overlap operator Sˆ for the adsorbed system is used instead for the separate systems. In some cases, this procedure causes the incorrect expansion of the wave functions of the total system (or the expansion coefficients), hence the violation of the orthonormal condition, leading to the physically incorrect results. In such cases, the norm-conserving pseudopotentials or the all-electron method should be used instead. We verified that it is not the case in the present study. We also note that the number of orbitals of the subsystems must be chosen carefully to avoid the incomplete basis set problem. Results and Discussion Adsorption Energies, Geometries, and Vibration Frequencies of Hydrogen on Pt(111). First, we calculated the adsorption energies of hydrogen on the neutral Pt(111) surfaces in UHV to confirm the accuracy and reliability of our interface setting. The adsorption energy is defined by
Eads,H ) -
(
)
nH 1 Etot(H/Pt) - Etot(H2) - Etot(Pt) nH 2
where Etot(H/Pt), Etot(H2), and Etot(Pt) are the total energies of the combined system, the hydrogen molecule, and the Pt slab, respectively. nH is the number of hydrogen atoms adsorbed on the surface. A positive value means that the adsorption is
10892 J. Phys. Chem. C, Vol. 112, No. 29, 2008
Hamada and Morikawa
TABLE 1: Adsorption Energies of Hydrogen (Eads,H) at High-Symmetry Sites on the Neutral Pt(111) Surface at ΘH e 1 ML (kJ/mol)a unit cell
NPt
atop
bridge
fcc hollow
(3 × 3)
3 4 5 6 7 8 9
47.0 32.4 42.9 40.1 40.7 39.7 37.3
43.4 32.6 38.5 39.6 37.5 37.7 36.2
50.1 41.9 45.1 47.4 44.6 45.4 44.1
45.8 36.5 40.5 42.2 39.4 39.7 37.3
3 4 5 6 7 8 9
54.8 39.7 50.0 49.5 46.1 47.6 43.9
50.4 44.5 48.3 48.9 5.5 47.4 45.8
1/3 ML 53.3 50.0 54.8 53.5 49.9 51.3 50.8
49.8 43.8 47.6 47.8 44.2 46.2 45.1
(2 × 2)
3 5
56.6 47.2
(3 × 23)
3 5
54.1 46.6
50.3 45.7
54.7 47.8
1/12 ML 55.3 52.3
51.9 47.3
a The dependence of Eads,H on the number of Pt layers (NPt) is also shown. The definition of the adsorption energy is explained in the text.
TABLE 2: Pt-H Bond Length (nm) at High-Symmetry Sites on the Neutral Pt(111) Surface at ΘH e 1 MLa
(1 × 1)
NPt atop bridge 5
0.155
NPt
atop
bridge
3 4 5 6 7
2265 2256 2270 2262 2270
1354
3 4 5 6 7
2282 2265 2259 2265 2259
(2 × 2)
3 5
2282 2265
(3 × 23)
3
2285
fcc hollow
hcp hollow
0.176
1 ML 0.185
0.185 0.185
(3 × 3)
5
0.155
0.175
1/3 ML 0.186
(2 × 2)
5
0.155
0.175
1/4 ML 0.185, 0.185, 0.186 0.185
(3 × 23)
5
0.155
0.175
1/12 ML 0.185, 0.186, 0.186 0.182,0.188, 0.188
a The bond lengths using five-layer slabs are shown. By changing the number of Pt layers (NPt), the changes of the bond lengths are less than 1%. The coordination numbers of Pt atoms are 1 (atop), 2 (bridge), and 3(fcc and hcp hollow sites). Because no symmetry constraint is adopted in the present calculations, the H atom is slightly displaced from the ideal high symmetry position in some cases. In such cases, all bond lengths are shown.
exothermic. The adsorption energies for high symmetry sites are summarized in Table 1, and the optimized Pt-H bond lengths (dPt-H) are listed in Table 2. Convergence of the adsorption energies with respect to the slab thickness is also shown. The fcc hollow site is the most stable adsorption site, except for the 1/3 ML case using a (3 × 3) surface unit cell with a three-layer slab. This indicates that a three-layer slab is not sufficient to obtain the accurate adsorption energies, and by increasing the number of Pt layers, the most stable adsorption site is converged to the fcc hollow site. We verified that the adsorption energies are converged within the chemical accuracy of 1 kcal/mol (4.12 kJ/mol) with five-layer slabs by repeating the calculations up to nine layers with (1 × 1) and (3 × 3) unit cells (Table 1). As already shown by Ka¨lle´n and Wahnstro¨m,19 at least five layers are necessary to obtain the accurate adsorption energies that are comparable with the experimental data.
fcc hollow
hcp hollow
1 ML (1 × 1)
1/4 ML 55.0 57.3 46.4 51.1
unit cell
unit cell
hcp hollow
1 ML (1 × 1)
TABLE 3: Pt-H Stretching Frequencies (cm-1) at High-Symmetry Sites of Pt(111) at ΘH e 1 MLa
(3 × 3)
1361
1157 1151 1151 1151 1145
1/3 ML 1276 1056 1074 1306 1056 1074 1068
1151 1151
1081 1080
1/4 ML 1050 1059 1/12 ML 1052
a The dependences of the frequencies on the number of Pt layers (NPt) are also shown.
The calculated νPt-H in UHV for the high symmetry sites together with the convergence test with slab thickness are listed in Table 3. We obtain νPt-H for fcc and hcp hollow sites of ∼1100 cm-1 and for atop sites of ∼2200 cm-1, in agreement with those obtained by the previous DFT calculations.21,22,25,30 The maximum error of frequency due to the use of a thin threelayer slab is estimated to be 23 cm-1 for the atop and fcc hollow sites. Because the error in frequency is small (∼1%), νPt-H using three-layer slabs is reported in the following. Electric Field Effect. Next, we examine the electric field effect dependence on the vibration frequency shift (vibrational Stark effect) on the νPt-H of the atop site. To investigate the effect of ΘH on the Stark tuning rate of νPt-H for the atop hydrogen systematically, we examined several hydrogen coverages and hypothetically put hydrogen atoms on atop sites at ΘH e 1 ML, whereas we assumed that fcc hollow sites are fully occupied and put additional hydrogen atoms on atop sites at ΘH> 1 ML. νPt-H and the corresponding dPt-H are plotted in Figure 3a,b for ΘH e 1 ML and ΘH > 1 ML, respectively. The calculated νPt-H and dPt-H show a good correlation: the larger the bond length, the higher the frequency becomes. Although Stark tuning rates at all coverages considered here are negligibly small at an electric field below -2.7 V · nm-1, at more negative electric fields, they increased to 2.26, 3.02, 2.36, 1.84, 5.97, and 5.07 cm-1 · V-1 nm for 1/12, 1/4, 1/3, 1, 4/3, and 2 ML, respectively. Wasileski et al.34 reported a Stark tuning rate of 4.5 cm-1 · V-1 nm, and Tomonari and Sugino33 reported ∼4.9 cm-1 · V-1 nm by using cluster models. The difference between the present results and the previous calculations may be due to the different treatment of the substrate. Similar discrepancy is also found in the theoretical study of the vibrational Stark effect on CO on the Pt(111) surface.47 By assuming the thickness of the electrical double-layer to be 0.3 nm,28,33,48,34 we obtain Stark tuning rates of 7.6, 10.1, 7.9, 6.1, 19.9, and 16.9 cm-1 · V-1 for 1/12, 1/4, 1/3, 1, 4/3, and 2 ML respectively. The Stark tuning rate is increased slightly at ΘH > 1 ML compared with ΘH e 1 ML. However, the calculated Stark tuning rates are much lower compared with the experimental value of 130 cm-1 · V-1.8,10 Thus the electric field effect alone cannot account for the large frequency shift observed in the experiments. To gain more insight into the field effect on the Pt-H vibrational frequency and its coverage dependence, we follow
Density-Functional Analysis of Hydrogen on Pt(111)
J. Phys. Chem. C, Vol. 112, No. 29, 2008 10893 The equilibrium position in the presence of the electric field q0F is obtained from the condition dE/dq ) 0 and by neglecting the higher-order term as
q0F )
µD F K0
Next, the total energy in the presence of the electric field is expanded in terms of q up to the third order as
1 Etot(q, F) ) E0F + KF(q - q0F)2 + GF(q - q0F)3 2 where E0F is the total energy at equilibrium, KF is the force constant, and GF is the anharmonicity parameter in the presence of the field. By collecting the coefficients in the second order, we obtain
KF ) K0 +
6G0µD - 2aD F K0
and the force constant-field slope can be derived as
dKF 6G0µD - 2K0aD ) dF K0 If we use the harmonic oscillator approximation, then the harmonic vibrational frequency νh is given by
νh )
Figure 3. Pt-H stretching frequency (upper panel) and bond length (lower panel) in ultrahigh vacuum as a function of surface charge at (a) ΘH e 1 ML and (b) ΘH > 1 ML. The values of the applied electric fields are also shown.
the analysis that was first given by Lambert53 and was later generalized by Wasileski et al.,34 which is useful in understanding the nature of the energetics and the vibrational properties of the adsorbed systems under the electric field. The total energy of the system can be expanded in Talyorlike series in terms of the displacement of the adsorbate q and the electric field F. For simplicity, we consider the zero-field limit, where the effect of polarizability can be neglected. By taking into account the terms up to the third order in q and to the first order in F and by rearranging these terms, the total energy can be written as 0 Etot(q, F) ) Etot (q) - µ(q)F
1 0 (q) ) E0 + K0q2 + G0q3 Etot 2 where E0 is the total energy at equilibrium, K0 is the force constant, and G0 is the anharmonicity parameter at zero field. The induced dipole moment µ(q) is expressed in terms of q up to second order
µ(q) ) µs + µDq + aDq2 The static and dynamic dipole moments are defined by
µs ) -
∂Etot ∂F q)0
and
µD ) -
∂2Etot ∂F ∂ q q)0
The higher-order (second order in q and first order in F) term aD is usually small but plays a non-negligible role in some cases.
1 2π
KF MA
where MA is the mass of the adsorbate. Then, the vibrational Stark-tuning slope is
dνh 3G0µD - K0aD ) νh dF K2 0
Note that this relation applies at zero field but can be generalized to the finite-field case along the lines of Wasileski et al.34 Although the Stark-tuning slope dK/dF is primarily determined by the combined quality 6GµD /K and -2aD, the former term dominates in the case of adsorbates that form a polar bond (hence, a large dynamic dipole moment) with the substrate.34 Note that when the vibration is purely harmonic (G0 ) 0) and the dipole moment is linear in q (aD ) 0) the vibrational frequency is field-independent. The above analysis can be adopted in the case that more than one atom is adsorbed on the surface by replacing the displacement q with the normal coordinate Q and the mass of the adsorbate with identity. We applied the analysis to the following simple systems as illustrative examples: one is the neutral Hatop/Pt(111) (1 × 1) at 1 ML (fcc sites are empty) and another is the neutral H/Pt(111) (1 × 1) at 2 ML where atop and fcc hollow sites are fully occupied. Parameters as obtained here are listed in Table 4, together with those obtained by Wasileski et al.34 for hydrogen adsorbed on an atop site of the Pt13 cluster. In both the 1 and 2 ML cases, the dynamic dipole moment µDs is small compared with that induced by adsorbates such as Na, reflecting the fact that the induced static dipole moment µss is small. Consequently, 6GµD/K is small, and non-negligible contributions arise from the -2aD term. By increasing the hydrogen coverage, the bare force constant K and the anharmonicity parameter G decrease as the hydrogen coverage increases. However, a larger contribution from µD results in the larger 6GµD/K, hence, the larger vibrational Stark tuning slope at high hydrogen coverage. We note that the Stark tuning slopes calculated by the above procedure are underestimated compared with those calculated
10894 J. Phys. Chem. C, Vol. 112, No. 29, 2008
Hamada and Morikawa To summarize, the small vibrational Stark effect can be understood by the fact that the induced dipole moment is small. Moreover, the larger vibrational Stark tuning slope at high coverage is originated from the increase in the dynamic dipole moment. By using the parametrization of the energy and the polarization (dipole moment) at zero field, the coverage dependence of the vibrational Stark shift can be semiqualitatively understood in terms of the dynamic dipole moment. Because the peak intensity of the vibrational band is proportional to the square of the dynamic dipole moment, the above analysis indicates that the experimentally observed sharp increase in the band intensity of the Pt-H stretching mode of atop hydrogen at potentials more negative than 0.1 V(RHE)8–10 is partly due to an increase in hydrogen in the neighboring hollow sites. Solvent Effect. At the electrode/solution interface, the solvent water molecules may play an important role, and the effect should be incorporated in the modeling of a realistic interface. The significance of the solvent effect on the reaction energy of the methanol dehydrogenation was discussed by Okamoto et al.51 To model an electrical double layer (solvent effect), we introduced an icelike-thin-water layer (water bilayer) on the Pt surface, as shown in Figure 4. The bilayer model was successfully used in the theoretical studies of HER.29,30 Note that although the term “bilayer” is originally used for the icelike structure (H-up, Figure 4a) it is also used to represent water layers in the H-down configuration (Figure 4b) in the recent literature. We calculated the adsorption energies of water bilayer Eads,w and the adsorption energy of hydrogen in the presence of w the water bilayer Eads,H , defined by
Eads,w ) - [Etot(water/Pt) - Etot(water) - Etot(Pt)] and w Eads,H )-
Figure 4. Side and top views of the structures of (a) H-up and (b) H-down water bilayers on Pt(111) and H atoms on (c) atop(1), (d) atop(2), (e) atop(3) with the H-up bilayer, (f) bridging, (g) fcc hollow, and (h) hcp hollow with the H-down bilayer sites. In the H-up (H-down) water bilayer configuration, dangling (non H-bonded) -OH bonds of water molecules are directed toward the vacuum (metal surface).
TABLE 4: Bonding and Polarization Parameters and Corresponding Stark Tuning Slopes of H/Pt(111) at Zero Field in UHVa coverage (ML)
1
2
H/Pt13b
G (eV · nm-3) K (eV · nm-2) µs (D) µD (e) -2aD (e · nm-1) 6GµD/K (e · nm-1) dK/dF (e · nm-1) νh (cm-1) dνh/dF (cm-1 · V-1 · nm) dνh/dF (DFT) (cm-1 · V-1 · nm)
-1.7497 × 104 1.9361 × 103 0.1160 -0.0090 0.2601 0.4859 0.7460 2285 0.44 1.84
-1.5181 × 104 1.7381 × 103 0.3982 -0.0802 0.8615 4.2048 5.0663 2165 3.16 5.07
-1.87 × 104 2.25 × 103 -0.11 1.2 6.7 8.0 2506 4.40 4.45
a Parameters are obtained by using Pt(111) (1 × 1) three-layer slabs. See the text for the notation. b Parameters are obtained by using the H/Pt13 cluster by Wasileski et al.34
by DFT. This is presumably because dν/dF values from DFT are obtained at the finite field, whereas the above parameters were estimated at the zero field. However, we find that this analysis can account for the field-dependent vibrational frequency of hydrogen semiquantitatively.
1 [E (water ⁄ H ⁄ Pt) - Etot(water ⁄ Pt) nH tot nH E (H )] 2 tot 2
where Etot (water/Pt), Etot (water), and Etot (water/H/Pt), and Etot(Pt) are the total energies of the water bilayer adsorbed Pt surface, the isolated water bilayer, the water bilayer and the hydrogen coadsorbed Pt surface, and the bilayer adsorbed Pt surface, respectively. The adsorption energies of hydrogen in UHV and in the presence of water for high symmetry sites at 1/3 ML are summarized in Table 5 together with the adsorption energies of the water bilayer, and the corresponding structures are depicted in Figure 4c-h. In contrast with the UHV case, the fcc hollow site is no more stable, and the atop site (atop(2), Figure 4d) is the most stable adsorption site. In the presence of the H-down (H-up) water bilayer (Figure 4a,b) the adsorption energies become slightly higher (lower) and the energy difference becomes smaller (except for the hcp-hollow site). The most stable adsorption site is the atop(2) site (Figure 4d), where the adsorbed H is located just below an oxygen atom of a water molecule lying parallel to the surface. On this site, the hydrogen atom is stabilized by a hydrogen-bond-like interaction with the water molecule above it, and the Pt-H bond length is elongated. This result is in agreement with Ishikawa et al.32 that the atop site is the most stable site at the Pt/solution interface. The potential energy surface (PES) of hydrogen on the Pt surface is strongly modified by the presence of water molecules. In addition, the PES is affected by the orientation of water molecules. As already shown by Sa´nchez,49 Zhao et al.,50 and Rossmeisl et al.,28 the orientation of water molecules depends
Density-Functional Analysis of Hydrogen on Pt(111)
J. Phys. Chem. C, Vol. 112, No. 29, 2008 10895
TABLE 5: Adsorption Energies of Hydrogen on Pt(111) (3) in High-Symmetry Sites at 1/3 ML Coverage in UHV w (Eads,H) and with the H-down or H-up Water Bilayer (Eads,H ) and the Adsorption Energies of Water Bilayers (Eads,w) (kJ/mol)a atop(1) atop(2) atop(3) bridge fcc hollow hcp hollow Eads,H
UHV 48.3
50.0
54.8
47.6
58.6
38.8
47.2
42.5
H-down Eads,w 50.9 w Eads,H
57.3
67.5
56.4 H-up
Eads,w 45.9 w Eads,H
46.
47.7
43.7
44.0
a There are three nonequivalent sites in a Pt(111)(3 × 3) cell in the presence of a water bilayer, and the coverage of water molecules is 2/3 ML. All the adsorption energies for H on atop sites of particular interest and the lowest values for other adsorption sites are shown. Atop(1) is a site where no water molecule is above, atop(2) is a site where there is a water molecule lying parallel to the surface, and atop(3) is a site where there is a water molecule whose OH bond points toward the vacuum (H-up) or the Pt surface (H-down). In the H-down structure, atop(3) is unavailable because the H atom of the water molecule lies right above the atop site.
Figure 6. Pt-H stretching frequency (upper panel) and bond length (lower panel) of (a) atop(1) and (b) atop(2) sites in the presence of H-down water bilayer as a function of surface charge. Electric fields are also shown. Adsorption geometries used are explained in the text.
Figure 5. Total energy of the water-bilayer-adsorbed Pt(111) (3 × 3) surface referenced to that of H-down bilayer at zero-charge ∆Etot, as a function of surface charge. Three-layer slabs are used in the calculations. Most stable structures at negatively and positively charged states are shown in insets (a) and (b), respectively. Red, white, and gray balls indicate O, H, and Pt atoms, respectively.
on the external field. In the bilayer model, half of the water molecules lie parallel to the surface, and the -OH bonds in the other half of the water molecules are pointing toward the vacuum (H-up, Figure 4a) or the surface (H-down, Figure 4b). At zero field, the H-down structure is more stable than the H-up structure, although the energy difference is small. This implies that the H-up and H-down structures coexist at a finite temperature. As shown in Figure 5, by applying the negative (positive) field, the H-down (H-up) structure becomes more stable. In addition to this, the water molecules lying parallel to the surface turn into the O-up (O-down) configuration in response to the electric field. Dominant water molecules are in H-down or O-up configurations at the negative field and in H-up or O-down configurations at the positive field. Because the relative stability of the high symmetry adsorption sites is not changed by applying the electric field in the absence of the water layer (UHV), the PES and, consequently, the diffusion property of hydrogen at the electrochemical interface, depend on the
electric field not directly but via the interaction with water molecules. Thus, the diffusion of hydrogen on the Pt surface in an electrochemical environment (in the presence of water) is quite different from that in UHV. Hydrogen diffuses from fcc hollow sites to neighboring hollow sites via bridge sites avoiding atop sites in UHV,19 whereas in the electrochemical condition, it is predicted to diffuse between adjacent atop sites via bridge or fcc and hcp hollow sites.31 The calculated values of νPt-H as a function of the electric field for atop(1) and atop(2) at 1/3 ML (fcc hollow sites are empty) and 4/3 ML (fcc hollow sites are fully occupied) are shown in Figure 6. The frequency shift of νPt-H for atop(1) is little affected by water, and the vibrational Stark shifts are as small as those in UHV (0.1 cm-1 · V-1 · nm at 1/3 ML and 1.86 cm-1 · V-1 · nm at 4/3 ML in the presence of the water bilayer). νPt-H for atop(2) is significantly modified by the electric field. At the zero field, Pt-H bond length is elongated by the attractive interaction between hydrogen and water above, thus νPt-H is much lower than that in UHV. By applying the electric field, water molecule prefer the O-up configuration by the electrostatic interaction, and the distance between the interacting oxygen and hydrogen atoms increases (Pt-H distance decreases). Consequently, νPt-H increases to approach the UHV value. This behavior is inconsistent with the experimental observation. This can be explained as follows: On the actual electrode surface, under the potential at which a hydrogen evolution occurs (and νPt-H can be observed), a negative electric field is applied to the electrode surface. In such a case, the hydrogen atom does not interact
10896 J. Phys. Chem. C, Vol. 112, No. 29, 2008
Figure 7. Pt-H stretching frequency of atop(1) in the presence of the water bilayer as a function of potential (a) determined from the electrostatic potential at the oxygen site in the lower layer (V1) and in the upper layer (V2) and determined from the excess charge-potential relation from the previous first-principles molecular dynamics study.31 The origin of the potential is set to that of the neutral state.
strongly with the water molecule because water is already in an O-up configuration, and the water-hydrogen distance is large. The electric field dependence of νPt-H of atop(2) presented here does not correspond to the frequency shift observed in the experiment situation. Now let us consider the potential dependence of νPt-H, instead of the field dependence, to compare more precisely our results with experiments. In the above discussion, we assumed the double-layer thickness to be 0.3 nm to convert the electric field to the potential. This is an ambiguous assumption because the double-layer thickness depends on the solution and the electrolyte concentration. In the presence of the water layer, by looking at the electrostatic potential at the Pt nuclear sites and the oxygen nuclear sites, we can estimate the change in the electrode potential relative to that in the solution. Although the absolute value of the electrostatic potentials at nuclear sites cannot be determined exactly (because we use pseudopotentials), differences can be calculated accurately, and the potential dependence of the frequency can be estimated in a lessambiguous way. In Figure 7a, we show νPt-H of atop(1) at 4/3 ML as a function of potential determined from the electrostatic potential at the oxygen in the first water layer closest to the surface (V1) and in the upper water layer (V2). The frequency shifts thus obtained are estimated to be ∼0 cm-1 · V at 1/3 ML and 16 cm-1 · V-1 (from V1) and 14 cm-1 · V-1 (from V2) at 4/3 ML. Note that at lowest potentials the frequency change seems to saturate. The reason is not yet clear, but it is possibly due to the numerical error in the calculation of the frequency under strong electric fields. In the previous work31 we determined the excess charge-potential relation at the water/Pt(111) interface by taking the difference between the average electrostatic potentials at the oxygen sites in the bulklike water region (as described above) and the Pt sites in the electrode. By assuming that the same charge-potential relation holds for the present system, we obtain the frequency shift at the rate of 51 cm-1 · V-1 at 4/3 ML, as shown in Figure 7b. This can be considered to be the most realistically determined frequency shift, although ambiguity still remains. For example, hydrogen coverage is not taken into account in determining the excess charge-potential relation. By modifying the description of the water/electrode interface, a more quantitative discussion will
Hamada and Morikawa
Figure 8. (a) Adsorption energy of hydrogen at the atop site in UHV Eads,H, (b) Pt-H stretching frequency νPt-H, and (c) Pt-H bond length dPt-H as a function of hydrogen coverage. At low coverage (ΘH e 1) (open diamond), fcc hollow sites are empty, and at high coverage (ΘH > 1) (filled diamond), they are fully occupied. The three-layer slab is used. At coverages of 1.5 and 1.75 ML, there are two and three atop hydrogen atoms in a unit cell, respectively, and their vibrational modes are hybridized. Hybridization between the vibrational modes of hydrogen on the atop sites and on the fcc sites is negligibly small.
be possible. The vibrational Stark tuning rate thus obtained is about 2.5 times higer than that estimated without the water layer, but it is still less than half of the experimental value of 130 cm-1 · V-1.8,10 Hydrogen Coverage Effect. Having examined the field effect on the hydrogen adsorbed Pt(111) surface, we now turn to the hydrogen coverage effect. Because hydrogen atoms always prefer the fcc hollow site at ΘH e 1 ML, we assume that atop hydrogen appears after the fcc hollow sites are fully occupied, as discussed above. Here, it should be noted that the hydrogen coverage on the Pt(111) electrode surface is estimated to be ∼2/3 ML at the equilibrium potential.52 Thus, the present result may not rigorously correspond to the actual situation in the experiments, but it is sufficient to show the significance of the coverage effect on the vibrational property of adsorbed hydrogen. The coverage dependence of the hydrogen adsorption energy using the three-layer slab is shown in Figure 8a. To illustrate how hydrogen atoms interact with neighboring H, the adsorption energies at ΘH e 1 ML, where fcc hollow sites are empty, and at ΘH > 1 ML, where they are fully occupied, are shown. At ΘH e 1 ML, the change of the adsorption energy is small, within ∼7 kJ · mol-1. Note that by increasing the slab thickness to five layers, the differences in the adsorption energies are affected by no more than 1 kJ · mol-1. Our results indicate that the lateral interaction between Pt-Hatop is small, and their effect on the Pt-H frequency is expected to be small. The dipole-dipole interaction is also small because the induced dipole moment is considerably small (0.12 D for hydrogen adsorbed on the atop site at 1 ML). By increasing the hydrogen coverage from 1 to 2 ML in the presence of hydrogen on the fcc hollow site (Hfcc), the adsorption energy is decreased almost linearly, indicating the repulsive interaction between adsorbed hydrogen atoms. Kunimatsu et al.9,10 suggested the repulsive interaction between adsorbed hydrogen from the Frumkin isotherm, which is in good agreement with our results. The coverage dependence of the νPt-H and the bond length are show in Figure 8b,c. It can be clearly seen that at ΘH > 1 ML the νPt-H rapidly decreases as the hydrogen coverage
Density-Functional Analysis of Hydrogen on Pt(111)
Figure 9. Projected density of states (PDOSs) (upper panel) and crystal orbital overlap populations (COOPs) (lower panel) of hydrogen on the Pt(111) (1 × 1) surface at (a) 1 ML and (b) 2 ML. PDOSs and COOPs for hydrogen on the atop site (Hatop) are indicated by solid lines and on the fcc site (Hfcc) by dotted-dashed line. PDOSs for surface Pt d-band are shown by dashed lines. COOPs near Fermi level are magnified and displayed in the insets (the same vertical scales are used for both 1 and 2 ML coverages). Black, red, and blue lines are for excess charges of 0.00 e/Pt, 0.02 e/Pt, and 0.04 e/Pt, respectively. In (c), COOP between Hatop and Hfcc at 2 ML on the neutral surface is also shown.
increases and the corresponding bond length is elongated. The change in the frequency is significant from ∼2260 to ∼2140 cm-1. Our results clearly show that the hydrogen coverage effect is quite large on the νPt-H, suggesting the large contribution from the effect of hydrogen coverage to the experimentally observed large potential shift of the νPt-H. Kunimatsu et al. suggested that the double-layer effect (vibrational Stark effect) on the frequency shift is small because the concentration of the electrolyte has little effect on the observed frequency shift.9,10 Our results are in good agreement with their suggestion. However, in order to explain quantitatively the experimentally observed frequency shift, the field effect should be taken into account: At the potential where the HER occurs, the hydrogen coverage is considered to be high. Then, the Stark shift becomes higher and contributes to the frequency shift, although the Stark tuning rate depends on the hydrogen coverage. Analysis of the Electronic Structure. To investigate the electronic origin of the vibrational Stark effect and the hydrogen coverage dependence of the Pt-H vibrational frequency, we calculated the PDOSs onto the atomic orbitals and the COOPs as explained above. PDOSs onto the H s orbital and COOPs between the H s orbital and the substrate orbitals for H on the atop site at 1 and 2 ML are shown in Figure 9a,b, respectively. In both 1 and 2 ML cases, the Fermi level is located slightly above the bonding and antibonding boundary between the H s and the substrate d states. As the negative electric fields are applied (substrate is negatively charged), PDOSs and COOPs are almost unchanged
J. Phys. Chem. C, Vol. 112, No. 29, 2008 10897
Figure 10. PDOSs onto the clean and hydrogen-adsorbed neutral Pt surface d-bands in UHV. Arrows indicate the d-band centers.
and slightly shifted downward relative to the Fermi level. The nearly rigid shift of adsorbed PDOSs indicates that the Stark effect on the electronic structure is not significant. As seen in the insets of Figure 9, the application of negative electric fields increases the occupation of the antibonding state, leading to the weakening of Pt-H bonding. The magnitude of the shift is larger in the 2 ML case than in the 1 ML case, which is more consistent with the larger vibrational Stark shift at ΘH > 1 ML than at ΘH e 1 ML. The larger antibonding peak also contributes to the increase in µD. We also find the non-negligible overlap of wave functions between Hatop and Hfcc from the COOP analysis (Figure 9c). The dominant character of COOP between them is antibonding, indicating that there is a repulsive interaction between Hatop and Hfcc that is stronger than that between the hydrogen atoms on the atop sites. The repulsive interaction between Hatop and Hfcc may contribute to the destabilization of the Pt-H bonds at high hydrogen coverage. In Figure 10, we plot the PDOSs of Pt d-bands of clean, 1 and 2 ML hydrogen-adsorbed Pt(111) surfaces, together with the positions of the d-band centers (denoted by arrows) relative to the Fermi level. As the coverage increases, the apparent filling of the d-states increases (downward shift of the d-bands), and the d-band center relative to the Fermi level rapidly decreases. This can be understood in terms of s-d hybridization.54 When a hydrogen atom is adsorbed on a clean Pt surface, a part of the d-states below the Fermi level is transferred to the states above the Fermi level because of the hybridization with the hydrogen s-state. The loss of the d-states is compensated by the upward shift of the Fermi level and finally, the apparent filling of the d-states increases. The lowering of the Pt d-band center causes the weakening of the Pt-H bond.55 Consequently, Pt-H stretching vibrational frequency decreases. The d-band model clearly explains how the νPt-H decreases upon increasing the hydrogen coverage. Xu et al.7 and Kunimatsu et al.10 attributed the large tuning rate of the Pt-H frequency to the shift of the work function or
10898 J. Phys. Chem. C, Vol. 112, No. 29, 2008 the Fermi level of the electrode surface. It should be emphasized that the shift in the Fermi level of the electrode surface cannot be independent of the electric fields just outside of the electrode surface and the coverage of hydrogen. The surface excess charge, which induces a small shift of the Fermi level of the electrode surface as shown above, is directly related to the electric fields outside of the electrode surface by the Gauss’s law. The work function change of the Pt electrode is induced by the coverage of hydrogen. Kunimatsu et al. showed that the Pt-H frequency is uniquely dependent on the SHE. We think that this dependence should come from the Pt-H frequency dependence of both the electric fields and the coverage of hydrogen. This point should be studied further theoretically as well as experimentally. Conclusions Density-functional theory calculations were carried out on hydrogen adsorbed on the Pt(111) electrode in an electrochemical environment by taking into account electric field, solvent, and hydrogen coverage effects. These effects were systematically examined to investigate the important factors determining the stability and vibrational property of hydrogen at the electrochemical interface. We find that the field effect on the adsorption energies and vibrational frequencies of hydrogen on Pt is negligibly small, and the vibrational Stark tuning rate is about 10 cm-1 · V-1 at low coverages and becomes slightly higer (∼20 cm-1 · V-1) at high coverages in the ultrahigh vacuum. By explicitly including water molecules, the PES of hydrogen on the Pt surface is significantly modified, and it is strongly dependent on the orientation of the water molecules. By including the solvent effect on the νPt-H, the Stark tuning rate is increased further to ≈50 cm-1 · V-1, but it is still lower than the experimentally observed value of 130 cm-1 · V-1. νPt-H rapidly decreases by increasing the hydrogen coverage. The frequency shift is caused by the weakening of the Pt-H bond associated with the lowering of the surface Pt d-band center. The results presented in this work clearly show that it is necessary to take into account the electric field, the water solvent and the hydrogen coverage effects to account fully for the experimentally observed large potential dependence of the νPt-H. Acknowledgment. We thank Minoru Otani, Osamu Sugino, Yasuharu Okamoto, and Tamio Ikeshoji for fruitful discussions and comments. This work was partially supported by a Grantin-Aid for Scientific Research in Priority Areas (Development of New Quantum Simulations and Quantum Designs, grant no. 1706400) from the Ministry of Education, Culture, Science, Sports and Technology, Japan. The numerical calculations were carried out at the Cybermedia Center of Osaka University, the Supercomputer Center of the Institute for Solid State Physics of The University of Tokyo, the Information Techonology Center of The University of Tokyo, and the Information Synergy Center of Tohoku University. The molecular graphics used in this article were generated by the XCrySDen program package.56 References and Notes (1) Nichols, R. J.; Bewick, A. J. Electroanal. Chem. 1988, 243, 445. (2) Ogasawara, H.; Ito, M. Chem. Phys. Lett. 1994, 221, 213. (3) Peremans, A.; Tadjeddine, A. Phys. ReV. Lett. 1994, 73, 3010. (4) Tadjeddine, A.; Peremans, A. J. Electroanal. Chem. 1996, 409, 115. (5) Nanbu, N.; Kitamura, F.; Ohsaki, T.; Tokuda, K. J. Electroanal. Chem. 2000, 485, 128. (6) Ren, B.; Xu, X.; Li, X. Q.; Cai, W. B.; Tian, Z. Q. Surf. Sci. 1999, 157, 427–428.
Hamada and Morikawa (7) Xu, X.; Ren, B.; Wu, D. Y.; Xian, H.; Lu, X.; Shi, P.; Tian, Z. Q. Surf. Interface Anal. 1999, 28, 111. (8) Kunimatsu, K.; Senzaki, T.; Tsushima, M.; Osawa, M. Chem. Phys. Lett. 2005, 401, 451. (9) Kunimatsu, K.; Uchida, H.; Osawa, M.; Watanabe, M. J. Electroanal. Chem. 2006, 587, 299. (10) Kunimatsu, K.; Senazki, T.; Samjeske´, G.; Tsushima, M.; Osawa, M. Electrochim. Acta 2007, 52, 5715. (11) Kunimatsu, K.; Seki, H.; Golden, W. G.; Gordon, J. G.; Philpott, M. R. Surf. Sci. 1985, 158, 596. (12) Zou, S.; Weaver, M. J. J. Phys. Chem. 1996, 100, 4237. (13) Lambert, D. K. Electrochim. Acta 1995, 41, 623. (14) Hohenberg, P.; Kohn, W. Phys. ReV. 1964, 136, B864. (15) Kohn, W.; Sham, L. J. Phys. ReV. 1965, 140, A1133. (16) Hammer, B.; Nørskov, J. K. Nature 1995, 376, 238. (17) Olsen, R. A.; Kroes, G. J.; Baerends, E. J. J. Chem. Phys. 1999, 111, 11155. (18) Papoian, G.; Nørskov, J. K.; Hoffmann, R. J. Am. Chem. Soc. 2000, 122, 4129. (19) Ka¨lle´n, G.; Wahnstro¨m, G. Phys. ReV. B: Condens. Matter Mater. Phys. 2001, 65, 033406. (20) Watson, G. W.; Wells, R. P. K.; Willock, D. J.; Hutchings, G. J. Phys. Chem. B 2001, 105, 4889. (21) Ba˜descu, S. C.; Salo, P.; Ala-Nissila, T.; Ying, S. C.; Jacobi, K.; Wang, Y.; Bedu¨rftig, K.; Ertl, G. Phys. ReV. Lett. 2002, 88, 136101. (22) Ba˜descu, S. C.; Jacobi, K.; Wang, Y.; Bedu¨rftig, K.; Ertl, G.; Salo, P.; Ala-Nissila, T.; Ying, S. C. Phys. ReV. B: Condens. Matter Mater. Phys. 2003, 68, 205401. (23) Le´gare´, P. Surf. Sci. 2004, 559, 169. (24) Greeley, J.; Mavrikakis, M. J. Phys. Chem. B 2005, 109, 3460. (25) Ford, D. C.; Xu, Y.; Mavrikakis, M. Surf. Sci. 2005, 587, 159. (26) Okamoto, Y. Chem. Phys. Lett. 2006, 429, 209. (27) Blum, L.; Marzari, N.; Car, R. J. Phys. Chem. B 2004, 108, 19670. (28) Rossmeisl, J.; Nørskov, J. K.; Taylor, C. D.; Janik, M. J.; Neurock, M. J. J. Phys. Chem. B 2006, 110, 21833. (29) Taylor, C. D.; Kelly, R. G.; Neurock, M. J. Electrochem. Soc. 2007, 154, F55. (30) Sku´lason, E.; Karlberg, G. S.; Rossmeisl, J.; Bligaard, T.; Greeley, J.; Jo´nsson, H.; Nørskov, J. K. Phys. Chem. Chem. Phys. 2007, 9, 3241. (31) Otani, M.; Hamada, I.; Morikawa, Y.; Sugino, O.; Okamoto, Y.; Ikeshoji, T. J. Phys. Soc. Jpn. 2008, 2, 024802. (32) Ishikawa, Y.; Mateo, J. J.; Tryk, D. A.; Cabrera, C. R. J. Electroanal. Chem. 2007, 607, 37. (33) Tomonari, M.; Sugino, O. Chem. Phys. Lett. 2007, 437, 170. (34) Wasileski, S. A.; Koper, M. T.; Weaver, M. J. J. Chem. Phys. 2001, 115, 8193. (35) Morikawa, Y. Phys. ReV. B: Condens. Matter Mater. Phys. 2001, 63, 033405. (36) Morikawa, Y. Phys. ReV. B: Condens. Matter Mater. Phys. 2004, 69, 041403. (37) Troullier, N.; Martins, J. L. Phys. ReV. B: Condens. Matter Mater. Phys. 1991, 43, 1993. (38) (a) Vanderbilt, D. Phys. ReV. B: Condens. Matter Mater. Phys. 1990, 41, 7892. (b) Laasonen, K.; Pasquarello, A.; Car, R.; Lee, C.; Vanderbilt, D. Phys. ReV. B: Condens. Matter Mater. Phys. 1993, 47, 10142. (39) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (40) Methfessel, A.; Paxton, A. T. Phys. ReV. B: Condens. Matter Mater. Phys. 1989, 40, 3616. (41) Wang, J. G.; Hammer, B. J. Chem. Phys. 2006, 124, 184704. (42) Otani, M.; Sugino, O. Phys. ReV. B: Condens. Matter Mater. Phys. 2006, 73, 115407. (43) Sugino, O.; Hamada, I.; Otani, M.; Morikawa, Y.; Ikeshoji, T.; Okamoto, Y. Surf. Sci. 2007, 601, 5237. (44) Sawada, H.; Morikawa, Y.; Terakura, K.; Hamada, I. Phys. ReV. B: Condens. Matter Mater. Phys. 1997, 56, 12154. (45) Hoffmann, R. ReV. Mod. Phys. 1988, 60, 601. (46) Aizawa, H.; Tsuneyuki, S. Surf. Sci. 1998, 399, L364. (47) Lozovi, A. Y.; Alavi, A. J. Electroanal. Chem. 2007, 607, 140. (48) Weaver, M. J. Appl. Surf. Sci. 1993, 67, 147. (49) Sa´nchez, C. G. Surf. Sci. 2003, 527, 1. (50) Zhao, J.; Chan, C. T.; Che, J. G. Phys. ReV B: Condens. Matter Mater. Phys. 2007, 75, 085435. (51) Okamoto, Y.; Sugino, O.; Mochizuki, Y.; Ikeshoji, T.; Morikawa, Y. Chem. Phys. Lett. 2003, 377, 236. (52) Markovic, N. M.; Ross, P. N., Jr. Surf. Sci. Rep. 2002, 45, 117. (53) (a) Lambert, D. K. Solid State Commun. 1984, 51, 297. (b) Lambert, D. K. J. Chem. Phys. 1988, 89, 3847. (54) Terakura, K. J. Phys. F: Met. Phys. 1977, 7, 1773. (55) Hammer, B.; Morikawa, Y.; Nørskov, J. K. Phys. ReV. Lett. 1996, 76, 2141. (56) Kokalj, A. Comput. Mater. Sci. 2003, 28, 155. Code available at http://www.xcrysden.org/.
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