Theoretical Investigation of Hydrated Hydronium Ions on Ag (111)

J. Phys. Chem. B 2001, 105, 7227-7238

7227

Theoretical Investigation of Hydrated Hydronium Ions on Ag(111) P. Paredes Olivera,† A. Ferral,‡ and E. M. Patrito*,‡ Unidad de Matema´ tica y Fı´sica and Departamento de Fisicoquı´mica, Instituto de InVestigaciones en Fisicoquı´mica de Co´ rdoba (INFIQC), Facultad de Ciencias Quı´micas, UniVersidad Nacional de Co´ rdoba, Ciudad UniVersitaria, 5000 Co´ rdoba, Argentina ReceiVed: January 7, 2001; In Final Form: May 15, 2001

We investigated the adsorption of hydronium ions on Ag(111) in conditions that simulate the structure of the double layer using the ab initio quantum mechanical Moller-Plesset second-order method. The most representative points of the potential energy surface for bare hydronium on Ag(111) were first investigated. Then, the ion was hydrated with 1, 2, and 3 water molecules, and the structures of the hydronium-water complexes were studied on Ag(111) under different externally applied homogeneous electric fields. Bare hydronium adsorbs via the hydrogen atoms with C3V or Cs symmetry. For these coordinations, the potential energy surface has a small corrugation: the binding energy on the hcp hollow site (-56 kcal/mol) is only 2 kcal/mol more stable than on the ontop site. On the other hand, adsorption via the oxygen atom is destabilized due to the Pauli repulsion with the metal. The equilibrium geometry of the trihydrated complex (H9O4+) has the water molecules located between the hydronium ion and the surface, indicating that hydronium does not specifically adsorb. The surface reaction leading to H9O4+ from adsorbed water and hydronium is very exothermic (-32 kcal/mol) mainly due to the formation of hydrogen bonds. The electric field has a smaller influence on the adsorption of the hydrated ion than on the bare ion due to the screening of the water molecules. The different contributions to the binding energy in the presence of electric fields were considered. The polarization contribution is more important for H9O4+ than for H3O+ and leads to a stabilization of the trihydrated complex at small positive electric fields.

Introduction A complete description of the hydrogen evolution reaction

2H+(aq) + 2e-(m) ) H2(gas)

(1)

requires an understanding of the interactions among hydrated protons, water, adsorbed hydrogen, and the electrode surface. This problem has been approached experimentally by simulating the electrochemical double layer in ultrahigh vacuum (UHV). Adsorbed hydronium ions were first reported by Wagner and Moylan with HF and H2O1 and with H and H2O2 coadsorbed on Pt(111) using electron energy loss spectroscopy (EELS). The electrochemical reaction Had + H2Oad f H3O+ ad + emetal

(2)

was later identified3 unambiguously in UHV by coadsorbing H and H2O on Pt(111) and Cu(110) and isotopically substituting Had by Dad. Hydronium ions were also observed under UHV with H and H2O coadsorbed on Pt(100)4 and Pt(110)5 and with SO3 and H2O coadsorbed on Pt(111).6 Under electrochemical conditions, hydronium ions coadsorbed with bisulfate anions were detected by infrared reflection absorption spectroscopy (IRAS) on Pt(111).6-8 Hydronium was also observed9 on Au(111) in perchloric acid by means of surface-enhanced infrared absorption spectroscopy. * Corresponding author. E-mail: [email protected], FAX: 54-351-4334188. † Unidad de Matema ´ tica y Fı´sica. ‡ Departamento de Fisicoquı´mica.

The nature of the adsorbed hydronium species was investigated recently by Masel5 and co-workers who obtained EELS spectra compatible with hydrated hydronium ions such as H5O2+, H7O3+, and H9O4+. Concerning the geometry of adsorbed hydronium, IRAS spectra of hydrated H3O+ adsorbed on Pt(111) at 110 K7 were compatible with a hydronium ion having C3V symmetry with the molecular C3 rotation axis perpendicular to the surface. From a theoretical point of view, the structure of hydrated proton clusters in vacuum has been studied by several authors by means of ab initio calculations at different levels of theory.10-15 On metal surfaces, the adsorption of hydrated hydrogen atoms on the Cu(100) surface was investigated at the Hartree-Fock level by Lorentz and co-workers16-18 in connection with the hydrogen evolution reaction. The adsorption of ions on metal surfaces has been studied using quantum mechanical methods to understand the nature of the bonding and the magnitude of ion-surface interactions with the final goal of building a detailed picture of the electrochemical double layer. Ab initio studies of ionic adsorption have been mainly restricted to monoatomic ions such as the halogen and alkali ions19-27 and small polyatomic anions such as SCN-.25,28 Recently, we investigated the adsorption of several polyatomic oxyanions such as sulfate,29,30,33 bisulfate,30,33 carbonate,31,33 bicarbonate,32,33 nitrate,33 perchlorate,33 and phosphate.33 Even though the presence of external homogeneous electric fields perpendicular to the surface was considered in some of these studies32,33 in order to model the environment of the double layer, the hydration of the ions was not taken into account. This is a more demanding task from a computational point of view because larger adsorbate sizes have to be

10.1021/jp010066w CCC: $20.00 © 2001 American Chemical Society Published on Web 07/07/2001

7228 J. Phys. Chem. B, Vol. 105, No. 30, 2001

Paredes Olivera et al.

Figure 1. 28-Atom silver cluster with a hydronium ion on a hcp hollow site.

considered. In the case of a sulfate anion hydrated with three water molecules, we did not observe a strong effect of the water molecules on the main features of the anion-surface bonding.34 But in the case of ions that do not specifically adsorb, the hydration of the ion is expected to play a crucial role on the nature of the hydrated ion-surface bonding. This has been shown recently by Head and co-workers for the hydrated fluoride ion on Al(111).35 In the present work we investigated the adsorption of hydronium ions on Ag(111) using the ab initio quantum mechanical Moller-Plesset second-order method (MP2). To model the environment of hydronium in the electrochemical interface, the hydration of the ion was considered and the electrode polarization was simulated by applying external homogeneous electric fields perpendicular to the metal surface. To build a complete picture of the energetics of adsorbed hydrated hydronium ions, the following adsorbates are considered: H2O, H3O+, H5O2+, H7O3+, and H9O4+. After presenting the structural and energetic aspects of these adsorbates, the surface reaction for the formation of the hydrated complexes is discussed. The nature of the hydronium-surface bonding is investigated in detail and, in the final part, the adsorption of the ions in the presence of homogeneous external electric fields is considered. Surface Modeling and Theoretical Methods The cluster method was used to model the Ag(111) surface. In the case of ions, the cluster model of the surface must be large enough to accommodate the charge transferred to/from the cluster29,36 and to adequately describe image charge interactions.31,33 The long-range coulombic interactions between the charged adsorbate and the metal surface also require that clusters employed to study surface interactions for ions be larger than those clusters used for neutral adsorbates. We investigated the convergence of the hydronium binding energy with cluster size and found that for clusters larger than about 30 atoms the binding energy is converged. We chose the 28 metal atom cluster shown in Figure 1, which has 12/10/6 atoms in each layer. The silver atoms in the primary chemisorption site were described using 11-electron atoms, and the remainder of the atomic electron density was replaced by relativistic effective core potentials (RECP) of the Huzinaga type.37-39 The rest of the atoms had one electron in the valence shell. The basis set employed for the 11-electron silver atoms is a (7s 1p 2d/3s 1p 2d) RECP basis set. The contraction coefficients were obtained by fitting to the atomic orbitals and orbital energies as obtained from relativistic Hartree-Fock calculations in which the Darwin

Figure 2. First layer of the metal cluster. Shaded atoms are 11-electron silver atoms. Labels (from left to right) indicate surface sites: ontop, hcp hollow, bridge, and fcc hollow. (a) cluster with Cs symmetry and (b) cluster with C3V symmetry.

and mass-velocity corrections are taken into account. Two different silver clusters were used in the calculations. Both had 28 atoms as shown in Figure 1 but differed in the number of 11-electron atoms in the first layer, as shown in Figure 2. The cluster with 8 atoms having 11 valence electrons (Figure 2a) was used to investigate the adsorption on bridge, hollow, and ontop sites under Cs symmetry. The cluster whose first layer had only 6 silver atoms with 11 valence electrons (Figure 2b) was used to perform most of the calculations of trihydrated hydronium under C3V and C3 symmetries. We also performed some calculations under Cs symmetry on the 28-atom cluster (Figure 1) having 10 atoms with 11 electrons in the first layer and one atom with 11 electrons in the second layer. We obtained the same binding energies as with the 28-atom cluster, which has 8 atoms with 11 electrons in the first layer (Figure 2a), indicating that the number of 11 electron atoms in the primary chemisorption site is enough. The labels in Figure 2a indicate the adsorption sites investigated. The sites are defined taking as a reference the position of the oxygen atom of hydronium. The electronic structure of the metal cluster also needs to be considered in order to obtain reliable binding energies. The work of Siegbahn and co-workers40-42 showed that metal clusters of even modest size are adequate to study chemisorption processes for neutral adsorbates, provided that the metal cluster electronic structure is adequately chosen. Basically, the adsorbate electrons must fit into the electronic structure of the cluster. For example, in the case of a radical adsorbate that has a singly occupied

Hydrated Hydronium Ions on Ag(111)

J. Phys. Chem. B, Vol. 105, No. 30, 2001 7229

orbital, the electronic state of the cluster must also have a singly occupied orbital with the right symmetry for the adsorbatemetal bond to be formed. The metal cluster must also have a high density of states close to the Fermi level. This is generally the case for the large clusters used in ion-surface studies. The metal cluster in Figure 1a has the five highest occupied MOs in an energy range of 0.7 eV. That is, the average energy spacing of these MOs is 0.14 eV, which represents a high density of states for a metal cluster of this size. The oxygen and hydrogen basis sets employed were (9s 5p 1d/4s 2p 1d) and (4s 1p/2s 1p), respectively.43 The metal cluster was built using the bulk metal distance of 2.884 Å for silver.44 The calculations were performed with the electronic structure program TANGO-95.45 This is a quantum mechanical electronic structure program largely developed for calculations on systems containing metal atoms. The adsorbate geometries were optimized at the Hartree-Fock level. After each geometry optimization, the adsorbate surface distance was further optimized at the MP2 level of theory. The metal atoms were kept fixed in all geometry optimizations. Binding energies were calculated by subtracting the total energy of the bare substrate and the bare adsorbate from the substrate-adsorbate composite energy. Thus, for a bare hydronium ion, the binding energy is defined as

BE ) EH3O+-cluster - Ecluster - EH3O+

Figure 3. Potential energy for hydronium on different surface sites as a function of the oxygen-surface distance.

(3)

Negative values of binding energies indicate a stabilization of the substrate-adsorbate system with respect to the bare adsorbate and bare metal cluster. The binding energies of the hydrated hydronium complexes (H5O2+, H7O3+, and H9O4+) were calculated according to eq 3 using the appropiate adsorbate. Electric fields perpendicular to the surface were taken into account by adding the corresponding terms to the Hamiltonian. The energy gradients were computed analytically45 in order to perform geometry optimizations in the presence of external electric fields. Since the adsorbate-metal cluster systems investigated in this work have a net charge of +1, they are never strictly at equilibrium because of the net force from the interaction between the charge and the external electric field. Even though the total energy of the system has a linear dependence on translation of the molecule along the electric field direction, the energy first and higher derivatives are invariant to these translations, making it possible to define a unique optimized structure for the system. To determine the optimized geometry, it is necessary to introduce constraints46,47 that counteract the net force on the system. The optimized structures of charged molecules in an electric field are dependent on the type of constraint used,46,47 and the choice of constraint depends on the physical situation being modeled. In our case, the net force appears on the adsorbate atoms because the metal atoms are kept fixed (the energy gradients on these atoms are zeroed). This net force was evenly divided over each of the atoms, and the corresponding net forces on each atom were subtracted from the energy gradient. Results and Discussion Adsorption of Bare Hydronium. The potential energy curves for hydronium adsorbed on the ontop, hcp hollow, bridge, and fcc hollow sites (Figure 2a) of Ag(111) are shown in Figure 3. The energy of every point in the curves was obtained by fixing the oxygen-metal surface distance while optimizing the position of the hydrogen atoms. On the ontop and bridge sites

Figure 4. Side view of equilibrium hydronium geometries on ontop, hcp hollow, bridge, and fcc hollow sites.

hydronium has a binding energy of -54 kcal/mol, while on the hcp hollow site the binding energy is -56 kcal/mol. On the fcc hollow site, the binding energy is only 0.6 kcal/mol more stable than on the hcp site. The differences in the binding energies on both hollow sites are too small to determine the most stable site. The hcp hollow site was considered for all of the calculations involving the hollow site. The equilibrium geometries in the minimum of the potential energy curves are shown in Figure 4. For the sake of comparison, the ions on the different adsorption sites have been plotted on the same metal cluster. On the hcp hollow site, the geometry optimization was started with the hydrogen atoms pointing toward the metal atoms. For this case, the ion lies flat on the surface for all points of the potential energy curve, but when the optimizations are performed with the staggered geometry (hydronium rotated 60 degrees), the ion tilts as shown in Figure 5a. In this case the binding energy is -55 kcal/mol. The same trends were observed on the fcc hollow site. Figure 4 shows that the staggered hydronium on the fcc hollow site is slightly tilted as compared to the flat ion geometry on the hcp hollow site. On the ontop site, the ion lies nearly flat on the surface for all points of the potential energy curve. But on the bridge site, the ion tilts with one hydrogen atom pointing toward the surface (Figure 4). On this site, the ion decomposes into an adsorbed hydrogen atom and a water molecule when it is pressed against the surface at distances slightly shorter than the equilibrium distance in Figure 3. Protontransfer reactions for bare and hydrated adsorbed hydronium ions are considered elsewhere.48 On the hcp hollow site we also found other local minima in the potential energy function for which the ion adsorbs with Cs rather than with C3V symmetry, as shown in Figures 5b and 5c. The binding energies for these configurations are around -56 kcal/mol. In all cases, hydronium adsorbs via the hydrogen atoms and never via the oxygen atom. We conclude that the potential energy surface shows a small



Figure 6. (a) Hydronium effective charge and (b) hydronium OH bond lengths as a function of oxygen-surface distance for different adsorption sites.

Figure 5. Equilibrium structures of hydronium adsorbed on the hollow site with Cs symmetry.

corrugation for all of the hydronium coordinations that have one, two, or three hydrogen atoms pointing toward the surface. However, the binding of hydronium is destabilized when it adsorbs via the oxygen atom. This will be discussed in the hydronium-surface bonding section. There are no reports of ab initio calculations of hydronium binding energies. But in the case of Pt(111), Masel and coworkers5 estimated a hydronium surface interaction of -54 kcal/ mol based on an image dipole model.49 This value on Pt(111) is very close to our hydronium binding energies on Ag(111). Binding energies of molecules and ions do not differ too much among the noble metals.36,50 For example, sulfate binding energies on silver and gold differ by only 10%,29 and the same trend is observed for halide binding energies on the most stable sites of Ag and Pt.27 Another example is bisulfate for which we obtained30 a binding energy of -58 kcal/mol on Ag(111), whereas Bockris and co-workers obtained a value of -51 kcal/ mol on Pt(111) based on the modeling of adsorption isotherms.51 Figure 6a shows the hydronium effective charge calculated from a Mulliken population analysis as a function of the distance from the surface for the different adsorption sites. On the ontop and hcp hollow sites, the charges remain virtually constant at around +0.85, which shows that hydronium remains mainly as an ionic adsorbate. The fact that the ion effective charge is lower than 1 indicates charge transfer from the metal surface. However,

on the bridge site, the ion effective charge decreases rapidly as it approaches the surface. In this case, the ion is being reduced and begins to decompose into water and an adsorbed hydrogen atom.48 As shown in Figure 4, the ion has the right geometry to decompose on this site. The relaxation of hydronium as it approaches the surface is shown in Figure 6b. The horizontal line in the figure corresponds to the OH bond length of hydronium in vacuum (0.96 Å). The OH bond involving the H atoms closer to the surface (labeled d1) is more elongated than the other OH bonds. In the case of hydronium lying flat on the hcp hollow site, all OH bond lengths are the same, and the same happens for the OH bonds on the ontop site. In this case the relaxation is small. On the other hand, the d1 bond length of hydronium on the bridge site increases rapidly, which indicates the breaking of this bond as a consequence of the decomposition of hydronium.48 Adsorption of Water. Before presenting the results for hydrated hydronium, we will consider the adsorption of water on Ag(111). It is not the aim of this paper to perform a complete investigation of the water-silver bond on different binding sites. Therefore, the binding energy of water was calculated only on the ontop site (see Figure 2a). Ab initio calculations have determined that this is the preferred binding site on metals such as Hg52,53 and Al.54 We obtained a binding energy of -8 kcal/ mol for a water coordination having the oxygen atom in contact with the surface and the hydrogen atoms in the plane perpendicular to the surface. The geometry of water in vacuum was used in the calculation. For such a low binding energy, we do not expect that the relaxation of water may have an important contribution to the binding energy. When the binding energy



TABLE 1: Binding Energy, Hydration Energy, and Enthalpy Change for Complex Formation (all energies in kcal/mol) H2O H3O+ H5O2+ H7O3+ H9O4+

BE

∆Hhyd

∆Hcomplex

-8 -56 -39 -37 -26

-38 -64 -86

-13 -29 -32

of an adsorbate is small, cluster effects may be important. Therefore, we also calculated the binding energy of water on a 7-silver cluster, which has an atom in the middle (for ontop coordination) surrounded by an hexagon of six atoms. Because of the symmetry, this cluster has no dipole moment (whereas the cluster of Figure 2a has a small dipole that may produce an artificial interaction with the water molecule) but has the disadvantage of a low density of states due to the small size. On this cluster we obtained a binding energy of -7 kcal/mol. The binding energies calculated on the 28- and 7-atom metal clusters compare very well with a binding energy of -6.4 kcal/ mol reported for the ontop site of Ag(100) using the density functional theory.55 We could not determine the tilting of the water molecule on either cluster because we obtained a binding energy difference of less than 0.1 kcal/mol between the upright and flat water configurations. We also obtained a small energy difference when the water molecule coordinates to the surface via the hydrogen atoms. These facts point to the limitations of the cluster model to study the coordination of physisorbed adsorbates such as water as it is documented in the literature. For two studies of water adsorption on Hg52,53 using perturbation theory, no agreement was reached with respect to the tilting of water. We attribute this to the different metal clusters used to model the surface in both studies. Despite these limitations, the calculated binding energies are in agreement with our previous calculation on silver (Table 1c, ref 56) based on the bond order conservation method.50 In ref 56 we obtained a value of -8.6 kcal/mol for water coordinated on the ontop site via the oxygen atom. Therefore, we took the value of -8 kcal/mol for the binding energy of water. Adsorption of Hydrated Hydronium. In this section we report on the hydration of adsorbed hydronium with 1, 2, and 3 water molecules. For each hydrated structure, many geometry optimizations starting from different initial conditions were performed in order to avoid local minima in the potential energy surface. The adsorbates considered in this section are H5O2+, H7O3+, and H9O4+. Their equilibrium geometries were optimized in vacuum, and the vacuum energy is the reference for the calculation of the corresponding binding energy according to eq 3. Figures 7-9 show the equilibrium structures obtained. The addition of the successive water molecules produces the detachment of the hydrogen atoms of hydronium from the surface until in the trihydrated complex (Figure 9), the water molecules are located between the ion and the metal surface, showing that hydronium does not specifically adsorb. The binding energies of the different complexes are listed in Table 1. The decrease in binding energies with the addition of water molecules will be discussed in the hydronium-surface bonding section. Table 2 shows the geometric parameters of the hydrated complexes on the surface as well as in vacuum. It also contains the data for some configurations of bare hydronium in the minimum of the potential energy surfaces of Figure 3. The OH bond length of hydronium involving hydrogen atoms in contact with the surface (d1, see labels in Figures 7 and 8) enlarges

Figure 7. Equilibrium structure of monohydrated hydronium with the water molecule in (a) a plane perpendicular to the surface and (b) rotated 90 degrees with respect to (a).

Figure 8. Equilibrium structure of H7O2+.

Figure 9. Equilibrium structure of H9O3+.

with respect to the vacuum value. This weakening of the bond is a general trend found for most adsorbates and is a consequence of charge transfer from the metal toward antibonding orbitals of the adsorbate.50 The OH bonds of the water molecules (d3) also undergo a small relaxation that is nearly the same for



TABLE 2: (a) OH Bond Lengths (labeled d1, d2, and d3) and Hydrogen Bond Lengths (HB) for the Adsorbed Species and for the Species in Vacuuma and (b) Oxygen-Surface Distance for the Oxygen Atom of Hydronium (O1) and the Oxygen Atom of Water (O2) for the Different Species (a) OH Bond Lengths d1 species O+

H3 (C3v) H3O+ (Cs) H5O2+ H7O3+ H9O4+

d2

adsorbed

vacuum

0.974 0.983 0.971 0.978

0.962 0.962 0.954 0.953

d3

HB

adsorbed

vacuum

adsorbed

vacuum

adsorbed

vacuum

0.962 0.993 0.985 0.984

0.962 1.061 1.000 0.982

0.947 0.947 0.950

0.950 0.948 0.947

1.596 1.613 1.591

1.366 1.521 1.608

(b) Oxygen-Surface Distance O1 H2O (ontop) H3O+ (ontop) H3O+ (hcp) inv. H3O+ (hcp) H3O+ (fcc) H5O2+ H7O3+ H9O4+ a

O2 2.60

2.813 2.78 2.40 2.46 2.80 2.96 4.57

4.09 3.68 3.49

The labels are defined in Figures 7-9.

both bonds. The hydrogen bond is more relaxed for H5O2+ than for H9O4+. In the latter, virtually the same bond length as in vacuum is observed. In Figure 7a the water molecule is in the Cs plane of symmetry. For this structure the oxygen lone pair orbitals of water on either side of the plane interact with an OH group in hydronium. In Figure 7b the geometry optimization was started with the hydrogen atoms of water on either side of the plane of symmetry. The structure in Figure 7b has virtually the same energy (to within 1 kcal/mol) as that in Figure 7a (Table 1). This means that both lone pair orbitals of the water molecule are involved in the hydrogen bonding. This is effectively reflected in the geometry of water in Figure 7b. The plane of the water molecule in Figure 7b forms an angle of 4.5 degrees with the line along the hydrogen bond. Thus, the plane of the water molecule is nearly collinear with the hydrogen bond, which favors the interaction of both lone pair orbitals of water. For the water dimer, on the other hand, this tilt angle is 55 degrees57 as a consequence of the bonding of an OH group from one water molecule to one of the oxygen lone pair orbitals on the second water molecule. The geometry of H9O4+ was optimized in C3V and C3 symmetries using the metal cluster of Figure 2b. The constraints of C3V symmetry do not allow the water molecules to tilt, but this is possible in C3 symmetry. The geometry optimization in C3 symmetry was started with a structure that had the hydrogen atom of each water molecule pointing toward the oxygen atom of the next water. However, the optimization converged to the structure shown in Figure 9 which has C3V symmetry. The H9O4+ geometry was also optimized under Cs symmetry using the metal cluster of Figure 2a in order to allow the complex to move away from the hollow site, but the oxygen atom of hydronium always remained on this site. For both the bare hydronium ion and the trihydrated complex, the geometry optimizations produced structures that had the hydrogen atoms of the ion pointing toward the surface. For H9O4+, we started the geometry optimization with the hydronium ion on the surface (“specifically adsorbed”) and the water molecules above the ion. But in the successive iterations, the ion moved up leaving the water molecules in between. To evaluate the energy difference between the equilibrium structures

of H3O+ and H9O4+ (shown in Figures 1 and 9) and the corresponding inverted structures with the oxygen atom of hydronium pointing toward the surface, we calculated the potential energy surfaces (PES) in a wide range of distances as shown in Figure 10. The inverted hydronium has the oxygen atom in contact with the surface and the hydrogen atoms pointing away from the surface. The inverted H9O4+ complex

Figure 10. Potential energy for H3O+ and H9O3+ adsorbed with the hydrogen atoms pointing toward the surface and in the inverted configuration. For the inverted species, the adsorbate-surface distance corresponds to the oxygen-surface distance, while for the other structures it corresponds to the hydrogen-surface distance.



is a specifically adsorbed hydronium via the oxygen atom with the three water molecules on top of it. The PES were calculated using the H3O+ and H9O4+ geometries optimized in vacuum. The hydronium binding energy obtained from Figure 10 is -55 kcal/mol, which is very close to the value of -56 kcal/mol obtained from Figure 3 where for each oxygen-surface distance the geometry of H3O+ was optimized. This small difference shows that the internal relaxation of the ion has only a small contribution to the value of the binding energy. However, the PES for the inverted hydronium ion shows a binding energy of only -37 kcal/mol. It is 18 kcal/mol less stable than hydronium with its hydrogen atoms pointing toward the surface. The same effect is observed for the inverted H9O4+ complex, which has a binding energy of -10 kcal/mol and is thus 16 kcal/mol less stable than the structure of Figure 9. Therefore, a specifically adsorbed trihydrated hydronium is very much destabilized with respect to the nonspecifically adsorbed ion. The most stable geometry of trihydrated hydronium (Figure 9) supports the model of Schmickler58 for electrochemical proton-transfer reactions in which the rate-determining step is the transfer of a proton from a hydronium ion in the second water layer to a water molecule in contact with the metal, from where another proton is passed on to the metal surface. Table 2b shows the distance to the surface of the oxygen atom of hydronium (O1) and the oxygen atom of water (O2) for the different adsorbates. The value of 2.60 Å for the oxygen-surface distance of water is in the range of values reported by Toney et al.59 For the positively charged Ag(111) surface, they found that the O atom distribution has a leading edge at 1.95 Å and a fairly broad peak at 2.7 Å above the surface. These spacings are compatible with an oxygen-down average orientation of the water molecule.59 The position of the oxygen atom of bare hydronium lies between 2.4 and 2.8 Å above the surface, depending on the orientation and the surface site. The hydronium-surface distance is shorter than the watersurface distance in accordance with the respective bond strengths (Table 1). On the fcc hollow site, the oxygen atom is closer to the surface than on the hcp hollow site because in the former the hydrogen atoms are pointing toward bridge sites (staggered configuration), whereas in the latter the hydrogens point toward metal atoms (eclipsed configuration). The addition of water molecules detaches the ion from the surface and the oxygensurface distance for hydronium increases from 2.80 to 4.57 Å, whereas for the water molecules, this distance decreases from 4.09 Å to 3.49 Å. For H9O4+, the water molecules coordinate to the surface via the hydrogen atoms (Figure 9), which leads to an oxygen-surface distance of 3.49 Å. This value is in the range reported by Toney et al.59 for the cathodic silver surface; they found the leading O edge at 3.05 Å and a sharp peak in the O height distribution at 3.7 Å. This is interpreted59 in terms of water binding to the cathodic surface via one or two hydrogen atoms. For the adsorption of H9O4+, the surface metal atoms also have a net negative charge (as for the cathodic surface) due to the polarization that hydronium induces on the metal cluster. The metal polarization will be further discussed in the hydronium-surface bonding section. Surface Formation of Hydrated Hydronium Complexes. Table 1 summarizes the binding energies of water, hydronium, and the hydronium complexes as well as the hydronium hydration energies. With all of these quantities, we can now evaluate the enthalpy change of the surface reaction: + H3O+ ads + nH2Oads f [H3O‚(H2O)n]ads

(4)

in which the adsorbed hydrated complex is formed from

adsorbed water and hydronium.The enthalpy change of eq 4 is given by

∆Hcomplex ) -BEH3O+ - nBEH2O + ∆Hhyd + BEcomplex (5) where binding energies are negative according to the definition, eq 3. ∆Hhyd is the hydration energy of hydronium in vacuum and is also negative. In eq 4, we assume that the n water molecules do not interact among themselves. Equation 5 corresponds to the thermodynamic cycle in which a hydronium ion and n water molecules are desorbed into vacuum, the hydronium-water complex is formed in vacuum and then adsorbed on the surface. All of the quantities involved in the calculation of ∆Hcomplex are given in Table 1, which shows that the formation of all the hydronium complexes is exothermic. For H7O3+ and H9O4+, the enthalpy change is more exothermic than for H5O2+ due to the higher contribution of the hydration energy. Therefore, under UHV conditions, bare adsorbed hydronium ions will readily form the hydrated complexes in the presence of water. These results for Ag(111) can be extrapolated to other metals for two reasons. First, the hydration energy (which does not depend on the metal) has an important contribution in eq 5. Second, the binding energies of molecular adsorbates do not change much among the different metals, as discussed in the adsorption of bare hydronium section. In particular, the binding energy of -54 kcal/mol estimated by Masel and co-workers5 on platinum is very close to our value on Ag(111). Therefore, the data in Table 1 support the formation of a mixture of hydrated hydronium complexes as observed on Pt(110).5 Hydronium-Surface Bonding. To rationalize the trends in hydronium binding energies with respect to hydration and orientation of the ion, we need to consider the different mechanisms that contribute to the binding energies of adsorbates. There are many techniques for analyzing the nature of the bonding of adsorbates to cluster models of metal surfaces.60 One such method is the so-called constrained space orbital variation (CSOV) method,61,62 which allows the decomposition of the binding energy of adsorbates into its many contributions. In general, the contributions to the binding energy of ions arise from the following processes: (a) the Pauli repulsion due to the nonbonding overlap of the occupied orbitals of the adsorbate and the metal cluster (its effect is to lower the binding energy); (b) metal polarization induced by the adsorbate; (c) polarization of the adsorbate; (d) donation of charge from the surface to the adsorbate, and (e) charge transfer from the adsorbate to the metal surface. Except for the Pauli repulsion, all of the other contributions increase the magnitude of the binding energy. In the case of ions, an important contribution to the binding energy arises from the metal polarization. From a classical point of view, the polarization that a point charge induces in a metal is represented as an image charge appearing within the metal. This interaction scales with the square of the charge according to Coulomb’s law. In ref 33 we showed that the binding energy of polyatomic oxyanions with one (HSO4-, ClO4-, HCO3-, NO3-), two (SO42-, CO32-), and three (PO43-) negative charges does scale with the square of their charge. The contributions of charge transfer and Pauli repulsion to the binding energy are evident when comparing the binding energies of anions with the same formal charge, such as sulfate and carbonate, which are 159 and 196 kcal/mol, respectively, on the hollow site of Ag(111).33 The higher binding energy of carbonate is coherent with its higher charge transfer toward the metal with respect to that of sulfate (0.52 and 0.35 electrons, respectively). Carbonate is also expected to have a lower Pauli repulsion than sulfate



due to its smaller size (carbonate has 32 electrons while sulfate has 50). The same trends were reported27 for the halogen anions adsorbed on silver surfaces: the main contributions to the binding energy arise from the Pauli repulsion, the metal polarization, and the charge transfer to the metal surface. For Cl-, Br-, and I- anions, the Pauli repulsion increases with the number of electrons of the adsorbate while the metal polarization shows the reverse trend. The charge donation contributes between 10 and 15 kcal/mol to the binding energy.27 The extent of metal polarization can be evaluated from the accumulation and depletion of charge of the different layers of the metal cluster. A Mulliken population analysis of the charges of the silver atoms shows that when a bare hydronium is adsorbed on the surface (Figure 1) it polarizes the electron density of the metal cluster, leading to an accumulation of charge on the first layer. Table 3 shows that the 12 atoms of the first layer have an excess of 0.30 electrons (with respect to the bare metal cluster), whereas the remaining 16 atoms of the other two layers have lost 0.44 electrons. The adsorption of trihydrated hydronium (Figure 9), on the other hand, leads to an accumulation of only 0.22 electrons on the first layer and to a depletion of 0.27 electrons for the other two layers. This shows that the water molecules screen the metal polarization with the corresponding destabilizing effect for the adsorbed hydrated hydronium. The water molecules also inhibit the charge transfer from the metal toward the adsorbate. For the bare hydronium ion there is a charge transfer of 0.14 electrons, whereas for H5O2+, H7O3+, and H9O4+, the charge transfers are 0.09, 0.07, and 0.05 electrons, respectively. The charge transfer from the metal leads to a decrease of the effective charge of the bare ion from +1 to +0.86. For the hydrated complexes, the effective charge of hydronium is also +0.86, although the charge transfer from the metal is smaller. This is due to the charge transfer from the water molecules hydrogen bonded to hydronium. Table 3 also shows that the extent of charge transfer and metal polarization that the inverted adsorbates produce are comparable with those of the ions in their equilibrium geometries. For bare hydronium, the charge transfer from the metal to the adsorbate is the same (around -0.14 electrons), irrespective of the orientation of the ion, and the extent of metal polarization is comparable. For the trihydrated complex, the charge transfer is small in both configurations and the extent of metal polarization is virtually the same. Therefore, these processes do not explain the differences in binding energies among the inverted and the equilibrium structures. These differences arise from the Pauli repulsion between the electron density of the adsorbate and that of the metal cluster. The contribution of the Pauli repulsion can be estimated by evaluating the overlap of the electron density of the bare cluster and the bare adsorbate at a separation distance corresponding to the equilibrium distance of the adsorbate/metal cluster system:

overlap )

∫Fmetal‚clusterFadsorbate dr ) 4∑∑∫|ψi|2|ψj|2 dr i

(6)

j

where the index i runs over the occupied molecular orbitals (MOs) of the metal cluster and j over the occupied MOs of the bare adsorbate. For the hydronium configuration shown in Figure 1, this overlap is 8.0 × 10-3 a.u. while for the inverted hydronium the overlap is 14 × 10-3 a.u., which explains the lower binding energy of inverted hydronium. For both cases, ca. 50% of the total overlap arises from the overlap of the electron density of the highest occupied MO of the metal cluster

TABLE 3: Accumulation (positive numbers) and Depletion (negative numbers) of Electron Density (in atomic units) for the Different Layers of the Metal Cluster and for the Whole Metal Cluster as Obtained from Mulliken Populations (reference is the bare cluster) H3O+ inverted H3O+ H9O4+ inverted H9O4+

1st layer

2nd and 3rd layers

charge transfer

0.30 0.22 0.22 0.28

-0.44 -0.38 -0.27 -0.27

-0.14 -0.15 -0.05 0.01

with the occupied MOs of hydronium. The same trend is observed for the trihydrated complex. It is interesting to compare our results with those of Head and co-workers who studied hydrated halide adsorption on the cathodic Al(111) surface.35 For trihydrated iodide on Al(111), the water molecules have one hydrogen atom pointing toward the ion in a structure with C3V symmetry. Due to the spherical symmetry of the ion, there is no preferential orientation for the hydrogen bonding and the water molecules are located above the ion, thus allowing its specific adsorption. In this configuration, the water molecules do not screen the metal polarization and, consequently, these authors obtain the same binding energy for the bare ion as for the trihydrated iodide. For hydronium, on the other hand, the water molecules push the ion away from the surface (Figure 9) as a consequence of two driving forces: the preferential orientation of the hydrogen bonding with the water molecules and the fact that adsorption via the oxygen atom of hydronium is highly destabilized by Pauli repulsion (Figure 10). In the case of the trihydrated fluoride ion, Head and co-workers found35 a destabilizing effect of the water molecules, even though they are located on top of the ion. In this case, the adsorbate has C3 rather than C3V symmetry, with the water molecules forming a crown structure on top of the fluoride. Due to the smaller size of the fluoride ion, water molecules hydrogen bonded to it are pushed toward the surface to distances that are repulsive for the bare water molecules. We found the same trend for H9O4+. The oxygens of the water molecules in H9O4+ are located at 3.49 Å above the surface, while from the PES of three water molecules (with the same geometry as that in Figure 9 but without the hydronium ion) we found that the oxygen atoms are located at 3.65 Å. Therefore, hydronium also pushes the waters against the surface with the corresponding destabilizing effect. Electric Field Effects. To model adsorption processes in electrochemical interfaces, the potential of the metal electrode has to be taken into account. Several approaches have been considered in the literature. In semiempirical methods, such as the ASED method in which the most important parameters are the orbital ionization potentials (OIP), the electrode potential is modeled by shifting the OIPs, which produces a change in the energy levels of the metal cluster.63,64 In the case of ab initio calculations, several approaches have been employed. One approach is to add (remove) electrons to (from) the metal cluster in order to model negative (positive) potentials. Depending on the number of electrons and the surface of the cluster, different surface electron charge densities can be obtained.35 The drawback of this approach is that it leads to systems with unpaired electrons that have convergence problems.65 To vary the surface charge density in a continuous way, another approach has been to renormalize the electron density matrix so that a metal cluster can have a fractional charge.66 This approach has been used with small metal clusters (Hg366 and Pt567), since there can be an important redistribution of the surface charge66 for clusters with three or more atomic layers.

Hydrated Hydronium Ions on Ag(111) The electrode polarization can also be treated as an external uniform electric field applied in a direction perpendicular to the metal surface. This approach has been used in the study of adsorbates such as CO,68-70 CN,71 NO,70 and atomic oxygen coadsorbed with ions,72 as well as in our previous studies of anion adsorption.32,33 For large metal clusters, a linear variation of the cluster HOMO energy as well as the cluster surface charge was found with the electric field,33 indicating that the main features of electrode polarization are taken into account. This is still an approximation, since electric fields in the double layer are not homogeneous. In this section we take this approach and we investigate electric fields effects on several adsorbate properties such as geometry, binding energy, and charge transfer. Electric field perpendicular to the surface in the range (0.01 au ) (5.2 × 107 V/cm were considered. These fields are comparable to those present in an electrochemical cell because an externally applied potential of 1 V creates an electric field of ∼107 V/cm at the electrode surface.73 The effects of the electric field were studied comparatively for bare hydronium and the trihydrated ion. Figure 11 shows the influence of the electric field on the binding energy of the adsorbates. The direction of a positive field is defined in the inset of the figure. This field produces an energy lowering (due to the alignment of the water dipole with the field) for a bare water molecule oriented as shown in the inset. For bare hydronium adsorbed on a hollow site, the binding energy decreases for positive electric fields (Figure 11). The electric field affects the different contributions to the binding energy outlined in the hydroniumsurface bonding section. The most important contribution in the case of ions is the metal polarization.33 Positive fields remove electrons from the surface, increasing the electrostatic repulsion with the positive adsorbate. Another effect is to lower the energy levels of the metal cluster, thus inhibiting the charge transfer from the metal to the adsorbate with the corresponding destabilizing effect. While at zero field there is a charge transfer of 0.14 electrons to the adsorbate (Table 3), the charge transfer is only 0.04 electrons at a field of +0.01 au. On the other hand, negative fields, which inject electrons into the surface, increase the binding energy as expected. Also, for a field of -0.01 au, the charge transfer to hydronium increases to 0.22 electrons. For H9O4+ we observe (Figure 11) the same trends as for H3O+. However, positive electric fields also stabilize H9O4+ on the surface. This is due to the contribution of the adsorbate polarization which for H9O4+ is more important than for H3O+. To explain this, we will decompose the binding energy for the process of adsorbing an ion on a polarized metal surface:


Figure 11. Binding energies of H3O+ and H9O3+ as a function of external electric field. The inset shows the direction of a positive electric field perpendicular to the surface. This positive fields aligns a water molecule as shown in the figure.

Ion in vacuum + metal cluster (electric field) f adsorbed ion (electric field) (7) into the following contributions:

Relaxation: Ion in vacuum (vacuum geometry) f ion in vacuum (surface geometry) (8) Polarization: Ion in vacuum (surface geometry) f ion in a vacuum (surf. geom., elect. field) (9) Adsorption: Ion in vacuum (surf. geom., elect. field) f adsorbed ion (surf. geom., elect. field) (10) In step 8, the geometry of the ion is changed from its equilibrium geometry in vacuum to the geometry that the ion has on the surface. We will refer to the energy change of this step as the relaxation energy. In step 9, an electric field is applied to the

Figure 12. Decomposition of binding energy into adsorption, polarization, and relaxation contributions for (a) H3O+ and (b) H9O3+ as a function of external electric field.

relaxed ion, and the energy change of this process is the polarization energy of the ion. Finally, in step 10, both the ion and metal cluster representing the surface are subject to the same electric field and they are brought together for the adsorption process to take place. The energy change of this step is the adsorption energy. We will refer to the energy change of the whole reaction, process 7, as the binding energy which is decomposed into relaxation, polarization, and adsorption energies. Figure 12 shows the different contributions to the binding energy for H3O+ and H9O4+. The influence of the electric field



Figure 13. Perpendicular height of hydrogen atoms of H3O+ (empty circles) and H9O3+ (filled circles) above the surface as a function of external electric field.

is qualitatively the same for the bare and the hydrated ion. The electric field mainly affects the adsorption and polarization energies. However, the relative contributions of both processes are different. For H3O+, the adsorption energy is the main contribution to the binding energy. For H9O4+, the adsorption energy is smaller and, therefore, the polarization contribution is more important. For both ions, the polarization contribution has a stabilizing effect to the bonding at positive electric fields. Figure 12b shows that the adsorption and relaxation energies of H9O4+ are small and virtually the same at a field of +0.0025 au. An extrapolation of the lines to more positive electric fields shows that the adsorption energy will soon drop to zero and change sign, indicating a repulsive behavior between the surface and the adsorbate. Indeed, any geometry optimization at electric fields more positive than +0.0025 led to desorption of H9O4+. Therefore, the stabilization of the hydrated ion at low positive electric fields is mainly due to the polarization contribution to the binding energy. Figures 13-15 illustrate the effect of the electric field on the relaxation of adsorbed H3O+ and H9O4+. The metalhydrogen distance is plotted in Figure 13 for the hydrogen atoms closer to the surface (for H9O4+ they correspond to the hydrogen atoms of the water molecules, see Figure 9). The surface distance curves in Figure 13 follow the same trends as the adsorption contribution to the binding energy of Figure 12. The changes in adsorbate-surface bond lengths with electric fields are a measure of the ionicity of surface bonds. For example, the halogen and oxygen metal surface bond lengths are affected by the electric field because for these atoms there is a charge transfer of about 1 electron from the metal surface toward the adsorbate.61,62 The smaller changes in H9O4+-surface bond lengths with electric field indicate that ionic bonding is less important than for bare hydronium, as expected from the screening of the water molecules. The contribution of the water molecules to the H9O4+-surface bond can be estimated by calculating the binding energy of three water molecules with the same geometry as that in H9O4+. We obtained a value of -10 kcal/mol while the binding energy of H9O4+ is -26 kcal/ mol, thus showing that ionic bonding is less important for H9O4+ than for H3O+. Figure 14 shows the internal relaxation of H3O+ and H9O4+ as a function of the electric field. The changes in the hydronium OH bond length (labeled d1) correlate with the changes in the adsorption energy (see Figure 12). At the most negative fields where the interaction of the adsorbate with the surface is stronger, the OH bond weakens. This is a general trend that we have observed with all adsorbates33 and is coherent with the

Figure 14. Internal relaxation of H3O+ (empty circles) and H9O3+ (filled circles) as a function of external electric field.

Figure 15. Orientation of a water molecule in H9O4+ adsorbed on the hcp hollow site for different external electric fields: +0.025 au (black circles) and -0.01 au (white circles). The figure shows the plane containing a water molecule and one of the three OH bonds of hydronium. Bond lengths in Å.

picture of conservation of bond order on metal surfaces.50 The same is observed for the water OH bond closer to the surface (labeled d2). Figure 14 shows that the OH bond length of hydronium in H9O4+ (labeled d1) is longer than that of the bare ion at all fields. This is because the interaction of hydronium with the three water molecules in H9O4+ (-86 kcal/mol, the hydration energy) is stronger than the interaction of H3O+ with the metal surface (-56 kcal/mol). This leads to a weakening of the OH bond in H9O4+ with the corresponding bond enlargement. The hydrogen bond in H9O4+ (labeled HB) is the most affected by the field. Its decrease with negative fields indicates that proton transfer from hydronium to a water molecule is favored. The effect of the electric field is more important on the orientation of the water molecules than on the internal relaxation of the bonds as shown in Figure 15. The water molecules rotate around the hydronium ion and their hydrogens get closer to the surface at the most negative fields. This shows

Hydrated Hydronium Ions on Ag(111) that the water dipole tends to align with the negative field, which is energetically more favorable. Conclusions The adsorption of H2O, H3O+, H5O2+, H7O3+, and H9O4+ was investigated on Ag(111) at the Hartree-Fock + MP2 level of theory using metal clusters to model the surface. The adsorption of the ions was studied in the absence and presence of external electric fields comparable to those present in the electrochemical interface. Bare hydronium adsorbs under C3V and Cs symmetry with binding energies around -56 kcal/mol on the hollow site. Adsorption always occurs via the hydrogen atoms, and the potential energy surface shows a small corrugation on the different surface sites. Under Cs symmetry, there are a number of structures very close in energy that adsorb via one or two hydrogen atoms. Adsorption via the oxygen atom is destabilized by the Pauli repulsion with the electron density of the metal. The addition of water molecules to a bare adsorbed hydronium has the effect of detaching the hydrogen atoms of the ion from the surface as a consequence of hydrogen bond formation. When three water molecules are added, they locate between the metal and the ion. This shows that trihydrated hydronium does not specifically adsorb. The lower binding energy of H9O4+ (-26 kcal/mol) with respect to that of bare hydronium (-56 kcal/mol) is due to the screening of the metal polarization induced by the water molecules. Charge transfer from the metal to hydronium is also inhibited. The surface reaction for the formation of the hydrated complexes from water and hydronium is exothermic and has an important contribution from the formation of the hydrogen bonds. The enthalpy changes for the formation of H5O2+, H7O3+, and H9O4+ are -13, -29, and -32 kcal/mol, respectively. The exothermic formation of the complexes is predicted on metals other than silver. In the presence of external electric fields, the binding energies of the adsorbates were decomposed into adsorption, relaxation, and polarization contributions. The adsorption contribution is more important for bare hydronium than for the trihydrated complex. The polarization of the adsorbate is more important for H9O4+ than for H3O+ and leads to a stabilization of H9O4+ at moderately positive electric fields. However, H9O4+ desorbs at higher fields since the adsorption contribution changes sign and becomes repulsive. The effect of the electric field on the internal relaxation of the ions is smaller for H9O4+ than for the bare ion due to the screening of the water molecules. For H9O4+, the hydrogen bonds are the most affected by the field. The hydrogen bond length decreases with negative fields, indicating that proton transfer from hydronium to a water molecule will be favored. Acknowledgment. E.M.P. thanks Fundacioń Antorchas for Grant A-13532/1-102 and Consejo Nacional de Investigaciones Cientı´ficas y Tećnicas (CONICET) for PEI grant 0305/97. P.P.O. thanks Agencia Nacional de Promocioń Cientı´fica y Tecnolo´gica (grant 06-00000-02148), Fundacioń Antorchas (grant A-13532/73), CONICET (PEI grant), and CONICOR. We also thank the support of Agencia Nacional de Promocioń Cientı´fica y Tecnolo´gica for grant 06-03195; CONICET for grant PICT 0180, and SECYT-UNC for grant 163/99. A.F. thanks CONICET for the fellowship granted. References and Notes (1) Wagner, F. T.; Moylan, T. E. Surf. Sci. 1987, 182, 125. (2) Wagner, F. T.; Moylan, T. E. Surf. Sci. 1988, 206, 187.

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Theoretical Investigation of Hydrated Hydronium Ions on Ag (111)

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