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Available online at www.sciencedirect.com

Electrochimica Acta 53 (2008) 6149–6156

Electronic interactions decreasing the activation barrierfor the hydrogen electro-oxidation reaction

Elizabeth Santos a,b,∗, Wolfgang Schmickler c

a Faculdad de Matematica, Astronomıa y Fısica - Universidad Nacional de Cordoba, Cordoba, Argentinab Zentrum fur Sonnenenergie und Wasserstoff-Forschung, Helmholtzstr. 8, D-89081 Ulm, Germany

c Institute of Theoretical Chemistry, University of Ulm, D-89069 Ulm, Germany

Received 10 August 2007; received in revised form 2 December 2007; accepted 11 December 2007Available online 25 December 2007

bstract

A unified model for electrochemical electron transfer reactions which explicitly accounts for the electronic structure of the electrode recentlyroposed by us is applied to the hydrogen oxidation reaction at different metal electrocatalysts. We focus on the changes produced in the transitiontate (saddle point) as a consequence of the interactions with d-bands. We discuss different empirical correlations between properties of the

etal and catalytic activity proposed in the past. We show which role is played by the band structure of the different metals and its interactionith the molecule for decreasing the activation barrier. Finally, we demonstrate why some metals are better electrocatalysts for the hydrogen

lectro-oxidation reaction than others.2007 Elsevier Ltd. All rights reserved.

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eywords: Electrocatalysis; Electron transfer reactions; Bond-breaking; d-Ban

. Introduction

The question: What determines the catalytic activity of anlectrode? is of central importance for electrochemical sci-nce and its technological applications. Much research has beenocused on this issue, in particular for the oxygen reduction andydrogen oxidation, and several ideas have been advanced with-ut much success. Thus, properties like the d-character [1], theosition of the d-band center [2], or the density of states at theermi level have been considered, but none of them has a clearelation to the catalytic activity. In the absence of proper theo-ies, correlations with other properties such as the work functionave been sought [3]. The most famous of these is so-called theolcano plot [4,5] of the rate of the hydrogen evolution versushe energy of adsorption, which we shall discuss in greater detailelow.

Recently, we have proposed a unified model for electro-hemical electron transfer reactions on metals, which explicitlyccounts for the electronic structure of the electrode. It applies

∗ Corresponding author. Tel.: +731 50 31342; fax: +731 50 22819.E-mail address: esantos@uni-ulm.de (E. Santos).

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013-4686/$ – see front matter © 2007 Elsevier Ltd. All rights reserved.oi:10.1016/j.electacta.2007.12.049

drogen oxidation

oth to simple and to bond-breaking reactions, and points outwo key factors required for electrocatalysis: a high density of-states near the Fermi level and strong interaction of the latterith the valence orbital of the reactant [6–10]. First calcula-

ions had been performed with idealized band shapes in order tonderstand the way in which this catalysis works. Very recently,e have briefly reported on the application of our theory to

he hydrogen oxidation reaction [11]. In this communication,e shall enlarge on this topic and discuss our results in greateretail.

. The model

Our approach is an extension of the electron transfer the-ry proposed previously [12,13]. The details of the theory areiven in these publications; here, we summarize those aspectshich are essential for understanding the application to hydro-en oxidation. Explicitly, we consider the reaction of a biatomicomonuclear molecule at a metal electrode. The Hamiltonian

f the system contains the contributions of the molecule, theetal which acts as a catalyst, the solvent and the corre-

ponding interactions between these subsystems. In order toescribe the molecular bond between the two hydrogen atoms,

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150 E. Santos, W. Schmickler / Electr

e employ the extended Huckel approximation taking intoccount the repulsion by orbital overlap. The Marcus–Hushheory [14,15] is applied for the reorganization of the solventnd the Anderson–Newns model [16,17] for the interaction ofhe valence orbital with the metal. Other interactions, such aspin–spin repulsion on the reactant and image charge, are alsoonsidered. Then, the Hamiltonian is solved within the Green’sunctions formalism. For a homonuclear molecule, the densityf states of the reactant is affected by the presence of the metalnd can be described by the following expression:

Molec = 1

π

∑σ

{Δ

(z − εσ − β)2 + Δ2+ Δ

(z − εσ + β)2 + Δ2

}

(1)

The sum is over the two spin states σ = ±1; the first term cor-esponds to the bonding and the second one to the anti-bondingrbital. The parameter β is related to the dissociation energyf the molecule De and thus determines the energy separationetween both orbitals. The effective energy of the orbital of oneonstituent atom is given by εσ :

˜σ± = εo + Sβ − 2λq

+U 〈nσ∓〉 − γ (1 − 〈nσ−〉 − 〈nσ+〉) + Λ (2)

Here ε◦ is the energy of the atomic orbital relative to theermi level; it can be tuned by the applied electrode potential.he second term accounts for the orbital overlap S between bothtoms. The third term is the shift produced by the fluctuationsf the solvent, where λ is the reorganization energy according toarcus–Hush theory, and q the normalized solvent coordinate.riefly, a solvent coordinate q corresponds to a solvent config-ration which would be in equilibrium with a particle of chargeq. The fourth and fifth terms account for the spin–spin and

ipole–dipole interactions respectively. 〈ni〉 is the occupation ofhe spin orbital i:

ni〉 =∫ EF

−∞ρidz (3)

Here ρi is the density of states of the spin orbital, and Δ andare the so-called chemisorption functions, which are related

o the density of states of the metal and the coupling constantetween metal and molecule Vk:

∑k

|Vk|2z − εk + iδ

= −iΔ(z) + Λ(z) (4)

denotes the shift of the orbital energy caused by the interactionith the metal, and Δ the level broadening. Both parameters are

nterrelated through a Hilbert transform:

(z) = 1P

∫ ∞ Δ(z′)dz′ (5)

π −∞ z − z′

here P denotes the principal part.Within our model the potential energy of the system can be

alculated as a function of various system parameters such as

apsw

ica Acta 53 (2008) 6149–6156

he effective solvent coordinate, the bond distance and the dis-ance of the reactant to the metal surface. Simultaneously, theccupation probabilities of the orbitals can be calculated. Fig. 1hows contours plots of such potential energy surfaces at a fixedistance of the reactant to the metal projected onto the plane ofhe solvent coordinate and the bond distance r for three differentases: the reduction of a molecule (a) the dissociation withoutlectron transfer (b), and the oxidation (c). In all the cases wean follow the energy of the system and the occupation of theolecular orbitals along the whole reaction path. The initial state

s a neutral molecule corresponding to a minimum at the solventoordinate q = 0, and with the bond distance at its equilibriumalue r = ro. The reaction goes through a saddle point (marked bystar) to the valley at higher bond distance centered at a solventoordinate qf, which is different in the three cases considered. Inhe first case, the reduction of the molecule produces two anionsa). Then the valley at higher separation between the atoms isentred at qf = +2. For the dissociation of the molecule to twotoms, the center of the final valley is located at qf = 0, and inc) the molecule oxides to two cations with the valley at qf = −2.n all cases the system has to overcome a saddle point situatedt intermediate value of the solvent coordinate q and the bondistance r. We note that the surfaces in this figure are meanto demonstrate the typical reactions paths, therefore they haveeen calculated for a constant chemisorption function Δ, whichorresponds to the non-catalytic coupling to a sp-wideband ando the absence of a d-band.

For the electron transfer reactions the presence of the solvents essential: the resulting ions are stabilized by their interactionith the solvent. Therefore, model calculations performed for

eactions on a metal surface in the gas phase, which can nowa-ays be routinely performed with the aid of quantum-chemicalackages, can only describe the pure dissociation A2 → 2A,ut not electron transfer with bond breaking. They may stilllluminate certain aspects of these reactions, but are necessar-ly incomplete. Another most important aspect absent in theas phase is the electrode potential, which determines the ratend the direction of electrochemical reactions. In our model, ahange in the electrode potential shifts the Fermi level of theetal with respect to the energy levels in the solution.

. Selection of system’s parameters for the oxidation ofydrogen

As a special case we have investigated the overall reaction:2 → 2H+ + 2e−. First results have already been published [11].he initial state is the stable molecule, and the final state consistsf two protons stabilized by the interaction with the solvent. Inhe critical stage of this reaction, a thermal fluctuation of theolvent configuration raises the bonding orbital of the moleculeo the Fermi level EF of the metal, two electrons are transferredrom the molecule to the metal, the molecular bond is broken, andhe system relaxes into two solvated protons. Thus, a good cat-

lyst must lower the energy of the system as the bonding orbitalasses EF. We shall focus on the changes produced in the tran-ition state (saddle point) as a consequence of the interactionsith d-bands. We shall show which role is played by the band

E. Santos, W. Schmickler / Electrochimica Acta 53 (2008) 6149–6156 6151

Fig. 1. Potential energy surfaces contour plots showing three possible reaction paths (yellow arrows) for the bond breaking of the molecule A obtained with differentf Syste( f thet

sbtt

mshHt(mihtbtEaelltmswewt

4

ap

b

Δ

rathe contributions to Δ(z) vanish outside the bands. We employthis simple model in order to investigate the effects on the acti-vation state of the reaction of different properties of the bands,such as position (εc), width (wd) and coupling factor (Vk). We

amilies of parameters. The stars indicate the saddle points for the reaction paths.b) U = 8.0 eV, εo = −4.0 eV; (c) U = 5.0 eV, εo = −2.0 eV. The density of states ohe occupation.

tructure of the different metals for decreasing the activationarrier. Finally, we shall demonstrate why some metals are bet-er electrocatalysts for the hydrogen electro-oxidation reactionhan others.

The choice of the parameters for hydrogen oxidation wasade according to the following criteria: The Coulomb repul-

ion U between two electrons on the same atomic orbital ofydrogen was taken as 4.54 eV [18], and the tight-binding (oruckel) constant for the hydrogen molecule was chosen such

hat it reproduces the binding energy of the hydrogen molecule4.55 eV). The energy of reorganization for the proton was esti-ated in the following way: The hydration energy of the proton

s about 11.5 eV; at the surface, the proton has roughly lost aboutalf of its solvation sheath. Therefore, the energy of reorganiza-ion, which is caused by the interaction with heavy particles, haseen taken as 3 eV, roughly one quarter of the solvation energy ofhe proton. The effective coupling constants |Veff|2, described inq. (7) below, were taken from the published values by Hammernd Nørskov [2,19]. According to Eq. (2) the relative position oflectronic energy levels in the solution with respect to the Fermievel EF depends on the electrode potential. Our aim is to calcu-ate relative values for the energies of activation and to explainhe great variation observed in catalytic activity with different

etals. Therefore, we choose the same, well-defined referencetate for all metals. We have chosen the electrode potential athich a hydrogen molecule in the bulk of the solution has an

nergy of −4λ, which according to the estimates given aboveould roughly be the energy of the final state of this reaction,

wo protons on the electrode surface.

. Model calculations with idealized band shapes

In previous works [7,8], we have analyzed the effect of ide-lized d-bands on electrochemical reactions in general. For thisurpose we have considered a semi-elliptical ideal shape for the

Fbw

2

m parameters: Δ = 0.2 eV, De = 3.75 eV, λ = 0.8 eV. (a) U = 5.0 eV, εo = −4.3 eV;molecule is shown schematically for the start and end points. Shadows indicate

ands as proposed by Newns [17] (see Fig. 2):

(z) = Δo

[1 −

(z − εo

c

wo

)2]1/2

θ[w2

o − (z − εoc)2]

+ d

⎡⎣1 −

(z − εd

c

wd

)2⎤⎦

1/2

θ[w2d − (z − εd

c)2] (6)

The first term represents the sp-band, and the second term rep-esents the d-band with centers εo

c and εdc and half-width wo,

nd wd respectively. The two Heaviside functions θ ensure that

ig. 2. Level broadening Δ and shift Λ for the superposition of two semi-ellipticands; wideband: Δo = 0.2 eV, wo = 10 eV, εo

c = 4.3 eV; thin band: Δd = 0.2 eV,

d = 1 eV, εdc = 3.0 eV.

6152 E. Santos, W. Schmickler / Electrochimica Acta 53 (2008) 6149–6156

Fig. 3. Density of states for the hydrogen molecule at the transition state forvarious coupling strength |Veff|2 with a thin d-band (wd = 1 eV) located at theFermi level. |Veff|2: 0 eV2 (full, black line), 1 eV2 (dashed, red line), 5 eV2 (dot-tot

trim

e0

tdstacfmabaipcnastttd

E

FEs

odcVtaeb10 eV (Fig. 5).

However, there are also other properties of the bands affect-ing the energetic of the system. Fig. 6 shows the influence ofthe position of the d-band on the activation barrier. (a) and (b)

ed, green line), 10 eV2 (dotted-dashed blue line). Shadows indicate occupationf the states. (For interpretation of the references to colour in this figure legend,he reader is referred to the web version of the article.)

ake in a first approximation, the latter factor as a constant andeplace it by a single effective value Veff. Thus the sum over kn Eq. (4) reduces to the surface density of states ρMet(z) of the

etal and we have:

(z) = π|Veff|2ρMet(z) (7)

In addition to the d-band, we consider an sp-band of semi-lliptic form with a width of 10 eV and a coupling constant of.2 eV with the reactant.

The electronic interaction between the molecular orbitals andhe metal at the transition state play the key role in decreasinge activation barrier of electrochemical reactions. Therefore, wehall analyse in more details the influence of different factors onhis state. In the case of reduction reactions, the interaction of thenti-bonding orbital is determining, while the bonding orbital isrucial for oxidation such as the particular case considered hereor hydrogen. Fig. 3 shows the density of states for the hydrogenolecule at the transition state for various coupling strength withthin d-band (width wd = 1 eV) located at the Fermi level. Theonding orbital crosses the Fermi level at the transition statend is partially occupied. The charge of the elongated molecules about +1 at this position. The interaction with the d-bandroduces a broadening of this orbital, and for enough stronglyoupling it even splits into bonding and anti-bonding parts, butow with respect to the metal. The anti-bonding orbital is alsolittle affected. However, its contribution to the energy of the

ystem is not important because it lies far more positive thanhe Fermi level. Effectively, the electronic contribution to theotal energy is given by the integral up to the Fermi level ofhe product between the energy coordinate z and the molecular

ensity of states ρMolec:

elec =∫ EF

−∞z ρMolec(z) dz (8) F

a

ig. 4. Integrand of Eq. (6), z.ρMolec(top) and electronic contribution given byq. (6) (bottom) as a function of the energy coordinate z obtained from datahown in Fig. 3. Symbols same as in Fig. 3.

Thus, it is clear that a broadening and shift of the molecularrbitals to more negative values of the energy coordinate z willecrease the electronic contribution. The effects of the couplingonstants can be observed in Fig. 4. The d-band with the highereff produces the more negative shift, the higher broadening and

hus it shows the greater area below EF. Then the net effect ofn increasing coupling constant Veff is a decrease of the totalnergy. A decrease on the activation barrier of about 0.7 eV cane produced by the presence of a band with a coupling factor of

2

ig. 5. Dependence of the activation energy with the coupling factor |Veff|2 ford-band with constant width wd = 1 eV and fixed position εd

c = EF.

E. Santos, W. Schmickler / Electrochim

F(|

cehw

w

atF(tHtbΔ

eTWtoe

5

uo

F

ig. 6. Dependence of the activation energy with the position of the d-band εdc .

a) wd = 1 eV, |Veff|2 = 1 eV2; (b) wd = 1 eV, |Veff|2 = 10 eV2; (c) wd = 3 eV,Veff|2 = 10 eV2.

orrespond to bands with the same width wd = 1 eV but differ-

nt coupling constant ((a) |Veff|2 = 1 eV (b) |Veff|2 = 10 eV)). (c)as the same coupling constant than (b) but its width is bigger:d = 3 eV. When the interaction between metal and molecule iseak (a) the optimal position of the d-band is near the Fermi level

rtom

ig. 7. Surface densities of d-band states of the metals considered. The integral over

ica Acta 53 (2008) 6149–6156 6153

nd the behaviour is almost symmetric. For stronger interactionshe optimal position shifts towards more negative values than theermi level (b), this effect being more important for wider bandsc). It is noticeable that the presence of a band far more positivehan the Fermi level still has an influence on the bonding orbital.owever, we have to keep in mind that the effect of d-bands on

he molecular orbital is not only due to the broadening producedy Δd but also by the shift produced by Λd. While the effect ofd is limited to an interval 2 wd around εd

c , the influence of Λdxtends asymptotically over a wide energy range (see Fig. 2).his is also the cause of asymmetry in the curves shown in Fig. 6.hen the position of the d-band is located at energy lower than

he EF, we have the effect of both Δd and Λd on the bondingrbital, while if it is located over the EF, only the effect of Λd isvident.

. Model calculations for real systems

Calculations with idealized band shapes are very useful fornderstanding the way in which a catalysts acts. In order to applyur model to real systems and predict their catalytic activity, we

equire the key factors: the densities of states of the metal, andhe coupling with the reactant. Fig. 7 shows the d-band densitiesf states of nine different metals for which we have performedodel calculations. The position and the shape of the d-bands

the densities has been normalized to unity. The coupling factors are also given.

6154 E. Santos, W. Schmickler / Electrochimica Acta 53 (2008) 6149–6156

Ffm

dFwcAtwmot

idwtTeriT

Ffl

Fig. 10. Density of states for the molecule at the saddle point for some of the met-als shown in Fig. 7: ideal metal with a wide sp-band (full, black line), Ag(1 1 1)(dashed, green line), Ni(1 1 1) (dashed, red line), Pt(1 1 1) (dotted, blue line).(r

ca

stBnoFhtoetot

ig. 8. Experimental values compiled from [5] and [26] of the exchange currentor hydrogen oxidation reaction as a function of the position of d-bands for theetals shown in Fig. 7.

iffer widely. Ir and Re have wide bands centered almost at theermi level. The bands of Ni, Co and Pt are somewhat thinner, butith a higher density of states (DOS) at EF. Rh is an intermediate

ase between these two groups. On the other hand, Ag, Cu andu have very thin bands with a high DOS at the centre, but

hey are localized several eV below EF. The coupling constants,hich are given in the same figure, are very different from oneetal to the other and there is no correlation with the features

f the bands. They depend on the extension of the orbitals, andhus increase when going down a column of the periodic table.

Before turning to the results of our own calculations it is ofnterest to compare experimental data for the exchange currentensity of the hydrogen electrode with two metal characteristicshich have been invoked in the recent literature: the position of

he d-band center, and the density of states at the Fermi level.he corresponding plots are shown in Figs. 8 and 9. For the

xperimental data we show both the highest and the lowest valueeported in the literature; we shall comment below on the spreadn these values. It is evident that no correlation exists at all.he systems are too complicated, and the band structures are to

ig. 9. Experimental values compiled from [5] and [26] of the exchange currentor hydrogen oxidation reaction as a function of the density of states at the Fermievel for the metals shown in Fig. 7.

ttethisAtiiEtd

fcimdSh

For interpretation of the references to colour in this figure legend, the reader iseferred to the web version of the article.)

omplex to obtain a simple link between the catalytic activitynd one single metal property.

From the metal densities of states and the coupling constantshown in Fig. 7 we are able to calculate the chemisorption func-ions Δ and Λ, which determine the energetic of the reaction.y means of relatively simple calculations, which imply theumerical evaluation of the integral given by Eq. (8), we havebtained potential energy surfaces (similar to those shown inig. 1) and the corresponding occupation probability for theydrogen orbitals for all these metals. As discussed in section 4,he key factor for catalysis is the broadening, or even splitting,f the bonding orbital of H2 as it passes the Fermi level, whichntails a reduction of the energy of activation. The structure ofhe metal bands is reflected in the structure of the molecularrbitals at the transition state. The higher the coupling constant,he stronger is this effect. As an example, we have consideredhree metals with different characteristics in their band struc-ures. The effect of the d-bands on the molecular orbitals and thelectronic contribution to the energy of the system at the transi-ion state are shown in Figs. 10 and 11. Pt(1 1 1) and Ni(1 1 1)ave both a high DOS near the Fermi level. Thus, the bond-ng orbitals are considerably broadened. However, this effect istronger on Pt(1 1 1) because of the higher coupling constant.g(1 1 1) has also a higher coupling constant than Ni(1 1 1) but

he center of the band lies much lower. Ag(1 1 1) splits the bond-ng orbital into a large peak near EF and a smaller peak, whichs roughly centered in the middle of the d-band (∼5 V belowF). However, the smaller peak produces a bigger lowering of

he electronic energy contribution as can be observed in Fig. 11,ue to its position at lower values of the energy coordinate z.

Finally, we show in Fig. 12 a plot of the experimental valuesor the exchange current density versus the activation energyalculated from our model. Except for Au and Ag, the exper-mental values in the literature vary by at most one order of

agnitude. This is the kind of variation to be expected when

ifferent measuring techniques or different surfaces are used.everal of the data are 40–50 years old, but since that time thereas been no significant advance in the measurement of kinetic

E. Santos, W. Schmickler / Electrochim

FEs

dtstvtm

Ffwe

dtrIoowttwlitaatilsg

finrdiatmrNsre

ig. 11. Integrand of Eq. (6), z.ρMolec(top) and electronic contribution given byq. (6) (bottom) as a function of the energy coordinate z obtained from datahown in Fig. 10. Symbols are the same as in Fig. 10.

ata–indeed, judging from a recent tendency to measure evenhe rates of fast reactions solely by cyclic voltammetry thereeems to have been a decline in experimental skill. In any casehere is no reason why these data are not trustworthy, and the

ariation of the rate over six orders of magnitude is real. Wherehere has been a significant advance is the pretreatment of noble

etal electrodes by flame annealing. This may explain the large

ig. 12. Experimental values compiled from [5] and [26] of the exchange currentor hydrogen oxidation reaction as a function of the activation barrier calculatedith our unified model. The dotted lines are linear fits of the lower and higher

xperimental values.

t

rotttantaiicwitmieoa

ica Acta 53 (2008) 6149–6156 6155

iscrepancy in the data for gold and silver. The data point withhe high exchange current for silver was measured in our labo-atory by pulse methods and with the flame treatment [20,21].n the cited work, we measured the rate of hydrogen evolutionn three principle surfaces of silver, and found the same orderf magnitude for the exchange current in all cases, though thereas a definite difference between the crystal planes. Needless

o say, that we believe this data point, which is very close tohe value of Doubova and Trasatti [22], to be particularly trust-orthy. Similarly, for polycrystalline gold we measured in our

aboratory practically the same rate as the higher value indicatedn figures [23,24]. Therefore, we believe that for gold and silverhe higher rate constants are more likely to be correct. Indeed,s a general rule the higher values for the rates should be moreccurate, since inadequate, i.e. too slow, techniques or bad elec-rode preparation usually results in too low values. Bearing thisn mind, we observe a very clear correlation between our calcu-ated values and the experimental data. This is the first time thatuch a correlation has been based on calculations rather than oneneral arguments.

The general trend of our calculated results can be understoodrom the densities of states and the coupling constants shownn Fig. 7. Thus, Ir, Re, Pt, Rh all have a high density of statesear the Fermi level and high coupling constants, therefore theeaction is very fast at these metals. Co and Ni have a highensity of states, but a very small coupling just as Cu, whichs worse because its d-band lies well below the Fermi level. Aund Ag have intermediate coupling constants and d-bands belowhe Fermi level, and therefore have intermediate rates. The sp

etals, which comprise Hg, Pb, Cd, In, all have d-bands wellemoved from the Fermi level and are therefore bad catalysts.ote that this argument can be made for any electron transfer

tep, so that the general trend should be the same, whatever theate determining step for the overall reaction–as long as it is anlectron transfer step, but this seems always to be the case forhe hydrogen reaction.

A venerable concept for explaining trends in the hydrogeneaction is the so-called volcano curve which results from a plotf the rate versus the energy of adsorption of a hydrogen atom inhe gas phase [4,5]. All of the experimental data in Fig. 11 lie onhe ascending branch of the volcano curve for the simple reasonhat all points on the descending branch pertain to metals thatre covered by an oxide film in aqueous solutions, a fact that wasot known when this plot was first constructed. The tendencyo form oxide films correlates with high energies of hydrogendsorption, it just indicates a highly reactive surface. Thus theres no experimental evidence that high adsorption energy as suchmplies a low reaction rate. As a justification for the volcanourve it is sometimes argued that the reaction should be fastesthen the free energy of adsorption is close to zero, because then

t is easy for the reactant to get to the surface and to leave it, sohis should be the location of the maximum rate. While this argu-

ent, known as Sabatier’s principle, may be applied to reactions

n the gas phase, it cannot be used in electrochemistry: the freenergy of adsorption of a charged species like a proton dependsn the electrode potential. Taken to its logical conclusion thisrgument would mean, that for each metal the current-potential

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156 E. Santos, W. Schmickler / Electr

urves should take the form of a volcano curve, with the apexeing at the potential where the free energy of adsorption is zero,nd negative transfer coefficients at high overpotentials–this isssentially the argument given in a recent article by Trasatti andchmickler [25]. Needless to say, such a behaviour has nevereen observed. Therefore, we believe that the volcano curve forhe hydrogen evolution reaction should be laid to rest next to theydrogen in statu nascendi.

Our model has a strong relation to the work of Hammernd Norskov. In a seminal paper these authors showed that thedsorption of hydrogen on metal surfaces is governed by the veryoncepts that we use: the position of the d-band and its couplingtrength to hydrogen. The difference between their work andurs is, that they consider the energetic of the ground state ofhe adsorbed hydrogen, while we consider the activated state ofn electron transfer reaction, in which a solvent fluctuation shiftshe bonding orbital past the Fermi level. It is satisfying that bothhe adsorption and the oxidation reaction can be understood byhe same principles. Indeed, this seems to be the reason for theood correlation between hydrogen adsorption energies and theeaction rate observed in the ascending branch of the defunctolcano plot.

The quantitative aspects of our model can be significantlymproved by using more results of quantum-chemical calcula-ions, and we are developing our work in this direction. However,e do not expect that this will change our understanding of elec-

rocatalysis or lead to a different trend in the calculated energiesf adsorption.

. Conclusions

We have successfully applied our unified model for electro-hemical electron transfer reactions to the hydrogen oxidationeaction at different metal electrocatalysts. We have demon-trated that the key point for decreasing the activation barriers played by the changes produced in the transition state (saddleoint) as a consequence of the interactions with d-bands. Weave discussed different empirical correlations between prop-rties of the metal and catalytic activity proposed in the past.s could be observed from the previous discussion, in order

o explain the catalytic effects of different materials the details

f the band structure and also the coupling constants betweenolecule and metals must be considered. Simplified attempts

onsidering separately the position of the band center, the den-ity of states at the Fermi level, the width of the band, etc.

[[[

ica Acta 53 (2008) 6149–6156

annot explain the experimental data. The correlation betweenur calculated results and the experimental data is the first cor-elation for the hydrogen reaction that is based on a detailedodel.

cknowledgments

We thank Cristian Sanchez from the University of Cordoba,rgentina, Axel Groß, Kay Potting, and Florian Wilhelm from

he University of Ulm for supplying us with the metal densities oftates. We participate in the COST D36 Action project Structurend Reactivity Relationship of nanoarrays.

Financial support by the Deutsche ForschungsgemeinschaftSchm 344/34-1, Sa 1770/1-1), by the European Union (NENAroject) and by CONICET (Argentina) is gratefully acknowl-dged.

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