Mechanism of Molecular Oxygen Reduction at the Cathode of a PEM

May 15, 2008 - ... The reactions considered are O2(ads) ↔ O(ads) + O(ads) (1), O2H(ads) ↔ O(ads) + OH(ads) (2), H2O(ads) ↔ H(ads) + OH(ads) (3),...
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8464

J. Phys. Chem. C 2008, 112, 8464–8475

Mechanism of Molecular Oxygen Reduction at the Cathode of a PEM Fuel Cell: Non-Electrochemical Reactions on Catalytic Pt Particles Stephen Walch,* Abhishek Dhanda, Masoud Aryanpour, and Heinz Pitsch Department of Mechanical Engineering, Stanford UniVersity, California 94305 ReceiVed: December 3, 2007; ReVised Manuscript ReceiVed: February 13, 2008

Various catalytic reactions in proton exchange membrane (PEM) fuel cells are discussed, and the effects of different steps, parallel pathways, and side reactions are analyzed for the oxygen reduction reaction (ORR) mechanism. A suitable mechanism table is formulated for the prominent pathway of ORR. The kinetics of the proposed nonelectrochemical reactions on platinum surfaces are then studied using the B3LYP density functional theory (DFT) with the Wadt and Hay relativistic ECPs and basis sets augmented with a 4f function on Pt. The reactions considered are O2(ads) T O(ads) + O(ads) (1), O2H(ads) T O(ads) + OH(ads) (2), H2O(ads) T H(ads) + OH(ads) (3), OH(ads) + OH(ads) T O(ads) + H2O(ads) (4), and OH(ads) + O(ads) T O(ads) + OH(ads) (5). Calibration calculations are carried out for reaction 1 on a single Pt atom using the CASSCF/MRCI method with a cc-pVDZ/relativistic ECP basis set for Pt and the aug-cc-pVDZ basis set for O. Comparison with B3LYP DFT calculations shows that the latter method overestimates binding energies by more than a factor of 2, but the barrier heights with respect to reactants are accurate. This result is consistent with calculations for the outer minimum for molecular oxygen on Pt(111), where the computed binding energy is about a factor of 2 larger than what is found from experiments. We find that, while a Pt2 cluster gives qualitatively correct results, the results are strongly influenced by cluster size effects, and inclusion of nearest neighbor atoms in at least the top and second layers is necessary for accurate energetics. The rates computed within the conventional transition state theory plus a Wigner estimate for tunneling using barriers obtained from the largest clusters show that the second, fourth, and fifth reactions are most important on the surface of catalytic Pt particles. Solvation effects were investigated using a model consisting of cyclic (H2O)n structures and were found to be small. 1. Introduction Proton exchange membrane (PEM) fuel cells might play a major role in future energy systems for a wide range of applications. However, the performance of PEM fuel cells needs to be significantly improved to create an economic rival to conventional power generation systems. A major obstacle comes from the slow electrochemical reactions at the cathode electrode causing large potential losses in PEM fuel cells. The standard reversible potential for O2 reduction reaction is calculated to be 1.23 V, but because of slow kinetics, the working voltage lies near 0.8 V, even on platinum electrodes.1 Understanding the chemical phenomena involved requires a detailed knowledge about the important reactions at the atomic level. To go beyond a single-step representation of the electrochemistry in a PEM fuel cell, a suitable reaction mechanism has to be formulated which includes both chemical and electrochemical (electron transfer) steps. The two main aspects of this are to establish a reaction mechanism and to estimate kinetic rate data. The factors affecting the oxygen reduction reaction have been reviewed recently by Markovic et al.,2,3 Adzic et al.,4 and other groups. The focus of most of the work on the oxygen reduction reaction (ORR) processes occurring on platinum electrodes has been the experimental characterization and analysis. Experimental data are available for the dependence of ORR kinetics on various environmental parameters such as pressure, temperature, humidity, reactant concentrations, and electrolytes.5–11 Empirical models are obtained on the basis of these results for * Corresponding author.

representing the overall system dynamics. A relatively detailed understanding of the fundamental reactions has been obtained from these studies and was further complemented by computational studies of several researchers.12–24 Different reaction pathways exist for the overall oxygen reduction reaction.3 On platinum electrodes, O2 reduction reaction is considered to proceed either through a direct electroreduction to H2O or through a parallel pathway with H2O2 as an intermediate species.25 However, the direct reduction pathway is more prominent at the working voltage regime.26 The overall reduction reaction is inherently irreversible even on platinum electrodes.3 The efficiency is further reduced by the simultaneous occurrence of parasitic reactions which compete in establishing a mixed potential.27,28 The oxidation of adsorbed impurities present in the electrolyte may constitute a possible side reaction, which result in a parasitic anodic current.28 Others, like the corrosion reaction, are considered to be a source of adsorbed species which block the active sites for oxygen reduction.27,29 In addition to the surface blocking effect, the interactions between the adsorbed species are also shown to affect the reaction kinetics.30 The oxygen reduction reaction includes a series of single electron transfer reactions intermediated by a few chemical steps, which constitute the overall mechanism. Many authors believe that the first electron transfer reaction is the rate determining step for oxygen reduction in acidic media,14,31 while others attribute the overall rate to a chemical reaction.25,32 The concept of RDS implies that other reactions are very facile as compared with the RDS and hence can be considered in a quasi-equilibrium state.32 Since

10.1021/jp7114127 CCC: $40.75  2008 American Chemical Society Published on Web 05/15/2008

Mechanism of Molecular Oxygen Reduction

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H2O is a key species in the overall reaction, the mechanism has also been suggested to be affected by the relative humidity values for the Nafion electrolytes.10 Nevertheless, the formulation of a reliable reaction mechanism requires investigating all individual steps. The first group of reactions, which are the subject of this paper, are thermal reactions on the Pt(111) and (100) surfaces. This set includes the dissociation of O2, O2H, and H2O as well as two hydrogen-exchange reactions on catalytic Pt surfaces. There have been a number of computational studies of the reactions considered here. Michaelides and Hu13 studied the dissociation of water, recombination of O and H, and recombination of OH and H on the Pt(111) surface using a plane wave DFT method. They also considered the bonding of OH on a Pt(111) surface in on-top, bridge, and 3-fold sites.33 Li and Balbuena20 studied the dissociation of O2 on a Pt5 cluster using a method similar to the present work. However, ref 20 is mainly focused on the electrochemical process, and thus the results are not directly comparable to the reactions considered here. Wang and Balbuena34 did consider dissociation of O2 on a Pt cluster using molecular dynamics simulations and found that the dissociation proceeds via an asymmetric path. Quite recently Jacob79 has studied some of the same reactions considered here using a large 35 Pt atom cluster. In recent years, quantum computations have been performed to calculate the energetics of electrochemical reactions 16,35 using different methods and basis sets. The aim of the present study is to develop a chemical reaction mechanism for the chemical reactions involved in the ORR from a series of consistent ab initio calculations. It is required that all reactions be simulated with the same level of theory and basis sets. The consistency of the computations is important to explicitly capture ratios of individual reaction rates. We will first provide an estimate of the accuracy of the DFT calculations employed here, particularly considering the tendency to overestimate binding energies discussed later. In the following, we will investigate two issues: (i) the accuracy of the B3LYP/DFT method and basis set and (ii) the accuracy of the Pt2 cluster model widely used in the literature.18,36,37 The present paper is focused on nonelectrochemical reactions. In a later paper, we will discuss the electrochemical reactions, which involve protonation and electron transfer, and the overall set of reaction rate constants will be used in kinetic Monte Carlo calculations to predict experimental observables. The structure of the paper is as follows. The compilation of the chemical mechanism is presented in section Chemical Mechanism. The computational method is described in section Computational Method, which is followed by the results obtained from the quantum simulations. 2. Chemical Mechanism The kinetics of the ORR have been analyzed by several authors and various possible reaction mechanisms have been proposed.2,3,5,8,25,29,38 Different chemical processes take place in the cathode layer of PEM fuel cells. These processes include the usual oxygen reduction reaction and other side reactions that interfere with the overall kinetics. In acid electrolytes, the overall reduction of oxygen to water can take place through different reaction pathways.3 For Pt electrodes, the prominent global pathway for ORR is considered to be the direct four-electron reduction reaction25 given by

O2 + 4H+ + 4e- T 2H2O

(6)

However, a parallel pathway is also observed, where H2O2 is generated as a byproduct of a two-electron reduction

reaction.26,39,40 The adsorbed peroxide can be reduced to water or desorbed and diffuse into the bulk of the solution.39,40

O2 + 2H+ + 2e- T H2O2(ads)

(7)

H2O2 + 2H+ + 2e- T 2H2O

(8)

On platinum and platinum family metals, the direct fourelectron reduction pathway is dominating.25 From rotating ring disk electrode (RRDE) experiments, the relative contribution of the parallel pathway has been found to be less than 1%.26 However, this fraction only takes into account the amount of H2O2 getting desorbed and reaching the ring electrode, implying that the ratio might be higher. A study of both reaction pathways is hence necessary in order to correctly model the overall reaction kinetics. The current work will investigate the direct four-electron reduction pathway for the purpose of quantifying the complete mechanism by ab initio methods. Future works will focus on the kinetics of the electrochemical reactions, the indirect parallel pathway, and parasitic side reactions. The overall reduction reactions (6-8) proceed through several elementary reaction steps which include both chemical and electrochemical reactions. Numerous experimental studies on the ORR have contributed to proposing various reaction mechanisms for the direct four-electron reduction pathway.5–8,31Tafel plots for ORR on Pt in acidic environments exhibit a 120 mV per decade slope at high current densities and a 60 mV per decade slope at low current densities.31 The kinetics of the ORR mechanism at high current densities is explained in terms of the initial charge transfer step being the rate-determining step (RDS).31,41 On the other hand, the 60 mV per decade slope at low current densities can be associated with either a chemical or an electrochemical RDS. The possible chemical RDS follows a quasi-reversible initial electron transfer step.41 The slope difference is also explained in terms of the effect of the adsorption energetics, where the interaction of the adsorbed species results in Temkin adsorption conditions at low current densities and Langmuir adsorption conditions at high current densities.31,42,43 The indirect reduction with H2O2 as intermediate has also been proposed to be the reason for this difference in Tafel slope.44 Different propositions regarding the RDS are supported by suggesting different reaction mechanisms for the overall reaction. One possible mechanism for ORR is given by Yeager et al. 25 where the dissociation of the adsorbed O2 is considered to be the rate determining step:

O2(ads) T O(ads) + O(ads)

(1)

O(ads) + H+ + e- T OH(ads)

(9)

OH(ads) + H+ + e- T OH2

(10)

The electrochemical reactions 9 and 10 constitute the rest of the mechanism and are considered to be quasi-reversible. Recent studies demonstrate that the nature of bonding of the adsorbed O2 to the Pt surface affects the overall reduction kinetics and the reaction pathway.36 For the end-on adsorption of the O2 molecule, the indirect mechanism is favored, whereas the bridge bonding to the Pt surface favors the direct process.14,36 This corroborates the experimental observance of peroxide at high potentials, where high coverages reduce the number of dual sites required for bridge adsorption. Hence, for the direct reduction pathway, reaction 1 could become rate limiting at lower current densities. This view also suggests the formation of peroxide at the anode electrode of PEM fuel cells from the reduction of

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the crossovered O245 since the anode is believed to have relatively high coverages at all potentials.42 On the basis of the experimental current-potential relationship, another reaction pathway has been proposed, which includes reactions 9 and 10 and

O2 + H+ + e- T O2H(ads)

(11)

O2H(ads) T O(ads) + OH(ads)

(2)

as the elementary steps.28,32,38,41 For high current density regions, the first electrochemical reaction 11 is thought to be the rate determining step in this mechanism.28,31,38,41 This view was further supported by the ab initio studies of Anderson et al.1,14,16 The first electron transfer step 11 was proposed to be rate determining for low current densities also, where the interactions between adsorbed species leads to a higher slope value.43 However, the dissociation reaction (2) could be a possible candidate for the chemical RDS since it also satisfies the high Tafel slope criterion.41 Tafel experiments prove that the breaking of the oxygen bonds cannot occur before the rate determining step in-order to obtain the observed reaction order of unity with respect to oxygen. However, all proposed reactions 1, 11, and 2 satisfy this criterion. Anderson et al. 36 calculated a very low activation barrier for the dissociation reaction 2 that supports the electrochemical step being the RDS for both high and low current densities. However, an excess of adsorbed O and OH species at high coverages could make the net forward direction slower for reaction 2. A change of mechanism with variation of humidity has also been suggested, where both reaction 11 and reaction 2 become slow at high humidity conditions10 leading to dual rate determining steps. Further investigations are hence required in order to establish the existence of the RDS and comprehend the overall reaction mechanism for the oxygen reduction reaction. The overall reaction kinetics are also affected by the presence of H2O in the electrolyte. In the fast scan cyclic voltammetry experiments, the same coverage values of oxygen containing species are observed in both O2-rich and O2-lean environments. This leads to the conclusion that the source of oxygen containing adsorbed species is actually H2O rather than O2.9,28,44 H2O molecules from electrolyte undergo electrochemical water discharge reactions producing adsorbed OH and O species according to the reactions 12 and 13.28 +

-

H2O T OH(ads) + H + e

(12)

OH(ads) T O(ads) + H+ + e+

(13) -

Net H2O T O(ads) + 2H + e

(14)

Many studies propose that a monolayer of adsorbed OH exists on the surface which is produced mainly from reaction 12.1,30 This monolayer is oxidized to PtO only at relatively higher anodic potentials as compared with the standard potential of reaction 12.1,29,30 This is also suggested by experimental investigations using low energy electron diffraction (LEED)46 and Fourier transform infrared (FTIR) spectroscopy.47 Symmetric peaks have been observed for the anodic and cathodic scans in cyclic voltammetry curves showing the quasi-reversibility of the water discharge reaction 12 on Pt electrodes.30,46 Another viewpoint is that water is completely oxidized on Pt surfaces producing Oads species.27,28 One possible pathway for O formation is reaction 14, which is a combination of the water discharge reactions 12 and 13 with OHads as the intermediate species.28 Birss et al.,48 however, utilized electro-

chemical quartz-crystal nanobalance (EQCN) experimental results to conclude that the mechanism for the generation of oxides does not include OHads at any stage. Recent EQCN and auger electron spectroscopy (AES) experiments support this direct oxide generation pathway.49,50 The adsorbed O undergoes place exchange reactions at potentials higher than 1.15 V,29,49 which is higher than the working potentials of PEM fuel cells. Parthasarathy et al. 27 observed reaction 14 at potentials higher than 0.88 V, which suggests adsorbed O to be the dominating adsorbed species. The oxide reaction is considered as a parasitic reaction, that reduces the net output by establishing a mixed potential control.27 In addition to the electrochemical reactions 12-14, an alternative chemical pathway exists for the H2O dissociation step16

H2O(ads) T H(ads) + OH(ads)

(3)

al.16

Anderson et calculated a high activation barrier for this reaction 3 on platinum. However, the presence of adsorbed O reduces this barrier leading to a water disproportionation reaction 13,51,52

OH(ads) + OH(ads) T O(ads) + OH2(ads)

(4)

A combination of reactions 4 and 13 can provide another possible low energy pathway for the generation of O(ads) species, where each O(ads) generates two O(ads) species. This outlines the importance of studying the effect of interactions between the neighboring species. For example, adsorbed H2O is calculated to increase the barrier for the backward disproportionation reaction 4.13 Neighboring O(ads) and O(ads) species can participate in an H-exchange chemical reaction

OH(ads) + O(ads) T O(ads) + OH(ads)

(5)

The relative coverage of O(ads) and OH(ads) is affected by the relative kinetics of chemical reactions 3-5. Besides these redox surface reactions, side reactions such as Pt corrosion reactions are observed, which can have a profound effect on the overall kinetics. These metal ion reactions include the electrochemical dissolution of Pt and the chemical decomposition of Pt oxides.53,54

Pt T Pt2+ + 2e2+

Pt

(15) +

+ H2O T PtO + 2H

(16)

These corrosion reactions are responsible for the coarsening of the electrode surface by dissolution reaction 15 and redeposition step 16.55,57 As a result, the chemical kinetics of all surface reactions are affected by the change in the catalyst surface structure. In addition, the loss of Pt from the electrode to the electrolyte thereby reduces the electrochemically active area. These effects are promoted by potential cycling and the hydrogen crossover process.56 Hydrogen gas in the membrane reduces the Pt ions by the following reaction

Pt2+ + H2 T Pt + 2H+

(17)

These side reactions result in a parasitic current, which consequently lowers the cell efficiency because of the drop in the mixed potential. The uncertainty of the constituting reactions and the exact nature of intermediate reactant species requires a complete kinetic analysis of the above-mentioned reactions. The important reaction steps are tabulated in Table 1. The current work investigates the chemical reactions involved in the direct fourelectron reduction of oxygen on Pt electrodes in Nafion

Mechanism of Molecular Oxygen Reduction

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TABLE 1: Reaction Steps Constituting the Oxygen Reduction Reaction at Cathode Electrode of Pem Fuel Cells reaction type chemical

reaction O2(ads) T O(ads) + O(ads) O2H(ads) T O(ads) + OH(ads)

H2O(ads) T H(ads) + OH(ads) OH(ads) + OH(ads) T O(ads) + H2O(ads) OH(ads) + O(ads) T O(ads) + OH(ads) electrochemical O2(ads) + H+(aq) + e- T O2H (ads)

side reactions

reference 25, 36, 14 38, 32, 28,

41 16 51, 52, 13 this work 38, 32, 28,

41

OH(ads) + H+(aq) + e- T OH2

25, 28, 46,

O(ads) + H+(aq) + e- T OH(ads)

25, 28, 38,

H2O T O(ads) + 2H+(aq) + 2e-

27, 48, 49,

Pt T Pt2+(aq) + 2ePt2+(aq) + H2O T PtO + 2H+(aq) Pt2+(aq) + H2 T Pt + 2H+(aq)

55, 56, 57 55, 56, 57 55, 56, 57

30 32 50

electrolyte, that is, reactions 1-5. The kinetics of the corresponding electrochemical reactions, the indirect parallel pathway, and the parasitic corrosion reactions will be discussed elsewhere. 3. Computational Method 3.1. Platinum Cluster Model. The Pt atom is in the third transition row and has the atomic configuration [Kr]

4d104f145s25p66s15d9 5d10 6s25d8

where 6s15d9 is the ground-state configuration and the 5d10 and 6s25d8 states are 0.5 and 0.6 eV higher in energy. The 6s and 5d levels are considered to be valence; the 5s and 5p levels are semicore, and the 4d and 4f levels are core. Thus, normally 60 electrons are taken as core. As a third transition row element, an accurate description of the Pt atom requires inclusion of relativistic effects. In this work, we included these effects using the relativistic effective core potentials developed by Wadt and Hay.58 Two levels of effective core potential (ECP) were developed. The LANL2DZ potential replaces the 60 electron core, while the LANL1DZ potential also replaces the 5s25p6 configuration. Wadt and Hay also developed double-ζ level basis sets for use with their ECPs. We augmented these basis sets by a single Gaussian f function optimized for the Pt atom. We also carried out more accurate CASSCF 59,60/MRCI 61,62 studies for Pt + O2 f PtO2 using a 5/1 active space in Cs symmetry (3A′′ state). The cc-pVDZ/ECP basis set for Pt developed by Peterson63 was used with the Stuttgart 60 core-electron relativistic ECP, and the aug-cc-pVDZ64 basis set for O. We were only able to correlate the 6s and 5d levels of the Pt atom because of restrictions on the number of active orbitals in MOLPRO. We did carry out more extensive calculations on PtO using CC-pVTZ basis sets and correlating the 5s and 5p levels. This required uncontracting the 5s and 5p shells and optimizing a (1s1p1d) shell of correlating functions to allow correlation of the 5s and 5p semicore levels. These calculations were then used to extrapolate the results for PtO2. Five neutral reactions were studied using both a Pt2 model and larger clusters to describe the Pt(111) and (100) surfaces; for example, a planar Pt10 cluster was one model for the Pt(111) surface. The Pt10 cluster includes all of the nearest neighbors

in plane Pt atoms with respect to the central Pt2 for a Pt (111) surface (Pt-Pt distance 2.77 Å). In the calculations, the central Pt2 and additional O/H atoms used the LANL2 ECP with the LANL2DZ +1f/ cc-pVDZ, Pt/O,H basis sets, and the remaining Pt atoms used the LANL1DZ basis set with the LANL1 ECP. Calculations for the singlet and triplet states of Pt2 indicate that the Pt-Pt bond is mainly Pt 6s6p like and the 5d levels are only weakly coupled. A CASSCF/MRCI calculation for Pt2 at a bond length of 4.75 au found the singlet state, which has a Pt-Pt 5dσ bond, to be only 0.15 eV below the triplet state, which has the 5d electrons in 3dδ orbitals. Thus, we have adopted a cluster model in which the Pt atoms are assumed to be in a 6s15d9 atomic configuration, and we assume the 5d levels are only weakly interacting. In this situation, the energy is only weakly dependent on the couplings of the 5d levels, and with simple wave functions, the best representation is with all of the 5d singly occupied orbitals high-spin coupled. (Note that attempts to couple these orbitals low-spin would require a broken symmetry UHF based calculation to get physically meaningful results.) Thus for Pt10, we use a spin multiplicity 11 state. Similar conclusions have been reached by Kua and Goddard III65 who also note that the metal-metal bonding mainly involves the metal 6s level ,and the metal to O bonding is mainly through the metal 5d levels. This suggests that, within the high-spin model, the Pt2 and Pt10 clusters should give fairly similar results. Most of the calculations used the DFT method with the B3LYP66 hybrid67 functional, and were carried out with Gaussian03.68 The CASSCF/MRCI calculations used the MOLPRO69 system of programs. Rate constants were calculated for each of the reactions based on the Pt2 model. In each case, frequencies and partition functions were calculated using Gaussian, and reaction rates were computed using the conventional transition state theory

k ) κkBT/hfact/freact exp(-E0/kBT)

(18)

where fact and freact are the partition functions with respect to the zero-point level of the molecule for the saddle point and reactants respectively (with the imaginary frequency excluded in the case of the saddle point,) and E0 is the activation energy including a zero-point correction. In the cases involving transfer of an H atom, tunneling was estimated using a Wigner correction70

κ ) 1 + 1 /24 (pω*/kBT)2

(19)

where ω* is the imaginary frequency. In other cases, the transmission coefficient κ is taken as unity. Rate constants were also calculated for all five reactions using barrier heights from larger clusters which represent the Pt 111 and Pt 100 surfaces. (See discussion in section 3.4.) Since the Pt cluster geometry is frozen in these calculations, normal modes involving the Pt atoms are not expected to be meaningful. Also the much larger mass of the Pt atoms compared with the O and H atoms would be expected to lead to weak coupling to modes involving the Pt atoms. We therefore used the pre-exponential factors computed from the Pt2 model and corrected the rate constants for the changed barrier heights by a factor exp(-∆Ee/ kBT), where ∆Ee is the change in barrier height compared with the Pt2 model. 3.2. Choice of 4f Exponent for Pt. The exponent for the 4f function on Pt was optimized by minimizing the energy at the MP2 level for a single Pt atom. This gave exponents of ∼1.0 for a single 4f function and ∼1.5 and ∼0.5 for two 4f functions. In general, the optimal exponent for a correlating function is larger than the optimal exponent for a polarization function.

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TABLE 2: Energetics for Pt + O2 outer minimum

saddle point

inner minimum

CASSCF/MRCI cc-pVDZ/ aug-cc-pVDZ CASSCF/MRCI Extrapolated to CC-pVTZ/CV based on PtO

-0.4

1.1

-0.8

-0.6

0.9

-1.0

DFT DFT DFT DFT DFT

-0.9 -1.0 -0.7 -0.8 -0.9

0.9 0.9 1.1 1.0 0.9

-1.4 -1.4 -0.5 -1.5 -1.6

Figure 1. Pt + O2 f PtO2.

authors

De, eV

ROO, Å

0.0

2.6

-0.4

Eichler and Hafner71 Sidak and Anderson36 PW experiment

0.72 0.9 1.3 0.4,75 0.576

1.39 1.38 1.37 1.3777

method

cc-pVDZ/aug-cc-pVDZ cc-pVDZ/cc-pVDZ LANL2DZ/cc-pVDZ LANL2DZ + 1f/cc-pVDZ LANL2DZ + 2f/cc-pVDZ

MP2 LANL2DZ + 1f*/cc-pVDZ

Indeed, optimizing a single 4f function at the B3LYP level for Pt2 (which mainly makes it of the 4f function to polarize the 5d levels of Pt) gives an exponent of 0.4. We also found that, in B3LYP calculations for Pt2 using the two 4f functions, only the 0.5 exponent affected the energy. Thus, the 0.5 exponent was nearly optimal for B3LYP calculations and was used in the DFT calculations. For MP2 calculations, we used the exponent of 1.0, which had been optimized at the MP2 level. 3.3. Calibration Calculations for Pt + O2. Table 2 shows energetics for the Pt + O2 reaction at various computational levels, while the structures are shown in Figure 1. The structures were taken from the DFT calculations with LANL2DZ+1f/ccpVDZ basis set, and the same geometry was used at all levels of calculation with the exception of the MP2 calculations where the geometries were reoptimized at the MP2 level. From Figure 1, one sees the formation of an outer minimum with the O2 molecule still intact and a saddle point leading to an inner minimum in which the O2 bond has been broken and replaced by two PtO bonds. The CASSCF/MRCI results show a significant bond strength (0.4 eV) for O2 bound to a Pt atom in the outer minimum, followed by a barrier of 1.1 eV with respect to reactants (1.5 eV with respect to the outer minimum), and an inner well bound by 0.8 eV. The outer minimum corresponds to a physiadsorbed state, and the bonding may be thought of as a dative bond between a lone pair on the oxygen and the 5d9 Pt configuration. Calculations were carried out for PtO with ccpVDZ basis sets including correlation of the 5s and 5p levels (core-valence correlation). This gives an increase of 0.10 eV in the strength of the PtO bond. Of this, 0.06 eV comes from the larger basis set and 0.04 eV comes from core-valence correlation. Assuming the effect on PtO2 is twice that of PtO, a rough estimate of the effect of the larger basis set and corevalence correlation on the PtO2 system was obtained by adding 0.2 eV to the binding energy of each of the structures in Figure 1. By comparing it now to the DFT calculations, the calculations with the cc-pVDZ/aug-cc-pVDZ basis set are the most comparable to the CASSCF/MRCI calculation, since they use the same basis set. The barrier is slightly lower than that of the CASSCF/MRCI results, but the well depths for both the outer and the inner minima are significantly deeper. In the case of the inner minimum, DFT gets 0.9 while CASSCF/MRCI gets 0.4 or more than a factor of 2. While it is possible that further improvement in the basis set used for the CASSCF/MRCI calculations would reduce this error somewhat, it seems unlikely from the estimates above that the effect would be much more than 0.1 eV. In the case of the outer minimum for Pt2 plus O2 on the Pt(111) surface, a similar discrepancy exists. Corresponding

TABLE 3: Characterization of the Outer Minimum for Pt2O2 in the Twofold Site ωOO, cm-1 850 873 842,78 875,76 87075

experimental studies are able to measure the bond length, OO stretching frequency, and adsorption energy. DFT calculations71 show two distinct adsorption sites. One of these sites has the O2 directly above a Pt2 as in our calculations, while the other has the O2 in a 3-fold hollow (fcc) site. Table 3 shows the calculated binding energy, OO bond length, and OO vibrational frequency for the calculations of Eichler and Hafner,71 Sidak and Anderson,36 and the present work compared with experiment. From Table 3, it is seen that all three DFT calculations give reasonable OO bond lengths and vibrational frequencies, but overestimate the binding energy. In the present calculations, taking the larger experimental estimate, the binding energy is overestimated by a factor of about 2.6. This compares to a factor

Figure 2. (a) The Pt16 cluster. Blue atoms are top layer and red atoms are second layer. The Pt10 cluster omits the second layer atoms. (b) The Pt20 cluster. Blue atoms are top layer, red atoms are second layer, and purple atoms are third layer. (c) The Pt14 cluster. Blue atoms are top layer and red atoms are second layer. The Pt8 cluster omits the second layer atoms.

Mechanism of Molecular Oxygen Reduction

Figure 3. (a) Pt2O2 f PtOO. (b) Pt2OOH f Pt2O-OH. (c) Pt2H2O f Pt2OHH. (d) Pt2OHOH f Pt2H2OO. (e) Pt2OHOfPt2OOH.

of 2.3 for DFT compared with CASSCF/MRCI results for Pt + O2. The comparable ratios suggest that the CASSCF/MRCI results are close to experiment as would be expected, and that DFT overestimates the binding energy by more than a factor of 2 in both cases. Comparing results with and without augmentation of the oxygen basis set shows little effect. The one DFT case which differs significantly from the others is the LANL2DZ case without f functions, which in particular gets the inner well too weakly bound. This is an expected result since bonding of O atom to Pt involves the Pt 5d levels, and these require f functions for polarization. We also looked at the MP2 method for this system, and this gives results that are very different from what we obtained with the CASSCF/MRCI method. In particular, the outer well is not bound; the barrier is too high by more than a factor of 2, and the inner minimum is bound by a factor of 2 less. It is probable that these errors result from an inability of perturbation theory based methods to accurately represent a potential energy surface with a large amount of multireference character. Note that, in these calculations, the 4f exponent is taken as the MP2 optimized value of 1.0, denoted by 4f*.Taking these considerations together, we believe DFT is a cost-effective method that should give reasonable results for these systems. 3.4. Calculations with Larger Clusters. Figure 2 shows larger clusters which were used. The Pt10 cluster was used for

J. Phys. Chem. C, Vol. 112, No. 22, 2008 8469 the (111) surface, and the Pt8 cluster was used for the (100) surface. In both cases, these clusters include a central Pt2 molecule surrounded by the surface nearest neighbors. We also considered clusters with nearest neighbors in the second layer below the surface, which gives the Pt16 and Pt14 clusters for the (111) and (100) surfaces, respectively. Finally, we considered a Pt20 cluster for the (111) surface, which includes third layer Pt atoms. We note that, while we have examined the convergence with respect to cluster size systematically in this work, some authors believe that a slab calculation using a periodic boundary condition is necessary for accurate results. We intend to test this conjecture in future calculations; however, it is necessary to separate cluster size effects from effects due to the choice of method (e.g., the DFT functional used). As an example, the hybrid functionals such as B3LYP, which we have calibrated against ab initio calculations in this work, are not available in the present periodic boundary condition DFT codes. Thus, we need to examine what systematic errors are introduced by less reliable functionals in order to separate true cluster size effects from bias in the computational method. As an example, preliminary calculations by us using VASP and the default functional for Pt2O2 lead to well depths twice that found with B3LYP, and a similar result was found using the local density approximation (LDA) as implemented in Gaussian. In the preliminary calculations, we assumed a local plane of symmetry including the central Pt2 and the following atoms: (i) the two O atoms for reactions 1 and 2, (ii) the O atom and one H atom for reaction 3, and (iii) two O atoms and one H atom for reactions 4 and 5. However, this constraint leads to difficulties because O atoms tend to prefer 3-fold sites, and OH radicals prefer bridged sites. Thus, we relaxed this constraint in subsequent calculations, and the results reported here had no symmetry imposed. We obtained fully optimized stationary point structures for all five reactions on the Pt10 and Pt8 clusters, which represent the (111) and (100) surfaces, respectively. These geometries were then used in single point calculations of the energy with the larger clusters. 4. Thermal Reactions on Pt2 and Larger Clusters We consider five thermal reactions, which, based on the discussions in section Chemical Mechanism, constitute the dominant pathway in chemical reactions at the cathode of PEM fuel cells. These are

O2(ads) T O(ads) + O(ads)

(1)

O2H(ads) T O(ads) + OH(ads)

(2)

H2O(ads) T H(ads) + OH(ads)

(3)

OH(ads)+OH(ads) T O(ads) + H2O(ads)

(4)

OH(ads) + O(ads) T O(ads) + OH(ads)

(5)

Figure 3 shows the structures for these reactions on the Pt2 cluster and the energetics are given in Table 4. For reaction 1, calculations were carried out for a 3A′′ surface. As with Pt + O2, there is an outer physisorbed minimum, a saddle point, and an inner minimum, where the O2 bond has been broken and replaced by two PtO bonds. Comparing to the work of Sidik and Anderson36 all three structures are more tightly bound in our calculations due to the addition of the 4f function on Pt. However, the energy difference between the outer minimum and the saddle point is approximately the same 0.7 eV. It should be noted that Sidik and Anderson did not obtain

8470 J. Phys. Chem. C, Vol. 112, No. 22, 2008

Walch et al.

TABLE 4: Binding Energies (Electronvolts) for O and OH to Pt Clusters

TABLE 5: Energetics on (a) Pt Clusters (111) and (b) Pt Clusters (100) Surface

system

Pt14 100

Pt16 111

(a) reaction

structure

Pt2

Pt10

Pt16

Pt20

O bridged OH bridged

-4.15 -3.70

-3.79 -3.41

1

outer saddle point inner outer saddle point inner outer saddle point inner reactant low-spin reactant saddle point product reactant saddle point product

-1.34 -0.62 -1.44 -1.94 -1.89 -3.54 -1.05 -0.27 -0.70

-1.42 -0.06 -1.58 -2.26 -1.97 -3.77 -1.00 0.23 -0.23 -0.96 -0.04 0.80 0.0 0.0 0.69 0.0

-1.67 -0.54 -1.58 -2.40 -2.62 -3.63 -0.58 0.96 0.71 -1.61 0.40 0.04 0.0 0.0 0.38 0.0

-1.95 -0.72 -1.65 -2.37 -2.81 -3.46 -0.59 0.74 0.50 -1.26 0.65 0.23 0.0 0.0 0.22 0.0

saddle points for 1 and 2 but rather obtained approximate minimum energy pathways as a function of O-O distance. The saddle point for O2 dissociation is 0.6 eV below the Pt2 + O2 reactants. This implies that it is possible for O2 to dissociate on Pt2 without a barrier, at least in vacuum. A more accurate assessment could be made with variational transition state theory, which takes into account the vibrational zero-point energy perpendicular to the reaction coordinate and may lead to a barrier. For a PEM fuel cell, the cathode is in contact with water, and thus, the O2 has to displace water molecules to bond to the Pt surface. This process would also lead to a barrier. For reaction 2, the calculations were carried out for a 2A surface. The inner well structure obtained in our work has the O and OH on opposite sides of the Pt2, which is unphysical in terms of a Pt surface. A similar situation is observed for the outer minimum of reaction 3. Later, we discuss larger clusters, which remove this difficulty. For the present, we find in agreement with Sidik and Anderson36 that the barrier for the dissociation of O2H is less than 0.1 eV. The outer minimum is bound by 1.9 eV compared with about 2.1 eV obtained by Sidik and Anderson. The inner well in our case is bound by 3.5 eV compared with approximately 3.3 eV for Sidik and Anderson.36 For reaction 3, the calculations were carried out for a 3A surface and give a binding energy for H2O to Pt2 of 1.1 eV. As noted above, it is likely that DFT overestimates this binding energy, but compared with the binding energy of O2 in the outer minimum, this implies it is uphill by 0.9 eV to displace two water molecules and bind one O2 molecule to Pt2. The outer minimum structure has the O of the H2O approximately colinear with the two Pt atoms, which is unphysical. This defect is corrected by using larger clusters. For the Pt2 cluster, the saddle point for dissociation is 0.3 eV below the reactants energy. However, the saddle point for larger clusters is higher in energy than the reactants. For reaction 3, Michaelides and Hu13 found that water was bound by 0.34 eV, and the barrier to dissociation was 0.68 eV. In our calculations, we find a binding energy around 1.0 eV for Pt(100) and (111) and barriers to dissociation of 1.3 eV for the (111) surface and 1.4 eV for the (100) surface. Thus, our calculations have the water more tightly bound, but we agree with the previous work in that the barrier to dissociation exceeds the binding energy by about 0.3 eV. The calculations were carried out for a 3A surface for reaction 4 and a 2A′′ surface for reaction 5. The barrier for reaction 4 is about 0.2 eV, and for reaction 5, it is about 0.5 eV. 4.1. Rate Constants at 300 K Based on Pt2 Cluster Results. Table 6 shows thermal rate constants at 300 K for reactions 1-5 based on the results with the Pt2 cluster. Here, the forward direction is indicated by f, and the reverse direction is indicated by r. In all cases, transition state theory assumes the reactants are thermally equilibrated over the available rotational-vibrational levels. From Table 5a,b, it is seen that the comparatively significant rates are for reactions 2f, 4f, and 4r. After these three steps, reaction 5 has the fastest rate constant which is smaller by at least 6 orders of magnitude. 4.2. Results on Larger Clusters. Table 4 shows energetics for bonding O and OH above the central Pt2 of the Pt16 (111) and Pt14 (100) clusters. We find the OH bonds at a bridged site, while the O atom in each case moves toward a 3-fold site. In

2 3 4

5

0.0 0.17 0.07 0.0 0.52 0.0

(b) reaction

structure

Pt2

Pt8

Pt14

1

outer saddle point inner outer saddle point inner outer saddle point inner reactant low-spin reactant saddle point product reactant saddle point product

-1.34 -0.62 -1.44 -1.94 -1.89 -3.54 -1.05 -0.27 -0.70

-1.73 -0.32 -2.27 -2.43 -2.40 -3.77 -0.58 0.14 -0.33 -1.07 -0.14 0.18 0.0 0.0 0.37 0.0

-1.85 -0.89 -2.34 -2.41 -2.26 -4.02 -0.55 0.46 0.08 -1.42 0.09 0.28 0.0 0.0 0.33 0.0

2 3 4

5

0.0 0.17 0.07 0.0 0.52 0.0

TABLE 6: Rate Constants at 300 K A, molecule- rate, molecule sec-1 sec-1 reaction E0, eV 1f 0.68 2.8 × 1r 0.81 9.4 × 1010 2f 0.01 3.8 × 1012 2r 1.29 7.8 × 1012 3f 0.63 0.53 × 1012 3r 0.41 3.4 × 1012 4f 0.06 2.1 × 1012 4r -0.02 2.9 × 1012 5 f ) 5r 0.40 1.2 × 1012 1012

1.2 × 2.8 × 10-3 2.6 × 1012 2.2 × 10-9 1.6 × 101 4.8 × 105 2.1 × 1011 6.3 × 1012 2.5 × 105 101

κ

rate plus tunneling, molecule sec-1

1.0 1.0 1.0 1.0 1.22 1.22 1.93 1.93 7.05

1.2 × 101 2.8 × 10-3 2.6 × 1012 2.2 × 10-9 2.0 × 101 5.9 × 105 4.1 × 1011 1.2 × 1013 1.8 × 106

the case of the (111) surface, this is a 3-fold hollow site in agreement with the earlier work of Jacob et al.72 Our binding energy for O at the 3-fold hollow site is 3.79 eV, which is slightly larger than that of Jacob et al.72 Using the same level of theory, we find that the O-O bond strength in O2 is 5.36 eV, and the O-OH bond strength in O2H is 3.11 eV. By combining these numbers with those in the previous paragraph, the following energies are obtained with respect to reactants: two O atoms, -2.22 and -2.94 eV on the (111) and (100) surfaces, respectively, and O + OH, -4.09 and -4.74 eV on the (111) and (100) surfaces, respectively. Figures 4 and 5 show the stationary point structures for the Pt10(111) and Pt8(100) clusters, respectively. By looking first at the Pt10(111) results shown in Figure 4, it is seen that for reaction 1 the O2 is approximately directly above the central Pt2 in the outer minimum, much like in the Pt2O2 case. However, at the saddle point the O2 has broken symmetry and in the

Mechanism of Molecular Oxygen Reduction

Figure 4. (a) Pt10O2 f Pt10OO. (b) Pt10HO2 f Pt10OHO. (c) Pt10H2O f Pt10OHH. (d) Pt10OHOH f Pt10OOH2. (e) Pt10OHO f Pt10OOH.

product the dissociated O atoms are at 3-fold sites. For reaction 2, both the outer minimum and the saddle point have broken

J. Phys. Chem. C, Vol. 112, No. 22, 2008 8471 symmetry, and the product has O in a 3-fold site and OH in a bridged site. For reaction 3, the H2O starts out directly above a surface Pt atom; however, as the reaction progresses, the OH moves toward a bridged site, and the H atom ends up at a position near an on-top site. For reaction 4, the OH plus OH end has both OH in bridged sites, while the H2O plus O end has the H2O at an on-top site and the O atom in a 3-fold site. The saddle point has the two O atoms roughly above the central Pt2. For reaction 5, the minimum corresponds to OH in a bridged site and O in a 3-fold site, but the saddle point corresponds to moving the bridged OH to another bridged position closer to the O atom. From this position, it is clear that the forming OH can move to an equivalent minimum, which is the mirror image of the first minimum. Looking now at the Pt14(100) results shown in Figure. 5, it is seen that for reaction 1 there is nearly a plane of symmetry, much like in Pt2, This suggests somewhat less tendency for O atoms to go toward a 3-fold site on the (100) surface, possibly because the 3-fold sites have one longer Pt-Pt bond as compared with the (111) surface. However, for reaction 2, it is seen that the reaction involves essentially bridged sites for O and OH in the outer minimum and saddle point and distorted bridged sites for the product, which suggest some repulsion of the negatively charged O and OH. For reaction 3, the H2O starts out at a slightly distorted on-top site for the outer minimum; the saddle point has distorted bridged sites, and the product corresponds to bridged sites. For reaction 4, the reactant has both OH in bridged sites with one moved toward an on-top site, and the product has the O in a bridged site and the H2O in an on-top site, with the saddle point in between. Reaction 5 is seen to involve O and OH in slightly distorted bridged sites. Table 5 also shows energetics for all five reactions on the Pt10, Pt16, and Pt20 (111) clusters and on the Pt8 and Pt14 (100) clusters. One new feature in the larger clusters is the consideration of a low-spin reactants minimum for reaction 4. For the product of reaction 4, since H2O is a singlet state and since bonding one radical orbital of an O atom to a radical orbital on Pt leads to the same number of radical orbitals (one), the product and saddle point should have the same spin multiplicity as the Pt cluster. However, for the reactant, each OH forms a bond to a radical orbital of the Pt cluster, and this leads to a cluster with multiplicity of two less than the multiplicity of the Pt cluster. This cluster is denoted by low-spin. From Table 5, we see that for the reactant the low-spin cluster is 1 eV or more below the high-spin cluster. This requires a mixing of surfaces of different spin multiplicity in order to couple reactants and products, and even if the coupling between the surfaces is strong, the barrier to the forward reaction is increased by greater than 1 eV. This means that reaction 4 will only be important in the reverse direction. Table 7a,b shows the computed barrier heights for the forward direction of reactions 1-5 on all of the clusters. Table 8 shows the best estimates of barrier heights for the forward and reverse directions of reactions 1-5 on the Pt20(111) and Pt14(100) clusters compared with what was obtained on the Pt2 cluster. From Table 7, it is seen that the Pt10(111) and Pt14(100) clusters give significantly different barriers than the Pt2 cluster. Generally, the barrier heights increase, which is consistent with disruption of bonding to Pt atoms, which are nearest neighbors to the central Pt2. Second and third layer Pt atoms lead to further changes; however, these effects are smaller than what was seen for adding nearest neighbors in the first layer. We only considered clusters with a second layer of Pt atoms (i.e., Pt14) for the (100) surface. Note that in Table 7a the differences in

8472 J. Phys. Chem. C, Vol. 112, No. 22, 2008

Walch et al. TABLE 7: Barrier Heights As a Function of Cluster Size for (a) Pt(111) and (b) Pt(100) (a)

Pt2

Pt10

Pt16

Pt20

O2 HO2 H2O H2O O f OH O f

0.72 0.05 0.78 0.17 0.52

1.36 0.29 1.23 0.80 0.69

1.13 -0.22 1.54 0.04 0.38

1.23 -0.51 1.33 0.23 0.22

(b)

Pt2

Pt8

Pt14

O2 HO2 H2O H2O O f OH O f

0.72 0.05 0.78 0.17 0.52

1.41 0.03 0.72 0.18 0.37

0.96 0.15 1.01 0.28 0.33

TABLE 8: Best Estimates of Barriers reaction

Pt2

Pt20 111

Pt14100

1f 1r 2f 2r 3f 3r 4f 4r 5f ) 5r

0.72 0.82 0.05 1.65 0.78 0.43 0.17 0.10 0.52

1.23 0.93 (0.0) (1.09) 1.33 0.24 (1.91) 0.23 0.22

0.96 1.45 0.15 1.76 1.01 0.38 (1.70) 0.28 0.33

TABLE 9: Best Estimates of Rates (sec-1) reaction 1f 1r 2f 2r 3f 3r 4f 4r 5f ) 5r

Figure 5. (a) Pt8O2 f Pt8OO. (b) Pt8O2H f Pt8OOH. (c) Pt8H2O f Pt8OHH. (d) Pt8OHOH f Pt8OH2O. (e) Pt8OHO f Pt8OOH.

Pt20 111 3.7 × 10-8 4.2 × 10-5 1.8 × 1013 4.8 1.3 × 10-10 8.9 × 108 3.7 × 10-20 8.2 × 1010 1.8 × 1011

Pt14 100 1.2 × 10-5 8.4 × 10-14 5.5 × 1010 3.3 × 10-11 2.8 × 10-3 4.0 × 106 1.2 × 10-16 1.2 × 1010 2.7 × 109

barrier height between the Pt16 and the Pt20 clusters range from 0.1 to 0.3 eV. Since the change in adding a third layer is smaller than adding a second layer, one might speculate that adding further layer would have an effect less than the difference between adding two and three additional layers, that is, the difference between the Pt16 and the Pt20 clusters given above. Thus, for these reactions, we believe the barrier height is converged to within a few 0.1 eV. For reaction 2 on the (111) surface, it is seen that the barrier for the forward reaction on the Pt16 and Pt20 clusters is negative. This occurs because these are single point calculations, and if we had optimized the saddle point geometry for the larger cluster, we would have obtained a smaller or zero barrier. Thus, we reduce the best estimate of the barrier reported in Table 7 to zero. Also in Table 7, the barrier for 4f is computed assuming a crossing of surfaces of different multiplicity as discussed above. Using the best estimates of the barrier heights from Table 8 and correcting the rates in Table 5 for the change in barrier heights leads to the rates given in Table 9. Here we see that the largest rates are 2f, 4r, and 5f ) 5r. Thus, considering the larger clusters 4f is no longer important and the reduction of the barrier for reaction 5 makes it also important in the mechanism. Interestingly, 3r also has a significant rate considering the larger clusters. However, by analogy to the forward rate for reaction 4, this rate may be greatly reduced if we consider the low-spin surface where the OH plus H product forms two bonds to the surface. Thus, we expect reaction 3r will not be important.

Mechanism of Molecular Oxygen Reduction

J. Phys. Chem. C, Vol. 112, No. 22, 2008 8473 TABLE 10: Effects of Solvation on Energetics in Electronvotls for Reactions 2, 4, and 5

Figure 6. Solvation model for HO2.

While we expect the relative rates to be accurate, the absolute rate constants may well be in significant error due to the limitations of the DFT method and of the cluster method. This is due to the extreme sensitivity of the rate constant to the barrier height and our estimate of remaining errors in barrier height of a few 0.1 eV. For example, an error of 0.1 eV in the barrier height leads to an error of ∼50 in the rate constant at 300 K. Jacob79 has also considered some of the same reactions using a 35 Pt atom cluster based on the earlier work of Jacob et al.72 In principle, this calculation should be more accurate than the present work with respect to cluster size effects. However, in these calculations, constrained optimizations were carried out to define approximate minimum energy paths, and the paths are very different in the reactants-to-products direction than in the products-to-reactants direction. This implies true minimum energy paths were not obtained and true saddle points are not obtained. This leads to serious discrepancies between estimates of barriers obtained in their work and that obtained in our work, for example, for the dissociation of HO2 to OH and O a barrier of ∼17 kcal/mol (or ∼0.7 eV) is reported, whereas Sidak and Anderson36 report less than 0.1 eV, which is in agreement with the present work. One other difference compared with our work is that we assumed we should keep the d electrons high-spin coupled. This is based on the assumption that the d electrons are only weakly coupled and thus a high-spin calculation should give about the same energy as a low-spin calculation and is easy to do with simple wave functions. The low-spin wave function is very difficult to describe by methods like DFT and at the very least requires symmetry broken solutions. Jacob has tried to obtain the lowest spin state for each cluster, but this may introduce errors of unknown magnitude. 4.3. Effects of Solvation. Since the PEM fuel cell chemistry is happening in a water environment, we also considered the effect of solvation on the reaction rates by adding explicit water molecules. Here, we considered reactions 2f, 4, and 5 since these are the most important reactions in the mechanism based on their computed rates. We first considered a simple solvation model for O2H, which is the reactant in reaction 2f). Here, we are considering cyclic structures similar to what is found for (H2O)n clusters.73 The OH end of O2H has an OH bond and an additional in-plane oxygen lone pair of O(2s) character, while the O end has two in-plane oxygen lone pairs of O(2s) and O(2p) character. In the case where one water is hydrogen bonded to an OH bond, we find that two waters bridge the O2H, while in the case where bonding is to an oxygen lone pair on each O, three waters are needed to bridge the O2H, leading to the structure shown in Figure 6. The remaining O2H orbitals not involved in hydrogen bonds are of O(2p) character and are approximately perpendicular to the plane; see Figure. 6. These orbitals are used in

reaction

reactant

saddle point

product

(2) (2) + 5H2O (4) (4) + 5H2O (5) (5) + 6H2O

0.0 0.0 0.0 0.0 0.0 0.0

0.5 0.5 0.17 0.14 0.52 0.47

0.07 0.07 0.0 0.0

forming bonds to the Pt surface and are not available for hydrogen bonding; thus, this model is suitable for describing reaction 2f, and we also find this model is reasonable for reactions 4f and 4r. For reaction 5, we used six waters of solvation to be consistent with the model above. We note that a similar model of solvation has been used by Woon74 in describing reactions of astrophysical importance. Table 10 shows the effect of explicit waters of solvation on reactions 2f, 4f, and 4r. Here, we see that the effect on reaction 2f is essentially zero, which is reasonable since the OO bond only elongates by of the order of magnitude of 0.1 Å, and thus there is little change in the O2H charge distribution. For reaction 4, there is a more significant effect, which is consistent with stronger hydrogen bonding for H2O as compared with OH. Here, by considering the effects of solvation, the barrier for 4f is lower by 0.03 eV, while the barrier for 4r is higher by 0.04 eV. For reaction 5, we see a reduction in the barrier height by 0.05 eV. These corrections would lead to small changes in the rates for reaction in a humid environment. 5. Conclusions A comprehensive chemical mechanism for PEM fuel cell reactions was discussed in the Introduction. In this paper, we present results for a subset of this mechanism consisting of five nonelectrochemical reactions on catalytic platinum particles. The B3LYP density functional theory (DFT) method was used with the Wadt and Hay relativistic ECPs and basis sets LANL2DZ plus addition of a 4f function on Pt to study five chemical reactions on Pt(100) and (111) surfaces. Calibration calculations were carried out for the reaction Pt + O2 f PtO2 using the CASSCF/MRCI method with a ccpVDZ/relativistic ECP basis set for Pt and the aug-cc-pVDZ basis set for O. Comparison to B3LYP DFT calculations showed that the binding energies are overestimated by more than a factor of 2, but the barrier heights with respect to reactants are accurate. This result is consistent with calculations for the outer minimum of molecular oxygen on Pt(111), where the computed binding energy is about a factor of 2 larger than the experimental results. In spite of the overestimation of the binding energy, the computed OO bond length and vibrational frequency are found to be in good agreement with the experimental data. This establishes that O2 is strongly bound in the outer minimum, and the bond length is substantially elongated from approximately 1.2 Å to 1.37 Å. The computed bond strength De of OO is 5.4 eV, and the barrier to dissociate O2 to two O atoms on the Pt surface is 0.7 eV. The computed bond strength De OH-O in O2H is 3.1 eV, and the barrier to dissociation to O plus OH on the Pt surface is found to be less than 0.1 eV, in agreement with the work of Sidik and Anderson. We find that, while a Pt2 cluster gives qualitatively correct results, the results are strongly influenced by cluster size effects, and inclusion of nearest neighbor atoms in at least the top and second layers is necessary for accurate energetics.

8474 J. Phys. Chem. C, Vol. 112, No. 22, 2008 Conventional transition state theory, using the barrier heights from the largest clusters and the frequency analysis from the Pt2 clusters plus a Wigner estimate for tunneling, shows that reactions 2f, 4r, and 5 are important on the surface of catalytic Pt particles. We find that OH bonds at a bridged site, while O favors a 3-fold hollow site. The binding energy for an O atom at a 3-fold hollow site on the (111) surface is computed to be 3.8 eV in good agreement with the literature results. Finally, the effects of solvation were computed using a solvation model consisting of cyclic (H2O)n structures. The solvation effects are shown to be relatively small. While we believe the computed barrier heights are accurate to within a few 0.1 eV, we note that a change in barrier height of 0.1 eV leads to an error in rate constant of about a factor of 50 at 300 K. Thus, while we expect relative rate constants to be more accurate, there may therefore be significant errors in the absolute value of individual rate constants. Acknowledgment. This work was supported by Honda R&D Co. Ltd., Wako, Japan. References and Notes (1) Anderson, A. Electrochim. Acta 2002, 47 (22-23), 3759. (2) Markovic, N. M.; Ross , P. N., Jr. In Interfacial Electrochemistry: Theory, Experiments and Applications; Wieckowski, A., Ed.; Marcel Dekker: New York, 1999821. (3) Markovic, N. M.; Schmidt, T. J.; Stamenkovic, V.; Ross, P. N. Fuel Cells 2001, 1 (2), 105. (4) Adzic, R.; Lipkowski, J.; Ross, P. N., Eds. Electrocatalysis, 197, Wiley-VCH: New York, 1998. (5) Parthasarathy, A.; Srinivasan, S.; Appleby, A. J.; Martin, C. R. J. Electrochem. Soc. 1992, 139 (9), 2530. (6) Zinola, C. F.; Castro Luna, A. M.; Arvia, A. J. Electrochim. Acta 1994, 39 (13), 1951. (7) Beattie, P. D.; Basura, V. I.; Holdcroft, S. J. Electroanal. Chem. 1999, 468, 180. (8) Parthasarathy, A.; Srinivasan, S.; Appleby, A. J. J. Electrochem. Soc. 1992, 139 (10), 2856. (9) Wakabayashi, N.; Takeichi, M.; Itagaki, M.; Uchida, H.; Watanabe, M. J. Electroanal. Chem. 2005, 574 (2), 339. (10) Xu, H.; Song, Y.; Kunz, H. R.; Fenton, J. M. J. Electrochem. Soc. 2005, 152 (9), A1828. (11) Neyerlin, K. C.; Gasteiger, H. A.; Mittelsteadt, C. K.; Jorne, J.; Gu, W. J. Electrochem. Soc. 2005, 152 (6), A1073. (12) Li, T.; Balbuena, P. B. J. Phys. Chem. B 2001, 105 (41), 9943. (13) Michaelides, A.; Hu, P. J. Am. Chem. Soc. 2001, 123 (18), 4235. (14) Anderson, A.; Albu, T. J. Electrochem. Soc. 2000, 147 (11), 4229. (15) Norskov, J. K.; Rossmeisl, J.; Logadottir, A.; Lindqvist, L.; Kitchin, J. R.; Bligaard, T.; Jonsson, H. J. Phys. Chem. B 2004, 108 (46), 17886. (16) Anderson, A.; Neshev, N.; Sidik, R.; Shiller, P. Electrochim. Acta 2002, 47 (18), 2999. (17) Zhdanov, V. P.; Kasemo, B. Surf. Sci. 2004, 554 (2/3), 103. (18) Anderson, A.; Cai, Y.; Sidik, R.; Kang, D. J. Electroanal. Chem. 2005, 580 (1), 17. (19) Rossmeisl, J.; Logadottir, A.; Norskov, J. K. Chem. Phys. 2005, 319 (1/3), 178. (20) Li, T.; Balbuena, P. Chem. Phys. Lett. 2003, 367 (3/4), 439. (21) Taylor, C. D.; Neurock, M. Curr. Opin. Solid State Mater. Sci. 2005, 9 (1-2), 49. (22) Nilekar, A.; Xu, Y.; Zhang, J.; Vukmirovic, M. B.; Adzic, R. R.; Mavrikakis, M. AIChE Annual Meeting, Conference Proceedings 2005, 10619–10619. (23) Zhdanov, V. P.; Kasemo, B. Electrochem. Commun. 2006, 8 (4), 561. (24) Gu, Z. H.; Balbuena, P. B. J. Phys. Chem. A 2006, 110 (32), 9783. (25) Yeager, E. Electrochim. Acta 1984, 29, 1527. (26) Markovic, N. M.; Gasteiger, H. A.; Ross, P. N. J. Phys. Chem. 1995, 99 (11), 3411. (27) Parthasarathy, A.; Dave, B.; Srinivasan, S.; Appleby, J. J. Electrochem. Soc. 1992, 139 (6), 1634. (28) Wroblowa, H. S.; Rao, M. L. B.; Damjanovic, A.; Bockris, J. O. J. Electroanal. Chem. 1967, 1, 139. (29) Angerstein-Kozlowska, H.; Conway, B. E.; Sharp, W. B. A. J. Electroanal. Chem. 1973, 43, 9. (30) Wang, J. X.; Markovic, N. M.; Adzic, R. R. J. Phys. Chem. B 2004, 108, 4127.

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