Role of Adsorbate Coverage on the Oxygen Dissociation Rate on Sr- Doped LaMnO3 Surfaces in the Presence of H2O and CO2

Sr-doped LaMnO3 (LSM) is a promising oxygen reduction reaction electrocatalyst in solid oxide fuel cells and other electrochemical devices. The presence of CO2 and H2O has been reported to promote the oxygen dissociation reaction on LSM surfaces. Here, we investigate the coadsorption mechanism of O2 with H2O or CO2 by combining first-principles calculations of the (0 0 1) surface containing 25−100% Sr with thermodynamic adsorption models. The molecules were found to chemisorb by formation of charged oxygen, hydroxide, and carbonate species, and the adsorption energies were exothermic up to monolayer coverage. Low concentrations of H2O or CO2 do not compete with O2 for adsorption sites under relevant conditions. However, their presence contributes to the total amount of oxygen-containing species. The increased coverage of oxygen species provides a quantitative explanation for the reported enhancement in oxygen dissociation kinetics in the presence of H2O/CO2. This study thereby provides insights into oxygen exchange mechanisms on LSM surfaces.


INTRODUCTION
Sr-doped LaMnO 3 (LSM) is one of the most studied perovskite materials for solid oxide fuel cell (SOFC) cathodes because of its high electronic conductivity, good oxygen reduction kinetics, and thermal and chemical stability with yttria-stabilized zirconia. 1−3 For the same reasons, LSM has also been applied in composite electrodes in solid oxide electrolyser cells 4 and catalytic layers and/or electronically conducting phases for mixed conducting membranes and catalytic membrane reactors. 5 At intermediate temperatures (600−800°C), the main limiting factor for the performance of SOFCs has been ascribed to the oxygen reduction reaction (ORR) at the cathode. 3,6 Oxygen surface exchange and surface diffusion of oxide ions have been identified as two key processes that control the ORR. 7 Surface exchange kinetics remains an elusive property because it involves several steps including adsorption and dissociation of molecular oxygen, reduction (charge transfer), and incorporation of oxygen species into the cathode or electrolyte. Depending on the specific application and electrode characteristics, there are multiple possible reaction pathways, and it is inherently challenging to separate individual reaction steps. 8,9 LSM has been found to catalyze oxygen exchange mainly through the homoexchange mechanism where LSM provides surface sites for the adsorbates to dissociate, diffuse, and reassociate. 10 Oxygen is subsequently incorporated into the electrolyte at the triple-phase boundaries, which may be the limiting step of the ORR. 11 On the other hand, the heteroexchange mechanism involves lattice oxygen and thereby requires oxygen vacancies at the surface. Although LSM exhibits low bulk oxygen vacancy concentration, heteroexchange may be facilitated by fast diffusion along grain boundaries. 12,13 In the case of typical mixed conducting c a t h o d e m a t e r i a l s s u c h a s L a 2 N i O 4 + δ a n d Ba 0.5 Sr 0.5 Co 0.8 Fe 0.2 O 3−δ , dissociative adsorption of oxygen rather than incorporationhas been reported to limit the oxygen surface exchange. 14,15 In situ isotope-labeled gas-phase exchange experiments have been used to investigate the oxygen exchange reaction. By flowing gas mixtures of 18 O 2 and 16 O 2 over a catalyst bed, the oxygen dissociation rate can be measured directly as the steady-state concentration of the dissociation product, 18 O 16 O. In such experiments, the oxygen exchange rate can be directly related to the oxygen adsorbate concentration in the case of the homoexchange mechanism. With this approach, Huang et al. recently showed that the presence of H 2 O and CO 2 could enhance the oxygen dissociation rate on LSM surfaces. 16 By adding 2500−3000 ppm of CO 2 or H 2 O to pure 0.05 bar oxygen, the oxygen dissociation rate increased by a factor of 1.5−2 and the results showed that both CO 2 and H 2 O participated in the exchange reaction. The detailed understanding of this improvement is still unclear; possible explanations could be the presence of additional oxygencontaining surface species such as hydroxide or carbonate or changes in the reaction mechanisms and/or barriers as suggested for La 0.6 Sr 0.4 Co 0.2 O 3−δ 17 and SrTiO 3 . 18 In the case of other materials systems, few studies have been performed on the effect of steam on oxygen surface exchange: isotope exchange followed by SIMS measurements has revealed enhanced oxygen surface exchange for mixed conductors such as La 0.6 Sr 0.4 FeO 3−δ 19 and PrBaCo 2 O 5+δ 20 in the presence of steam, which was ascribed to faster water adsorption and dissociation at surface oxygen vacancies, that is, heteroexchange. On the other hand, the presence of CO 2 impurities usually has an adverse effect on oxygen surface exchange kinetics because of undesirable reactions and/or degraded performance of the cell. 21,22 In this work, we predict the equilibrium adsorbate concentrations on LSM surfaces by combining first-principles calculations and thermodynamic models for gas adsorption. The (La, Sr)O-terminated (0 0 1) surface is selected as the model system as it is shown to be the favored termination in theoretical and experimental studies. 23,24 We consider the cases of O 2 /CO 2 and O 2 /H 2 O coadsorption as a function of partial pressures and temperature. The role of coadsorption can thereby be evaluated in comparison with measured oxygen dissociation rates under given environmental conditions. 16 The surface adsorption reactions were described by considering chemisorption and dissociative adsorption. Adsorption of CO 2 by formation of a carbonate species can be described by bonding with an LSM surface oxide ion where *La/Sr denotes a surface La or Sr-site and H ad + is associated with a surface oxide ion, that is, OH O • in Kroger− Vink notation. 29 Third, the dissociative adsorption of oxygen can be described by the formation of peroxide species or oxide ion adsorbates on La/Sr sites By also considering the coverage dependence of the adsorption energetics, the temperature and pressure ranges, where the surface becomes saturated and coadsorption becomes competitive, can be evaluated. Thereby, we present a quantitative comparison of the changes in overall oxygen coverages and the enhancement in the oxygen dissociation rate by addition of H 2 O and CO 2 reported by Huang et al. 16 2. COMPUTATIONAL METHODS 2.1. First-Principles Calculations. Spin-polarized density functional theory (DFT) calculations were carried out using VASP 30 and the projector-augmented wave method. 31 PBE-generalized gradient approximation (GGA) 32 was used with the DFT + U approach by Dudarev et al. 33 and the on-site Coulomb interaction parameter for Mn was set to 4.0 eV based on previous studies. 34 −37 The energy cutoff for the planewave basis set was 400 eV. The included valence electrons were La 5s 2 p 6 d 1 6s 2 , Sr 4s 2 5p 6 6s 2 , Mn 3p 6 d 5 4s 2 , and O 2s 2 p 4 .
The surface of Sr-doped LaMnO 3 was modelled as a symmetric (La, Sr)O-terminated (0 0 1) slab with a thickness of 11 atomic layers and 2 × 2 cell expansion in the lateral directions (108 atoms). The periodic images of the slab were separated by a vacuum region of about 25 Å. The calculations were performed with a 4 × 4 × 1 k-point grid, and the atomic positions were optimized until the residual forces were within 0.03 eV Å −1 . In order to avoid spurious structural distortion upon gas adsorption, the orthorhombic structure was used, and the lateral lattice parameters 7.78 and 7.99 Å were obtained from a 2 × 2 × 2 cell with a Sr-dopant concentration of 12.5%. The octahedral tilting in the slab was a + b − c − in Glazer notation.
By use of symmetric slabs, the surface dipole between the terminating (LaO) + and (MnO 2 ) − layers in stoichiometric (0 0 1) slabs was avoided. 23 The excess positive charge of the additional 4(LaO) + layer in the 2 × 2 slab was compensated by four Sr-dopants. Slabs terminated with three different Sr concentrations were considered: 4(La 0.75 Sr 0.25 O) 0.75+ , 4(La 0.5 Sr 0.5 O) 0.5+ , and 4(SrO) 0 , that is, 25, 50, and 100% Sr, respectively. The tendency for segregation of Sr to the surface of LSM was thereby taken into account. 36 In the case of the slab with 25% Sr on the surface, the remaining two Sr-dopants were introduced in the subsurface layer to obtain a charge neutral cell. The overall Sr concentration was thereby 16.7% for the slabs terminated with 25−50% Sr and 33.3% for the fully SrO-terminated slab.
Because of the inherent challenge of representing the hightemperature paramagnetic state of LSM, ferromagnetic (half-metallic) ordering was imposed, 38 and the magnetic moment of Mn was 3.8− 4.0 μ b . Selected calculations were pursued with G-type antiferromagnetic ordering as it has been suggested as more appropriate to represent paramagnetic systems. 38 Although the antiferromagnetic ordering could not be retained upon adsorption, it has previously been shown not to be important for adsorption calculations in LaMnO 3 . 39 The adsorption energies, ΔE i ads , were calculated as the total energy difference of the adsorption reactions for coverages of 0.25, 0.5, and 1 monolayer. The adsorbates were generally introduced on both sides of the slab, while for some configurations, complete convergence was only achieved with the adsorbate on one side of the slab. The difference in adsorption energy for these two approaches was relatively small (typically ±0.1−0.17 eV). For calculations with higher coverages, the adsorbates were arranged in several symmetrically inequivalent configurations in order to obtain the lowest energy structure. Interactions between different adsorbates were investigated in the case of H 2 O and O 2 according to reaction 5 (Supporting Information), but otherwise not considered. The calculated coverages may therefore be overestimated close to saturation, while the relative coverages of the different adsorbates can be expected to be less affected.
The adsorption thermodynamics were evaluated based on the adsorption energy and configurational and vibrational entropy of the adsorbates. The vibrational frequencies were obtained according to the finite displacement method implemented in VASP with four 0.015 Å displacements of the vibrating species along the crystallographic axes. The vibrational entropy of the adsorbates, S i vib , was thereby calculated from the normal mode frequencies, v j , according to where β j = hv j /kT. 40 Changes in the vibrational frequencies of the LSM surface oxide ion were also included in the cases of 1/2O 2 (peroxide), CO 2 , H 2 O adsorption. The change in zero-point energy upon adsorption, ΔZPE, was calculated using the same frequencies according to Δ∑ j (hvj/2). The adsorption entropies, ΔS i ads , were obtained with the gaseous reference states taken from thermochemical tables 41 and therefore include the loss of translational entropy upon adsorption. Because of the challenges with the O 2 molecule within GGA, the chemical potential of O 2 was corrected based on the approach by Wang et al. 42 by normalizing the calculated enthalpies of formation of a range of binary nontransition metal oxides to the experimental values. The correction amounted to −1.14 eV for the total energy of the O 2 molecule ( Figure S1).

Thermodynamic
Model. The thermodynamic model computes equilibrium coverage for each adsorbate species by minimizing the total free energy of the system. Here, we list the energetic terms included in the model. For each adsorption species i, the total adsorption Gibbs energy associated with it is a function of its coverage Θ i .
Here, ΔH i ads = ΔE i ads (Θ i ) + ΔZPE is the adsorption enthalpy for oxygen adatoms, water molecules, and carbon dioxide molecules as obtained from DFT calculations and Δμ i = kT ln(p/p 0 ) is the change in chemical potential of the gas species with varying partial pressure. The configurational entropy is given by the coverages of all adsorbates and is separated into contributions from the adsorbates associated with the oxygen and cation sites on the surface. The surface oxygen sites can be occupied by O ad − , H ad + , and carbon in CO 3,ad 2− , while the cation sites can be occupied by OH ad − , O ad 2− , and oxygen in CO 3,ad 2− . Although each cation site can accommodate only one OH ad − or O ad 2− , both oxygen atoms of CO 3,ad 2− can be accommodated because of the specific adsorbate configuration upon carbonate formation. That is to say, each adsorbed CO 2 molecule occupies one oxygen site and one cation site on the surface. The total configurational entropy can thereby be written as The total Gibbs energy of the system can thereby be described as where the sum over i covers all possible adsorbate species. The equilibrium coverages under given conditions were solved by varying the coverages of the coadsorbates and determining the combination of the lowest energy.
For the convenience of further analysis, we also define three additional coverage terms. First, the number of vacant cation adsorption sites, Θ free , because these are limiting, allows for analyzing whether the surface is saturated by competitive adsorption Second, the total number of adsorbed oxygen species on the surface, Θ O tot Third, the total number of adsorbed species on the surface, that is, counting only one of the oxygen atoms of CO 2 3. RESULTS 3.1. Adsorbate Configurations and Energies. Adsorption of CO 2 on LSM (0 0 1) was determined to be energetically most favorable by chemisorption of carbonate species as shown in Figure 1 for coverages of 0.25−1. The carbonate adsorbates were formed by bonding to an LSM surface oxide ion. For coverages of 0.25 and 0.5, the surface oxide ion(s) relaxed out of the LSM surface, leaving  Chemistry of Materials pubs.acs.org/cm Article undercoordinated manganese in the subsurface layer ( Figure  1a,b). The most stable configuration for dissociative adsorption of H 2 O was determined to involve a hydroxide species bridging two surface cations, preferably La 3+ , and a proton associated with a LSM surface oxide ion and directed toward the hydroxide species (Figure 2). Similar configurations of chemisorbed H 2 O have been observed by scanning tunneling microscopy studies of the SrO-terminated surface of the layered perovskite Sr 3 Ru 2 O 7 . 43 In some cases (Θ < 0.5, 25− 50% Sr), the surface oxide ion relaxed out of the surface, leaving undercoordinated Mn in a similar manner as for the carbonate adsorbates. Figure 3 shows oxygen chemisorbed as peroxide species bound to LSM surface oxide ions (reaction 3). The O−O bond lengths were 1.46−1.50 Å, that is, slightly longer than the nominal 1.4 Å, which may be ascribed to the additional bonding to the surface cations.  Figure 4d shows the adsorption of an oxygen molecule with a bond length of 1.4 Å. In principle, the (0 0 1) surface contains four additional symmetrically equivalent sites for oxygen bridging Sr−La, but higher coverages resulted in significant restructuring of the surface and thus not considered further.
Bader charge analysis revealed that the bridging oxide ions attained essentially the same charge as the bulk oxide ions of LSM, O −1. 25 . In comparison, the charge of oxygen in the dioxide configurations was significantly smaller: O −0.7 for the dimer groups in Figure 3 and O −0.5 for the O 2 molecule in Figure 4d, indicating that these species can be described as peroxide (O 2 2− ) and superoxide (O 2 − ), respectively.   Chemistry of Materials pubs.acs.org/cm Article The calculated adsorption energies for LSM with 25, 50, and 100% Sr in the surface layer are shown as a function of adsorbate coverage in Figure 5 with corresponding linear fits. The adsorption energies were slightly less exothermic with increasing Sr content for all adsorbates, particularly at the lowest coverages. The adsorption energy of CO 2 showed the strongest coverage dependence, which may be ascribed to its larger size and the number of bonds to La/Sr, that is, steric and chemical interactions, respectively. In comparison, the  (Figure 4a,b). The adsorption energies of bridging oxide ions exhibited a complex behavior and a strong dependence on both Sr content and adsorbate coverage. The most exothermic values (Θ ≤ 0.5, 25−50% Sr) may to a larger extent reflect the instability of the polar surfaces, as also evidenced by restructuring in some cases (e.g., Figure 4e). Notably, reverse segregation of Sr could be substantiated by considering the segregation energy for Sr combined with the adsorption energy of a bridging oxide ion. A segregation energy of −0.43 eV per Sr from the subsurface to surface was obtained by comparing the slabs with 25 and 50% Sr in the surface layer, while the adsorption energy of O 2− was −0.71 eV, more exothermic for the surface with 25% Sr. Accordingly, the most stable configuration was obtained with lower Sr content in the surface layer by including oxygen adsorbates. However, defects and mixed terminations must be considered for the complete understanding of the surface chemistry of LSM. 44,45 Table 1 summarizes the thermodynamic parameters for adsorption and the respective site occupancies for the adsorbates. The vibrational frequencies of the adsorbates are provided in Table S1, and the temperature dependence and linear fit of the adsorption entropies are shown in Figure S2. Overall, the obtained adsorption energies are significantly exothermic for all three gases. In the case of CO 2 , less exothermic chemisorption energies of −1.4 and −1.1 eV were previously obtained for the undoped material based on DFT calculations (using GGA and a different carbonate adsorption geometry) and adsorption isotherms on LaMnO 3.15 powders, respectively. 25 The present values for the Sr-doped surfaces range from −2.41 to −0.74 eV (Θ CO 2 = 0.25). These values may be compared to the formation enthalpies of La 2 O 2 CO 3 and SrCO 3 from CO 2 and the binary oxides, −1.5 46 54 It should be noted that several computational studies have been performed for oxygen adsorption on the MnO 2terminated LaMnO 3 (0 0 1) surface. 34,37,55,56 The strong exothermic adsorption of both H 2 O and CO 2 implies that these may enter competitive regimes. Consequently, the presence of H 2 O may displace CO 2 and prevent carbonate formation on the surface as reported for SrTiO 3 and BaZrO 3 . 18,53 For the calculations of equilibrium adsorbate coverages, the peroxide configuration was considered because of the favorable energetics at higher coverages and across Sr contents compared to the bridging oxide ions. The restructuring observed for some of the bridging configurations may reflect permanent changes in the surface that alter the catalytic properties. Moreover, it remains uncertain if the most exothermic adsorption energies for the bridging configuration were associated with other aspects of the computational approach related to charge balance and surface polarity.
3.2. Adsorbate Coverages. The equilibrium adsorbate coverages were sought by minimizing the total Gibbs energy of the system as described in Section 2.2. To show how each energetic term changes with adsorbate coverages, Figure 6 displays the two-dimensional energy landscapes for CO 2 /O − coadsorption at T = 1073 K, p O 2 = p CO 2 = 1 bar, and 50% Srdoped surface. Figure 6a shows Figure 6b. The configurational entropy, −TS config , is minimized at intermediate total coverage, as both low coverage and saturation are low-entropy states (Figure 6c). The total Gibbs energy of the system is the sum of the previous three terms, with the first two being the dominant terms. In this case, the lowest energy is obtained for Θ O = 0.31 and Θ CO 2 = 0.29. A similar plot for O 2 /H 2 O coadsorption is shown in Figure S4. Following this method, the equilibrium surface coverages were surveyed for temperature and oxygen partial pressure  Figure 7 shows the case for O 2 /CO 2 coadsorption. Under the considered conditions, Θ O is hardly influenced by the presence of CO 2 because of the availability of a significant amount of adsorption sites for both species throughout the pressure ranges (Θ free ). These results show that coadsorption of O 2 and CO 2 is not in competition with each other. Despite the noncompetitive nature of the CO 2 adsorption, CO 2 adsorbates provide extra oxygen-containing surface species that may be involved in the oxygen exchange reactions. There is a significant contribution from CO 2 to Θ O tot even at relatively low p CO 2 : 10 −1 bar CO 2 increases Θ O tot by a factor of 1.7 at 673 K and by a factor of 3.5 at 1073 K relative to the CO 2 -free case. CO 2 adsorption becomes negligible for partial pressures lower than 10 −7 bar at 1073 K. Figure 8 shows the calculated adsorbate coverages for O 2 / H 2 O coadsorption in the same temperature and partial pressure range on the 50% Sr-doped LSM surface. The effect of H 2 O on O 2 adsorption qualitatively resembles that of CO 2 , that is, Θ O remains almost constant with varying p H 2 O . There are major differences as well. Adsorption of H 2 O is energetically less favorable compared to that of CO 2 at low coverage but more favorable at high coverage because of weaker adsorbate interactions (Table 1). Consequently, starting from p H 2 O = 10 −10 bar at 673 K, Θ H 2 O is initially lower than Θ CO 2 under equivalent conditions but increases with a steeper slope with increasing partial pressure. A competitive adsorption regime is entered at around p H 2 O > 10 −3 bar with minor suppression of Θ O .
Equivalent coverage plots for the 25% and 100 Sr-doped LSM surfaces are provided in Figures S5−S8. The qualitative trends remain similar to those of the 50% Sr-doped surface, in line with the relatively small changes in adsorption energies as shown in Figure 5. There is a moderate decrease in total   Chemistry of Materials pubs.acs.org/cm Article adsorbate coverages going from the 25% Sr-doped surface to the 100% Sr-doped surface because of the less exothermic adsorption energies with increasing Sr content.

DISCUSSION
In this section, we discuss possible connections between surface adsorbate concentrations and the oxygen dissociation rate by comparison with the experimental results from Huang et al. 16 We first assume a simple model for the relationship between the oxygen dissociation rate, R diss , and the total number of active species on the surface, Θ act This model assumes that R diss follows an Arrhenius relationship with an activation energy, E a , that is constant and not affected by coadsorption. The prefactor Θ act represents a nonlinear term because of changes in surface coverage with respect to temperature and partial pressures. In ref 16 Figure 9 shows Θ O+H 2 O+CO 2 as a function of inverse temperature under the same gas environments on the 50% Sr-doped surface, assuming that Θ O+H 2 O+CO 2 is an appropriate representation of Θ act in eq 13. The Arrhenius relationships are fitted and shown by the dashed black lines. The result shows that changes in Θ O+H 2 O+CO 2 with temperature represents a minor contribution to the apparent activation energy: −0.16 eV (for pure O 2 ) and −0.19 to −0.23 eV (for coadsorption) in the high-temperature regime (973−1123 K). This effect gradually disappears as temperature goes down and the surface becomes saturated. Now, we discuss whether Θ O+H 2 O+CO 2 is a good representation of active species contributing to surface dissociation by referring back to measurements in ref 16. Following eq 13, under the same temperature, the ratio of [ 16 O 18 O] in the two gas environments should be the same as the ratio of the r e s p e c t i v e Θ a c t . In other words, the ra-  Figure 9, Θ O changes very little with the addition of H 2 O or CO 2 because of the noncompetitive nature of the adsorption. Therefore, if the oxygen exchange mechanism remains unchanged in the presence of H 2 O and CO 2 , these results indicate that Θ O is not the only source of active surface species.
The two remaining candidates that we consider for Θ act are Θ O+H 2 O+CO 2 and Θ O tot . In Figure 10, we show the ratios as in (a) 0.5 atm O 2 plus 3000 ppm H 2 O versus pure O 2 and (b) 0.5 atm O 2 plus 2500 ppm CO 2 versus pure O 2 in comparison to the ratio of the measured oxygen exchange rates. The colored bands represent the uncertainty due to the different Sr contents in the surface layer. Looking at Figure 10a, Figure 10b, the ratio between Figure 9. Effect of CO 2 and H 2 O on equilibrium Θ O+H 2 O+CO 2 predicted in this work in three gas environments varying with temperature (solid lines) on the 50% Sr-doped surface. The three gas environments are all at p O 2 = 0.5 atm, with the addition of 3000 ppm H 2 O (blue) and 2500 ppm CO 2 (green). For comparison, Θ O in presence of CO 2 /H 2 O (dashed lines) shows that there is a negligible effect of coadsorption on Θ O under these conditions. The contribution of coverage to the apparent activation energy for each case is fitted and shown by the dashed black lines. Figure 10. Comparison between predicted Θ O tot , Θ O+H 2 O+CO 2 , and experimentally measured 16  The above quantitative comparison shows that it is reasonable to consider Θ O+H 2 O+CO 2 as the prefactor Θ act in eq 13. This will partly eliminate the nonlinear characteristic of the Arrhenius fitting of the oxygen dissociation rate. In Figure 11a Figure 11b for the 50%-Sr doped surface. Here, Θ O+H 2 O+CO 2 is the calculated value from this work under the experimental thermodynamic conditions. Assuming [ 16 O 18 O] ∝ Θ O+H 2 O+CO 2 exp(−E a /kT), we obtain a uniform activation energy of 0.81 eV for all three atmospheres. The good consistency among all three sets of data after the prefactor normalization indicates that eq 13 is a plausible model for interpreting experimental surface kinetic data and that the increase in Θ act is possibly the predominant contributor to the enhancement of the oxygen dissociation rate in the presence of CO 2 and H 2 O.
Figures S10 and S11 presents equivalent renormalized dissociation rates for the 25 and 100% Sr-doped surfaces. Similar to the 50% Sr-doped case, the renormalization allows for a uniform activation energy across gas atmospheres. Activation energies of 0.78 and 0.87 eV were obtained for the 25 and 100% Sr-doped surfaces, respectively.
The present work demonstrates that an increased concentration of oxygen-containing surface species in the presence of small amounts of CO 2 or H 2 O (Θ O+H 2 O+CO 2 ) can account for the increase in the oxygen exchange rate according to the homoexchange mechanism. This concentration effect, of course, is not expected to be the only factor that could contribute to the enhanced surface oxygen exchange rate on LSM. It is reasonable to expect that different surface species, such as surface hydroxide and carbonate, can affect the reaction mechanisms in different ways through interactions with the surface and oxygen adsorbates. This could potentially explain some discrepancies between the predicted Θ O+H 2 O+CO 2 ratio and experimental oxygen exchange rates. Discrepancies can also be ascribed to several limitations of the model, including the use of a single pristine (0 0 1) surface, lack of interactions between coadsorbates, and computational accuracy (particularly the rather large correction applied to the oxygen adsorption energies, see Section 2.1 and the Supporting Information).
We conclude that the ORR is affected by CO 2 /H 2 O in the following way when these gases are added in small amounts into O 2 gas. First, our predicted adsorption concentrations have shown that trace amounts of CO 2 /H 2 O do not hinder surface oxygen adsorption of O 2 . Second, the simple Arrhenius model, as in eq 13, leads to quantitative agreement with experimental oxygen dissociation rates. This result indicates that the increase of active oxygen species provided by coadsorbed CO 2 and H 2 O can be correlated with promotion of homoexchange. These two points imply that the presence of CO 2 /H 2 O in the predicted regime will not impede the ORR. In the regime where dissociative adsorption of oxygen is the rate-limiting step, CO 2 /H 2 O coadsorption promotes the overall ORR by providing extra active oxygen species on the surface. In terms of the role of surface coverage and heteroexchange rate on the electrode performance of SOFCs, H 2 O or CO 2 does not take part in the overall fuel cell reactions. Nevertheless, the increased concentration of oxygen species on the cathode in the presence of H 2 O and/or CO 2 may promote the kinetics of intermediate reactions that increase performance.

CONCLUSIONS
First-principles calculations and thermodynamic models were used to investigate oxygen, water, and carbon dioxide adsorption on the (La, Sr)O-terminated (0 0 1) LSM surface as functions of temperature and partial pressures. The calculated surface coverages showed that adsorption of oxygen was hardly influenced by trace amounts H 2 O or CO 2 because of the noncompetitive nature of coadsorption. However, CO 2 and H 2 O do contribute significantly to the total number of oxygen-containing surface species, even at low partial pressures. By assuming that these species take part in the oxygen homoexchange reactions, the increase in coverage was