Surface termination effects on the oxygen reduction reaction rate at fuel cell cathodes

The results of first principles calculations of oxygen vacancy and oxygen adsorbate concentrations are analyzed and compared for the polar (La,Sr)O and MnO2 (001) terminations of (La,Sr)MnO3 fuel cell cathode materials. Both quantities strongly depend on the average Mn oxidation state (La/Sr ratio). In thin symmetrical slabs, the cation nonstoichiometry also plays an important role by modifying the average Mn oxidation state. The surface oxygen vacancy concentration for the (La,Sr)O termination is more than 5 orders of magnitude smaller when compared to the MnO2 termination. The vacancy and adsorbed oxygen migration energies as well as the dissociation barriers of adsorbed molecular oxygen species are determined. The encounter of adsorbed atomic oxygen and surface oxygen vacancy is identified as the rate determining step of the oxygen incorporation reaction. Since the increase of atomic and molecular oxygen adsorbate concentration is limited by the typical saturation level in the range of 20% for charged adsorbates, the overall oxygen incorporation rate is predicted to be significantly smaller for the (La,Sr)O termination.


Introduction
Solid oxide fuel cells (SOFCs) continue to attract great attention as a promising source of ecologically clean and efficient electricity generation. The key factor, largely determining the SOFC performance, is the oxygen reduction reaction (ORR) rate at the surface with further oxygen incorporation into the cathode. [1][2][3][4] La 1Àx Sr x MnO 3Àd (LSM) was one of the rst ABO 3 -type perovskites employed as a SOFC cathode material, which is still used in the form of porous composites with the respective electrolyte material, to increase the average ionic conductivity. In our previous investigation, 5 we studied in detail oxygen adsorption, dissociation and migration on the (001) MnO 2 -terminated LM surface while LaO one is much less studied.
For undoped LaMnO 3Àd (LM), the MnO 2 (001) termination was calculated to be the most stable termination; 5 however, with increasing Sr doping the (La,Sr)O termination is predicted to become energetically more favorable. 6 Also, for a given average cation composition, it is frequently found that the surface exhibits a higher Sr content and/or an increased ratio of A-site to B-site cations either already introduced during lm preparation by pulsed laser deposition 7 or upon annealing. [8][9][10] Segregation effects are also supported by theoretical calculations. 6 Similar trends of A-cations and, in particular, Sr surface segregation were also found for perovskite La 1Àx Sr x Co 1Ày Fe y O 3Àd (LSCF, see e.g. ref. [11][12][13] solid solutions, emphasizing the importance of better understanding of defect formation and oxygen reduction kinetics on the AO-type termination. When comparing the different (001) terminations of LSM, the fact that these terminations represent polar surfaces has to be properly taken into account. The formation of polar terminations is rather frequent for oxides. The physics and chemistry of a broad class of oxide polar surfaces are summarized, for instance, in review articles. 14,15 The pure polar terminations of a macroscopic sample are electrostatically unstable and must reconstruct to avoid the "polar catastrophe" due to a huge dipole moment. This could be achieved in several ways. In this paper, we assume that the LSM (001) surface polarity is negated by surface rumpling and the electron density redistribution near the surface. There are also other options to compensate for surface dipole moments, such as surface oxygen vacancy formation, 16 structural changes through the formation of extended structural defects such as steps and trenches, 17 or structural reconstruction through a complete rearrangement of the terminating planes into an ordered pattern of AO and BO 2 stripes. 18 However, a comprehensive study of these options, which strongly depend on particular experimental conditions, extends far beyond the goals of this article.
In the present paper, we analyze the oxygen vacancy ðV $$ O Þ formation, oxygen (both atomic and molecular) adsorption and dissociation on LSM (001) (La,Sr)O-and (001) MnO 2 -terminated surfaces (also comparing with previous results for (001) MnO 2 (ref. 5,19,20)). To some extent, the nominal polarity of (LaO) + and (MnO 2 ) À layers may be decreased by surface rumpling and also by the electron density redistribution near the surface (see the discussion in Section 3.1). Nevertheless, the remaining polarity strongly modies the defect formation and adsorption energies, and thus strongly inuences the oxygen exchange surface reaction kinetics. It might also act as a driving force for surface reconstruction at elevated temperatures. Despite the importance of this phenomenonalso for related (Ba,Sr,La)-(Fe,Co,Mn)O 3 perovskitesit has rarely been systematically investigated. Also, the commonly neglected effect of different Mn oxidation states in slabs with different cation stoichiometry has to be taken into account. Based on our results, a semiquantitative comparison of the oxygen reduction kinetics on LSM (001) MnO 2 and on (La,Sr)O termination layers is given. The focus of the present investigation is on the relative differences between the (001) (La,Sr)O and (001) MnO 2 terminations, rather than on absolute reaction rates or absolute values of defect energetics.

Computational details
In this study, LSM refers to all possible (La,Sr)MnO 3 compositions; the abbreviation LM represents Sr-free lanthanum manganate bulk or slabs, while LS25M is used for systems in which 25% of La ions are substituted with Sr, and LS50M for 50% Sr doping, respectively. While a high Sr content, such as in LS50M, is rarely used for SOFC cathode materials, it is still within the solubility limit 21 and allows us to explore a larger range of Mn oxidation states. Calculations were performed using the DFT method, 22 as implemented in the computer code VASP5.4. 23 Core electrons are substituted with US PAW 24 potentials (Table A1 in the ESI †), and the GGA-PBE 25 exchangecorrelation functional is employed. To make the results comparable to our previous calculations on the MnO 2 termination (ref. 5,26,27), we here used the GGA approach without the Hubbard +U term. Despite the fact that this neglect could affect the absolute values of reactions including electron transfer, [28][29][30] it is expected not to skew the relative difference of such reaction energies for different slab terminations, which are the main goal of the present study. The difference of V $$ O concentrations for AO and BO 2 terminations is the most important contribution to the slower O exchange kinetics at the AO surface (Section 3.4), and since the charges of the oxide ions in the surface plane do not differ much between AO and BO 2 terminations (Table A2 †), the respective surface V $$ O formation energies will be similarly affected by the +U correction for both terminations. For early 3d transition metals such as Mn, the formation energies of different negatively charged oxygen adsorbates on the respective oxides change monotonically with U. 31,48 While the magnitude of the +U correction might vary according to the different number of electrons transferred to different adsorbed species (Table A5 †), this difference in the correction is not expected to override the pronounced E ads differences as shown in Fig. 7.
Moreover, it was shown that for the experimental orthorhombic geometry, such an approach correctly reproduces the A-type anti-ferromagnetic (AAF) structure of LM experimentally observed at low temperatures 26,32 and the basic defect properties of many ABO 3 perovskites and their solid solutions. 3,5,[33][34][35][36][37] The kinetic energy cut-off is set to 520 eV. Brillouin zone sampling is performed by the Monkhorst-Pack scheme 38 with 30 and 20 k-pointsÅ À1 for the bulk and the surface calculations, respectively.
Depending on the temperature and degree of (non)stoichiometry, three types of structural distortions have been observed in La 1Àt MnO 3Àd , one rhombohedral R 3c and two orthorhombic Pnma. 39,40 These distortions could be a combination of the octahedral tilting, rotation and Jahn-Teller octahedral deformation. 41 Energetically, the difference between rhombohedral and orthorhombic phases in the LM bulk does not exceed 0.05 eV per ABO 3 formula unit. Experimentally, the orthorhombic phase of LM can easily be converted into the rhombohedral one by annealing in N 2 at 600 C, 42 indicating that both structures are very close in energy, whereas the ideal cubic perovskite is considerably (by $0.3 eV) less favorable. Therefore, it is essential to introduce a lattice distortion into the modeling. The spin-polarization of B cations also strongly affects the energy of the structure. Diamagnetic solutions are considerably (by z1 eV) less favorable than magnetic solutions whereas the energies of FM and all high-symmetry A-, C-, GAF states lie close together, within 0.1 eV per formula unit. The choice of the exact magnetic structure is not expected to signicantly affect the results, as long as it is consistent for all calculations (at cathode operating temperatures, LSM anyway loses its magnetic order and becomes paramagnetic).
In our slab calculations, we employed the ferromagnetic state (Mn in a high spin state) with a rhombohedral structure, which is lowest in energy. In this structure, the oxygen octahedra rotate alternately in all three main directions, whereas in the orthorhombic structure along the direction normal to the basal plane all octahedra rotate in the same direction ( Fig. 1a and b). For defect calculations in the bulk, an 8 ABO 3 -unit pseudo-cubic 2 Â 2 Â 2 supercell was used. High-symmetry structures were constructed in such a supercell for 0, 25 and 50% relative Sr concentrations, creating bcc and simple cubic Sr-sublattices, respectively. Two concentrations of oxygen vacancies (d ¼ 0.125 and 0.25) were simulated by removing neutral oxygen atoms. This leads to an increased electron density of the nearest Mn ions (thus, decreasing their oxidation state). The electron density inside the oxygen vacancy is negligible (#0.1 e), and the vacancy can thus be denoted as a doubly positively charged defect, V $$ O , in the standard Kröger-Vink nomenclature. The oxygen vacancy formation energies are calculated according to In the (001) surface calculations, seven-layer 2D symmetric slabs were used (i.e. sequence AO-BO 2 -AO-BO 2 -AO-BO 2 -AO or BO 2 -AO-BO 2 -AO-BO 2 -AO-BO 2 ; total thickness about 3.5a 0 which corresponds to z14Å), separated along the z axis by a 5a 0 vacuum gap. The surface cell is made of eight AO or BO 2 units Fig. 1c). There are two, eight and four nonequivalent surface oxygen lattice sites for 0, 25 and 50% Sr concentrations, respectively. The removal/adsorption of a surface oxygen atom from these terminations (symmetrically on both sides) leads to a surface defect concentration of 12.5% (1/8 defect per AO or BO 2 surface formula unit). The lattice constants were optimised in the bulk defect calculations (leading to a small energy reduction, #0.05 eV per formula unit). For the slab calculations only the atomic coordinates were optimized, with the lattice constants kept xed at the respective bulk values.
The calculated binding energy for a gas-phase O 2 molecule is À5.9 eV (the combination of pseudopotentials and exchangecorrelation functionals used in the plane wave VASP code is known to overestimate the experimental value of 5.12 eV and thus the vacancy formation energy; however, this does not affect the differences of the defect and adsorbate formation energies that are the main focus of the present study. The calculated bond length of 1.23Å is close to the experimental value of 1.21 A). The lattice constants and angles in rhombohedral LM, LS25M and LS50M are a 0 ¼ 7.88Å, a ¼ 90.85; a 0 ¼ 7.81Å, a ¼ 90.54; and a 0 ¼ 7.77Å, a ¼ 90.50, respectively.
The oxygen adsorption was modeled on a 7-layer LaOterminated symmetric non-stoichiometric La 4 Mn 3 O 10 (001) slab. Such 7-layer slabs have been found to suffice for a good convergence of the main properties such as V $$ O formation energy with a slab thickness 5,26,27 and are used here for consistency with a previous study. The electron charge redistribution in the terminating planes of this slab is similar to that for stoichiometric slabs with an even number of layers. 27 The total dipole moment normal to the (001) surface is naturally cancelled by the slab's symmetry, but two local dipole moments remain at the surfaces (charged surface and subsurface layer; also the adsorbate layer, if present, is charged) which are oriented in opposite directions. Transition states were calculated by the NEB method 43 with eight intermediate images. The effective atomic charges were calculated with the Bader method. 44 The atomic structures are visualized using VESTA soware. 45

Results and discussion
In order to nally elucidate the effect of AO versus MnO 2 surface terminated slabs (including the surface dipoles) on the oxygen incorporation rate, we rst analyze separately the oxygen vacancy formation (Section 3.1), oxygen (O/O 2 ) adsorption (Section 3.2) and dissociation (Section 3.3), and then combine all these results in the discussion of the ORR kinetics in Section 3.4. In all sections, it is important to properly account for the fact that in thin symmetrical slabs, the two different terminations have different overall cation stoichiometries, and thus the average Mn oxidation states, which, in turn, affect all processes involved in the electron transfer. This issue thus far has barely been discussed in the literature. As shown in the following sections, both the surface oxygen vacancy formation and the oxygen adsorption are affected by a set of key parameters: most importantly the Mn oxidation state, reduced oxygen coordination number, lattice distortions and surface dipole effects, which are not always easy to disentangle, even through computer modelling.

Oxygen vacancy formation
In general, surface defect formation energies are expected to differ from bulk values; however, one has to carefully distinguish between the true surface effects and other contributions. In the present investigation, we use symmetrical slabs (with identicaleither (La,Sr)O or MnO 2terminations on both sides), which have the benets of a zero total electric dipole moment and good computational efficiency. This leads to a different overall ratio of A-site to B-site cations for AO and BO 2 terminated slabs. For the 7-layer La 4 Mn 3 O 10 and La 3 Mn 4 O 11 slabs used here, this results in Mn oxidation states of +2.67 and +3.25 (Table 1), which differ considerably from the bulk Mn 3+ value and may strongly modify V $$ O formation and oxygen adsorption energies. This deviation should decrease asymptotically to zero for very thick slabs, but in practical calculations still directly affects the vacancy formation energy E V $$ O and adsorption energies as discussed below.
For all LM and LSM compositions discussed here, the AO and BO 2 layers of the perovskite structure are charged (Table A2 in the ESI †). The layer charges for the bulk materials decrease from 0.96 e per formula unit for LM, down to 0.69 e per formula unit for LS50M (gray circles in Fig. 2), as expected for a partial substitution in the AO layers with Sr 0 La and increasing Mn oxidation state in the BO 2 layers. While for the same average Mn oxidation state, the BO 2 layer charges for the bulk, central and surface layers of the slabs are quite similar, and the AO surface layer charges are systematically, by 0.2-0.25 e per formula unit, lower than those for AO layer deeper inside the slab. Also, the splitting into sub-planes is different for AO and BO 2 surface layers ( Fig. A1 in the ESI †). The surface rumpling can partially compensate for the surface dipole; for the BO 2 termination, the subsurface AO layer also shows a pronounced distortion with La/Sr outward displacement.
The decrease of the Mn oxidation state due to the variation of the La/Sr ratio and/or the formation of V $$ O affects the electronic structure of both the bulk and the slabs, so that the Fermi energy increases (it is plotted in Fig. 3a relative to the deep reference O 2s states, see ref. 36 for more details). Interestingly, different slopes are observed for the bulk and AO and BO 2 terminations. A similar effect was found for the surface work functions of the symmetrical 9-layer ABO 3 slabs, which increase more steeply for the BO 2 termination when moving through the element row, from B ¼ Ti to Ni. 46 Fig. 3b shows the V $$ O formation energy E V $$ O for the bulk and the central layer of the slabs (cf. also Table A3 in the ESI †). The data for the bulk and MnO 2 -terminated slabs agree very well.
O in the central layer of AO terminated slabs is slightly lower, which might be affected by the electron density redistribution towards the surface AO layer with an excessive positive charge that correspondingly decreases the Mn effective oxidation state in the inner layers and lowers E V $$ O (cf. the differences in layer charges in Fig. 2). Overall, the trend of these E V $$ O with the Mn oxidation state is very similar to the variation in the bulk Fermi level (Fig. 3a). The bulk V $$ O formation energies for LM and LS50M as well as the decrease for LS50M are in good agreement with literature values in ref. 47 and 48 (with U eff ¼ 0) and experimental data on La 0.9 Sr 0.1 MnO 3 , discussed in ref. 49. The fact that the bulk E V $$ O is rather similar for LM and LS25M was also noticed in ref. 50, although the use of the GGA+U method resulted in different absolute energies.   Finally, Fig. 3c displays E V $$ O for the surface oxygen vacancies (cf. also  Fig. 3c. A similar energy difference in surface vacancy formation energies for the (001) LM LaO and MnO 2 terminations was also observed for larger, 16-layer slabs calculated using the GGA+U functional (these slabs were cation-stoichiometric, but exhibited a nonzero surface dipole). 28 The true surface effect on E V $$ O has two contributions: (i) contributions originating from under-coordinated atoms in the surface layer. Qualitatively, one might expect that V $$ O formation is facilitated in both termination layers, because the number of Mn-O surface chemical bonds broken upon oxygen removal is smaller compared to the bulk. This effect is well known in covalent semiconductors and the so-called E 0 centers (dangling bonds) in amorphous silica 52 as well as for perovskites with neutral surface AO and BO 2 layers such as SrTiO 3 (e.g. it was found that E V $$ O is reduced by 0.8 eV on the TiO 2 termination but is almost unchanged on SrO, 28 whereas Alexandrov et al. 53 estimated even larger changes of 1.4 eV and 1 eV; for BaZrO 3 , and E V $$ O was reduced by 0.5 eV on the ZrO 2 termination 54 ). (ii) Contributions which are related to the fact that the AO and BO 2 (001) terminations are polar. To some degree, this polarity is attenuated by small relaxations of the surface layer (outward displacement of Mn ions at the MnO 2 termination, 32 and oxide ions at the LaO termination, cf. Fig. A1 in the ESI †). Furthermore, in a perovskite, such as (La,Sr)MnO 3 with cations easily changing their oxidation state, one could expect the polarity to be partially compensated by the increased Mn oxidation state in the MnO 2 termination layer. However, the data in Table A2 † indicate a less positive surface Mn charge, i.e. an opposite trend, which can rather be interpreted as an increased Mn-O bond covalency (but the MnO 2 surface layer charge hardly deviates from that of bulk with the same Mn oxidation state, cf. Fig. 2). A charge transfer of z+0.1 e per formula unit for the MnO 2 termination and zÀ0.15 e for the LaO surface was found in ref. 28. However, this electron density redistribution does not suffice to fully compensate for the surface dipoles, and the remaining polarity affects the defect formation and oxygen adsorption energies.
In the LaO termination layer with a formal charge of +1 e, the surface polarity is expected to disfavor the surface V $$ O formation. Obviously, the polarity effect dominates here over the reduced number of broken chemical bonds, leading to an overall increased E V $$ O : In contrast, for the MnO 2 termination, the negative excess surface charge is expected to favor V $$ O formation. Despite the additional contribution from the reduced number of broken bonds at the surface, the overall decrease of E V $$ O at the MnO 2 termination remains quite moderate. The total difference of 1-1.2 eV in the surface E V $$ O for the two terminations (for a given average Mn oxidation state) leads to a large difference in the surface V $$ O concentrations at 1000 K by more than 5 orders of magnitude (cf. Table A7 †). This strongly affects the ORR rates, as discussed in Section 3.4. The decreased ½V $$ O on the AO termination will also make it more susceptible to effects from segregation processes or poisoning by impurities.

Atomic and molecular oxygen adsorption
Let us rst discuss the adsorption of atomic O species. Our previous GGA studies 5,26 showed that atomic oxygen on the MnO 2 termination prefers to be adsorbed atop the surface Mn ion (Fig. 5d) with a binding energy of À1.1 eV (with respect to O in a gas-phase O 2 molecule). This is in qualitative agreement with the À1.9 eV found with the B3LYP hybrid functional. 55 In contrast, on the (001) LaO-terminated LM surface the only stable oxygen adsorption site is the "hollow" position (the bridge between the two nearest La ions) (Fig. 5a), in agreement with hybrid LCAO calculations, 55 plane wave GGA calculations 19 and atomic O adsorption on the LaO termination of La 2 NiO 4 . 56 The adsorption energy depends strongly on the Mn oxidation state (see Fig. 7a below) and can reach À4.3 eV. It might, at rst glance, seem unexpected that the O is adsorbed on such a hollow site and not atop a La cation. However, this O position relative to the underlying La cations is exactly the site that O would take if a full MnO 2 layer was grown on top of the LaO layer. The La-O ad distance of 2.0-2.2Å is signicantly shorter than the La-O bulk distance of z2.7Å. Due to the rhombohedral distortion of the slab structure, two non-equivalent hollow positions with different adsorption energies are available, and the presence/absence of Sr leads to more congurations. The effective atomic charges, interatomic distances and the energies of adsorbed species are collected in Table A5 in the ESI †.
The O adsorbed on the AO termination carries a signicant negative charge of À1.19 to À1.28 e (comparable to that for oxide ions) in the bulk (À1.22 to À1.27 e) and only slightly smaller than for O in the AO surface layer (À1. 33 57 This plot allows for a distinction of superoxide vs. peroxide species. On the AO termination the superoxide not only has a shorter O-O bond than the peroxide, but also significantly larger average distances to the surface A cations (Table A5 †). 1.20 e with that of bulk oxide ions, one might be tempted to assign it also to doubly charged peroxide O 2

2À
). The comparison between MnO 2 and AO terminations also emphasizes the inuence of the nature of adsorbate-slab interaction (partly covalent on MnO 2 but largely ionic on AO) on the character of the adsorbed species.  Table A2 †). Most probably, the very negative adsorption energies also contain a contribution from the stabilizing effect of the adsorbed oxygen species on the AO surface plane, which otherwise attempts to mitigate the structural disruption by pronounced surface rumpling as indicated in Fig. A1. † Despite the expected effect of the slab Fermi energy variation (blue dotted line in Fig. 7a), E ad,O on the MnO 2 termination is nearly independent of the Mn oxidation state. This results from the repulsion between negatively charged adsorbates O ad À (more negative for a lower Sr content, cf. Table A5 †) and the negative surface layer charge (also more negative for a lower Sr content), which apparently cancels the more favorable electron transfer for Sr-poor slabs with a higher Fermi level. Thus, for the MnO 2 termination we are le with a true termination effect on O adsorption caused by the surface dipole as indicated by the blue dashed arrows; however, since the position of the blue dashed line cannot be xed on an absolute energy scale, the picture here is only qualitative. Fig. 7a convincingly demonstrates the importance of considering the actual Mn oxidation states caused by the slab cation stoichiometry. Indeed, a direct comparison of the atomic O adsorption energies on the LaO and MnO 2 terminations of symmetrical 7-layer slabs 55,58 or 9-layer slabs 19 yields a difference in E ads,O of 3-4 eV. However, Fig. 7 clearly indicates that most of this difference is due to the Mn oxidation state variation, and only less than 1 eV is the true termination effect when comparing the data for a xed Mn oxidation state (e.g. Mn 3.3+ ).
For both terminations, the E ad,O 2 values for molecular adsorption are less negative than the sum of the two respective atomic O adsorption energiesi.e. O 2 dissociation is energetically favored. The energies, charges and distances are given in Table A5, ESI †. Molecular adsorption on the AO termination occurs in a tilted conguration (Fig. 5b), but for LS25M and LS50M also in a horizontal conguration (Fig. 5c)  . Peroxide species in the horizontal conguration were also found to be the most stable ones on the LaO termination of La 2 NiO 4 in ref. 56, with a tilted superoxide being by 0.14 eV less favorable. On the MnO 2 termination only tilted superoxide is present (Fig. 5e). Fig. 7b shows the molecular adsorption energies; the trends and their interpretation are very similar to that of atomic adsorption. The more negative E ad,O and E ad,O 2 for the AO termination should lead to much larger adsorbate coverages compared to the MnO 2 termination (for the same Mn oxidation state).  Table A5. † The dotted lines indicate the slope of the Fermi level (Fig. 3a), but with an opposite sign since electrons are transferred to adsorbed species.
However, the increase will be limited by saturation effects which arise for charged adsorbates and tend to limit the coverages to about 20%. 5 This point will become important in the kinetics discussion in the last section.

Dissociation barriers
Earlier, we have modelled in detail the dissociation of molecular oxygen species on the MnO 2 termination for an orthorhombic LM slab 5 and do not expect large differences for adsorption energies in the present slightly rhombohedrally distorted slabs. The oxygen molecule dissociation without V $$ O assistance on the defect-free AO termination is modelled here for several initial congurations. Fig. 8a illustrates the path starting from the "horizontal" LS25M conguration. The O 2 dissociation is rather a straightforward process, with simultaneous elongation of the O-O bond and gradually closer approach to the surface La/Sr ions (Fig. 8b). Aer dissociation, the two adsorbed O ions occupy neighboring hollow positions (Fig. 8c), with a mutual repulsion energy of z0.5 eV. The NEB-obtained O 2 dissociation barrier for this conguration is only 0.6 eV. In turn, Fig. 9 exemplies the O 2 dissociation starting from a tilted conguration. Here the path is more complicated, since one O ion has to travel a rather large lateral distance to reach its nal site, and the energy barrier also turns out to be larger, 0.9 eV.
The trends in dissociation barriers for LM, LS25M and LS50M AO-terminated slabs are revealed in Fig. 10. The energies of the dissociation transition states E TS (relative to O 2 in the gas phase) become systematically more negative with the decrease of the dissociation energy DE diss (Fig. 10a, Table A6 †). Note that the DE diss depends mainly on the average Mn oxidation state, with some additional contributions stemming from different adsorption congurations. The scattered actual dissociation barriers (Fig. 10b) show a clear trend of decrease for more negative DE diss , which corresponds to the Bell-Evans-Polanyi principle. 59,60 Interestingly, the dissociation barrier calculated for adsorbed peroxide on the LaO termination of La 2 NiO 4 (ref. 56) (1.35 eV for DE diss ¼ 0.4 eV) also nicely ts into this plot.
Let us now compare the O 2 dissociation barrier on the AO termination of LS50M (Mn 3.33+ ) with that on the LM MnO 2 termination (Mn 3.25+ ) since both refer to similar Mn oxidation states. On the AO termination, the barriers of 0.7-1.3 eV considerably exceed that of 0.6 eV found for the LM MnO 2 termination in ref. 5. This may be related to the dissociation pathway on AO being more complicated than on MnO 2 where it proceeds from a peroxide bridging between two surface Mn ions to two separate O atoms attached to exactly these two Mn ions. The variation of the energy barrier with Mn oxidation states is expected to be roughly similar for both terminations because a lower oxidation state (higher Fermi level) favors the electron transfer to antibonding p* orbitals of the oxygen molecule and thus facilities the dissociation. Owing to the low V $$ O concentration in the AO surface layer, dissociation processes with V $$ O assistance are not considered for the AO termination here. For the AO termination of La 2 NiO 4 , a strongly decreased dissociation barrier of 0.28 eV was obtained for molecular oxygen  The initial state (horizontal configuration), (b) transition state (energy higher by 0.60 eV than the initial state), and (c) one frame after the transition state (energy 0.14 eV lower than the initial state). The final state geometry is similar to that given in Fig. 9c. species vertically inserted into a V $$ O ; 56 but such a reduced barrier cannot outweigh the effect of the extremely low vacancy concentration on the AO termination of the LSM slabs.

Discussion of the energy prole and kinetics for the oxygen incorporation reaction
The energy proles for the oxygen incorporation reaction on the AO termination based on the results from the previous section are shown in Fig. 11. The overall ORR proceeds steeply downhill, being more exothermic for slabs with a low Sr content (cf. the larger vacancy formation energy E V $$ O in Fig. 3b). However, one has to keep in mind that at realistic operational temperatures, the Gibbs free energy prole contains a large positive entropy contribution (ÀTDS 0 z 2 eV at 1000 K) due to the loss of translational and rotational degrees of freedom of the O 2 molecule. 3    combination of D* and V $$ O data in ref. 61; for LM with pronounced oxygen excess 62 even lower values are expected. Such a concentration corresponds to a contribution of +1.7 eV congurational entropy at 1000 K ðÀTDS config ¼ RT ln½V $$ O Þ: Thus, despite the largely downhill energy prole, the real reaction kinetics is not necessarily fast.
The V $$ O formation energies for the AO termination are higher by 0.5-0.7 eV compared to bulk with a comparable Mn oxidation state (Fig. 3c). At 1000 K this corresponds to a decrease of the V $$ O concentration by roughly 3 to 4 orders relative to the bulk (these numbers are compiled in Table A7 †). Therefore, ORR mechanisms which proceed via direct O 2 adsorption into a V $$ O on the AO termination can be ruled out. In other words, the thermally activated dissociation rate of O 2,ad 2À adsorbed on the perfect AO termination is higher than the rate of O 2 adsorption into a surface V $$ O followed by subsequent fast dissociation. Both the atomic and molecular oxygen adsorption energies on AO terminations are very negative (range of À4.5 to À2 eV per O Fig. 7a and À5 to À2.5 eV per O 2 Fig. 7b). This means that at SOFC operating temperatures in air the concentration of adsorbed oxygen species could become so high that it reaches the plateau of $20% coverage, limited by the mutual repulsion of charged adsorbates. 5,63 The adsorbate coverages calculated with reasonably estimated DS 0 add values are also given in Table  A7. † Because of the more negative DH 0 add for the formation of two atomic species compared to one molecular adsorbate ( Fig. 7a and b), O ad 2À on AO and O ad À on MnO 2 are always in majority. Only for molecular oxygen species on the MnO 2 termination, smaller coverages in the range of 10 À4 to a few % are obtained. This means that the molecular adsorbate coverage on the AO termination is increased from these values to the saturation limit of z20%, i.e. varying by a factor of 4 to 2000.
Since the chemisorption is assumed to proceed without a signicant barrier, this is not the rate limiting step. Three processes could be potentially considered as the rate determining step on the AO termination: (i) the O 2 dissociation, with a barrier of 0.1-0.8 eV (Fig. 11) Notwithstanding the fact that the same step is rate determining for the AO and MnO 2 terminations (at least, at comparably high pO 2 (ref. 5) as relevant for a cathode material), the ORR is expected to be much slower for the former termination. On one hand, the adsorption energies for atomic as well as molecular oxygen species are much more negative on the AO termination compared to MnO 2 (for the same Mn oxidation state), but since the coverage by charged adsorbates approaches a saturation at about 20% 5 this more favorable adsorption energetics can only partially be translated into a higher concentration of O 2,ad À/2À and O ad À/2À (the latter being the relevant concentration for the rate determining step). On the other hand, the surface V $$ O concentration is lower by more than 5 orders of magnitude on the AO termination, and the migration barrier for the O ad 2À À V $$ O encounter is more than 0.6 eV higher (Table A7 †) which corresponds to a 3 orders of magnitude decrease of the O ad 2À À V $$ O encounter rate at 1000 K. Although these numbers are only a rough estimate, it indicates that even if most of the surface on a real SOFC cathode has a (La,Sr)O termination, even small patches of the MnO 2 termination (or any other terminations more active than (La,Sr)O) in the percent range might still make a signicant contribution to the overall ORR kinetics. This is in line with the observation for thin lm La 0.6 Sr 0.4 CoO 3Àd cathodes that already the addition of a monolayer of only 4% Sr strongly decreases the exchange rate of a freshly deposited lm. 65 While we are not aware of direct experimental determinations of adsorbed oxygen coverage on exclusively AO-or BO 2 -terminated perovskites, a recent ambient-pressure XPS investigation demonstrated distinct differences in the water adsorption of LaO-and FeO 2 -terminated LaFeO 3 . 66

Conclusions
The energetics of V $$ O formation as well as molecular and atomic oxygen adsorption were analyzed and compared for the polar (La,Sr)O and MnO 2 (001) terminations of (La,Sr)MnO 3 slabs. Distinct differences are noticed (more negative adsorption energies and higher V $$ O formation energies for the (La,Sr)O termination), which can however not be rationalized with a simple electrostatic picture. For comparably thin symmetrical slabs (used in practical calculations), the effect of cation offstoichiometry also has to be considered, which affects the average Mn oxidation state (neglecting this may lead to errors of several eV). When comparing data for the same Mn oxidation state, V $$ O formation energy is higher by 1-1.2 eV in the (La,Sr) surface layer than for the MnO 2 termination, which drastically decreases ½V $$ O (also relative to bulk). Interestingly, not only the adsorption energies differ between the terminations, but also the adsorbate charges (O 2,ad 2À and O ad 2À for (La,Sr)O but rather O 2,ad À and O ad 2À for MnO 2 ). The fact that the adsorption energies are much more negative on the (La,Sr)O termination can only partly be translated into higher adsorbate coverages, because they meet the saturation limit of about 20% for charged species. For both terminations, an encounter of adsorbed atomic oxygen species and V $$ O is expected to be the rate determining step of oxygen exchange, and the extremely low surface V $$ O concentration predicts the rate on the (La,Sr)O termination to be much slower than that on MnO 2 . Thus, the MnO 2 terminated fraction of the (La,Sr)MnO 3 polar surfaces is expected to mainly contribute to the oxygen reduction reaction even if present in only small amounts.
The main trends found here for the (La,Sr)MnO 3 system (decreased ½V $$ O and increased adsorbate coverage on the AO termination) are expected to hold also for related (Ba,Sr,La)(Fe,Co,Mn)O 3 perovskite cathode materials. However, the detailed dependence on the cation composition is far from trivial to predict since the decreased ½V $$ O and increased adsorbate coverage exert a counteracting effect on the oxygen exchange rate. The contribution of the AO termination to the overall rate is expected to become larger in materials with a less negative oxidation energy which increases the bulk ½V $$ O and typically makes the adsorption energies less negative (i.e. decreases adsorbate coverages). Then, a larger part of the more negative adsorption energy for the AO termination may actually translate into increased oxygen coverages before the saturation limit is met.

Conflicts of interest
There are no conicts of interest to declare.