DFT+U Analysis on Stability of Low-Index Facets in Hexagonal LaCoO3Perovskite:Eff ect of Co3+Spin States

Dan WuGong-ong ChenChao-yiGeZhen-peng HubcXue-hao HeXin-gang Li

a.Tianjin Key Laboratory ofApplied Catalysis Science&Technology(Tianjin),Tianjin 300072,China

b.Collaborative Innovation CenterforChem ical Science&Engineering(Tianjin),Tianjin 300072,China

c.School of Physics,NankaiUniversity,Tianjin 300071,China

d.Department ofChem istry,School of Science,Tianjin University,Tianjin 300072,China

DFT+U Analysis on Stability of Low-Index Facets in Hexagonal LaCoO3Perovskite:Eff ect of Co3+Spin States

Dan Wua,b,Gong-dong Chena,b,Chao-yiGea,b,Zhen-peng Hub,c?,Xue-hao Hed,Xin-gang Lia,b?

a.Tianjin Key Laboratory ofApplied Catalysis Science&Technology(Tianjin),Tianjin 300072,China

b.Collaborative Innovation CenterforChem ical Science&Engineering(Tianjin),Tianjin 300072,China

c.School of Physics,NankaiUniversity,Tianjin 300071,China

d.Department ofChem istry,School of Science,Tianjin University,Tianjin 300072,China

By the fi rst-princip les calculations,m ost studies indicated that the(1ˉ102)-CoO2term ination of LaCoO3cannot be stabilized,which disagreesw ith the experimentalobservation.Besides the crystalstructure,we found that the spin statesof Co3+ions could affect surface stability, which previously were not well considered.By exam ining the diff erent states of Co3+ions in hexagonal-phase LaCoO3,including low spin,intermediate spin,and high spin states,the surface grand potentials of these facets are calculated and compared.The results show that the spin states of Co3+ions have an im portant influence on stability of the LaCoO3faˉcets. Diff erent from the previous results,the stability diagram s dem onstrate that the(1102)-CoO2term ination can stably exist under O-rich condition,which can get an agreementw ith the experimental ones.Furthermore,the surface oxygen vacancy formation energies(EOv) of stable facets are com puted in diff erent spin states.TheEOvof these possible exposed term inations strongly depend on the spin state of Co3+ions:in particular,theEOvof the HS states is lower than that of other spin states.This indicates that one can tune the pro perties of LaCoO3by directly tuning the spin states of Co3+ions.

DFT+U,Spin state,Surface,Perovskite

I.INTRODUCTION

In recent decades,perovskite oxides(ABO3)have aroused considerable interests as the cathodematerials in solid oxide fuel cells for use in many energy storage and conversion technologies,such as the oxygen evolution reaction(OER)and oxygen reduction reaction(ORR)[1?5].These oxides are also catalyticallyactive and cost-effective catalysts for many im portant chem ical reactions,such as NOx(including NO and NO2)storage reduction[6,7],CO oxidation[8],and m ethane combustion[9].Since those catalytic reactions are surface processes,studies on the surface properties of thosematerials play an im portant role in deep ly understanding the catalytic reactions.Usually,the experim ental observations believed that(001)facets,particularly(001)B-term inated surface,in perovskite oxides(ABO3)are stable and play a pivotal role in these catalytic chem ical reactions[10?14].However,to the best of our know ledge,the surface stabilities of perovskite oxides,especially for LaCoO3,are still under debate from theoretical calculations.For examp le,us-ing the cubic-phase structure of LaCoO3in the calculations,Kahnet al.[15]predicted the Co-term inated (111)surface and LaCoO-term inated(110)surface to be the most stable;Chenet al.[16]reported that the ground term ination was the(001)-LaO surface,transitioning to the(111)-LaO3facet in oxygen-rich condition;while Zhanget al.[17]found that the LaO-and CoO2-term inated(001)surfaceswere stable.

It is noticed that LaCoO3has a rhombohedral primitive cellw ithsymmetry[18?23],which belongs to the hexagonal phase,but the cubic phase was used in the previous calculations[15?17].As well known,results from the fi rst-princip les calculations are very sensitive to the geometric structure ofmaterials.Therefore,the com p lexity of p revious studiesmay com e from the difference on crystal structures of LaCoO3.Recently,Liuet al.exp lored the stability of low-index facets on the hexagonal-phase LaCoO3by using the fi rˉst-p rincip lesˉ analysis[24],and they found that the (1102)-LaO,(1104)-O2and(0001)-LaO3term inations were thermodynam ically stable w ith a non-spin(NS) state.Though a more accurate crystal structure was em p loyed in their calculations,the results were still in confl ict w ith the common sense from the experimentalists that the(001)-CoO2was stable and active in the reactions[11?14].Therem ight be som e key factors ig-noredin previous calculations,which can reconcile the disagreement between com putational result and experim ental observation.

Besides the crystal structure,the spin state of Co3+ion is another im portant factor which can aff ect the resultsof calculations,butwasnotwell considered before. As reported in Ref.[25?29],LaCoO3exhibits nonmagnetic behavior at low tem perature(below 90 K)where the Co3+ions are in the low spin(LS)states,and undergoes a transition from sem iconductor to metal over 500 K,coincident to the spin state transition from intermediate spin(IS)to high spin(HS).It has also been reported that the spin states of Co3+ions in LaCoO3can greatly affect oxygen vacancy formation on the surface[30]and theirm igration in the bulk[31].However, there is a lack of report on surface stability of LaCoO3w ith consideration of the effects of spin states of Co3+ions.To this point,the reason for the above disagreem ent may arise from the spin states of the Co3+ions in LaCoO3.It is necessary to perform calcu lationsw ith appropriate Co3+spin states to clarify the propertiesof LaCoO3surface system s for the in-depth researches.

In this work,we com pared the surface grand potentials(?)of low-index facets of hexagonal-phase LaCoO3,where the Co3+ions’spin states are in LS,IS (ferromagnetic(FM),and anti-ferromagnetic(AFM)) and HS(FM,and AFM)states,to get a com prehensive understanding of LaCoO3surface system s.We determ ined the stable surfaces of LaCoO3in special chemical conditions by com paring the surface grand potentials(?).As the spin states of Co3+ions change,the region of stability diagram undergoes a significant variation.In addition,theEOvof stable facets of LaCoO3were com puted in different spin states.It indicates that the energy of surface oxygen vacancy links strongly to the spin mom ent of Co3+ions.Our simulations indicate that the(1ˉ102)-CoO2-term inated facet in hexagonal LaCoO3can be stabilized in most spin stateswhen the Co3+ions’spin states are taken into consideration. And this agreeswellw ith the experim entalobservation.

II.COM PUTATIONAL DETAILS

A.M odels of bulk and slab

The space group of crystalline LaCoO3is(No.167),which can be constructed w ith either a rhombohed ral or a hexagonal m odel(FIG.1).The Jahn-Teller effect causes a slight distortion of CoO6octahedron in LaCoO3,resulting in a prim itive cell of rhombohedral structure[18]w ith lattice param eters ofa=b=c=5.344?A,α=β=γ=61.01?(FIG.1(a)).As shown in FIG.1(b),theexperimental latticeparameters of hexagonalm odel[18]area=b=5.426?A,c=12.991?A,α=β=90?,andγ=120?.

FIG.1(a)Rhombohedral p rim itive cell and(b)hexagonal unit cells of LaCoO3.G reen,blue,and red balls represent La,Co and O atom s,respectively.

FIG.2 The top and side view s of optim ized(a)(1ˉ102)-LaO,(b)(1ˉ102)-CoO2,(c)(0001)-LaO3,(d)(0001)-Co,(e) (ˉ1104)-LaCoO,and(f)(ˉ1104)-O2.G reen,blue,and red balls represent La,Co,and O atom s,respectively.

In order to discuss the thermodynam ic stability of the low-index surfaces,we constructed six slab models.Adapted from the m odels in Ref.[24],a sevenlayer nonstoichiometric slab of LaO(FIG.2(a))or CoO2(FIG.2(b))term ination was used to simulate the facet along the(1ˉ102)direction,a thirteen-layer nonstoichiometric slab of LaO3(FIG.2(c))or Co(FIG.2(d))term ination wasused to simulate the facet along the(0001) direction;and an eleven-layer nonstoichiometric slab of LaCoO(FIG.2(e))or O2(FIG.2(f))term ination was used to simulate the facet along the(ˉ1104)direction. The(1ˉ102),(0001)and(ˉ1104)directions in the hexagonal phase correspond to the(001),(111)and(110) directions in a pseudo cubic phase.The black fram es in FIG.2 represent the periodic boundaries.

B.General setup for com putation

Density functional theory(DFT)calculations were performed w ith the Viennaab initioSimulation Package(VASP)[32,33].Thenucleiand core electronswere treated w ith the projector augmented wave(PAW)[34] m ethod.Generalized gradient approxim ation(GGA) w ith the Perdew-Burke-Ernzerhof(PBE)[35]form was em ployed to describe the electron exchange and correlation.For relaxation of bulk LaCoO3(hexagonal phase),a p lane wave basis set w ith cut-off of 400 eV and a 7×7×3 Monkhorst-Pack[36]k-point mesh were used to get the optimal lattice parameters.The optim al parameters of hexagonal phase area=b=5.485?A andc=13.031?A.For the slab calculations,the p lane wave energy cutoff of 400 eV and a 3×3×1 ofk-point mesh were used to get the properties of different surfaces.A ll the atom s in the bulk and slab were allowed to relax until the maximum force on each atom was smaller than 0.05 eV/?A.In each slab model,a separation over 15?A in vacuum was introduced to m inim ize interactions between periodic im ages.

The oxygen vacancy formation energy(EOv)is calculated using the follow ing equation:

whereE(defect)is the totalenergy of the slab w ith one surface oxygen vacancy,E(perfect)is the energy of the ideal slab andE(O2)is the energy of the O2molecule in the gas phase,respectively.

The different Co-3d occupations result in three spin states of Co3+ions in LaCoO3,including LS of t2g6eg0(S=0),IS of t2g5eg1(S=1)and HS of t2g4eg2(S=2). Each spin statewas constructed by changing the initial m agnetic mom ent of Co3+ion,i.e.LS=0,IS=±2 and HS=±4,where thequantity is the diff erencebetween alpha and beta electrons in a certain Co3+ion.The initial configurations of all Co3+ionswere set by MAGMOM, and then NUPDOWN was chosen to control the total spin of the slab.The selection rule of spin was also app lied to get a reasonable energy when oxygen vacancy was generated.For exam ple,two total spin numbers of the defect slab(+2 or?2 from the total spin number of initial slab)were calculated and the lower energy wasaccepted.The spin state of calculated O2molecule is always triplet.The partially fi lled d states in the Co3+ions are not well described by the standard DFT calculations,where the norm al GGA m ethods give a zero band gap of LaCoO3on the contrast to the experimental value of about 0.6 eV[37].We thus performed the DFT+Uapproach,where the on-siteUandJwere treated asa singleeff ective parameter among the d electrons on the Co3+ions,Ueff=U?J[38?40].We fixedJ=0.49 eV[41]in allour GGA+Ucalculations,and varied the value ofUin determ ining an optimal param eterU(3.4 eV),which w ill be discussed later.

C.The surface grand potential

To com pare the stability ofdiff erent term inations,the surface grand potential(?)is imp lemented in the calculations,as defined in Ref.[42]

whereNLa,NCo,andNOare the numbers of La,Co, and O atom s in the slab,respectively,andμrepresents the chem ical potential of La,Co,and O atoms species. Since the surface is in thermodynam ic equilibrium w ith the bu lk LaCoO3(μLaCoO3=EbulkLaCoO3)and the chem ical potentials of each species are related to the chem ical potentialof the bulk crystal,we thushave the follow ing constraint:

W henμLaiselim inated by Eq.(2)and(3),we introduce:

Subsequently,the surface grand potential can be determ ined as:

The surface La,Co,and O atoms are assumed to form no condensate on the surface,and the chem ical potential of each speciesmust be lower than the energy of an atom in the stable phase.We thus obtain the follow ing upper lim its of the chem ical potentials:

By combining Eq.(3)and(9),the lower lim its can be determ ined as follows,

whereis the formation energy of LaCoO3bulk crystal w ith respect to the La and Co atom s in their bulk phases,and the O atom in the gas phase.Once?μCoand?μOare determ ined in the eff ective ranges, the accessible values of?are thus obtained.

III.RESULTS AND DISCUSSION

A.Determ ining the optim izedUparam eter

It iswellknown thatUparameter playsan im portant role in the determ ination of the valence structure and the crystal structure.Since the band gap is generally related to the electronic structure of the bulk LaCoO3, it is essential to determ ine an appropriateUvalue for Co element to correct them istake.Previous studies indicate that the ground state LaCoO3is a nonm agnetic sem iconductor w ith Co3+ions in the LS state[28,29]. Therefore,band gap scan calculations were performed w ith the param eterUvarying from 2.9 eV to 3.9 eV w ith an interval of 0.1 eV on the LS ground state.The band gap as a function of the exchange parameterUis shown in FIG.3.W ith the increase of parameterU,the value of the band gap linearly increases.W henU=3.4 eV is em ployed,a band gap of 0.61 eV is obtained,which well agrees w ith the experimental value [37].TheUparameter of 3.4 eV was thus used for the GGA+Ucalculations to investigate surface stability of LaCoO3perovskite.

B.Therm odynam ic stability in diff erent spin states w ith GGA+U

To exam ine the influence of spin states of Co3+ions on surface stability,the surface grand potentials(?)of low-index facets have been calculated(Table S1?S3 in supp lementary materials),where the Co3+ions’spin states are in LS,IS(FM,AFM)and HS(FM,AFM) states,respectively.The FM and AFM configurations can be considered as two lim its in energy w ith respect to the spin state of LaCoO3.To determ ine the accessible values of?,we should calculate the eff ective intervals of?μCoand?μOaccording to the formation energy of LaCoO3bulk crystal,as defined in Ref.[42].The obtained formation energy of hexagonal LaCoO3is?9.31 eV.On the basis of Eq.(11),?μCoand?μOare thus restricted w ithin the ranges of(?9.31 eV

The stability diagram of the surface grand potential?of diff erent term inations w ithin the allowed area is displayed in FIG.4(a)when the Co3+ions are in LS state.Only three term inations out of six low-index facets are found to be stable:(1ˉ102)-LaO,(0001)-LaO3and(1ˉ102)-CoO2.The calculated results indicate that the(1ˉ102)-LaO term ination is stable in low O chemical potential and low Co chem ical potential,while its com p lem entary,the(1ˉ102)-CoO2term ination is in rich O chem ical potential and rich Co chem ical potential.Additionally,the(0001)-LaO3facet shows a stability dom ain in moderate Co and rich O environment. FIG.4(b)reveals the?of diff erent facets of the low spin Co3+ions as a function of?μCow ith?μO=0 eV. It can be noted that the(1ˉ102)-LaO term ination is favored in a large interval(?9.31 eV

FIG.3 Band gap of hexagonal phase LaCoO3as a function of exchange param eterU.

FIG.4(a)Stability diagram of the low-index surfaces of hexagonal LaCoO3in LS state.The surface grand potential (?)is represented as functions of?μCoand?μO.(b)The surface grand potentials of diff erent term inations in condition of?μO=0 eV.

FIG.5(a)and(c)Stability diagram of the low-index surfaces of hexagonal LaCoO3in IS state w ith a FM and an AFM con figurations.The surface grand potential(?)is represented as functions of?μCoand?μO.(b)and(d)The surface grand potentials of diff erent term inations in condition of?μO=0 eV in IS state w ith a FM and an AFM con figurations.

FIG.5(a)shows the?of different term inations as functions of?μCoand?μOin IS statew ith a FM configuration.Our calcu lations suggest that(1ˉ102)-CoO2, (0001)-Co and(ˉ1104)-LaCoO areunstablebecause their surface grand potentials are always larger than that of at least one stable facet w ithin the allowed region.According to FIG.5(a),the(1ˉ102)-LaO term ination is the most stable one in O-and Co-poor conditions.The (0001)-LaO3and(ˉ1104)-O2term inationsare favored in a small region corresponding to O-and Co-rich environm ents,respectively.FIG.5(b)shows the?of different facets as a function of?μCoin O-rich condition (?μO=0 eV)in IS state w ith a FM configuration.It appears that the(0001)-LaO3and(ˉ1104)-O2term inations can be stabilized in a very lim ited area(?2.15 eV

As disp layed in FIG.5(c),the(1ˉ102)-LaO,(0001)-LaO3,(ˉ1104)-O2and(1ˉ102)-CoO2are thermodynamically most favorable when the IS state is in an AFM configuration.Com pared to the stability diagram of the ISstatew ith a FM con figuration,thearea of the(1ˉ102)-LaO and(0001)-LaO3facets hardly change,while the region of(ˉ1104)-O2term ination only exists in a very sm all domain.The(1ˉ102)-CoO2term ination em erges and becom esm ost stable in rich O and Co environment. FIG.5(d)plots the surface grand potential?of different facets as a function of?μCow ith?μO=0 eV in IS state w ith an AFM configuration.The(1ˉ102)-LaO term ination is favorable in a large interval(?9.31 eV

FIG.6(a)p lots the surface grand potential?of different term inations as functions of?μCoand?μOin HS state w ith a FM configuration.The calculated results indicate that only four term inationsare thermodynam ically stable:(1ˉ102)-LaO,(0001)-LaO3,(ˉ1104)-O2and(1ˉ102)-CoO2as shown in FIG.6(a).The(1ˉ102)-LaO term ination is stable at low O chem ical potential(O-poor lim it)and low Co chem ical potential(Copoor lim it),as the(0001)-LaO3facet shows a stability domain in moderate Co and rich O environment. In general,the(ˉ1104)-O2and(1ˉ102)-CoO2term inations become the stable facets in a sm all domain corresponding to Co-and O-rich conditions.FIG.6(b) p lots the?of different facets of the high spin Co3+ions w ith a FM configuration as a function of?μCow ith?μO=0 eV(O-rich condition).The results indicate that when?μCoranges from?9.31 eV to?4.60 eV,the(1ˉ102)-LaO term ination is favored.W hen?μCois restricted to(?4.60 eV

FIG.6(a)and(c)Stability diagram of the low-index surfaces of hexagonal LaCoO3in HS state w ith a FM and an AFM con figurations.The surface grand potential(?)is represented as functions of?μCoand?μO.(b)and(d)The surface grand potentials of diff erent term inations in condition of?μO=0 eV in HS state w ith a FM and an AFM con figurations.

As shown in FIG.6(c),when the HS state is in the AFM configuration,the(1ˉ102)-LaO,(0001)-LaO3and(1ˉ102)-CoO2term inations are the most favorable facets.The stable region of(1ˉ102)-LaO term ination of the AFM configuration is larger than that of the FM configuration.However,the area of(0001)-LaO3becomes smaller.And the(1ˉ102)-CoO2facet alm ost does not change.FIG.6(d)reveals the?of the lowest-energy facets of the high spin Co3+ions w ith an AFM configuration as a function of?μCoin O-rich condition(?μO=0 eV).According to FIG.6(d), the(ˉ1104)-LaCoO,(0001)-Co and(ˉ1104)-O2facets cannot beobtained;however,the(1ˉ102)-LaO,(0001)-LaO3and(1ˉ102)-CoO2term inations can be stabilized in som e specialCo environm ent,as?9.31 eV

According to the above calculations,as the Co3+ions’spin states change,the stability diagram of lowindex facets in hexagonal-phase LaCoO3undergoes a significant variation.Considering diff erent spin states of Co3+ionsand diff erentmagnetic configurations,one can find that(1ˉ102)-LaO term ination is stable in a large region w ith oxygen poor condition.M oreover,the (0001)-LaO3and(1ˉ102)-CoO2term inations can be stabilized in an oxygen rich condition,which is a typical experimentalenvironment for LaCoO3.And tuning the chem ical potential of Co can tune the final surface exposition of LaCoO3nanoparticle.The(1ˉ102)-CoO2term ination is favorable under suitable chem ical potential regions,which can reach an agreement on theoretical resultsand experimentalobservation.This corresponds to the spin states of Co3+ions in perovskite LaCoO3. The Co3+ions occupying octahedral sites surrounded by oxygen ions can introduce comp lex magnetic property in LaCoO3,which has influence on the Co?O and O?O bond strength on the surface.

C.Oxygen vacancy form ation energy of the stable facets

Surface oxygen vacancy p lays a key role in the catalytic oxidation reactions in perovskite LaCoO3.We therefore analyze how the spin states of Co3+ions change the fundamental properties of oxygen vacancy formation.In order to exp lore the properties of these possible exposed facets,theEOvof the surfaces have been calculated.As shown in Table I,it can be found that higher Co3+magneticmoments lead to lower oxygen vacancy formation energies,in good agreem entw ith the previouswork[30].They attribute the tendencies in the surface oxygen vacancy formation energies to varia-tions in the O p-band center,which can be described as the Co?O bond strength.This trend suggests that oxygen vacancy energetics link strongly to the spinmom ent of Co3+ions.Furthermore,whether the Co3+ions are in a LS,an IS-FM,an IS-AFM,a HS-FM or a HS-AFM configuration,the(1ˉ102)-LaO term ination has thehighestEOvam ong these surfaces.It indicates that the (1ˉ102)-LaO facetmay be not active,since O atom s are strongly bound.In the HS-FM configuration,theEOvof(1ˉ102)-CoO2term ination is close to zero(0.08 eV), which is lower than that of(0001)-LaO3term ination (0.20 eV).W hen the spin state of Co3+ions is in a HS-AFM configuration,theEOvof(1ˉ102)-CoO2facet is 1.05 eV,which ismore than the(0001)-LaO3term ination(0.69 eV).As a result,it can be predicted that the(1ˉ102)-CoO2-and(0001)-LaO3-term inated surfaces m ight have good activity of O atoms,which can p lay a critical role in the surface reaction processes.

TABLE I Oxygen vacancy formation energy(EOv)for possible exposed surfaces w ith diff erent spin configurations.

For com parison,we also calculated surface oxygen vacancy formation energies w ith NS polarized m ethod as used in Ref.[24].The NS oxygen vacancy form ation energy of the(1ˉ102)-LaO term ination is still themaximum.Moreover,theEOvof(1ˉ102)-CoO2term ination is greater than that of the(0001)-LaO3surface.Comparing theEOvin NS state of(1ˉ102)-LaO and(0001)-LaO3facets w ith previous work[24],it can be found that there is a certain degree of error even ifwe use the sam em ethod andm odel.It isbecause that therew illbe a variety of uncertain spin configurations in the calculation processwhen we ignore the spin states,since there are a lot of localm inimums on the energy surfacew ith diff erent spin configurations.In fact,the above resu lt also represents that the spin statesextrem ely aff ect surface oxygen vacancies.Therefore,considering the spin states of Co3+ions is an essential role in exp loring the surface properties of LaCoO3.

IV.CONCLUSION

We performed DFT+Ucalculations to study the effect of Co3+spin states on surface stabilities of several low-index term inations of the perovskite LaCoO3.And theEOvof possibleexposed facets iscalculated in different spin states.The parameterUisem p loyed to correct the on-site Coulomb and theelectron interactions for local d orbitals.It is found that the spin states of Co3+ions in hexagonal-phase LaCoO3have an im portant effect on the region of stability diagram s.For themost cases w ith diff erent spin states and spin configurations of Co3+ions,the(1ˉ102)-CoO2term ination can be stabilized in oxygen rich environment,which agrees well w ith the experimental observation.Moreover,the spin states of Co3+ions can aff ect surface oxygen vacancy. The higher Co3+spin states give out the lower oxygen vacancy formation energies.Our results reveal that the spin states of Co3+ions should be well considered for studying the properties of LaCoO3facets.

Supp lem entary m aterials:The surfacegrand potential(?)of different term inations in LS,IS(FM,AFM) and HS(FM,AFM)states are disp layed,which is expressed as functions of the excess O and Co chem ical potentials(?μCoand?μO).

V.ACKNOW LEDGM ENTS

This work was supported by the National Natural Science Foundation of China(No.U1232118, No.21203099),the National Basic Research Program (No.2014CB932403),the Program of Introducing Talents of Discip lines to China Universities(No.B06006), Research Program for Advanced and App lied Technology of Tianjin(No.13JCYBJC36800),Doctoral Fund of M inistry of Education of China(No.20120031120033), Fok Ying Tung Education Foundation(No.151008), and Special Program for App lied Research on Super Com putation of the NSFC-Guangdong Joint Fund (the second phase).We appreciate the supports from the National Super-Com puting Center at Tianjin and Guangzhou.

[1]E.P.M urray,T.Tsai,and S.A.Barnett,Nature 400, 649(1999).

[2]J.Suntivich,K.J.M ay,H.A.Gasteiger,J.B.Goodenough,and Y.Shao-Horn,Science 334,1383(2011).

[3]J.Suntivich,H.A.Gasteiger,N.Yabuuchi,H.Nakanishi,J.B.Goodenough,and Y.Shao-Horn,Nat.Chem. 3,546(2011).

[4]J.W.Desm ond Ng,Y.Gorlin,T.Hatsukade,and T. F.Jaram illo,Adv.Energy Mater.3,1545(2013).

[5]J.Jung,M.Risch,S.Park,M.G.K im,G.Nam,H.Y. Jeong,Y.Shao-Horn,and J.Cho,Energy Environ.Sci. 9,176(2016).

[6]C.H.K im,G.S.Qi,K.Dahlberg,and W.Li,Science 327,1624(2010).

[7]X.G.Li,Y.H.Dong,H.X ian,W.Y.Hern′andez,M. M eng,H.H.Zou,A.J.M a,T.Y.Zhang,Z.Jiang,N.Tsubaki,and P.Vernoux,Energy Environ.Sci.4,3351 (2011).

[8]K.S.Song,S.K.Kang,and S.D.K im,Catal.Lett. 49,65(1997).

[9]G.Saracco,G.Scibilia,A.Iannibello,and G.Baldi, App l.Catal.B 8,229(1996).

[10]Y.M.Choi,D.S.M ebane,M.C.Lin,and M.L.Liu, Chem.M ater.19,1690(2007).

[11]Y.L.Lee,J.K leis,J.Rossmeisl,and D.M organ,Phys. Rev.B 80,224101(2009).

[12]Y.L.Lee,J.K leis,J.Rossmeisl,Y.Shao-Horn,and D. M organ,Energy Environ.Sci.4,3966(2011).

[13]S.O.Choi,M.Penninger,C.H.K im,W.F.Schneider, and L.T.Thom pson,ACSCatal.3,2719(2013).

[14]M.W.Penninger,C.H.K im,L.T.Thom pson,and W. F.Schneider,J.Phys.Chem.C 119,20488(2015).

[15]S.Khan,R.J.O ldm an,F.Cor`a,C.R.A.Catlow,S. A.French,and S.A.Axon,Phys.Chem.Chem.Phys. 8,5207(2006).

[16]Z.Z.Chen,C.H.K im,L.T.Thom pson,and W.F. Schneider,Surf.Sci.619,71(2014).

[17]S.G.Zhang,N.Han,and X.Y.Tan,RSC Adv.5,760 (2015).

[18]P.G.Radaelli and S.W.Cheong,Phys.Rev.B 66, 094408(2002).

[19]S.M.Zhou,L.F.He,S.Y.Zhao,Y.Q.Guo,J.Y. Zhao,and L.Shi,J.Phys.Chem.C 113,13522(2009).

[20]M.Risch,A.Grimaud,K.J.May,K.A.Stoerzinger, T.J.Chen,A.N.M ansour,and Y.Shao-Horn,J.Phys. Chem.C 117,8628(2013).

[21]S.M ukhopadhyay,M.W.Finnis,and N.M.Harrison, Phys.Rev.B 87,125132(2013).

[22]P.Ravindran,P.A.Korzhavyi,H.Fjellv?ag,and A. K jekshus,Phys.Rev.B 60,16423(1999).

[23]A.M ineshige,M.Inaba,T.Yao,Z.Ogum i,K.K ikuchi, and M.Kawase,J.Solid State Chem.121,423(1996).

[24]X.Liu,Z.Z.Chen,Y.W.Wen,R.Chen,and B.Shan, Catal.Sci.Technol.4,3687(2014).

[25]G.Thornton,B.C.Tofield,and A.W.Hewat,J.Solid State Chem.61,301(1986).

[26]K.Asai,P.Gehring,H.Chou,and G.Shirane,Phys. Rev.B 40,10982(1989).

[27]S.Yam aguchi,Y.Okim oto,and Y.Tokura,Phys.Rev. B 55,R8666(1997).

[28]I.A.Nekrasov,S.V.Streltsov,M.A.Korotin,and V. I.Anisim ov,Phys.Rev.B 68,235113(2003).

[29]D.P.Kozlenko,N.O.Golosova,Z.Jirk,L.S.Dubrovinsky,B.N.Savenko,M.G.Tucker,Y.Le Godec,and V. P.G lazkov,Phys.Rev.B 75,064422(2007).

[30]W.T.Hong,M.Gad re,Y.L.Lee,M.D.Biegalski,H. M.Christen,D.M organ,and Y.Shao-Horn,J.Phys. Chem.Lett.4,2493(2013).

[31]A.M.Ritzm ann,M.Pavone,A.B.M u?noz-Garc′?a,J. A.Keith,and E.A.Carter,J.Mater.Chem.A 2,8060 (2014).

[32]G.K resse and J.Hafner,Phys.Rev.B 47,558(1993).

[33]W.Kohn and L.J.Sham,Phys.Rev.140,A 1133 (1965).

[34]P.E.Bl¨och l,Phys.Rev.B 50,17953(1994).

[35]J.P.Perdew,K.Burke,and M.Ernzerhof,Phys.Rev. Lett.77,3865(1996).

[36]H.J.M onkhorst and J.D.Pack,Phys.Rev.B 13,5188 (1976).

[37]A.Chainani,M.M athew,and D.D.Sarma,Phys.Rev. B 46,9976(1992).

[38]V.I.Anisimov,J.Zaanen,and O.K.Andersen,Phys. Rev.B 44,943(1991).

[39]H.Hsu,K.Um em oto,M.Cococcioni,and R.Wentzcovitch,Phys.Rev.B 79,125124(2009).

[40]L.Wang,T.M axisch,and G.Ceder,Phys.Rev.B 73, 195107(2006).

[41]C.L.M a and J.Cang,Solid State Commun.150,1983 (2010).

[42]F.Bottin,F.Finocchi,and C.Noguera,Phys.Rev.B 68,035418(2003).

ceived on March 16,2017;Accepted on March 21,2017)

?Authors to whom correspondence shou ld be add ressed.E-m ail: zphu@nankai.edu.cn,xingang li@tju.edu.cn