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PredictingCoreLevelBindingEnergiesShifts:SuitabilityoftheProjectorAugmentedWaveApproachasImplementedinVASP

NoèliaPueyoBellafont,1FrancescViñes,1,*WolfgangHieringer,2,3andFrancescIllas1

Correspondenceto:FrancescViñes(E-mail:francesc.vines@ub.edu)

1NoèliaPueyoBellafont,FrancescViñes,FrancescIllasDepartamentdeCiènciadeMaterialsiQuímicaFísica&InstitutdeQuímicaTeòricaiComputacional(IQTCUB),UniversitatdeBarcelona,C/MartíiFranquès1,Barcelona,Spain,08028.2WolfgangHieringerLehrstuhlfürTheoretischeChemie,UniversitätErlangen-Nürnberg,Egerlandstraβe3,Erlangen,Germany,91058.3WolfgangHieringerInterdisciplinaryCenterforMolecularMaterials(ICMM),UniversitätErlangen-Nürnberg,Henkestraβe42,Erlangen,Germany,91054.

Introduction

X-ray photoelectrons spectroscopy (XPS) —a.k.a. electron spectroscopy for chemicalanalysis (ESCA)— is nowadays a widespreadtechnique used for material bulk elementalanalysis, especially in surface science studies,givenitsremarkablesurfacesensitivity.1Indeed,it is not only sensitive to a particular materialsurface termination, but to the atoms andmolecules adsorbed onto, which makes it awell-suited technique to detect surface

species,2 and even capable to discern

adsorption conformations.3,4 The detection ofemerged electrons over time allows to in situfollowagivensurfaceprocess,fromadsorptionand diffusion, to surface reactionsheterogeneously catalyzed by the substrate,enabling the characterization of reactants,intermediates, and products, and, ultimately,getting informationof the reactionmechanismandkinetics.2,5,6

The discrimination of one from anotherspecies (or conformations) links to particularatomic core level (CL) binding energies and,more importantly, core level binding energy

ABSTRACT

HereweassesstheaccuracyofvariousapproachesimplementedinVASPcodetoestimatecore-levelbindingenergyshifts(ΔBEs)usingprojectoraugmentedwave(PAW)methodtotreatcoreelectrons.Performance of Perdew-Burke-Ernzerhof (PBE) and Tao-Perdew-Staroverov-Scuseria (TPSS)exchange-correlationdensityfunctionalsareexaminedonadatasetof68moleculescontainingB→Fatoms indiversechemicalenvironments,accounting for185different1s core levelbindingenergyshifts, forwhich experimental gas-phaseX-ray photoemission (XPS) data and accurate all electronΔBEs as well are available. Four procedures to calculate core-level shifts are investigated. Janak-Slater transition state approach yieldsmean absolute errors of 0.37 (0.21) eV at PBE (TPSS) level,similar to highly accurate all electronΔSCF approaches using same functionals, and close to XPSexperimental accuracy of 0.1 eV. Study supports the use of these procedures to assign ΔBEs ofmolecular moieties on material surfaces of interest in surface science, nanotechnology, andheterogeneouscatalysis.

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shiftswith respect to a given reference,whichprovide information about different chemicalenvironments and/or oxidation states. Thedevelopment of high resolution XPS (HR-XPS)technique allows nowadays to distinguish corebindingenergyshifts(ΔBE)toaprecisionofupto~0.1eV.6However,thedefinitecorrelationofoneobservedXPSpeaktoagivenatomwithinamoleculeandtoitschemicalenvironmentisbyno means straightforward. Usual proceduresare based upon gas phasemolecular data,7 orwell-definedsurfacescienceexperimentsundervery controlled conditions.2,6 A more solid,unbiasedidentificationviaaccuratecalculationssimulating the electron ionization processwould be very attractive. Along this line wavefunction and density functional theory (DFT)basedmethodshaveprovenitssuitabilityusingthe so-called ΔSCF approach,8 in which thebinding energy (BE) for a given atom CL isgained by the difference in total energybetween the neutral system, and that with anholeintheCLoftheatomunderinspection.

The BEs values obtained through the ΔSCFapproach are obtained at the final state—i.e.the excited core electron is removed from thesystem under scrutiny and the electronicstructure modified according to the electronhole. Indeed, by considering the electronicscreening of the core state and relativisticeffects,onecanobtainBEestimateswellwithintheXPSexperimentalaccuracyof0.1eV,eitherbased on Hartree-Fock (HF) calculations, orusingmethodswithinDFT.9,10 Suchahigh levelof accuracy for isolated molecules would bedesirable when they are adsorbed to a solidsurface, inordertodistinguishamongdifferentmolecularadsorptionconformations,aswellasto monitor heterogeneously catalyzedprocesses.

Specifically, it ishighlydesirabletocorrectlymodel adatoms and adsorbed molecules ontransitionmetal (TM) surfaces, given that theyare ubiquitous in heterogeneous catalysis assupported activephases.Onehas also to keepin mind that these systems play a key role inother fields as well such as nanotechnologydevicesandchemicalresolutioncomponents.A

recent systematic study identified the Perdew-Burke-Ernzerhof (PBE)11 and the Tao-Perdew-Staroverov-Scuseria (TPSS)12 DFT exchange-correlation functionals as best compromisessuited to simultaneously describe both maingroup molecules and TM surfaces.13,14 One ofthe most extended ways of tackling ab initiostudies of TM surfaces is to take advantage ofperiodic boundary conditions,15 and, especiallyfor TM, to use pseudopotentials to describecore electrons or the projector augmentedwave (PAW) method,16 being highly accurateand in extensive use. This formalism can beregardedasaneffectiveallelectronmethod inwhichatomiccoresarefrozenasintheisolatedatom in its spin polarized ground state. In thecase one is interested in core level bindingenergies, the PAW description of the atomiccore with a generated core hole can beemployed.17 Several implementations of thePAW method exist in the literature withdifferent specificities. Here we focus in theimplementation of Kresse of Joubert18 in theVienna ab initio simulation package (VASP)code.19Thisisacodespeciallydesignedtostudyperiodic systems yet also suited to finitesystems provided they are embedded in aperiodic box sufficiently large to effectivelyisolatethecontainedspecies.20

However, periodic slab models, despiteallowingforareasonabledescriptionofsurfaceprocesses on TM surfaces, hamper a rigorousapplication of the ΔSCF approach. This isbecause of two different reasons; i) theresulting system with the core hole isperiodicallychargedandii)thecoreholeusetobe simulated with a pseudopotential ratherthan the full electronic description of coreelectrons. Despite of these difficulties, it hasbeen shown that final state (FS)CLBEs canbeestimated by generating a core excited ionicPAW in the course of the correspondingcalculation, as above commented.17 Theapproach neglects relaxation of core electronsupon ionization,yetvalenceelectronscreeningisexplicitlydescribed.Inthisapproach,toavoiddealing with a periodically repeated chargedsystem, the excited electron is added to the

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bottomoftheformerconductionband—orthelowestunoccupiedmolecularorbital (LUMO) inthe case of isolatedmolecules—, see Figure 1.Thesystemthusmaintains itschargeneutralitywithin the imposed periodic boundaryconditions (PBC). While this approach seemsappropriate to describe XPS with conductingprobes, for isolated molecules a naïveapplicationof the sameapproachwould resultin actually modeling a X-ray absorption nearedge structure (XANES) spectroscopy process.NoticethatwithintheVASP implementationofthe PAW method, absolute BEs are notaccessible given that only valenceenergies arecalculated. Other implementations existwhereabsolute BE can be obtained by adding up thefrozen core energies,21 although so far its usehas been limited. Because of the limitation inperformingproperΔSCFintheemployedcode,we here focus on core level binding energyshifts (ΔBE), alleged however to be ratheraccurate17andwidelyusedinpracticetoassignXPSsignaturestocertainsurfacespecies.3-5,22-24

The precision of this particular FS approachhasbeenestimatedtobeof0.02-0.05eVintestcalculations on selected systems.17 Subsequentstudies reported larger deviations,3-5,24 and, inpractice, different approaches are frequentlyconsidered, seeking for the best appliedapproach, as the accuracy issue remainedunclear. Other approaches include initial state(IS)approximations,whichconsidersthatKohn-Sham(KS)eigenstateenergies in theelectronicgroundstateasapproximations toBE—similarto Koopmans theorem in Hartree-Fock, astatement recently discussed unambiguouslyshowing that while Koopmans theorem doesnot hold for the KS eigenvalues, it properlyreflectsthetrendsinΔBEs.25Theproperwaytodefine IS BEs from DFT calculations has alsobeendescribedbysomeofus.26Analternativeapproach is provided by the model known asJanak-Slater (JS) transition state method,27which, in a nutshell, considers half occupationoftheCLwhenestimatingBEsratherthanafullcore-holeas intheFSapproach,seeFigure1.28Here,theorbitalenergiesareusedasestimates

for CL BEs and total energies are actuallydisregarded.

To address the accuracy of the theseprocedures above described, here we takeadvantageof the recentevaluationofPBEandTPSSperformanceonestimatingΔSCFBEs andΔBEs for 1s CL for a large data set of 68molecules containing a wide variety offunctional groups for first row main groupelements B→F, considering up to 185 corelevels, for which accurate gas phaseexperimental BEs are known, see Table S1 insupplementaryinformation(SI).9,29-32Onlythesefunctionals have been assessed, since theultimate goal is to employ them to assign XPSfeaturesofatomsand/ormoleculesindifferentpositions and/or conformations on TMsupports. The ΔSCF calculations for this largeset of molecules have been previously carriedout using a full all electron description and anear Hartree-Fock limit basis set, obtainedwithinspinrestrictedopen-shell formalismsforbothHFandKSmethods.9

Figure 1. Sketch of initial state (IS), final state(FS), and Janak-Slater (JS) situations, aswell asFSn and JSn approaches where excited (half)electron is removed from the system, andconceptuallyplacedinvacuum,ν.

ComputationalDetails

In the present calculations data set moleculeswere isolated in an asymmetric box with PBCensuring a minimum vacuum distance in anydirectionof10Å.CalculationswerecarriedoutattheΓ-pointandusingacut-offkineticenergylimit of 415 for the plane-wave basis set. ThePAWapproachwasusedto treatcoreelectronsand PAW core orbital energies were used todeduce theBE shifts in all cases. An electronic

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convergence0.01eVÅ-1wereused,togethertoa 1st order Methfessel-Paxton smearing of 0.1eV width. Calculations were performed in aspin-polarizedandanonspin-polarizedfashion,although criterion of 10-6 eV and an ionicconvergenceforcecriterionofspin-polarizationeffect on BEs was found to be essentiallynegligible,andsofortheΔBEs.

Note that spin polarization is a necessity toproperlyestimateabsoluteBEs,eitherusingHFor KS formalisms. Indeed, its neglecting bycarrying out spin restricted HF or KS in whichthecoreholeisevenlydistributedamongαandβ spin-orbitals, yieldsdeviationsof coreorbitalenergiesofupto~10eV,21anerrorremediatedby carrying out calculations either spinunrestrictedoropen-shell.Despiteofthis,evenif BE values obtained from ΔSCF calculationsmay be affected by spin polarization effects,there is evidence that the effects on the ΔBEsare negligible.33 Consequently, only non spin-polarizedvaluesarediscussed in the following.AllcalculationshavebeencarriedoutusingtheVASPprogram.19

TheIS,FS,andJSBEsandthecorrespondingshifts, ΔBE, with respect to a reference havebeen obtained following the previouslyprescribed methodology, with the followingmodifications: i)BEsarereferredtotheenergyofanelectron invacuum(insteadof theFermienergy, EF).24 Vacuum energy level is obtainedin each computed case as the constant valueelectrostatic potential energy distant from themolecule. Note that this vacuum leveling hasbeen carried out independently for eachmolecule, studied 1s level, and approximation(IS,JS,orFSbased).Next, ii)forcasesinvolvinghighly-symmetry related cores different PAWtypeswereused for theseequivalentatoms toavoid delocalized electronic situations. In suchcases the PAW used for the atom underevaluationwaskeptasthestandardinuse,butthe PAW of the other atom(s) related bysymmetryreplacedbythePAW_hreferences.18Finally iii) for FS and JS, instead of the usualaddition of the excited electron —or halfelectron in the JScase—to theLUMO,amorephysically sound situation has been

contemplated, in which the excited (half)electronisremovedfromthesystem,hereafternamed FSn and JSnmethods, see Figure 1. Theresultingcharge iscompensatedinsidethePBCbox with an underlying counterchargebackgrounddistributedwithin thebox. The JSnapproach thus closely corresponds to Janak-Slater transition state approaches withinperiodic boundary conditions. Furthermore, bycomparison, this approach allows estimatingtheartificial screeningeffectof (half)electronsin the LUMO in the FS and JS approaches. Thepossible effect on ΔBEs of the box-dilutedcounterchargehasbeenevaluatedbydoublingthe cell dimensions, i.e. minimizing thebackground countercharge density, withnegligiblevariations—~0.03eV.Results

The BEs obtained using the JS, FS, JSn, and FSnprotocols on PBE and TPSS density functionalsare listed in Table S1 in SI, whereas thoseobtained at IS are listed in Table S2. The ΔSCFapproach using PAW DFT total energy values(not shown) give very discrepant results withrespect to experiments, since, as commented,only valence electron density energy is usedwhencoreelectronsaredescribedbythePAWpseudopotentials. However, IS BE values (i.e.,ground-state core orbital energies), despitebeingheavilyandunphysicallyunderestimated,capturetheexperimentalBEtrends(seeFigureS1 in SI), as expected from previous works.25Theshiftwithrespecttoexperiment,estimatedaccording to mean error (ME) and meanabsolute error (MAE), shown in Table S3 in SI,backs up an arbitrary shifting proceduresometimesusedwhenattemptingatcomparingthese calculated values with experimentalmeasurements.17

The underestimation of absolute bindingenergies by the ground-state core orbitalenergies in the IS approach —implying anegative relaxation energy in response to thepresence of the core hole— flips tooverestimation when applying any of the finalstate approaches —FS, JS, FSn, or JSn—, as is

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exemplifiedforC1sinFigureS2ofSI.Itisworthtohighlightthatoverall i)PBEvaluesarecloserto experimental ones thanTPSS and that ii) FSand JS values aremuch closer to experimentalvaluesthantheFSnandJSncounterparts,yetiii)the trend is better captured using FSn and JSnapproaches,and iv) JSandJSnvaluesaremuchclosertoexperimentalvaluesthanFSanFSn.AsinIS,MAE,seeTableS4,indicatesthepresenceof a systematic deviation which allows forshifting BE values to align them with theexperimentalones.

The not so unexpected inaccuracy ofabsoluteBEs,whichcanbe,inthebestcases,ofuptofeweV,cancelshoweverwhenestimatingcorelevelbindingenergyshifts.Toillustratethispoint, ΔBEs were separately gained for maingroup elements B→F with respect to a givensimple reference molecule: diborane (B2H6),methane (CH4), ammonia (NH3), water (H2O),and fluoromethane (CH3F) for B→F,respectively.A comparisonof theperformanceforFS,JS,FSn,andJSnincalculatingΔBEsversusexperimentalvaluesisprovidedinFigure2.

Figure 2. Calculated PBE and TPSS ΔBEs,ΔBE(Calc.) versus experimental values,ΔBE(Exp.), for a) FS, b) JS, c) FSn, and d) JSnmethods.AllvaluesaregivenineV.

Note,forinstance,howFSvaluestendtobeunderestimated at both PBE and TPSS levels,with PBE values slightly closer to experimental

values, althoughwith a clearwider dispersion.WhenapplyingtheJSapproach,valueswalktheline, and so the MAE decreases, see Table 1,althoughtheslightlybetterperformanceofPBEversus TPSS remains, though theunderestimationseemstovanish.However,theMAEvaluesforPBEandTPSSwithintheFSandJS approaches are 0.9 eV and 1.0 eV,respectively,andso,oflittleusewhentryingtodistinguish species/conformations within theaforementioned experimental precision of 0.1eV.

The situation is greatly improved whenremoving the excited (half) electron from thesystem, e.g. when carrying out FSn and JSnapproximations. The removal of the ejectedelectron clearly lines upΔBEs estimates eitheratfullcore-hole(FSn)orwithintheJanak-Slater(JSn) approximation. However, deviations arestillnoticeableintheFSncase,especiallyatPBElevel,withanunderestimationof-1.4eV,whichdrops to0.85eVatTPSS level.Noticehowtheartificial valence (half) electron screening byPAWCLestimationincreasederrorsby0.19and0.80eVatPBEandTPSSlevels,respectively,asobservedbycomparingFSandFSnvalues.

Table 1. Summary of the ΔBE(Calc.) statistical analysis for all the core level studied at PBE and TPSS performance. All values are given in eV.

PBE

FS JS FSn JSn ME -1.03 -0.28 -1.40 -0.21 MAE 1.62 0.90 1.43 0.37 TPSS FS JS FSn JSn ME -1.21 -0.42 -0.85 0.02 MAE 1.73 1.01 0.93 0.21

However the most important result is that

thehalfexcitedelectronremovalinJSnnotonlylines up estimates, but also deviations. As aresult, no clear underestimation can bediscerned,and,moreover,MAEvaluesdiminishto0.37and0.21eVforPBEandTPSSJSnlevels.As found for FSn, the half excited electronscreening was responsible of an averageincreaseoferrorsinΔBEsof0.53and0.8eVfor

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PBE and TPSS, respectively. More importantly,theΔBEs MAE at PBE and TPSS levels of 0.37and 0.21 eV are of the same accuracy ofcorresponding relativistic ΔSCF calculations of0.24 and 0.25 eV as obtained in an earlierwork.9Hence, for gasphasemolecules, the JSnmethod in combination with a PAW coredescription is capable to reach the same highdegree of accuracy for ΔBEs than all electronΔSCF using a fully uncontracted near Hartree-Fock limit basis set.9 Note that forthermochemistryofgasphasemoleculeshybridfunctionals, such as Becke-Lee-Yang-Parr(B3LYP), are slightly better than PBE or TPSS,with a MAE of 0.16 eV, as obtained fromrelativistic ΔSCF calculations on a subset ofdata,10 although its use is not advised fortreating TM systems, as the proper metallicbond delocalization is hindered when usinghybrids.14Lastbutnotleast,onehastokeepinmind that small, yet frequent,experimentalBEshifts which fall within the PBE and TPSS JSnaccuracies cannot be correctly backed up bysuch calculations, and improved accuracymethods should be used, as the abovecommented. Inanycase,TPSSseemstobethebestcompromiseandbettersuitedwhentryingto link experimental ΔBEs to ab initioestimations, both reaching a similar degree ofprecision. Note that the superior performanceof the JSn method (used with an PAW coredescription and periodic boundary conditionshere) may not be surprising based on itsanalogy to the original Slater transition statetheory.28

Conclusions

Inconclusion,weaddressedtheaccuracyoffullcore-hole (FS) and Janak-Slater (JS) approachesasimplementedinVASPinpredictingcorelevelbinding energies and, more specifically, corelevel binding energy shifts from core orbitalenergiesusingaPAWdescriptionoftheatomiccores,andunderperiodicboundaryconditions,on abroaddataset of 68molecules containingfirst row atoms (B→F) in a great diversity ofchemical environments, accounting for a total

number of 185 different 1s CLs. In addition tocurrentprocedureswecontemplatedremovingthe excited (half) electron from the molecularLUMOintheherecalledFSnandJSnapproaches.As expected, the PAW total BE estimatespredicted by the VASP code do not match CLBEs since core electron energies are notexplicitly accounted for. However, computedΔBEs estimates, i.e. relative BE shifts, line upwell with experimental trends. For PBE andTPSS exchange-correlation functionals ΔBEestimates using JSn approach yield meanabsolute errors of only 0.37 and 0.21 eV, andare thus of similar size to all electron ΔSCFcalculationswith saturatedbasis sets,9 therebyapproaching the experimental accuracy of HR-XPSof0.1eV.TheaccuracyoftheJSnapproachis useful not only for molecules, but alsopromises itsuse inassigningΔBEsofmolecularmoietiesonmaterialsurfaces,withconcomitantapplicationsinsurfacescience,nanotechnology,and heterogeneous catalysis, although itsaccuracy in such systems remains to beconfirmed.

Acknowledgments

This work has been supported by SpanishMINECO/FEDERCTQ2015-64618-Rgrantand,inpart, by Generalitat de Catalunya grants2014SGR97 and XRQTC, and by the NOMADCenter of Excellence project, which receivedfunding from the European Union’s Horizon2020 research and innovation programmeundergrantagreementNo676580.F.V. thanksMINECOforapostdoctoralRamónyCajal(RyC)research contract (RYC-2012-10129). F.I.acknowledgesadditionalsupportfromthe2015ICREA Academia Award for Excellence inUniversity Research. W.H. gratefullyacknowledges support from the DeutscheForschungsgemeinschaft through the “Clusterof Excellence – Engineering of AdvancedMaterials”locatedinErlangen,Germany.

Keywords:XPS·Corelevelbindingenergyshifts·PAW·DFT·Moleculardataset

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Additional Supplementary Information (SI) canbe found in the online version of the article:Molecular list with BE estimates at both PBEandTPSSunderFS,JS,FSn,andJSnapproachesisgiveninTableS1.TheISandcoreorbitalenergyestimates are listed in Table S2. A statisticalanalysis of BEs is shown in Tables S3 and S4.Element decomposed IS trends are shown inFigureS1,whereasFS,JS,FSn,andJSnBEtrendsforC1scasesareshowninFigureS2.

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GRAPHICALABSTRACT

NoèliaPueyoBellafont,FrancescViñes,WolfgangHieringer,andFrancescIllas

PredictingCoreLevelBindingEnergiesShifts:SuitabilityofProjectorAugmentedWaveApproachasImplementedinVASP

HereweassesstheaccuracyofvariousapproachesimplementedinVASPtoestimatecore-levelbinding-energyshifts(ΔBEs)usingprojector-augmented-wavemethodtotreatcoreelectrons.Differentexchange-correlationfunctionalswithindensityfunctionaltheoryaretestedona68moleculesdatasetaccounting185different1s(ΔBEs)forwhichexperimentaldataisavailable.Janak-SlatertransitionstateapproachyieldsanaccuracysimilartoallelectronΔSCFcalculations,andclosetoX-rayphotoemissionaccuracyof0.1eV.