— —< <

Importance of Madelung Potential inQuantum Chemical Modeling of IonicSurfaces

GIANFRANCO PACCHIONI,1* ANNA MARIA FERRARI,1´ 2 3ANTONIO M. MARQUEZ, and FRANCESC ILLAS

1Dipartimento di Chimica Inorganica, Metallorganica e Analitica, Universita di Milano, via Venezian`21, 20133 Milano, Italy; 2Departamento de Quimica Fisica, Facultad de Quimica, Universidad deSevilla, 41012 Sevilla, Spain; and 3Departament de Quimica Fisica, Universitat de Barcelona, CrMartii Franques 1, 08028 Barcelona, Spain

Received 21 January 1996; accepted 13 July 1996

ABSTRACT

The importance of the inclusion of the Madelung potential in cluster models ofionic surfaces is the subject of this work. We have determined Hartree]Fock allelectron wave functions for a series of MgO clusters with and without a large

Ž .array of surrounding point charges PC chosen to reproduce the Madelungpotential. The phenomena investigated include: the reactivity of surface oxygenstoward CO , atomic hydrogen, and Hq; the geometry and adsorption energy of2water and the vibrational shift of CO adsorbed at Mg2q sites; the electronicstructure and the hyperfine coupling constants of oxygen vacancies, theparamagnetic Fq centers. While some clusters give results which are virtuallysindependent of the presence of the PCs, other clusters, typically of small size,give physically incorrect results when the PCs are not included. The embeddingof the cluster in PCs guarantees a similar response for clusters of different size,at variance with the bare clusters, where the long range coulombic interactionsare not included. Q 1997 by John Wiley & Sons, Inc.

Introduction

n the past 5 years, a large and constantly in-I creasing number of quantum chemical studiesof ionic materials and, in particular of ionic oxides,has been reported.1] 46 The reason is the consider-

* Author to whom all correspondence should be addressed.

able interest in the theoretical description and inthe computer simulation of the electronic proper-ties of oxides and of their chemical behavior whichis relevant in chemistry, solid state physics, andmaterial science. Most of these studies have beenperformed using the cluster model approach4 inwhich the infinite oxide crystal is represented by

Ž . 5 ] 38just a few atoms or ions . This is the sameapproach largely employed to study adsorption on

( )Journal of Computational Chemistry, Vol. 18, No. 5, 617]628 1997Q 1997 by John Wiley & Sons CCC 0192-8651 / 97 / 050617-12

PACCHIONI ET AL.

metals, and is alternative to the more rigorous, butcomputationally less flexible, band structure ap-proach in which the periodic nature of the surfaceis explicitly taken into account.39 ] 49 Usually, clus-ter models of oxide surfaces consist of a smallnumber of ions surrounded by a large array ofpoint charges, PCs, determined in such a way toreproduce the Madelung potential in thechemisorption region.5 ] 29 The Ewald technique hasbeen used widely in this context.2 Recently, clusterstudies in which the exact Madelung potential hasbeen included in the Hamiltonian50 or where thecorrect embedding in the host crystal is taken intoaccount51 ] 53 have also been reported. However, itis not uncommon to see cluster studies of oxidesurfaces in which the long range coulombic inter-actions are totally neglected. In these studies, thecluster model consists only of a set of atoms with-out any representation of the Madelung potentialof the extended crystal. It is well known that theMadelung potential is a very slowly convergentseries, so that the use of truncated clusters withouta PC embedding may result in anomalous valuesof the Madelung field. Nevertheless, there isenough empirical evidence that clusters withoutany PC embedding give results consistent with thechemical intuition and which are not too differentfrom those obtained with a PC representation ofthe Madelung potential.30 ] 38

In this article, we present for the first time asystematic study of the results given by cluster

Ž .models of an ionic oxide surface, MgO 100 , withand without embedding in PCs. The problemsconsidered involve surface electronic structure,surface reactivity, vibrations of the adsorbedspecies, etc. We will show that, in general, theinclusion of the long range coulombic interactionsguarantees more stable results as a function of thecluster size, but that it is not uncommon thatclusters with and without PCs give similar results.We will also attempt a rationalization of this be-havior in terms of intrinsic ionic nature of theMgO clusters and of convergence of the Madelungpotential versus cluster size.

Computational Details

We have performed all electron Hartree]FockŽ .HF calculations on various Mg O cluster mod-n nels of the MgO surface. Some clusters are centeredaround an oxygen atom when the interaction oc-curs at this site, and we denote these clusters as

O Mg ; when the interaction occurs at a surfacen nŽ .cation the cluster is of the type Mg O Fig. 1 . Then n

clusters used are stoichiometric and include thesame number of Mg and O atoms. The Madelungpotential has been taken into account by embed-ding the clusters in a large array of PCs of nominalvalues of q2 or y2. This is consistent with thelargely ionic nature of bulk and surface MgO.16,28

Ž .For the surface models, a 13 = 13 = 4 array ofPCs has been chosen to simulate the Madelungpotential at the adsorption site.9 The presence ofthese charges around the cluster induces an artifi-cial polarization of the oxygen atoms at the clusterperiphery. Techniques have been developed to re-move this artifact;25, 27, 54 they are based on the use

Ž .of effective core potentials ECP to represent thefinite size of the ions. We have used this techniquein one case to compare the behavior of a MgOcluster with and without PCs and with PCs andECPs.

The reactivity of CO with surface, five-coordi-2Ž . Ž .nated O and step, four-coordinated O oxide5c 4 c

( ) 2yFIGURE 1. a O Mg cluster model of an O site of9 9( )the MgO 100 surface. Interchange of the first with the

second layer gives the Mg O cluster used to model a9 9Mg2q site. A O Mg cluster can be obtained by cutting5 5

( )the eight corners of the O Mg cluster. b O Mg cluster9 9 6 6( )model of an edge site of the MgO 100 surface. Clusters

with and without embedding in point charges have beenused.

VOL. 18, NO. 5618

MADELUNG POTENTIAL

anions has been modeled by means of O Mg ,9 9Ž . Ž . Ž .O Mg surface and O Mg step clusters Fig. 1 .5 5 6 6

The central Mg2q ion in Mg O and the fiven n

nearest-neighbor Mg2q ions to the central oxygenin O Mg clusters have been treated with an nw x 913s8 pr6 s3 p basis, which includes a good repre-sentation of the Mg 3s and 3 p orbitals; the other

2q w xMg ions have been treated with a 12 s7pr5s2 pbasis.9 In O Mg , the four Mg2q ions in the sec-9 9

w xond layer were treated with a 8 s4 pr2 s1 p SZbasis set.55 For the oxygen atoms of MgO we used

w x 55a 8 s4 pr4 s2 p DZ basis. For CO we used a2standard DZP basis set.56 To better identify thedifferent contributions to the interaction energy forclusters with and without PCs we have performed

Ž . 57,58a constrained space orbital variation CSOV .This technique allows one to measure the relativeimportance of polarization and charge transfer ef-fects in the bonding of an adsorbate to a surface.Details about this technique and its application tooxide surfaces can be found in refs. 7, 9, 16, and 22.We have also considered the interaction of a neu-tral H atom and a Hq proton with the surfaceoxygen of O Mg . The basis set for H is of DZP9 9quality;55 therefore, this basis is of higher qualitythan the DZ basis used for the MgO clusters, butwe do not expect any significant imbalance in thedescription of the interaction.

As an example of adsorption of a molecule witha permanent dipole moment we chose water inter-acting with surface cations of MgO. Two clustermodels of a surface Mg2q site have been consid-ered, Mg O and Mg O , with and without PCs.5 5 9 9Adsorption of CO on surface, five-coordinatedMg and on step, four-coordinated Mg sites has5c 4 c

Ž .been studied by means of Mg O surface , Mg O ,5 5 6 6Ž . Ž .and Mg O step clusters Fig. 2 . In this case we10 10

have also performed a full vibrational analysis todetermine the CO v by means of finite differencese

of analytical first derivatives. The Mg and O basisset is the same as that described previously,

w xwhereas for C and O a 9s5pr4 s3 p basis has beenused59 as in previous studies on this system.7,9,10

Finally, we have considered the electronic struc-ture of Fq color centers on the MgO surface. Theses

defects formally correspond to the removal of anOy ion. Therefore, an Fq center is paramagnetics

and the localization of the unpaired electron canŽ .be determined by electron spin resonance ESR

60 w xqexperiments. We have considered O Mg ,8 9w xq w xq qO Mg , and O Mg models of F cen-12 13 20 21 s

ters. The same clusters have been used recently fora study of the electronic properties of F centerss

FIGURE 2. The Mg O cluster model of a Mg2q10 10

Ž .cation at an edge site of the MgO 100 surface. Asmaller cluster, Mg O , has been used to model6 6adsorption at the same site. This second cluster has beenobtained from Mg O by removing the outer eight10 10ions.

and the reader is referred to ref. 61 for detailsabout the basis sets used. Determination of hyper-fine coupling constants has been done by perform-

² 2:ing unrestricted HF calculations; the value of Ss 0.75 guarantees that the eigenfunction corre-sponds to a pure doublet state. The calculationshave been performed with the HONDO-8.5 pro-gram package62 on IBM Risc 6000 workstations.

Results and Discussion

ADSORPTION AND REACTIVITY

CO on O2y Sites2

A previous study has shown that an O site of5cMgO is very unreactive and that CO does not2

Ž .form a stable surface carbonate at the 100 terracesof the MgO surface.15 Here we have performednew calculations and we have determined a sec-tion of the potential energy surface by optimizingthe CO structure for various fixed O CO2 5c 2distances. We have considered three models: abare O Mg cluster; the same cluster embedded inn n

Ž .PCs, and in PCs and ECPs n s 5, 9 . The potentialŽ .energy curves for CO on O Mg Fig. 3 are2 9 9

purely repulsive and similar with and withoutPCs; this seems to indicate a minor effect of thesurrounding PCs on the mechanism of interaction.Both curves show a nonmonotone behavior whicharises from the energetic balance between the priceneeded to bend CO and the energy gain due to2the formation of the surface carbonate.22 At a dis-tance of 2.8 bohr from the surface, the geometricalparameters of adsorbed CO are virtually indistin-2

˚Ž . Ž .guishable: r C O is 1.202 A and a OCO is 1388Ž .for the case with PCs, whereas r C O s 1.205

JOURNAL OF COMPUTATIONAL CHEMISTRY 619

PACCHIONI ET AL.

˚ Ž .A and a OCO s 1378 without. The similar geom-etry reflects a similar interaction. This is confirmedby the results of the CSOV analysis. The termscontributing to the final interaction energy are

Ž .similar with and without PCs Table I . This isparticularly significant for the donation and back-donation contributions, but also for the initialFrozen orbital term which accounts for the Paulirepulsion and the electrostatic attraction between

Ž .the interacting units Table I . On the other hand, asmaller cluster, O Mg , gives completely different5 5results with and without PCs. The potential energycurve computed with PCs is very similar to thoseobtained for O Mg and shows the same repulsive9 9

Ž .behavior Fig. 3 . When CO is adsorbed on bare2O Mg , however, the curve exhibits a deep mini-5 5mum separated from the dissociation limit by anactivation barrier. In this minimum, CO is still2unbound with respect to dissociation into neutral

Ž .fragments, but by 0.2 eV only Fig. 3 . The CSOVŽ .analysis Table I shows that the different behavior

of O Mg and O Mg q PCs must be ascribed to5 5 5 5the different initial repulsion and to the largercharge transfer from MgO to CO occurring when2

the PCs are not included. This is because thesurface O2y ion, unstable in the gas phase, isstabilized by the Madelung potential which, on asmall cluster like O Mg , can be very different5 5from that of the real surface; the consequence is aless stable and more reactive oxide.22

This is what happens at MgO step sites. Afour-coordinated oxygen is much more reactivethan a five-coordinated one because the Madelungpotential at these sites is lower than on the regularsurface sites.15 CO forms a stable surface carbon-2ate at the low-coordinated defect sites of the sur-face without energy barrier.15 The step site of MgOhas been represented by a O Mg cluster. The6 6geometry optimization with O Mg and O Mg q6 6 6 6PCs results in not too different geometries but in

Ž .quite different adsorption energies Table II . Inparticular, in the absence of external PCs the inter-

Ž .action is stronger, 2.4 eV versus 1.1 eV Table II ,and the CO molecule is slightly more activated,2as shown by a smaller OCO angle and by a longerŽ . Ž . Ž .r CO Table II . The CSOV analysis Table I helps

to understand the origin of the different reactivity.In particular, it shows that the larger stability of

FIGURE 3. Potential energy curves for the interaction of CO with a surface O2y site of MgO. Left: O Mg ; right:2 5 5O Mg . For each surface—CO distance the internal geometrical parameters of adsorbed CO have been reoptimized.9 9 2 2PC: the cluster is surrounded by a large array of point charges; no PC: the cluster is not surrounded by point charges;ECP: the cluster is surrounded by a large array of point charges and the nearest-neighbor Mg2+ ions to the cluster

( ) aoxygens are described by an effective core potential ECP . Two cases are reported for O Mg : ECP , each O ion is9 9( ) b (completely surrounded by ECPs 16 in total ; ECP : only the O ions in the first layer are surrounded by ECPs 8 in

)total .

VOL. 18, NO. 5620

MADELUNG POTENTIAL

TABLE I.( ) ( )CSOV Analysis for CO Adsorbed on O Mg and O Mg Surface and O Mg Edge Cluster Models2 9 9 5 5 6 6

a( )of the MgO Surface—Clusters with and without Point Charges PCs Have Been Considered.

O Mg —CO O Mg —CO O Mg —CO9 9 2 5 5 2 6 6 2

PCs No PCs PCs No PCs PCs No PCs

Cluster DE Dm DE Dm DE Dm DE Dm DE Dm DE Dm

Frozen orbital y7.20 — y7.20 — y6.58 — y8.32 — y5.41 — y5.27 —MgO polarization q0.79 y0.11 q0.84 y0.08 q0.61 y0.16 q0.01 y0.11 q0.87 y0.14 q1.06 y0.18MgO donation q4.77 y1.11 q4.96 y1.02 q4.88 y1.25 q5.48 y1.52 q5.10 y0.85 q5.54 y1.23CO polarization q1.27 q0.03 q1.33 y0.01 q1.23 q0.02 q1.66 y0.03 q1.75 q0.10 q2.04 y0.012CO donation q0.29 q0.09 q0.30 q0.07 q0.24 q0.10 q0.38 q0.11 q0.25 q0.16 q0.29 q0.062

aEnergy change, DE, in eV; dipole moment change, Dm, in a.u.

the cluster without PCs is primarily due to thelarger donation of charge from the surface to CO ,2in analogy with the O Mg case. This is shown not5 5only by the energy gain at the donation step, butalso by the large change in the dipole moment,which indicates substantial flow of charge fromthe oxide anion to the adsorbate. This means thatthe electrons are less bound to the oxide anion andmore easily transferred to an interacting molecule.Again, the role of the Madelung potential is essen-tial. The underestimation of this term leads to a‘‘too reactive’’ oxide, as already shown for the caseof O Mg .5 5

We consider now the effect of using ECPs torepresent the finite size of the ions instead of PCs.We used ECPs63 to represent the next shell ofMg2q ions at the cluster border. This is an ap-proach to the more elaborate ab initio model poten-tial of Barandiaran and Seijo.64 In O Mg this5 5means that the 12q2 PCs nearest neighbors to theO2y ions have been replaced by ECPs; in the firstlayer, the central O2y ion is surrounded by realMg2q cations. In O Mg , eight additional oxygens9 9

Ž .are present Fig. 1 and 16 ECPs have been used torepresent the nearest-neighbor Mg2q ions to theperipheral oxygens. In these models, each O ion isthus completely surrounded by either real Mg ionsor ECPs. To show how the use of ECPs reduces theartificial polarization of the O ions by the PCs, weconsider also a cluster in which only the surfaceoxygens are embedded in 8 ECPs, whereas thesecond layer oxygens are surrounded by PCs. Theresults for CO adsorption are graphically repre-2sented in Figure 3. On O Mg the effect of the5 5ECPs is rather small and the curves obtained withPCs or with PCs and ECPs are similar. This is notthe case of O Mg , in which the curve obtained9 9with the 16 ECPs is considerably different and, in

particular, is less repulsive, than with PCs. Thereason for the different response of the two clus-ters is that, in the first case, O Mg , there are no O5 5

ions at the cluster border in the first layer but onlyin the second; the addition of the ECPs changes thepolarization of these second layer oxygens butdoes not affect in a marked way the reactivity ofthe central surface oxygen. In O Mg , on the other9 9

hand, there are four surface O ions at the clusterborder which are artificially polarized by theneighboring charges, an artifact removed by theECPs. This polarization is large enough to changethe electrostatic potential and the charge densityaround the central oxygen, leading to a differentreactivity. The polarization of the second-layeroxygens, however, is nonnegligible. This is shownby the model in which only 8 ECPs in the clusterfirst layer have been included. The corresponding

Ž b .curve see ECP in Fig. 3 is between that ofO Mg q PCs and O Mg q PCs q 16 ECP. These9 9 9 9

results show the importance of removing the artifi-cial polarization of the border oxygens induced bythe PCs. The use of ECPs is an efficient way toeliminate or reduce this problem. It should benoted that the use of ECPs to replace the y2charges is much less important. In fact, the polariz-ability of the Mg2q cations is extremely low, anddoes not change appreciably when the neighboringions are described by simple y2 PCs or by PCsand ECPs.

It is possible to conclude that O Mg is proba-9 9

bly the smallest cluster that can be used to modeladsorption on an oxide anion of MgO. This is alsodue to the fact that the cluster is built of two layerswhich are almost neutral, at variance with theO Mg cluster in which each layer contains four5 5

Ž .cations and one anion or vice versa .

JOURNAL OF COMPUTATIONAL CHEMISTRY 621

PACCHIONI ET AL.

TABLE II.Equilibrium Properties of CO , H O, and CO2 2

2I 2 HAdsorbed on O or Mg Ions of MgO Surface.

System and properties PCs No PCs

( )O Mg —CO edge site6 6 2

˚( ) ( )z O—CO A 1.41 1.37e 2

˚( ) ( )r C—O A 1.22 1.24e( ) ( )a OCO degrees 137 134

( )D eV 1.13 2.42e

( )Mg O —H O surface5 5 2

˚( ) ( )z Mg—OH A 2.14 2.10e 2

˚( ) ( )r O—H A 0.94 0.94e( ) ( )a HOH degrees 110 112

( )D eV 0.64 4.12e

( )Mg O —H O surface9 9 2

˚( ) ( )z Mg—OH A 2.17 2.25e 2

˚( ) ( )r O—H A 0.94 0.94e( ) ( )a HOH degrees 110 110

( )D eV 0.62 0.26e

( )Mg O —CO surface5 5

˚( ) ( )z Mg—CO A 2.48 unbounde2q a ˚( ) ( )Dz Mg A 0.05 y0.33

( )D eV 0.24 unbounde

( )Mg O —CO edge6 6

˚( ) ( )z Mg—CO A 2.41 2.45e2q ˚( ) ( )D z Mg A 0.03 0.02

b y1( ) ( )Dv C—O cm 40 20e( )D eV 0.38 0.33e

( )Mg O —CO edge10 10

˚( ) ( )z Mg—C A 2.45 2.45e2q ˚( ) ( )D z Mg A 0.03 y0.02

b y1( ) ( )Dv C—O cm 48 31e( )D eV 0.34 0.30e

a 2q (Vertical relaxation of the surface Mg ions surface rum-)pling .

b ( ) y1Experimental Dv C—O = 21 cm ; ref. 67.e

H and HH on O2I Sites

We have seen that the O Mg cluster shows9 9virtually the same reactivity toward CO indepen-2dently of the inclusion of the Madelung potential.To confirm this result we have considered theinteraction of this cluster with a neutral H atomand with a proton. The potential energy curve forthe interaction with neutral H is repulsive, andfurther shows the very low reactivity of a surfaceoxygen of MgO when the Madelung term is prop-

erly described. The two curves for O Mg and9 9Ž .O Mg q PCs are very similar Fig. 4 . Conditions9 9

Žare different for the interaction with a proton Fig..5 . Here there is a strong and attractive electro-

static interaction. The interaction energy can bedivided into the sum of three contributions: theinteraction of a q1 charge with the surface electro-static potential; the polarization of the surface inresponse to the presence of the charge; and thecharge transfer from the surface oxygen to the

Ž .empty orbitals of the proton Table III . Thesecontributions can be distinguished by computing acluster with a q1 PC and a cluster with a real Hq

ion. The interaction energy curve for Hq on O Mg9 9Ž .is much deeper than for O Mg q PCs Fig. 5 .9 9

This is because the electrostatic potential in thetwo cases is different65; in particular, without PCs,the EP is smaller. The other two terms, the clusterpolarization and the charge transfer, are almost

Ž .identical with and without PCs Table III . Wehave repeated the calculation with O Mg and5 5O Mg q PCs and we found a reversed behavior:5 5the interaction of the proton is stronger for the casewith PCs. The reason is primarily the differentvalue of the electrostatic potential in O Mg and9 9O Mg , although there are also differences in the5 5

Ž .cluster polarization see Table III . In the absenceof surrounding PCs, the electrostatic potential os-cillates strongly as a function of the number of

Žcations or anions on the cluster surface or, in

FIGURE 4. Potential energy curve for the interaction ofa neutral H atom with a surface O2y site of O Mg .9 9

VOL. 18, NO. 5622

MADELUNG POTENTIAL

FIGURE 5. Potential energy curve for the interaction ofa proton with a surface O2y site of O Mg .9 9

. 65other words, of the cluster size . Therefore, animportant conclusion is that even when the use ofclusters without representation of the long rangecoulombic potential is acceptable for the adsorp-tion of neutral molecules, these models should beused with great care to study the interaction ofcharged species or in general for cases in whichelectrostatic effects play a dominant role.

H O on Mg2H Sites2

We have studied the nondissociative adsorptionof water as an example of interaction of the MgOsurface with a molecule with permanent dipolemoment. We have considered the perpendicularapproach of the molecule on top of a Mg2q cation.Recent studies have shown that there are several

possible adsorption modes for this molecule,47,48

but our purpose is to compare clusters of differentsize with and without PC embedding. The clustersconsidered are Mg O and Mg O . The substrate5 5 9 9atoms have been kept fixed and a full geometryoptimization has been performed for the adsorbed

Ž .H O molecule Table II . The geometry of the2adsorbate is practically independent of the clustermodel used; the largest variations occur for the

˚Mg OH distance which goes from 2.10 A on2˚Mg O to 2.25 A on Mg O ; the clusters with PCs5 5 9 9

˚ Ž .are 2.14 and 2.17 A, respectively Table II . Theinternal H O geometrical parameters are virtually2the same for all models considered. Conditions arequite different when one considers adsorption en-ergy. The two clusters embedded in PCs give thesame adsorption energy, f 0.6 eV; on bare Mg O ,9 9

Ž .the D is reduced to 0.26 eV Table II . On bareeMg O , however, the computed D is 4.1 eV! This5 5 eis a strong deviation from the other results, whichis indicative of a completely different electrostatic

Ž .potential EP in the chemisorption region for thislatter cluster. The small geometrical distortions ofadsorbed versus free water molecule suggest ahighly electrostatic interaction with the surface.We have computed the EP along the normal to theMg2q adsorption site for the four models and weindeed found a totally different EP for Mg O5 5without PCs. In particular, the EP values com-puted at 4 bohr from the surface, close to theequilibrium position of the water molecule, are:Mg O q PCs s 1.98 eV; Mg O q PCs s 1.82 eV;9 9 5 5Mg O s 1.51 eV; and Mg O s y2.17 eV. We9 9 5 5notice that the EP values for the two clustersembedded in PCs are similar, consistent with thesimilarly computed D values. For bare Mg O ,e 9 9the EP is smaller but has the same sign of theclusters with PCs; for Mg O , on the other hand,5 5even the sign of the EP is reversed, indicating thatthis cluster is not well suited for the calculation ofadsorption energies of electrostatically boundmolecules.

TABLE III.( ) 2y ( )Energy Contributions eV to Interaction of Proton with Surface O Ion of MgO 100 Surface.

O Mg O Mg5 5 9 9

Cluster PCs No PCs PCs No PCs

( )a Electrostatic interaction 2.31 0.73 1.39 3.89( )b Surface polarization 1.70 2.93 2.09 2.23( )c Charge transfer 3.82 3.46 3.67 3.68

( ) ( ) ( )Sum a q b q c 7.83 7.12 7.15 9.80

JOURNAL OF COMPUTATIONAL CHEMISTRY 623

PACCHIONI ET AL.

CO on Mg2H Sites

Adsorption of CO on MgO is another exampleof interaction with surfaces dominated by electro-statics.7,9 The determination of the binding energyof CO on MgO is a delicate problem, which hasbeen the subject of a number of theoretical investi-gations.7,13,14,18,25,27,28 Here we do not address thispoint specifically, but rather compare clusters withPC embedding with bare MgO clusters. To thisend we have optimized the geometry of a COmolecule vertically adsorbed on a Mg2q cation ofthe MgO surface; the substrate is represented bythe Mg O cluster. In contrast to the previous case,5 5here the surface cation where CO is adsorbed wasallowed to relax in the optimization while all theother atoms of the cluster were fixed at the latticepositions of bulk MgO. The same process has beenconsidered for a step site, and the cluster used is

Ž .Mg O Fig. 1 . The response of the two ap-6 6proaches, with and without PCs, is quite differentfor the surface site. First, virtually no surface rum-pling is found with Mg O q PCs, in agreement5 5with experiment,66 whereas substantial relaxationof the position of the Mg2q ion is found with

w Ž 2q. xMg O see D z Mg in Table II . Second, while5 5ŽCO is bound on Mg O q PCs by 0.23 eV not5 5

.corrected by the BSSE , no binding at all is foundbetween CO and Mg O without PCs. This is a5 5qualitatively significant difference as it is experi-mentally established that CO is weakly bound at

ŽMgO terraces see, e.g., ref. 1 and references.therein . In this respect, the use of a cluster with-

out inclusion of long-range electrostatic terms leadsto qualitatively incorrect results, as already foundfor the case involving water.

This is not the case for the edge site. In fact, COis adsorbed at a Mg cation with practically the4 csame binding energy, 0.3 eV, and the same geome-try, irrespective of the presence of the external PCs

Ž .or the cluster size see Table II . With a moreexposed cation, the EP is dominated by the localcontribution from the ions around the adsorption

Ž .site and the effect of the distant ions or PCs isless important. This may explain the different re-

Ž .sponse of clusters of similar size Mg O or Mg O5 5 6 6in the description of the adsorption at differentsites like a surface or a step cation.

VIBRATIONAL FREQUENCIES: CO ON MGO

In a recent article, Pelmenschikov et al.38 sug-gested that molecular models of ionic materialswithout embedding accurately reproduce the vi-

brational shifts of adsorbed molecules. For COadsorbed on MgO, v shifts of 10, 21, and 60 cmy1

with respect to the free molecule have been mea-sured and assigned to CO adsorbed on five-, four-,

2q Žand three-coordinated Mg cations surface, step,. 67and corner sites, respectively . In ref. 38, it has

been shown that the v shifts of CO adsorbed onstep and corner sites are quantitatively reproducedby using HF wave functions and small MgO clus-ters without any representation of the Madelungpotential. No attempt has been done, however, toevaluate the importance of the Madelung term indetermining the CO vibrational frequency. Thus,we compare the adsorption of CO on Mg O ,6 6Mg O q PCs, Mg O , and Mg O q PCs clus-6 6 10 10 10 10

Ž .ter models of an edge site Fig. 2 . The use of twoclusters of different size will provide some infor-mation about the converge of the results withcluster size. No comparison is possible for thesurface site because, as mentioned above, no mini-mum is found for CO adsorbed on Mg O without5 5PCs.

We consider first the smallest model. The CO vshift computed with Mg O q PCs is of q40 cmy1 ;6 6the shift computed with Mg O is q20 cmy1. Both6 6

Žshifts are in the right direction the CO v ise.higher than in the gas phase . The value obtained

without PCs is in excellent agreement with theexperimental data, q21 cmy1,67 and with the re-sults of ref. 38. The obvious conclusion would bethat the presence of the PCs results in a too-largev shift.38 This is certainly true at the HF level oftheory but the question of the importance of corre-lation effects remains open. The v shift of COadsorbed on MgO has a largely electrostaticorigin.7,9 In particular, it is due to a combination ofthe wall effect, a term arising from the Pauli repul-sion due to the stretching of the molecule againstthe rigid surface,7 and a term due to the interac-tion between the surface electric field and the COdynamic dipole moment, dmrdr.9 This second termdominates when CO is adsorbed on free or ex-posed cations.9,10 One important contribution tothe CO v shift is therefore the CO dynamic dipolemoment, which in HF is much larger than the

Žexperimental value of y0.6 a.u. it is y1.0 a.u..9with the present basis set ; CASSCF calculations

where the active space consists of the 1p , 5s , 2p *,and 6s * orbitals give dmrdr s y0.7, much closerto the experimental value. Thus, correlation effectsreduce the value of the CO dynamic dipole mo-ment and may affect the value of the CO v shift.In fact, for uniform electric fields the field-induced

VOL. 18, NO. 5624

MADELUNG POTENTIAL

CO v shift is a function of both the slope and thecurvature of the dipole moment curve.68,69

We have computed the vibrational frequency ofthe CO molecule in the presence of uniform fields,F s 0.01 a.u. and F s 0.05 a.u., and of a distribu-tion of PCs simulating the edge site of MgO; inpractice, we replaced the ions of the Mg O q PCs6 6cluster by "2 PCs. The CO v has been deter-emined for both SCF and CASSCF wave functionsand compared with that of free CO. For a fieldF s 0.01 a.u. the CO v shift is virtually the same,q23 cmy1 in SCF, and q22 cmy1 in CASSCF. Fora larger field, F s 0.05 a.u., the shift at the SCFlevel, q112 cmy1, is much larger than in CASSCF,q69 cmy1. For the nonhomogeneous field givenby the PCs simulating the edge site we againfound a similar shift in SCF, q38 cmy1, andCASSCF, q33 cmy1. These results indicate that,for small electric fields, the CO v shifts computedat correlated and uncorrelated levels are similar,but for larger fields correlation effects lower Dvsubstantially. This is the case, for instance, of COadsorbed at corner sites where the shift of 60 cmy1

is largely due to the field]dipole interaction.10 Anadditional warning in computing small shifts ofthe order of a few cmy1 is that the BSSE can affectthese quantities as well as the adsorption energies.A proper consideration of this error may also benecessary when discussing accuracies within 2]3cmy1. Of course, the use of clusters with surround-ing PCs to determine vibrational shifts is not freefrom limitations; in fact, as already mentioned, thePCs induce an artificial polarization of the oxygenatoms at the cluster border with change of thecluster electric field and of the Pauli repulsionwith the adsorbed molecule. These effects, how-ever, can be reduced by placing, at the PCs posi-tions, ECPs or projector operators that account forthe finite size of the ions.25,27

Another important point to investigate is thecluster size dependence of the results. We haveconsidered a larger cluster, Mg O , and repeated10 10the geometry optimization and vibrational analysis

Ž .as for the Mg O case. The results Table II clearly6 6show that the adsorbate geometry and bindingenergy are relatively well converged for both mod-els with and without PCs and that similar valuesare found for the two clusters within our errorlimits. On the other hand, the CO vibrational shift

y1 Ž . y1 Ž .is 8 cm PC and 11 cm no PC higher in theŽ .larger cluster Table II compared with the smaller

one. While this is a small change in absolute value,it is relevant when the total shift is of the order of20]30 cmy1 as in the present case. In conclusion,

the computed shifts can be considered accuratewith error limits of "10 cmy1, but a more precisedetermination of this property may require consid-erably more refined models and theoretical meth-ods.

SURFACE ELECTRONIC PROPERTIES

As a last example of the importance of theinclusion of the Madelung potential we considerthe case of paramagnetic Fq centers on the surfacesof MgO. These centers are quite important in sev-eral adsorption processes because they exhibit amuch higher reactivity than that of the regularsurface.71 Furthermore, their electronic structurecan be characterized by means of ESR techniquesand the calculation of observable properties likethe hyperfine coupling constants, A, represents animportant test of the adequacy of the model used.Recent studies have shown that, on the electronicground state, the unpaired electron is entirely lo-calized in the vacancy, and that this is consistentwith a small value of A.60 A is the hyperfinecoupling constant of the electronic spin with thenuclear spin of the 25Mg nucleus; we have deter-

Žmined the isotropic part of A, a the Fermiiso.contact term , which is about 10 G in absolute

Žvalue according to experiment see ref. 60 and.references therein . We have considered clusters ofw xq w xqdifferent sizes, O Mg , O Mg , and8 9 12 13

w xqO Mg ; as usual, the clusters have been com-20 21puted with and without surrounding PCs. The aisovalues are reported for the four equivalent Mgions in the first layer and for the single Mg ion in

Ž .the second layer Table IV . When the largest clus-w xqter is considered, O Mg , the results with and20 21

Ž .without PCs are similar Table IV . The small aisovalues, about 4]5 G, are consistent with the un-

TABLE IV.Hyperfine Coupling Constants, a , foriso

+Paramagnetic F Centers on MgO Surface.s

( )a Giso

Mg first Mg secondCluster layer layer

q[ ]O Mg q PCs y6.0 y5.28 9q[ ]O Mg q PCs y5.5 y3.512 13q[ ]O Mg q PCs y4.2 y5.220 21

q[ ]O Mg 0.0 y5.78 9q[ ]O Mg 3.5 y44.912 13q[ ]O Mg y4.7 y1.120 21

( )Experimental ref. 60 f y8ry10 f y12

JOURNAL OF COMPUTATIONAL CHEMISTRY 625

PACCHIONI ET AL.

paired electron being localized in the vacancy andnot on the 3s levels of the Mg ions. The use ofsmaller clusters embedded in PCs gives essentially

Ž .the same result see Table IV . Small variations arefound in the a values as a function of the clusterisosize, but these oscillations are never larger than1]2 G, clearly indicating the same electronic struc-

Ž .ture for all clusters Table IV . On the contrary,dramatic changes occur when clusters without em-

w xqbedding are considered. In O Mg , a large a12 13 isoof y45 G is found for the Mg ion in the secondlayer, indicating a strong localization of the un-paired electron on this atom. This is different fromthe other clusters and in contradiction with the

w xqexperiment. The even smaller O Mg cluster,8 9on the other hand, gives no spin density at all on

Ž .the Mg ions in the first layer a is zero, Table IVisoand a small spin density on Mg2q in the secondlayer. Again, this contradicts the experimental ob-servation.

Clearly, the absence of the long range potentialleads to dramatic changes in the electronic struc-ture and in strong oscillations as function of thecluster size. This is not surprising if we think thatthe Madelung term is a slowly convergent series.The fact that some clusters exhibit similar behaviorwith and without PCs simply indicates a fortu-itously similar value of the truncated summationwith the infinite one.

Conclusions

In this study, we have considered the electronicproperties and the reactivity of MgO clusters withand without a PC representation of the Madelungpotential of the extended surface. Depending onthe size of the clusters considered, different resultsare obtained. In fact, for some clusters we found asimilar behavior with and without the surround-ing PCs. This is the case of adsorption of H andCO on the O Mg cluster model of a surface2 9 9oxygen, of the Mg O and Mg O models of6 6 10 10adsorption of CO at a step Mg2q site, and of thew xq qO Mg cluster used to describe the F cen-20 21 sters. For all these clusters, the results seem to bevirtually independent of the presence of the PCs.On the other hand, we have found a considerablenumber of cases in which clusters without embed-ding in PCs give results completely different thanthose with PCs and, more importantly, which arein contrast to the experimental evidence. This isthe case for smaller cluster models, like O Mg5 5

w xq w xqand Mg O , or of the O Mg and O Mg5 5 12 13 8 9models of surface Fq centers. This suggests thatsinclusion of the long range coulombic interactionsis essential when the clusters are small.

The reactivity and the electronic structure ofoxide surfaces is largely a function of the Madelungpotential at a given site. Therefore, several elec-tronic and chemical properties of ionic materialscan be explained simply in terms of electrostatics.For instance, the trends in core level binding ener-gies of oxygen anions72 and metal cations73 inalkaline-earth oxides can be easily rationalized interms of the Madelung potential at the site wherethe photoionization occurs. Also, the basicity ofoxide surfaces is a chemical property directly con-nected to the Madelung potential and not, as oftenassumed, to the net charge of an ion.22 In particu-lar, a larger Madelung potential results in a more

Žstable and less basic anion e.g., the surface sites of.MgO while a lower Madelung potential leads to a

Žstronger donor ability e.g., the edges and corner.sites of the surface . In this way, it is also possible

to understand the increasing basic character in theseries MgO, CaO, SrO, and BaO.22

From the previous discussion it is apparent thatthe Madelung potential is a crucial quantity indetermining the properties of an ionic material.Cluster models of an ionic oxide must correctlydescribe this contribution and the use of embed-ding in PCs is a simple, yet efficient, way to dothis. It has been suggested that in MgO values ofPCs lower than "2 give results in better agree-ment with the experiment.13,24 The use of PCs isless obvious for materials in which the bondinghas a mixed ionic-covalent character, like in SiO2or TiO . It is possible that clusters without repre-2sentation of the Madelung field give similar re-sults. In fact, the charge separation determiningthe ionic character of the material develops veryrapidly within a cluster, even when the size isrelatively small. This means that an ‘‘internal’’Madelung stabilization develops with the growthof the cluster. For instance, we have recently found

Ž .74that a Ti O cluster model of TiO 110 and a7 14 2Ž .75Cu O model of Cu O 111 surfaces, respec-28 14 2

tively, give similar results for the adsorption of COon cation sites with and without embedding inPCs. However, there is no guarantee that for a‘‘small’’ cluster the Madelung potential at a givensite resembles that of the real surface. Thus, for notcompletely ionic systems, where one may wonderwhich is the exact Madelung field, it is desirable tocompute the properties of interest as a function ofthe field. Usually, slight to rather large variations

VOL. 18, NO. 5626

MADELUNG POTENTIAL

Ž .up to 50% on the Madelung field do not result inlarge variations of the properties.76

In conclusion, we have shown that the use of anexternal field helps in stabilizing the Madelungpotential within cluster models of ionic materialsand strongly reduces the oscillations connectedwith the cluster size.

Acknowledgments

This work has been supported by the ItalianMinistry of University and Research, and CICytProject PB92-0766-CO2-01 and PB95-1247 of theSpanish Ministerio de Education y Ciencia. A. M.F. thanks the Computational Center of CatalunyaŽ .CESCA for the financial support for her stay atthe University of Barcelona through the HumanCapital and Mobility Programme. We are gratefulto NATO for Collaborative Research Grant No.941191.

References

1. J. Sauer, P. Ugliengo, E. Garrone, and V. R. Saunders, Chem.Ž .Rev., 94, 2095 1994 .

Ž .2. J. Sauer, Chem. Rev., 89, 199 1989 .Ž .3. E. A. Colbourn, Surf. Sci. Rep., 15, 281 1992 .

4. G. Pacchioni, P. S. Bagus, and F. Parmigiani, Eds., ClusterŽModels for Surface and Bulk Phenomena NATO ASI Series B,

.Vol. 283 , Plenum, New York, 1992.5. E. A. Colbourn and W. C. Mackrodt, Surf. Sci., 143, 391

Ž .1984 .6. R. Huzimura, Y. Yanagisawa, K. Matsumura, and S. Ya-

Ž .mabe, Phys. Rev. B, 41, 3786 1990 .7. G. Pacchioni, G. Cogliandro, and P. S. Bagus, Surf. Sci., 255,

Ž .344 1991 .8. K. J. Borve and L. G. M. Pettersson, J. Phys. Chem., 95, 7401

Ž .1991 .9. G. Pacchioni, G. Cogliandro, and P. S. Bagus, Int. J. Quant.

Ž .Chem., 42, 1115 1992 .10. G. Pacchioni, T. Minerva, and P. S. Bagus, Surf. Sci., 275,

Ž .450 1992 .Ž .11. K. J. Borve, J. Chem. Phys., 96, 6281 1992 .

Ž .12. D. Stromberg, Surf. Sci., 275, 473 1992 .¨Ž .13. K. M. Neyman and N. Rosch, Chem. Phys., 168, 267 1992 .¨

14. M. Polchen and V. Staemmler, J. Chem. Phys., 97, 2583¨Ž .1992 .

Ž .15. G. Pacchioni, Surf. Sci., 281, 207 1993 .16. G. Pacchioni, C. Sousa, F. Illas, P. S. Bagus, and F. Parmi-

Ž .giani, Phys. Rev. B, 48, 11573 1993 .Ž .17. K. M. Neyman and N. Rosch, Surf. Sci., 297, 223 1993 .¨

Ž .18. K. M. Neyman and N. Rosch, Chem. Phys., 177 1993 .¨19. A. Freitag, V. Staemmler, D. Cappus, C. A. Ventrice, K. A.

Shamery, H. Kuhlenbeck, and H. J. Freund, Chem. Phys.Ž .Lett., 210, 10 1993 .

Ž .20. G. Pacchioni and P. S. Bagus, Phys. Rev. B, 50, 2576 1994 .

21. G. Pacchioni, J. M. Ricart, and A. Clotet, Surf. Sci., 315, 337Ž .1994 .

22. G. Pacchioni, J. M. Ricart, and F. Illas, J. Am. Chem. Soc.,Ž .116, 10152 1994 .

23. A. Snis, I. Panas, and D. Stromberg, Surf. Sci., 310, L579¨Ž .1994 .

24. M. Nygren and L. G. M. Pettersson, Chem. Phys. Lett., 230,Ž .456 1994 .

25. M. Nygren, L. G. M. Pettersson, Z. Barandiaran, and L.Ž .Seijo, J. Chem. Phys., 100, 2010 1994 .

26. H. Nakatsuji, M. Yoshimoto, M. Hada, K. Domen, and C.Ž .Hirose, Surf. Sci., 336, 232 1995 .

27. J. A. Mejias, A. M. Marquez, J. Fernandez-Sanz, M. Fernan-dez-Garcia, J. M. Ricart, C. Sousa, and F. Illas, Surf. Sci.,

Ž .327, 59 1995 .

28. C. Sousa, J. A. Mejias, G. Pacchioni, and F. Illas, Chem. Phys.Ž .Lett., 249, 123 1996 .

29. K. M. Neyman, S. P. Ruzankin, and N. Rosch, Chem. Phys.¨Ž .Lett., 246, 546 1995 .

30. T. Ito, T. Tashiro, M. Kawasaki, T. Watanabe, K. Toi, and H.Ž .Kobayashi, J. Phys. Chem., 95, 4476 1991 .

31. K. Sawabe, N. Koga, K. Morokuma, and Y. Iwasawa, J.Ž .Chem. Phys., 97, 6871 1992 .

32. K. Sawabe, N. Koga, K. Morokuma, and Y. Iwasawa, J.Ž .Chem. Phys., 101, 4819 1994 .

33. K. Sawabe, K. Morokuma, and Y. Iwasawa, J. Chem. Phys.,Ž .101, 7095 1994 .

34. J. L. Anchell and E. D. Glendening, J. Phys. Chem., 98, 11582Ž .1994 .

35. Y. Yanagisawa, K. Takaoka, and S. Yamabe, J. Chem. Soc.Ž .Faraday Trans., 90, 2561 1994 .

36. H. Kobayashi, D. R. Salahub, and T. Ito, J. Phys. Chem., 98,Ž .5487 1994 .

37. Y. Yanagisawa, K. Takaoka, S. Yamabe, and T. Ito, J. Phys.Ž .Chem., 99, 3704 1995 .

38. A. G. Pelmenschikov, G. Morosi, A. Gamba, and S. Coluc-Ž .cia, J. Phys. Chem., 99, 15018 1995 .

39. M. Causa, R. Dovesi, C. Pisani, and C. Roetti, Surf. Sci., 175,`Ž .551 1986 .

40. R. Dovesi, R. Orlando, F. Ricca, and C. Roetti, Surf. Sci.,Ž .186, 267 1987 .

41. C. A. Scamehorn, A. C. Hess, and M. I. McCarthy, J. Chem.Ž .Phys., 99, 2786 1993 .

42. U. Birkenheuer, J. C. Boettger, and N. Rosch, J. Chem. Phys.,¨Ž .100, 6826 1994 .

Ž .43. W. Langel and M. Parrinello, Phys. Rev. Lett., 73, 504 1994 .Ž .44. J. Goniakowski and C. Noguera, Surf. Sci., 330, 337 1995 .

45. R. Nada, A. C. Hess, and C. Pisani, Surf. Sci., 336, 353Ž .1995 .

46. Y. Ferro, A. Allouche, F. Cora, C. Pisani, and C. Girardet,`Ž .Surf. Sci., 325, 139 1995 .

47. M. D. Towler, N. M. Harrison, and M. I. McCarthy, Phys.Ž .Rev. B, 52, 5375 1995 .

48. K. Refson, R. A. Wogelius, D. G. Fraser, M. C. Payne, M. H.Ž .Lee, and V. Milman, Phys. Rev. B, 52, 10823 1995 .

49. W. Langel and M. Parrinello, J. Chem. Phys., 103, 3240Ž .1995 .

JOURNAL OF COMPUTATIONAL CHEMISTRY 627

PACCHIONI ET AL.

50. M. A. Nygren, L. G. M. Pettersson, A. Freitag, V. Staemm-ler, D. H. Gay, and A. L. Rohl, J. Phys. Chem., 100, 294Ž .1996 .

51. C. Pisani, R. Orlando, and R. Nada, in Cluster Models forŽ .Surface and Bulk Phenomena NATO ASI Series B, Vol. 283 ,

G. Pacchioni, P. S. Bagus, and F. Parmigiani, Eds., Plenum,New York, 1992, p. 515.

52. C. Pisani, F. Cora, R. Dovesi, and R. Orlando, J. Electron`Ž .Spectrosc. Relat. Phenom., 96, 1 1994 .

53. A. Allouche, F. Cora, and C. Girardet, Chem. Phys., 201, 59`Ž .1995 .

Ž .54. V. Luana and L. Puejo, Phys. Rev. B, 41, 3800 1990 .55. S. Huzinaga, Ed., Gaussian Basis Sets for Molecular Calcula-

Ž .tions Physical Science Data, Vol. 16 , Elsevier, Amsterdam,1984.

56. T. H. Dunning and P. J. Hay, Modern Theoretical Chemistry,Plenum, New York, 1976.

57. P. S. Bagus, K. Hermann, and C. W. Bauschlicher, J. Chem.Ž .Phys., 80, 4378 1984 .

Ž .58. P. S. Bagus and F. Illas, J. Chem. Phys., 96, 8962 1992 .59. F. J. van Duijenevled, IBM Res. Rep. No. RJ 945, 1971.60. D. Murphy and E. Giamello, J. Phys. Chem., 99, 15172

Ž .1995 , and references therein.61. A. M. Ferrari and G. Pacchioni, J. Phys. Chem., 99, 17010

Ž .1995 .

62. M. Dupuis, F. Johnston, and A. Marquez, HONDO 8.5 forCHEM-Station, IBM Co., Kingston, NY, 1994.

63. W. J. Stevens, H. Basch, and M. Krauss, J. Chem. Phys., 81,Ž .6026 1984 .

Ž .64. Z. Barandiaran and L. Seijo, J. Chem. Phys., 89, 5739 1988 .65. A. M. Ferrari and G. Pacchioni, Int. J. Quant. Chem., 58, 241

Ž .1996 .66. V. E. Heinrich and P. Cox, The Surface Science of Meal Oxides,

Cambridge University Press, Cambridge, 1994.67. L. Marchese, S. Coluccia, G. Martra, and A. Zecchina, Surf.

Ž .Sci., 269r270, 135 1992 .Ž .68. D. K. Lambert, J. Chem. Phys., 89, 3847 1988 .

69. P. S. Bagus, C. J. Nelin, W. Muller, M. R. Philpott, and H.Ž .Seki, Phys. Rev. Lett., 58, 559 1987 .

70. G. Pacchioni, K. Neyman, and N. Rosch, J. Electron Spec-¨Ž .trosc. Relat. Phenom., 69, 13 1994 .

71. A. M. Ferrari and G. Pacchioni, J. Phys. Chem., 100, 9032Ž .1996 .

Ž .72. G. Pacchioni and P. S. Bagus, Phys. Rev. B, 50, 2576 1994 .73. P. S. Bagus, G. Pacchioni, C. Sousa, T. Minerva, and F.

Ž .Parmigiani, Chem. Phys. Lett., 196, 641 1992 .74. G. Pacchioni, A. M. Ferrari, and P. S. Bagus, Surf. Sci., 350,

Ž .159 1996 , Surf. Sci., to appear.75. T. Bredow and G. Pacchioni, Surf. Sci., to appear.76. C. Sousa, F. Illas, and G. Pacchioni, J. Chem. Phys., 99, 6818

Ž .1993 .

VOL. 18, NO. 5628