Final-State Screening and Chemical Shifts in Photoelectron Spectroscopy

PHYSICAL REVIEW B VOLUME 31, NUMBER 8 15 APRIL 1985

Final-state screening and chemical shifts in photoelectron spectroscopy

B. W. Veal and A. P. PaulikasMaterials Science and Technology Division, Argonne National Laboratory, Argonne, Illinois 60439

(Received 23 July 1984)

Photoelectron spectroscopic measurements of core-electron levels in cations of transition-series in-

sulators commonly show "satellite" features in the vicinity of the "main" photoelectron peaks. Inthis paper, the relationship between main lines and adjacent satellites is systematically examined for3d-series insulators. The spectral features are interpreted using a relaxation model that allows forthe possibility of different final-state screening conditions of the photoinduced hoyle. Systematictrends are examined by employing atomic calculations and utilizing transition-state theory to calcu-late electron removal energies for atoms in appropriately simulated chemical environments. It isdemonstrated that the main-line and satellite energies are both dependent on the cation charge envi-ronment but with different degrees of sensitivity. The consequence is that sensitivity to chemicalchange can be monitored in the observed main-line to satellite separation. Model predictions aretested by monitoring the dependence of the satellite separations on the cation valence state and onthe electronegativity of both cations and ligated anions. Systematic tests are applied to 3d-series in-sulators but more general applicability of the relaxation model is also discussed.

I. INTRODUCTION

It was established by Siegbahn and co-workers' thatsharp peaks could be observed in energy-analyzed pho-toemitted electrons following irradiation of a solid sampleby monochromatic x rays. These peaks correspond to thebinding energies (BE) of occupied core-electron levels.Since those binding energies are sensitive to local-chargeenvironments, it was expected that the binding energiesand hence the x-ray photoelectron spectroscopy (XPS)peaks would shift significantly as the chemical environ-ment (e.g. , valence state) was altered. Chemical shiftsare, of course, observed in XPS lines, sometimes withdramatic effect. For example, chemical shifts betweenXPS core levels for carbon atoms in different chemicalenvironments are sometimes 10 eV or more. ' Often,however, the chemical shifts are disappointingly small (2eV or less) even when valence changes, involving signifi-cant charge redistributions, occur. It has, of course, longbeen recognized that the XPS peaks do not directly mea-sure local ground-state charge environments. Because re-laxations or secondary excitations are always associatedwith core-hole production, it is generally difficult todetermine the precise correspondence between XPS peaksand ground-state properties.

Complicating the interpretation of chemical shifts isthe tendency, for cations in transition-element compounds(i.e., 3d, 4d, and 5 d, lanthanides, ' and ac-tinides ) to show satellite features in the vicinity ofXPS core lines. Typically, a single, relatively strong "sa-tellite" will appear at the high-binding-energy side of the"main line. " The low-binding-energy main line is almostuniversally the more intense one. The satellites appearwithin —1 Ry of the main line and tend to be associatedwith all core levels of the cation. These satellites are gen-erally called "shakeup" peaks.

Spectral complexity can also be introduced at core lev-

els by the exchange interaction between the core hole andthe localized electrons in an unfilled outer shell (multi-plet splittings). Splittings can be large at those shallowcore levels where the radial wave function is comparableto the radial function of the outer-shell local electrons.Structure may sometimes be introduced at deeper core lev-els, also. However, such effects appear to be generallysmall at the deep levels of 3d insulators, serving to pro-vide some apparent line broadening or weak substruc-ture.

&t is generally agreed that photoemission peaks (disre-garding peaks resulting from extrinsic loss processes) mea-sure the energy difference between the ground state of thesample and (suitably metastable) final states of the ionizedsample. Inevitably, creation of a deep core hole will causereadjustment of many electrons in the system including all"spectator" levels of the ion itself. All molecular orbitalsto which outer electrons of the ion contribute will also beperturbed. Thus, unavoidably, a complex multielectronresponse of the ion and its local environment will occur inassociation with photoejection. If one perceives the out-going photoelectron as being sensitive only to those finalmetastable states of a many-electron system (without giv-ing consideration to ongoing temporal processes exceptperhaps for their effect on linewidths), then one typicallyseeks to discover, and to characterize as completely aspossible, those final metastable ion states that exist in thecompany of the photoinduced core hole. Of course, thehope is that information relating to the ground-statechemical condition can also be inferred.

The substantial body of literature on the subject of sa-tellite structure contains speculations about the directionof charge flow following creation of a core hole and possi-ble configuration changes that might provide an identifi-cation of those final excited states that correspond to ob-served XPS peaks. The descriptive terms shakeup andshakedown have evolved, apparently to designate an exci-

31 5399 1985 The American Physical Society

B. W. VEAL AND A. P. PAULIKAS 31

tation or a relaxation (processes usually defined in relationto the energy state corresponding to the most intense"main" XPS line). There appears to be no clear distinc- .

tion between these terms except to indicate that one finalion state is either higher or lower in energy than a desig-nated (e.g. , main line) reference state.

In the recent literature, a growing body of evidencepoints to the importance of considering relaxation phe-nomena, following core-level photoejection, to account forboth the main-line and satellite features in insulating com-pounds. ' ' Varying levels of relaxation of the pho-toinduced ion (providing differing screening or polariza-tion conditions of the core hole) are thought to accountfor the observed XPS peaks. This view was advocated bythe authors in a study of 3s line shapes in transition-metalfluorides. The 3s line shapes were explained by consid-ering two final-state screening conditions. The screeningstate specifies a 3d population which, in turn, determinesthe amount of exchange splitting at the 3s level. Thecombination of two screening states, each with a different3d population, and the associated exchange splittings suc-cessfully predicted the observed line shapes. It was, furth-ermore, argued that different final-state conditions,reached in a relaxation response to the photoinduced hole,may account for the preponderance of structure that ap-pears in cation deep core-level photoemission spectra ofionic compounds.

Final-state relaxation and core-hole screening have beenconsidered by numerous other researches studying photo-emission spectra of metals and of adsorbates on metallicsubstrates. However, the screening arguments gen-erally are not offered for insulators. Some authors specif-ically exclude the possibility that screening 3d electronscan locally reside at the cation site in insulators. '

In this paper we examine the relationship of the dif-ferent final-state conditions to XPS core-level binding en-ergies observed for elements in different chemical environ-ments. The discussion will primarily focus on the energyseparations between main-line and satellite structures ininsulating compounds of 3d transition elements and onthe chemical sensitivity of these relative energies. Em-phasis will, therefore, be placed on extracting chemical in-formation from measurements of the internal electron-level structure.

II. THE SCREENING MADEL

A. Description

In the presence of a core hole, unfilled eigenlevels asso™ciated with the ion are pulled down (to higher binding en-

ergy) relative to the eigenlevels of the atom in its ground-state environment. One of these pulled-down levels couldbecome populated to locally charge-compensate the corehole. This compensation process represents a partialdeexcitation of the system and the kinetic energy of theoutgoing electron will correspondingly be increased by theamount of this deexcitation energy. This process, ofcourse, translates to a corresponding decrease in the ap-parent binding energy of the XPS line. Thus, if both thebare (unrelaxed) hole and the screened hole could be ob-served, then the screened condition would appear in XPSat the low-binding-energy side, with the bare hole at the

LOCAL DENSITY OF STATES-SCHEMATIC FOR TRANSITION METAL OXIDE-

4s-p n (E}

3dE) ———-- ————-- ————————

~&O2p

2p

4s-p(EXTENDEDORBITAL)

3d(LOCALORBITAL)

2p—

TRANSITION LIGAND TRANSITION METALMETAI WITH

CORE HOLEGROUND STATE

FICx. 1. A schematic representation of the local density ofstates at the cation and ligated sites in a (fully chemically ion-ized) transition metal oxide. Upon creation of a cation core holeby photoemission, other "spectator" levels of the cation arepulled down (to higher binding energy). It is then energeticallyfavorable for charge from neighboring (ligand) atoms to flow to-ward the ion to screen the core hole. The observed XPS bindingenergy for removal of a core electron will depend upon the radi-al distribution of the screening charge.

higher binding energy.Figure 1 illustrates the relaxation process which leads

to the final-state screening or polarization conditions.Here we schematically represent the local density of statesfor cations and ligands in the vicinity of the Fermi level

(EF) for a (fully ionized) transition-metal insulator thatcontains unfilled 3d levels. In the presence of the corehole, outer levels will be pulled down (in the case of a freeion or unscreened hole, by about a rydberg). This is gen-erally a sufficiently large shift in the level structure sothat the extended 4s-p orbitals will energetically overlapthe ligand 2p orbitals. Furthermore, both the cation s-p'sand the ligand 2p's are substantially extended spatially sothese levels strongly overlap, both in energy and in space.This strong orbital overlap provides favorable conditionsfor (partial) population of the cation s-p screening orbitals(from the distributed ligand 2p's) in response to the sud-den creation of a photohole (a resultant polarization con-dition). Although partial charge compensation might beaccomplished by this "nonlocal" s-p orbital occupancy,the "ground-state" ion (i.e., the fully relaxed ion) is real-ized with occupation of a "local screening" orbital that ispredominately 3d in character ' (see Sec. III). Electronsin the nonlocal screening orbitals may reside in thosestates for times well in excess of 10 ' sec (a typical"photoemission lifetime" as determined by observed XPSlinewidths). Thus, both final-state conditions are likely tobe sufficiently metastable so that both will produce sharpfeatures in the XPS spectrum. (Spectral complexity couldbe increased if time-dependent orbital repopulation wassignificant during the time frame of the photoemissionmeasurement. ) We shall see that the radial extent of the

FINAL-STATE SCREENING AND CHEMICAL SHIFTS IN. . . 5401

screening orbitals has a strong influence on the excitationenergies required to reach the different final screenedstates. Relative amplitudes of the screening states dependon the initial population probabilities and possibly upontemporal "trickle-down" processes wherein screening elec-trons fall from the nonlocal states to the less excited local-ly screened state.

The traditional view of photoemission in insulators isthat relaxation accompanying core-hole production occursvia an electronic polarization response in the solid. Ex-cept perhaps for the occupied atomiclike orbitals, all outerelectrons of the system are in chemically filled shells.Thus no free-electron charge (as in metals) is available toscreen a core hole. It is argued that the binding energy ofa core photoemission event will, nonetheless, be reducedby the polarization energy, a form of extra-atomic relaxa-tion. Estimates of relaxation energies accompanyingcore-electron photoejection have, for example, been re-ported for alkali and zinc halides. ' For transition-metal insulators, a similar kind of charge-compensationresponse can occur (nonlocal screening). However, wehave argued that charge compensation of a photohole canalso occur by occupation of a localized (d-electron) cationorbital. This electron charge is drawn from the hybri-dized ligand-p band.

Charge compensation of the core hole by means ofthese different processes represent two very differentfinal-state conditions. For d-electron compensation (localscreening), an excitonlike impurity (that is approximatelycharge neutralized) appears at the photoionized site. Nosignificant charge imbalance is now discernable at thescreened atom. The solid has, nonetheless, been deprivedof one electron. The hole must, therefore, redistribute in abubble of substantial spatial extent about the screenedhole. Thus, local charge compensation of the photoholeshould result in a spatially extended polarization cloudwith small internal field gradients, very similar to thephysical condition that results when an electron is directlyremoved from the ligand p band. (Coulomb repulsiondemands that the hole will be dispersed. ) In contrast, apolarization response which does not involve a charge-compensating 3d electron (nonlocal screening) leaves thesystem with a strong local Coulomb potential which mustbe compensated by polarization of the atoms in closelyneighboring shells. Thus a "local screening state" resultsin an extended polarization cloud while "nonlocal screen-ing" is associated with a more compact polarizationcloud.

In general, we expect that, for transition-element insula-tors, two final states will be observable. One state corre-sponds to a fully relaxed (locally screened) condition in-volving occupancy of a screening transition-series electronlevel. The second (nonlocal screening) state correspondsto a many-electron relaxed final state of the ion that ex-cludes occupancy of the localized transition-series (e.g.,3 d) electron level.

B. Relationship to shakeup and shakedown

The seemingly contradictory processes of shakeup (animplied excitation) and shakedown (an implied relaxation)

as mechanisms to explain cation satellite structure haveled to substantial confusion. When a core, hole is created,the system relaxes, both intra-atomically and extra-atomically, with a complex collective response, toward theground state of the ion. Metastable intermediate states(semirelaxed) may be encountered by the ion on its waytoward complete relaxation. Thus, multiple peaks couldbe observed. (In our view, the preponderance ofmultiple-peak structure that appears at XPS core levelswithin —1 Ry of the main line can be accounted for withthis simple relaxation model. ) Thus the terms shakeupand shakedown are consistent with the model consideredhere if we regard shakedown as a process by which thesystem adjusts to the sudden presence of the core hole inorder to reach the (fully or partially) relaxed final meta-stable states and if we regard shakeup as a term to desig-nate excitations of the final ion state measured withrespect to the fully reiaxed ion.

If a photoinduced core hole is suitably long lived andthe system response to creation of the deep hole is suitablyfast, then XPS will monitor the fully relaxed (groundstate) of the ion with its deep core hole. The correspond-ing XPS peak will, of course, occur at the lowest possiblebinding energy for this hole state. Any other XPS peakassociated with the core hole will represent an excitationwith respect to the fully relaxed ion state. The kinetic en-

ergy of the outgoing photoelectron from any higher bind-ing energy peaks will be degraded relative to the electronsassociated with the fully relaxed peak.

Reference 66 reviews the variety of assignments thathave been reported to account for satellites in transition-metal complexes. A ligand-to-metal 3d charge-transfershakeup process appears to be the most generally acceptedexplanation for the dominant satellite peaks in transition-element insulators. However, excitation assignments areusually made without first characterizing the fully relaxedhole state. Thus, in our view, this methodology is ofteninappropriate. The energetics of the final state requirethat charge flows (or relaxes) toward the cation tocharge-compensate the core hole. Thus a "charge-transferrelaxation" would always be a process associated withcore-level photoejection. Furthermore, the ligand- (bandorbital) to-cation 3d transition constitutes a processwhereby the ion is moving toward a highly relaxed condi-tion. (We have argued that this process produces thelow-binding-energy main XPS line. ) Thus, a ligand-to-3dshakeup assignment for the satellite would, in general, notappear to be appropriate.

Some authors are careful to point out that the intense,lowest-binding-energy XPS line must correspond to afully relaxed condition of the ion. However, if charge-transfer shakeup is then invoked to explain the satellite,are we to understand that a charge-transfer excitationfrom the fully relaxed state has occurred? In our view,this would be an acceptable perception of shakeup but it isa description that requires a clear understanding of thefully relaxed state (and would suggest that the satellite re-sults from a 3d-to-ligand charge transfer. )

In some cases, the final state of the ion may be left suf-ficiently excited that one could not reasonably view it ashaving been reached in a net relaxation process. In gen-


eral, however, this distinction has little value since thepoint where a "net" relaxation or excitation occurs cannotbe precisely defined.

III. INSIGHTS FROM ATOMIC CALCULATIONS

We shall make extensive use of a relativistic local-density atomic code to calculate eigenvalues and transi-tion energies for groups of atoms or ions systematicallyconfigured to simulate chemical changes. For example,Fig. 2 shows eigenvalues for "atomic" chromium with theouter electron configurations (3d 4p'), (3d 4p ),(3d 4p ), and (3d 4p ). The replacement of a localized3d electron with a more extended 4p e1ectron simulatesthe process of increased chemical ionization (e.g. , in-creased valence state) at the cation site. Increasing the ca-tion valence (usually) means that charge is drawn fromthe immediate vicinity of the cation and is redeposited onneighboring ligand atoms which closely surround the ca-tion. The net effect is qualitatively much like the processof converting the local 3d's into the extended 4p's, thusleaving a more positive potential at the cation site. Aproperly chosen set of atomic orbitals should reasonablyapproximate the spherical average of the radial chargedistribution centered at the cation site. To represent achange in cation valence will, of course, require a dif-ferent orbital set.

The eigenvalues of spectator levels (Fig. 2) move downas the outer electron charge is pushed further from the ca-tion center. The more localized the eigenfunctions ofthese spectator levels are, the more rapidly the levels move

down (although deep core levels all move at very nearlythe same rate since their charge is essentially all interiorto the outer orbitals where "chemical" effects occur).

Figure 2 indicates that substantial shifts in measuredbinding energies of cation core levels might be expected asthe ligand electronegativity or cation valence is altered.However, Fig. 2 represents ground-state conditions forchemically different environments, and spectroscopiesnever directly measure those ground states. In XPS thetotal energy difference between the ground state and somefinal ion state is measured.

For atoms, the excitation energy added to promote thetransition between a specified ground state and a specifiedfinal state can be obtained from transition-state (TS) cal-culations using the Dirac-Slater local-density formalism.Thus the energetics of a simulated photoemission processcan be examined using transition-state calculations. Withthe local-density code, excitation energies for (unscreened)ionization are calculated by removing —,

' of an electronfrom the core state. The excitation energy is then givenby the (negative of the) eigenvalue of the fractionally oc-cupied core level.

Figure 3 shows eigenvalues (upper dotted lines) at the2p3/z, 3p3/2, and 3d3/z core levels for the ground state ofthe "Cr atom" with configuration (3d 4p ). Also shownas (lower) dotted lines are eigenvalues for the ionizedatom: in Fig. 3(a), for a hole at the 2p3/2 level; in Fig.3(b), «r a hole at the 3d3/2 level; and in Fig. 3(c) for ahole at 3p3/2 We note that the electron-removal energy(i.e., the transition-state energy labeled unscreened ion inFig. 3) is approximately midway between the ground-stateand ion eigenvalues with the eigenvalues, in general, being

0

—IO—

ID

—560—4J

—570—

I I

pl/2

4s

I)c) EP3/2 LEVELI

-560

' screened2p&~& states

unscreenedion

4p.4d—

-600

-620

—640

(ei g.-atom)----- —-3d—

I(b) 3d3~~ LEVEL

I

3d --- 0"screened"3d3/~ states&' 4s-

(ei g.-atom) -----4p

unscreened .4dion —20

eI g,-lon) —--———

aI(c) 3P3&& LEvELI

—40 UJ

3d—screened

3p&&& states) 4s-(eI g.—a tom) —- —-=—. a.

-60unscreened .4d-Ion

(elg -lon)- —----—

—80

580—

(3d54p )

~2p 3/2

(3d44p ) (3d~4p ) (3d 4p )

CONF I GURATI ON

FIG. 2. Ground-state eigenvalues from atomic calculationsof several configurations of Cr(3d "4p "). These configurationssimulate varying levels of chemical ionization of the chromiumatom. Replacement of a localized 3d electron with a radiallyextended 4p places charge more remotely from the ion centerand thus corresponds to an increased level of chemical ioniza-tion. Localized levels (including 2p's and 3d's) move rapidly, innear unison, to higher binding energy as ionization is increased.Extended levels respond more slowly to chemical changes.

FIG. 3. Calculated electron-removal energies at the 2p3/2,3p3/2 and 3d3/2 levels for Cr(3d 4p ). The levels marked "un-screened" are transition-state (TS) calculations for electron re-moval from the isolated Cr(3d 4p') "atom. " These TS resultsfall approximately midway between the calculated eigenvaluesfor the ground state (dashed levels labeled eig.-atom) and calcu-lated eigenvalues for the hole state (dashed. levels labeled eig. -ion). Levels labeled "screened states" are TS calculations(electron-removal energies) of simulated screening conditions ofthe core-hole state. These levels represent the energy difference(excitation energy) between the ground state and the final statethat contains a core hole and an occupied outer (screening) elec-tron level (designated 3d, 4s, etc.).

31 FINAL-STATE SCREENING AND CHEMICAL SHIFTS IN. . . 5403

very different from ionization (TS) energies. The eigen-values represent the initial-state atom and final-state ion;the transition state represents the ionization energy re-quired to convert the atom from its initial state to its finalstate (including the energy associated with intra-atomicrelaxation of all spectator levels ). We shall see that TScalculations, particularly when screening conditions areproperly considered, can provide very accurate determina-tions of XPS core-level energies (see Sec. V E).

To simulate photoemission involving the screening con-ditions described in Sec. II, we remove —, of an electronfrom the core level and add —, of an electron into a screen-

ing orbital. For example, if screening is local (i.e., 3d), theexcitation energy E,„, for Cr 2p3/2 photoemission from a(fictitious) solid containing chromium ions in an environ-ment locally represented by the configuration (3d 4p )

would be Eexc E2p3/2 +E3d3/2 where E2p 3/2and

E3d are eigenvalues from the atomic calculation of3/2

ls 2s 2p&&22pq&z3s 3p (3d 4p ). Alternately, nonlocalscreening of the photohole would be calculated by placing

of an extended-state electron (e.g., a 4s or 4p) into thescreening orbital. For the configuration (3d 4p ), the en-

ergetics of the bare ionization process and various screen-ing conditions (3d, 4s, 4p, etc.) are shown in Fig. 3. Wesee that the electron-removal energy is greatest for the un-

screened final state and becomes progressively less as thescreening orbital becomes more localized. The solid linesshown in Figs. 3(a), 3(b), and 3(c) for the various screeningstates represent the multipeak (satellite) structure that onewould expect to observe for a "free chromium atom" ofground-state configuration (3d 4p ) if the atom could ac-quire the needed screening electrons (from a commonsource) during excitation. Note that the difference in re-moval energies for the various screened states is compar-able for ionization at the 2p, 3p, and 3d levels.

Important insights for interpreting XPS spectra are alsogained if one appreciates that the outer-electron states of a(fully relaxed) ion of atomic number Z that has a deepcore hole and a compensating (screening) outer electronare well approximated by the ground state of the neutralZ+1 atom. That is, to the outer electrons, a Coulomb-potential change produced by adding a sufficiently local-ized core hole is indistinguishable from the potentialchange produced by adding a proton to the nucleus. Toillustrate, we compare, in Fig. 4, outer-electron eigen-values for ground-state atomic iron Fe(3d 4s ) with cor-responding eigenvalues for (locally screened)Fe(ls'3d 4s ) containing a ls core hole and a compensat-ing 3d, and with eigenvalues for ground state Co(3d 4s ),the Z+1 analog of the excited Fe atom. We see that, forlevels outside (and including) the 2p shell, only minordifferences occur between corresponding core-level ener-gies of the highly excited Fe atom and the ground-stateCo atom (although 1s eigenvalues differ by more than 300eV). An application of the Z+1 model to predict satel-lite structure will be discussed in Sec. V D.

Clearly, the excitation energies, like the eigenvalues(Fig. 2), must depend on the ground-state charge (or"chemical" ) condition. The excitation (TS) energies at the2@3/2 level for the ground-state chemical ionization condi-

4s

~d5/2

-S8—

-62—

-64—CL

4J

Bp3/2

-700—

-720—

-740—

tions illustrated in Fig. 2 are shown in Fig. 5. Here wepresent excitation energies for the bare ionization (dashedline) and for local (3d) and nonlocal (4s, 4p) screening ofthe core hole. Recall (in these simulated chemical ioniza-

570—SCREENl N GORBITAL

3d

CLLUz 5go-Ld

)ObJlX

6l 0—

4s

BARE

L

(3d54p ) (3d 4p ) (3d 4p ) (3d 4p )

GROUND STATE CONF IGURATlON

FIG. 5. Dependence of electron-removal energies (TS calcula-tions) on simulated chemical ionization for the Cr 2p3/2 level.The dashed line represents simple electron removal while lineslabeled 3d,4s, 4p are energy differences between the ground state(noted on the abscissa) and the final state that contains a corehole and an occupied 3d, 4s, or 4p {screening) electron level.These results show that, for 3d screened final states, removalenergies are very insensitive to ground-state chemical changes.

-780Fe ( I s $d 4s2)

Fe (51 4s ) Co (5d 4s )

CONF I GURAT ION

FIG. 4. Calculated eigenvalues for Fe(3d 4s ) and forCo(3d 4s ) compared with eigenvalues for Fe{ls'3d 4s ). Thecomparison pf Fe(ls&3d74s2) and Cp{ls 3d 4s ) demonstratesthat a deep core hole {here at the Fe ls level) has a comparableeffect on the outer electron level structure as does a proton add-ed to the nucleus. Thus, screening of a deep core hole may beapproximated by the level structure of Z + 1 impurity.


tions) that the radial charge distribution at the metal siteis shifted outward as 3d electrons are replaced by 4p'sthus corresponding to an increase in valence. As thevalence state increases, the transition-state energy for theunscreened hole moves repaidly to higher binding energy.However, the TS energy for the locally screened levelshows only a small shift as the valence is changed. Thisresult explains why obserued XPS core leu-el shifts of cations can be so disappointingly small. Even if a largechange is made in the valence state of a cation, only avery small chemical shift will be observed in the intenseXPS line if the core hole is always screened by a localizedelectron.

Local screening shows little chemical sensitivity be-cause the transition from ground state to screened finalstate is essentially equivalent to an excitation from a (lo-calized) core level to a localized outer level. We saw inFig. 2 that localized levels move in near unison as thevalence state is altered. The transition energy from thecore level to the local outer level (unlike transitions to theextended outer level) is thus relatively independent ofchemistry. Figure 5 has shown that the locally screenedcation XPS peaks are very insensitive to chemicalchanges. However, substantially stronger chemical sensi-tivity is expected if the screening is nonlocal. Thus therelative separation between XPS main line and satellite(locally and nonlocally screened XPS final states) shouldbe sensitive to variations in the local cation charge envi-ronment. Thus we see the possibility that chemicalchanges can be monitored by measuring the relativeseparations between the main line and satellite. ' Figure 5suggests that the satellite separation is closely related tothe ground-state potential at the cation site. The greaterthe local positive charge at the cation site, the greater isthe expected satellite separation.

For 3d insulators, the low-lying nonlocal screeningstate will normally consist of 4s or hybridized 4s-4p bandstates that contain some admixture of 3d and ligand orbi-tals. If the character of the nonlocal screening state canbe estimated, then one can use the measured satelliteseparation to determine a configuration for the atomiccalculation that provides an estimate of the ground-statepotential at the cation site (e.g., see Fig. 5). To demon-strate the validity and general utility of the screeningmodel for interpreting XPS spectra, we systematically ex-amine, in the next section, experimental core-level spectrafor simple compounds observed under varying chemicalconditions and compare observed results with the modelpredictions.

IV. EXPERIMENTAL

Spectra displayed in this paper were recorded using aHewlett-Packard model No. 5950A photoelectron spec-trometer. A monochromatized Al Ko. x-ray source pro-vided incident x-ray radiation at 1486.6 eV. The overallinstrument resolution was -0.7 eV. A thermal electronsource, with adjustable filament temperature and ac-celerating potential, was used to flood the sample withelectrons to minimize sample charging. For each sample,Aood gun parameters were tuned to minimize spectral

broadening. Some of the samples were powder compactsheld onto a gold-coated substrate with an indium interfacelayer. Other samples were cut from ingots prepared bymelting or sintering. These samples were cleaved orscraped in situ with an alumina rod to expose a clean sur-face.

For this study, our intent was to choose relatively sim-ple and stable compounds which provide a range of chem-ical properties (e.g. , variable valence state and cation-ligand bond strength), while minimizing experimental dif-ficulties. We argue that satellite energies may quite gen-erally be used to discern chemical properties oftransition-element cations in different environments.However, we have not chosen to test the model predic-tions by extensively utilizing measurements reported inthe literature. In some cases, satellites are relatively weak,and- interfering structures from extrinsic loss processescan make data interpretation difficult (e.g. , see Sec. VD).For these reasons, tabulated values of satellite energies areparticularly inappropriate. Also, in situ sample reductionproblems (particularly for samples containing highvalence cations and heavier halides), inadequate valence-state isolation (frequently a problem with commerciallyobtained samples), and surface oxide contamination canprovide misleading results. For some compounds, satelliteenergies reported in the literature vary widely. Thus forthis study we chose systems which, in general, showstrong satellites. Surface oxides and in situ reduction ten-dencies were carefully monitored to ensure that their in-fluence on satellite positions was minimal.

The iron chloride samples were very hygroscopic. Sincespectral detail was sought at the weak Fe 3s levels, bothhydrous and anhydrous forms were measured to check forspectral distortion resulting from residual water (or oxy-gen) contamination. In the spectrometer, the hydratesshowed severe outgassing tendencies, probably associatedwith dehydration. The anhydrous FeC12 sample was asingle-crystal ingot which was loaded into the spectrome-ter from a nitrogen-gas atmosphere. The sample wasmounted with Torr-Seal epoxy (from Varian, Inc. ) andwas cleaved just prior to insertion. No oxygen or carboncontamination was observed on the cleaved surface. Aspectrum taken three days after initial loading into thevacuum system showed the presence of both carbon andnitrogen, but no apparent oxygen. No discernable differ-ences were noted between the (Fe 2p or Fe 3s) spectra ofingot FeC12 and powder FeC12 4H20.

For the FeC13 samples, only powder specimens wereavailable. For the hydrous material, severe outgassing ini-tially occurred in the spectrometer, probably resulting in asignificantly dehydrated sample. The anhydrous FeC13sample was loaded from a nitrogen-gas atmosphere. Theoxygen XPS signal was reduced by about a factor of 2 rel-ative to the hydrate, but it was not eliminated. Again,spectra for the "anhydrous" FeC13 and the (dehydrated)FeC13 6H20 samples were very similar. The presence ofresidual oxygen suggests that the sample surface is ratherpoorly characterized and may contain oxyhalide(s). How-ever, the Fe + state is apparently preserved in a predom-inately Cl environment. Spectral distortions at the Fe lev-els (at our level of signal-to-noise ratio) introduced by the

FINAL-STATE SCREENING AND CHEMICAL SHIFTS IN. . .

TABLE I. Satellite energy measured relative to cation 2p3/2level (Sc data are from Ref. 25).

Sc'+

FeF2FeA1204.FeC12FeBr2

ScF3Sc203ScC13ScBr3ScI3Sc2S3

E„, {eV)

6.35.75.44.8

12.311.49.58.47.49

Fe+

Zr'+

Ti'+

FeF3Fe203FeC13

ZrF4Zr02ZrC14

TiF4Ti02

E... (eV)

9.1

8.27.0

14.213.011.7

14.413.3

MnF&

I

f,p

Co F&

presence of oxygen appear to be small.In general, the trends reported here are confirmed by

measurements of satellite separations reported elsewherein the literature. Independent measurements of satellite

separations for the compounds reported in Fig. 10 appearin Refs. 4, 9, 13, 17, and 25. Data for the scandium com-pounds are from Ref. 25. 'Agreement between the citedmeasurements of satellite separations and our own mea-surements is usually within 3%. For the compounds ofFig. 10, the satellite energies (measured relative to the2p3/2 peak) are listed in Table I. The binding-energyreference scales used in Figs. 8, 11—16, and 18 were takenfrom the 2p3&2 levels of appropriate compounds listed. inRef. 2.

DISCUSSION

A. Typical core-level spectra and satellites

Figure 6 shows XPS spectra of the 2p levels in a seriesof 3d transition-metal difluorides (also see Ref. 4). Spec-tra are presented with the intense 2@3/2 peaks in align-ment. Except for ZnF2, satellites appear adjacent to thespin-orbit-split main lines. These satellite intensities sys-tematically increase, relative to the main line, with cationatomic number. The systematic behavior of the spectralfeatures for the Mn-Cu series of compounds illustratesthat the local screening condition (low BE peak) is dom-inant, especially for MnF2, where essentially no satellitestructure is observed. For ZnF2, which has no unfilled 3dlevels, only the nonlocal screening condition is possible.Consequently, no satellite structure (really no main line) isobserved except for weak plasmon peaks that also occuradjacent to the F 1s level.

The spectra of Fig. 6 show satelhtes at the 2p levels fordivalent transition-metal fluorides where satellites con-

Ni F&

1

~ ~

CUF&

I'. /~ ~ ~ ScF3

25

RELATIVE ENERGY (eV)FIG. 6. XPS spectra for spin-orbit-split 2p&/~ and 2p3/p lev-

els in a series of transition-element difluorides showing main-line and satellite features. Spectra are presented with the intense(main lines) of the 2p3/2 levels in alignment; the abscissa recordsthe binding energy in relation to the aligned main lines. For thecompounds of Mn-Cu, the main line corresponds to a locallyscreened {d"+') final state with the satellite resulting from non-local screening (d" final state). Since 3d screening cannot occurin ZnF2, no satellites appear and the peaks correspond to nonlo-cally screened final states. The nonlocal screening state for2p3/2 emission is indicated with the dashed line.

0

RELATIVE ENERGY (eV)FIG. 7. XPS spectra for the spin-orbit-split 2p levels of

CaF2, ScF3, and TiF4 displayed with 2p3/2 levels in alignment.Strong satellites on the high-binding-energy side replicate the 2pdoublet.


sistently appear about 6 eV removed from the intenselines. In Fig. 7 we show 2p spectra for 2+, 3+, and4+ cations of the compounds CaFz, ScF3, and TiF4,respectively. These (chemically) fully ionized cations arefrom the low-Z side of the 3d transition series. For thesecompounds, satellites are significantly more separatedfrom the main line (10—15 eV) than is the case for the di-fluorides. Here satellites replicate the main spin-orbitdoublet without overlapping it. A significant feature ofthe satellite spectra in Figs. 6 and 7 is their relative sim-plicity. Satellite spectra associated with a given core linetend to be characterized by a single peak.

B. Cation valence

Figure 8(a) shows the Fe 2p levels for Fe + and Fe +

ions in FeClz and FeC13. Consistent with the predictionsof Sec. III, we observe a small shift of the intense peak tohigher binding energy as Fe valence is increased and asubstantially larger shift of the satellite. The net effect isa small offset of the intense peak with an increasingseparation between main line and satellite as the Fevalence is increased. The spectra of Fig. 8 are presentedwith the Cl 2p core levels in alignment. Since the local-charge environment at the Cl site might be different in thetwo compounds, this alignment procedure may not be en-tirely appropriate. In support of this procedure, however,the absolute binding energies of the Cl 2p lines for thesetwo compounds, as reported in the literature, are nearlyequivalent. Also see Secs. VE and VI. While some un-certainty occurs in the relative positioning of the Fe +

and Fe + peaks, the main-line —to—satellite separationclearly and dramatically increases with increase of Fevalence.

Also shown in Fig. 8(b) are the Fe 3s levels. Thesespectra are further complicated by a large exchange split-ting, important when the 3s and 3d radial wave functionsare comparable. Following the procedure cited in Ref. 49(and using the same dependence of exchange splitting on

3d population), we calculate the 3s spectra. The calculat-ed results are shown immediately beneath the measuredspectra in Fig. 8(b). As in Ref. 49, the use of exchangesplitting and multiple screening states appears to satisfac-toiily account for the observed line shapes. For the Fe +compound, the 3s spectrum is noticeably compressed be-cause both the screening splitting and multiplet splittingare reduced relative to the Fe + compound.

C. Ligand electronegativity: Effect on cation spectra

sa t.

2 P3/2

The potential at the cation site in a binary ionic com-pound is affected by the relative ability of neighboringligands to withdraw charge from the metal atom. In gen-eral, as the ligand becomes more electronegative, we ex-pect that the potential at the cation site will become morepositive. (Of course, the cation potential can also be af-fected by the coordination number and relative orienta-tions of neighboring ligands. )

The process of increasing ligand electronegativity isqualitatively represented in Fig. 5 by moving to the righton the abscissa (moving electron charge outward from thecation center). Thus, we expect to see an increase in themain-line —to—satellite separation as ligand electronega-tivity is increased. This expectation is confirmed in Fig. 9where Fe 2p spectra are presented for the Fe + com-pounds FeF3, Feq03, and FeC13. Electronegativities(Pauling scale) for the ligands are 4.0, 3.5, and 3.0, respec-tively. Other systematic measurements of transition-element systems in the literature which dramatically illus-trate this correspondence between ligand electronegativityand satellite separation include a series of scandium com-pounds (ScF3, ScC13, Scq03, ScBr3, and Scl~), a corre-sponding (vapor-phase) Ti + series, ' and a Mn + series.

The satellite shift versus Pauling electronegativity is

2~&rzso t.~

2~IZZso t.

Fe CP&

(b) Fe&s

I~4'

~ eg

&eF~.

sat.A

Fe Cl~

W~~/, 9'

4—740 750 720 7I0 700 I 25 I I 5 l05 95 85

EIINDING ENERGY (eVj

FIG. 8. (a) Spin-orbit-split 2p-level spectra for Fe + andFe + chlorides showing the low-binding-energy main lines andprominent satellites. Note that the larger separation betweenmain line and satellite occurs for the higher valence cation. Themain line of FeC13 also displays a small chemical shift to higherbinding energy relative to the main line of FeClq. (b) Fe 3s lev-els in FeCl~ and FeC13. Predicted exchange-split doublets offsetby the screening splitting (6& for Fe + and 5& for Fe +) are com-pared with measured 3s spectra (see text).

1t

F 0-e203

FeCg ~==3

I

50 20 IO 0RELATlVE ENERGY (eV}

FIG. 9. XPS spectra for 2p levels in FeF3, Fe&03, and FeC13shown with 2p3/p levels aligned. Note that the satellite separa-tion from the main line increases with ligand electronegativity.


Tl F&

(a) K 2p's

I3

eCg& Fe Br2

4.0 3.5 5.0ELECTRONEGATIV I TY (b) F 1s

FIG. 10. Energy separations between main line and satellitesin XPS spectra of cation 2p3/2 levels for a number of ionic com-pounds. Satellite separations are plotted versus ligand electrone-gativity (Pauling scale). The satellite energies show a systematicdependence on electronegativity and cation valence. As thecharge environment at the cation site becomes more positive, thegreater is the satellite separation.

recorded in Fig. 10 for a number of representative seriesof compounds. We note the following.

(1) In all of the series, the satellite shift increases asligand electronegativity increases.

(2) Tht," splitting increases with increasing cationvalence as illustrated by the Fe + series and Fe + series.

(3) For highly electropositive cations (e.g. , Sc +), thesplitting is larger than for cations that have equivalentvalence (e.g., Fe +) but are less electropositive.

310 300 290

BINDING ENERGY (eV)FIG. 11. (a) XPS spectra of K 2p levels in KF. Spectra on

the high-binding-energy side, showing weak (apparently extrin-sic) electron-loss processes, are blown up 8 times. (b) F 1s spec-tra of KF similarly displayed. The F 1s peak is aligned with theK 2p3/2 peak (energy scale pertains to the K 2p levels). Notethe similar loss spectra following the F 1s and K 2p peaks.

satellite should be observable (unlike the case for K).In Fig. 11(a) we show the spin-orbit-split K 2p spectra

of KF with the high-binding-energy side enlarged 8 times.In Fig. 11(b) the F ls line is similarly displayed. Since aF 1s hole cannot be screened locally we expect to observea single F ls peak followed by extrinsic loss processes as-sociated with an 'electron traversing the solid. In princi-

D. Z+ 1 considerations: K'+ and Ca +

By applying the insights provided by the Z + 1 analogy(see Sec. III) to the analysis of K'+ and Ca + spectra,another important test of the screening model is obtained.For K + (e.g. , in KF) experiencing deep core photoioniza-tion, the Z+1 analogy suggests that the unscreened pho-toexcited ion is approximately equivalent to Ca +. ForCa, the ground-state atomic configuration is 3d 4s .Furthermore, in solids, we expect Ca to have a very small(hybridized) 3d population (a fraction of one electron).Thus we expect that the ground-state screening conditionof a deep hole in photoexcited K will be nonlocal. Theunfilled 3d bands, lying well above EF, are also highlydelocalized and consequently will be hybridized with ex-tended neighbor orbitals. Thus we expect that the K XPScore-level spectra will show no satellite structure attribut'-able to local screening states. On the other hand, Ca +(e.g., in CaFq), after having experienced deep core pho-toexcitation (but unscreened), is analogous to Sc +. Thelow-lying excited state should be predominantly 3d.(Atomic scandium has the configuration 3d'4s .) Thelow-binding-energy XPS peak at a Ca + core level thusshould correspond to a locally screened state. Thus the fi-nal state closely approximates the Sc + ion which con-tains an occupied 3d level. If a suitably metastable nonlo-cal screening state is also available, both the main line and

~W

(b)~+~t

(a) K 2p's

(b) S~

3 t 0 300 290

BINDING ENERGY (eV)FIG. 12. To demonstrate that the background (loss) spectra

following F 1s and K 2p spectra are of common origin, the K2p 1oss region is simulated by superimposing two F 1s spectraproperly scaled and offset to duplicate the spin-orbit com-ponents of the K 2p's. This offset-scaling procedure of the F 1sline nicely duplicates the K 2p loss region. Thus no K 2p satel-lite structure associated with different screening states of the 2pcore hole can be discerned.

5408 B. %'. VEAL AND A. P. PAULIKAS 31

pie, shakeup excitations associated with the F 1s hole arealso possible. However, KF is a wide-band-gap materialso they should be quite energetic, probably outside thespectral range displayed in Fig. 11. (In fact, strong satel-lite structure, exclusive to the F levels, is observed in thealkali and alkaline earth halides at 25—30 eV from themain line. ' ) If the structure following the K 2p's andF 1s is predominately extrinsic, then we should be able tosimulate the K 2p loss region by superimposing two F 1sspectra suitably scaled and offset to duplicate the spin-orbit components of the K 2p's. This simulation ispresented in Fig. 12(b), where it is compared to the raw K2p spectrum [Fig. 12(a)]. Both the magnitudes and shapesof the loss features in the simulated spectrum accuratelyreproduce the K loss spectrum. Surely no satellite peak,exclusive to the K line is apparent. For CaF2, the Ca 2pand F 1s spectra are displayed in Fig. 13. Using the F 1sline and the procedure outlined above, a Ca 2p spectrumis simulated and displayed in Fig. 14(b). We see that aportion of the experimental Ca 2p loss region is nicely ac-counted for, but a residual doublet persists. If this residu-al doublet corresponds to a screening state, it shouldreproduce the intense spin-orbit doublet (with a possiblelinewidth difference). Thus we add to the simulated spec-trum [Fig. 14(b)], the original Ca 2p spectrum (scaled by0.04 and offset by 10.8 eV). This final composite isshown in Fig. 15 compared with the Ca 2p XPS data. Wesee that a remarkably accurate reproduction of the mea-sured satellite spectrum is obtained. Thus we concludethat the satellite region consists of a single nonlocalscreening state superimposed on an extrinsic loss back-ground. The considerable difference in population ofthese two screening states apparently reflects differencesin the overlap between the initial (ground) state and thetwo possible final-state wave functions. In any case, Figs.11—15 demonstrate that multiple screening states are ab-sent in KF but are clearly present in CaFz, as predicted.

~ ~

~ ~ ~ ~

~ ~

(a) Ca 2p's

(b) Sim.

365 355 345

This analysis also demonstrates that considerable caremust be exercised in interpreting the satellite features.The Ca 2p spectra (Fig. 13) consist of three sets of spin-orbit-split doublets, but one doublet is contributed by ex-trinsic loss features common to the core lines of both ca-

(a)~ ~ ~ ~r~ ~ ~

~ ~ ~

(b)

C ~~ r

~ ~

~ ~ ~ ~' 'r

BlNDfNG ENERGY (eV}FIG 14 (a) XPS spectra of Ca 2p levels in CaF2 (b) Using

two superimposed F is spectra [Fig. 13(b)] properly scaled andoffset, the Ca 2p doublet is reproduced. Note that a portion ofthe high-binding-energy side is accurately reproduced but a resi-dual doublet is not accounted for.

(a) Ca 2p's

(a) Ca 2p's(b) Sim

365 355 345

(b) F 1s

365 355 345

B)NDING ENERGY (eV)FIG. 13. {a) XPS spectra of Ca 2p levels in CaF2. The high-

binding-energy side is blown up 16 times. (b) F 1s spectra inCaF2 similarly displayed {the energy scale pertains to the Cacore levels).

BINDfNG ENERGY (eV)

FIG. 15. (a) XPS spectra of Ca 2p spectra in CaF2. (b) Ca 2pspectrum (scaled by 0.04 and offset by 10.8 eV) added to thesimulation of spectrum (b), Fig. 14. The sequence of simulationsteps for the Ca 2p spectra (Figs. 13—15) indicates that a singlesatellite spectrum intrinsic to the Ca 2p's is superimposed on anextrinsic spectrum whose origin is also common to the F 1sspectrum. These results support the view that the Ca 2p satel-lite region contains a nonlocaHy screened final state with the in-tense lines corresponding to a locally screened final state. KF,in contrast, does not show multiple screening states (see Figs. 11and 12).


tion and ligand.The fact that K and Ca ions show very different but

predictable satellite structures provides strong evidence insupport of the screening model. The Ca cation, eventhough it has no occupied 3d electrons, shows behaviorwhich is typical of the cations in 3d transition-series insu-lators. The important common feature is that, when pho-toionized, the first unoccupied level is 3d.

E. Chromium compounds

The local screening condition for photoexcitation fromthe outermost (partially filled) shell of localized levels(e.g., for photoemission from a 3d level of a first longseries cation) assumes particular significance. The mea-surement of a 3d hole screened by an identical 3d meansthat the total energy difference (i.e., the transition-stateenergy) between the initial ground state and the finalscreened state is approximately zero (except for the energyrequired to move one electron across the work-functionbarrier and possible multiplet excitations which may ap-pear in the spectra). This screened final state correspondsto the level appearing at E =0 in the simulation of Fig.3(b). In the absence of multiplets, we expect that 3d emis-sion from transition-element insulators will appear in asingle 5-function line and will provide a "zero-energy"reference (i.e., the energy difference between nearly identi-cal initial and final states) for the photoemission spec-trum. Such a reference level is easily identified in the ex-perimental valence-band spectra of Cr20& shown in Fig.16(b). The sharp peak at the valence-band edge corre-sponds to excitation from the (nominally threefold occu-pied) 3d level of the Cr + ion. Reoccupation of the 3dlevel during measurement means that the 3d resonantpeak actually provides an approximate measure of theupper valence-band edge (assuming that the 3d state fillsfrom levels nearest E~). That is, with relaxation to a localscreening state, photoemission from the 3d level only re-quires enough energy to remove an electron from the

C&20g

02s p.

(b)

„pwzpt/2r:

/ I:.

I

I

I

I

I, I I

I585 575 565I

I

I

I

I

I

02p I

~ 3d sat.0 ~ ~

~ ~

~ ~II ~e ~

I

30 20I

jo

8lNDiNG ENERGY (eV)

FICx. 16. XPS spectra of {a) Cr 2p levels and (b) the valence-band region of Cr20&. The Cr 2p&&2 and Cr 3d peaks are shownin alignment to illustrate that satellite peaks occur at compar-able energies from the main line, both at the deep core levels andat the 3d level.

valence band.This point of view is also supported by molecular clus-

ter calculations of lanthanide trihalides reported by«scic « ~~."Mulliken analyses of the transition-stateion (an ion with —, hole) with the —,

' electron removed.from a 4f level, show an electronic relaxation from ligandorbitals to repopulate the depleted 4f shell. Thus the cal-culated 4f removal energy actually represents the removalenergy of the least-bound ligand orbital. This, of course,represents a fully relaxed molecular unit, a condition thatmay not always be probed by photoemission.

Analysis of the XPS valence-band measurement consti-tutes a problem separate from the analysis of 3d emission,requiring examination of the relaxation effects associatedwith removal of an electron from those valence bands(VB) which are predominately ligand orbitals. To the ex-tent that XPS measures the valence-band ground state, weexpect that the locally screened 3d peak will appear incoincidence with the upper valence-band edge. In Fig.16(b), experimental spectra confirm that the 3d peak inCr20& indeed occurs in coincidence with the upper VBedge.

However, in contradiction to these model predictions,cations ligated to highly electronegative anions show localscreening peaks that sometimes occur at anomalously lowbinding energies. In some compounds, a gap of 1—3 eVmay separate the locally screened peak from the valence-band edge. ' Local screening at the cation merely re-quires the removal of a total charge equal to approximate-ly one electron from the (usually six) ligand near neigh-bors. However, charge relaxation to compensate for aligand hole requires a polarization response from second-neighbor ligand atoms. (Near-neighbor cations are ion-ized and generally will not significantly contribute screen-ing charge. ) Thus, ligand screening requires a long-rangepolarization' response mediated by intervening cations.Since this collective response requires such long-range in-teractions, it may be that the system cannot relax in thetime frame of the photoemission experiment. Conse-quently it is likely that XPS does not monitor a fully re-laxed final state at the ligand site but comes much closerat the cation site. This view suggests that, for ligandphotoemission, a rather localized final hole state (at theligand site) is monitored. In contrast, for photoemissionfrom the outermost localized electron shell of cations, themore favorable relaxation conditions permit charge redis-tribution onto neighboring ligands resulting in the mea-surement of a more diffuse final hole state. As ligandsbecome less electronegative, the ions become larger, andligand-ligand overlap increases. For these materials, re-laxation of ligand valence-band electrons becomes morefavorable following photoemission and the locallyscreened outer (cation) level appears in closer proximity tothe valence-band edge, suggesting that more nearly com-plete relaxation has occurred.

We now examine the core-level satellite structure ofCr + compounds using the perspective described in Sec.III (see Fig. 5), considering ground-state configurations(3d "4p "). For Cr +, we regard three of the occupied delectrons to be atomiclike. To represent the nonlocalscreening (NLS) condition, then, we use a screening elec-

5410 B. %'. VEAL AND A. P. PAULIKAS 31

tron whose orbital makeup is equivalent to the occupiedconfiguration (of the ground state) that is in excess of thethree localized d electrons. VA'th this procedure, the NLScan have some 3d admixture. ' This is a somewhat arbi-trary procedure for quantifying the nonlocal screeningstate. The underlying assumption is that the NLS "polar-ization" state should be reasonably represented by occupa-tion of a low-lying hybridized band that exists separatefrom minimally hybridized atomiclike 3d levels. Calcu-lated results for both screening states at the 2p3/2 level areshown in Fig. 17.

For CrzOq, the observed separation between local andnonlocal screening peaks at the 2p3/2 level is 11.1 eV. InFig. 17 we see that this level separation is obtained fromatomic TS calculations for the ground-state configurationCr(3d 4p ). The calculated energy difference betweenthe locally screened 2p3/2 and 3d levels is 573.9 eV, inclose agreement with experiment (573.3 eV). The differ-ence between these experimental and theoretical numbers(0.6 eV) appears in Fig. 17 at the 3d level. (In this way,we have measured the 3d level using the screened 2p3/2core-level peak energies as our point of reference. )

For CrF&, the 2p3/2 satellite separation increases to 11.8eV. Again, using Fig. 17, we choose the ground-state con-figuration that matches the calculated energy differencebetween local and nonlocal screening states with the ex-perimental satellite separation. The increased separationof CrF&, relative to Cr20&, indicates a more positive cationpotential (that is represented by a configuration with

0—Cr~0&~ ~Cr F&

I

[Cr 3d3/~j

LOCALSCREENING

10—

Ct'W

~ 570—

ObJCL

580—

c' z&zizl

04

LOCALSCREENING

590—ONLOCALCREENING

{3d 4p ) (3d 4p ) (3d 4p )

GROUND STATE CONFIGURATION

FIG. 17. Calculated (TS) electron-removal energies (solidlines) for (3d"4p ") configurations for both local and nonlocalfinal-state screening conditions. For Cr20q and CrFq the Cr"ground-state configurations" are determined by matching theobserved satellite separations with the calculated local-nonlocalenergy separations (see text). The potential at the cation site inCrFq is seen to be slightly more positive than the correspondingsite in Cr20&. After fitting the spectra at the 2p3/2 level, com-parison is made between the measured 3d position and the cal-culated (local screening) 3d energy (E=0). The Cr "ground-state configuration" is also determined for K2Cr04. Here, Croccurs in the hexavalent state. Satellites are not apparent so theconfiguration is determined by monitoring the main line (localscreening) chemical shift relative to the Cr + compounds.

slightly reduced 3d occupancy). Again we use the 2p3/2levels as our point of reference and measure the energy ofan electron in the (locally screened) 3d level. The differ-ence between the theoretical (574.0 eV) and experimental(573.5 eV) 2p3/2 3d separations for local screening is 0.5eV, essentially equivalent to the measurement for Cr203.Thus for Cr compounds wh'ere a reference (zero energy)3d level can be observed, the analytical procedure correct-ly predicts the trends in the relative level placement thatare observed when the local cation potential is varied.Also, remarkably accurate determinations of peak separa-tions, hundreds of eV separated in energy, are obtainedfrom the local-density calculation of the screened holestates.

Using the configuration (3d 4p ) for CrzOs, we nowexamine the 3d shell. The calculated NLS peak occurs at7.5 eV, with the local screened peak, of course, at 0 eV. Asignificant prediction of this model picture is the expectedoccurrence of a NLS satellite peak near the 3d peak.Note, in Fig. 16, that the predicted peak is observed. Theobserved satellite separation at the 3d level is slightlygreater than the separation at the 2p's [Fig. 16(a)], al-though some reduction in the satellite separation ispredicted by the atomic simulation.

This analysis points to another useful insight. Atomiccalculations show that the excitation energy needed to re-move a localized 3d electron, in the absence of extra-atomic relaxation, will be —10 eV or more. This result isexperimentally confirmed for free atoms. The free-atom3d removal energies are always significantly greater than4s removal energies. Furthermore, the more highly ion-ized an atom is, the greater will be the removal energy foroccupied localized electrons. For the chemically ionizedCr + cation characterized by the configuration 3d 4pthe calculated (unscreened) removal energy is 15.8 eV.Thus, the fact that 3d's (or other local levels) frequentlyappear at or near the valence-band edge in ionic com-pounds is a strong indication that significant extra-atomicrelaxation, accompanyirig photoexcitation, has occurred.

As the Cr valence state is increased to the highly ion-ized Cr + condition (as in K2Cr04), a substantial increasein the local Cr potential is expected. Charge is drawnfrom 3d levels into molecular orbitals that are rich in 02p character. Unfortunately, core-level satellite featuresin K2Cr04 are apparently too weak and broadened to bediscernable from the extrinsic background and, of course,no reference 3d peak occurs since all outer electrons parti-cipate in molecular orbital formation. However, we sug-gest that a determination of the Cr core-level chemicalshift between Cr20& and K2Cr04 can be obtained by usingthe 0 1s line as a fixed energy reference. This procedureappears to be defensible since, with extended x-ray expo-sure, K2Cr04 chemically reduces, leaving superimposedCr + and (apparently) Cr + spectra. While the Cr~+ andCr + spectra show a large relative chemical shift, the oxy-gen (and potassium) lines remain unshifted during thereduction process. It seems reasonable, under these cir-cumstances, to infer that the local oxygen potentials forthe two compounds are very similar and that relativeshifts between Cr + and Cr + lines correspond to achange in the local Cr potentials (and not to spurious


charging or band-bending effects, which should affect allcore levels in a similar way). Using the 0 ls as a refer-ence, the chemical shift at the 2p3/2 peak for K2Cr04 rel-ative to Cr203 is 2.6 eV. This shift is very close to the2.8-eV binding-energy difference recorded in Ref. 2 forCr203 and K2Cr04. (However, the usual energy-referencedifficulties are encountered with the measurements ofRef. 2.)

Figure 17 would indicate that the final state corre-sponding to the intense 2p3/2 peak in K2Cr04 must bescreened locally. A Cr + ground-state potential represent-ed by the configuration (3d '4p '

) is suggested. For thisconfiguration, a NLS satellite would be expected at —15eV from the main line. Here the satellite is calculated(dashed line in Fig. 17) with the assumption that the orbi-tal composition of the screening electron is equivalent tothe ground-state configuration. (No moment-bearing, lo-calized 3d electrons are occupied in K2Cr04. Thus noground-state 3d electrons are excluded from the nonlocalscreening state as they were in Cr203. )

F. Satellite structure at the unfilled local shell

We have argued, in Sec. VE, that satellite structure,when apparent at deep core levels, will also be expected inthe vicinity of the partially filled, localized outer electronlevels. We expect these outer levels to show screeningbehavior much like that observed at the core levels. Wehave seen in Fig. 16 that a satellite associated with theCr +(3d ) peak does appear near the valence band ofCr203.

The 3d satellites are predicted for ionic compoundswhich have occupied atomiclike 3d states. If, however,we consider those compounds which are fully ionized(nominal 3d ions), then we have the remarkable cir-cumstance where strong satellites may be observed follow-ing the core levels (since empty 3d's are available forscreening) but no satellites can appear adjacent to thevalence band. An example of this situation is illustratedin Fig. 18 for ScF3. Very intense satellites follow the Sc

2p doublet, but no corresponding structure appears nearEF since no atomiclike 3d levels are available for ioniza-tion. Thus we see that, for insulators with strong cationcore-level satellites, corresponding satellite features mayor may not occur at the 3d level. The ability of the sim-ple screening model to predict their occurrence or absenceat the 3d level provides additional supporting evidence forits validity.

If the screening picture advocated in this paper iscorrect, then we should expect, for the 3d electrons, to ob-serve n —1 final-state multiplet structure at the satelliteposition. The low BE structure overlapping theligand —p-bonding orbitals also very likely contains multi-plet features but, in this case, the final states contain theoriginal 3d" electron count.

G. Iron compounds: An estimate of ground-statepotentials from XPS spectra

Exploiting the observation that cation deep core satel-lite separations are highly dependent on the local cationground-state potential, we suggest that with help from theatomic code an estimate of the potential at the cation sitecan be made. In Fig. 19 we show separations of the calcu-lated screened peaks for Fe ions as a function of variedground-state electronic configuration (3d "4p "). For theFe + ions, we hold a "localized 3d count" fixed at 6 (seeSec. VE) and screen (nonlocally) with an electron whosecharge distribution is equivalent to that of the remainingelectrons while for Fe +, we fixed a localized 3d count at5. Using the satellite data of Fig. 10 for the Fe com-pounds, in conjunction with the calculated curves of Fig.19, we find that Fe + ligated to fluorine neighbors rests in

a potential field represented by the configuration(3d 4p ). The d count is 5.8, 0.8 in excess of the nomi-nal Fe + ion configuration. This excess increases to 0.9and 1.1 for oxygen and chlorine neighbors, respectively.Similarly for Fe + ions ligated to fluorine, the excess dpopulation is 0.5 over the nominal Fe + ion value and in-

Sc F&

2pI~~ sot. p I /2,

:2p3/2'I l2—

Fe~+COMPOUNDS

Sc3p .i ~ ~e ~

~ 4 AJ:„'F2

I

4I5 405I

I

I

I

395

O

lX 8LLICA

LIJI—

LLI 4—M

I I I

40 30 20 IO 0

I

(Sd74I ') (pd64p2)

GROUND STATE CONFIGURATION

BINDING ENERGY (eV)

FIG. 18. XPS spectra of Sc 2p levels and the valence-band

region in ScF3. Strong satellites follow the 2p levels but (unlike

Fig. 16) no satellites occur adjacent to the valence bands.

FIG. 19. Calculated (TS) satellite separations (energy differ-ence between local and nonlocal screening of final state) as afunction of ground-state configuration for Fe + and Fe + ca-tions (solid lines). Experimental satellite energies are used inthis figure to estimate the ground-state potential at the cationsite.

5412 B. W. VEAL AND A. P. PAULIKAS 31

creases to 0.6, 0.6, and 0.7 for 0, Cl, and Br neighborsrespectively. Two trends (also noted for the Cr com-pounds discussed in Sec. V E) are observed:

(1) in a given valence state, the excess d count decreaseswith increasing ligand electronegativity (charge is moreeffectively pulled away by the more chemically active ion)and

(2) for a given ligand, the excess d count increases withincreasing cation valence state. Both of these trends aregenerally observed in Mulliken analyses of clusters orsolids.

We have pointed out that the nonlocal screening elec-tron wave function is somewhat arbitrarily specified.And, of course, uncertainty regarding this screening statewill be translated into a corresponding uncertainty in thededuced ground-state configuration. Thus, while we.canreadily monitor chemical trends involving charge redistri-bution, we cannot uniquely measure the ground-state po-tential. However, a more precise determination of thescreening states, possibly by applying molecular-clustertheory, in conjunction with the measured XPS satelliteseparations, should provide the capability for obtaining anaccurate ground-state description of ionic solids. Also, itmight provide a basis for extracting, in a straightforwardway (as demonstrated above, perhaps), a good approxima-tion to the ground-state potential directly from measure-ments of XPS satellite separations.

H. Lanthanides

For XPS spectra of lanthanide compounds, the locationof 4f-derived features relative to EF provides an impor-tant clue regarding the nature of the final-state screeningconditions. For light lanthanides, it appears that both lo-cal and nonlocal screening of deep hole states occur withcomparable probabilities. Strong satellites commonlyoccur at the core levels of I.a and Ce compounds ' andthe 4f peak of Ce + insulators appears near the valence-band edge. However, for compounds of heavierlanthanides (Z& -63), it appears that local screening isnot observed. In consequence, for the heavy lanthanides,4f spectra generally occur well away from EF (see Sec.VE) and the complex but well-understood 4f multipletstructures measure the 4f occupancy of the n —1 finalstate. Since screening for the heavy lanthanides is ap-parently nonlocal, chemical shifts are large, as confirmed,for example, by observation of large chemical shifts inmixed-valence compounds. SmB6 shows a chemicalshift of —10 eV between core levels (centroids) in the 2 +state relative to the 3+ state.

An even more dramatic feature of light lanthanide sys-tems (which display both screening conditions) resultsfrom the fact that local screening should occur via 4felectrons which are more localized than the 5s and 5pcore states. Thus the satellite structures associated withthe n =5 core levels are profoundly different from the sa-tellites associated with the deep core levels. Analysis ofthese materials, including La +, Ce +, and Ce + insula-tors, will be the subject of a subsequent paper.

I. Photoemission from ligands

Applying the Z+ 1 analogy to core-level photoemis-sion from ligands leads to rather different considerationsfrom those appropriate for the cation. The very elec-tronegative ligands (e.g. , from group VIA and VII') inionic compounds are characterized by a single valencestate and nominally have chemically filled shells. Forthese atoms, advancing from Z to Z+ 1 always involvesa valence change of one unit and, nominally, no change inthe population of the outermost electron shell. Thus, theouter electron levels of 0 (with an 0 ls hole) in an ion-ic compound should reasonably approximate the outerF' levels. (Recall that addition of a deep hole approxi-mates the addition of a proton. ) Consistent with this ob-servation, the ionic radii of 0 and F' are 1.40 and1.36 A, respectively. This very similar ionic size (with aslight contraction for the monovalent species) is charac-teristic of 2 —ions in group VIA and their 1 —neighborsin group VIIA. Thus, unlike the case for cation core lev-els, we would not expect to observe extra-atomic relaxa-tion involving the population of additional orbitals when aligand deep core hole is created. The ion always has achemically filled shell. Of course, on a less dramaticscale, an extra-atomic relaxation response will occur sincethe chemically filled shell of a ligand (of charge Z) is notequivalent to the chemically filled shell of its adjacent(charge Z + 1) neighbor. Some contraction of the outerp-shell orbitals occurs when the nuclear charge is in-creased (or a core hole is induced).

Since anion relaxation effects would generally appear tobe small, we expect that the energies of ligand XPS peaksshould be relatively sensitive to changes in the ground-state local anion potential. When anion shifts are small(apparently the usual case for binary metal-halide com-pounds when the cation is varied ' ), the indication maybe that the local halide potential is relatively the same inthe different compounds. Because satellite structure asso-ciated with local screening states is absent at the ligandcore levels, however, chemical information cannot be ex-tracted from the internal level structure in the straightfor-ward way afforded by the transition-metal cations.

J. Other considerations

It appears that, quite generally, the simple relaxationmodel discussed above will account for the main lines anddominant satellites in deep core (e.g. , 2p) XPS spectra of3d transition-element insulators. However, there are ex-ceptions, where predicted trends are not observed andwhere spectra are too complex to be readily explainedwith the simple model. In general, we expect that, forXPS spectra of 3d cations, the fully relaxed state will cor-respond to a locally screened ion and can be associatedwith a single XPS peak. [It may not always be true, how-ever, that this fully relaxed state is observable with XPS.For example, as noted above, the local (4f) screening stateapparently is not observable in compounds of heavylanthanides. However, we cannot identify 3d compoundsthat show this behavior. ] Some structure within the local-ly screened state might be contributed by multiplet excita-tions. One might expect, however, that cation satellite


spectra could represent a complex assortment of excita-tions (with a complex photoemission spectrum) ratherthan a single semirelaxed hole state characterized by non-local or band-type screening. For the simpler (e.g., binaryionic) compounds, such spectral complexity appears to bemore the exception than the rule. Typically a singlestrong satellite peak is observed. However, for com-pounds of copper and nickel, substantially greater spectralcomplexity is observed. Cation spectra for nickel halidesoften show two or more satellites. ' ' The main lineand first (lowest BE) satellite show behavior that is con-sistent with the trends predicted by the simple relaxationmodel discussed above with 3d screening accounting forthe intense peak. However, at least one additional satel-lite appears in the heavier nickel halides and shows aseparation from the main line that decreases with increas-ing ligand electronegativity. This would appear to be anexcitation of common origin for all the Ni halides. (ForNiF2, only a single satellite is apparent, probably becausethe first and second satellites have merged. ) For NiO, astill more complex spectrum is observed. ' Even the mainpeak is split into components separated by 1.8 eV.

For divalent copper compounds, predictions of thescreening model appear to be quite inappropriate. Satel-lites are generally composite, varying significantly be-tween the 2p&~2 and 2p3/2 peaks and showing a generallydecreasing satellite separation with increasing ligand elec-tronegativity. With the apparent strong tendency for lo-cal screening to occur in the 3d-series compounds, itseems likely that the main line corresponds to the fully re-laxed, locally screened peak (a conclusion also reached byRef. 24). The rather general systematics for halides inFig. 6 also favor this conclusion. However, satellites inthe Cu + compounds appear to be too complex to bedescribed by a single relaxation state.

VI. SUMMARY

We have utilized a relaxation model to account for XPScore-level binding energies and for the energies of prom-inent satellites that occur in compounds of transition-series elements. For purposes of this paper, illustrativeexamples have been confined to the first long series (3delements), but the concepts are also appropriate for the4d- and 5d-series compounds as well as for lanthanides(especially the light elements) and actinides. The oc-currence of spectral features (main line and satellite) is at-tributed to the presence of multiple screening conditionsof the photoinduced hole. The nature of the screeningelectrons and the ground-state potential determines theseparation of the satellite from the main line. Below wesummarize a number of considerations, discussed in thetext, that are relevant to deep core photoionization and tothe relaxation model.

a. Intra-atomic relaxation. Intra-atomic relaxation isalways associated with the production of a core hole. It isparticularly important when electrons in localized orbitalsare photoejected since their removal results in substantialreorientation of spectator levels involving large relaxationenergies.

b. Extra-atomic relaxation. The production of a core

hole leaves an unbalanced nuclear charge at the ion site.This increased positive charge pulls the electron levels ofthe ion to higher binding energy. It is now energeticallyfavorable for valence electron charge to be attracted fromneighboring atoms into the local potential well to screenthe core hole.

c. Character of screening ovbitaIs W. e expect thattransition-metal insulators will contain empty d statesthat are minimally hybridized (having essentially atomic-like character) as well as radially extended band states.Either type of state may serve to screen the core hole. Oc-cupation of extended-state wave functions is traditionallyviewed as a polarization response of the medium to thepresence of the local "impurity. "

d. The Z+1 approximation Fo.r a cation (of atomicnumber Z) with a deep core hole, a reasonably precisedescription of the electron states should be provided byrepresenting the ion as a Z+ 1 impurity in the solid. Toouter electron levels, the highly localized core hole ap-pears much like a proton added to the cation nucleus.Generally, in going from the Z to Z+ 1 atom, a d elec-tron (in transition-series compounds) is added. Similarlythe minimum energy state (fully relaxed state) of the ioninvolves the occupation of an additional d electron. Thisrepresents the local-screening condition. Thus screeningby filling a spatially localized orbital generally representsa larger deexcitation energy than screening with an ex-tended orbital (an excited-state condition of the ion).

e. Energetics —implications in XPS spectra. Sincescreening involves a deexcitation process, the kinetic ener-

gy of the photoelectron will be enhanced (by the screeningprocess) and the apparent XPS binding energy of thescreened state will thus be reduced -relative to the XPSbinding energy of the unscreened core hole. The low-binding-energy intense XPS line thus corresponds to amore fully relaxed condition than does the satellite. Thisinterpretation is consistent with a shakeup picture if weregard the main line as fully relaxed (i.e., locally screened)with the satellite being an excitation relatiue to this fullyrelaxed state.

f. Tempoval considerations. If multiple screening possi-bilities are observable, then time scales in the photoemis-sion process must play a fundamentally important role.Clearly, there is only one "ground-state" screening condi-tion. That is, if the core hole is sufficiently long lived,only orbitals for the least energetic of the possible screen-ing states will eventually become occupied to screen thecore hole. Thus, nonlocal screening states, to be observ-able as sharp satellites, must have lifetimes of at least—10 ' sec, the photoemission lifetime. The coupling be-tween those extended and local states of the cation deter-mine the electron residence time in the extended screeningstates.

g. Chemical shifts. The preceding analysis has shownwhy chemical shifts (involving the main line) are generallysmall for transition-element compounds, even when largecation valence changes are involved. The small shifts area consequence of local screening of the core hole, a relax-tion process which minimizes chemical sensitivity in XPSspectra. Greater chemical sensitivity is found at the satel-lite. Consequently, the relative spacing of local and nonlo-

5414 B. W. VEAL AND A. P. PAULIKAS 31

cal screening peaks (XPS main line and satellite) associat-ed with the cation is sensitive to the cation ground-statechemical environment. The peak separation increases aselectron charge is pulled away from cation site. Thus weargue that chemical-bonding information, including ca-tion valence state, can be obtained from measurements ofthe satellite separation relative to the main line. Unliketraditional measurements of absolute binding-energyshifts for studying chemistry, this approach does not re-quire the determination of an energy reference (an unsatis-factorily resolved problem for insulating materials).

VII. CONCLUSIONS

In this paper, we have, with several case studies, soughtto demonstrate that the intense, low-binding-energy peakassociated with XPS core-level photoemission measures,for 3d transition-element insulators, the energy differencebetween the ground state of the insulator and a final ionstate where the core hole is compensated by occupation ofan outer 3d electron acquired from surrounding ligand or-bitals. This viewpoint is supported by (fully relaxed) self-consistent field (SCF) calculations of ground-state andhole-state molecules, clusters, ' or "supercells, "where population analyses of the ground state and holestate consistently show that the core hole is predominatelycompensated by a 3d (or, for lanthanides, a 4f) electron.Thus, while energetics considerations generally supportthe local-screening interpretation of the intense peak, XPSmeasurement time considerations could, in principle, ex-clude it. The systematic studies reported in this papersupport the view that the local-screening description isgenerally appropriate for the final core-hole state associat-ed with the intense peak in 3d insulators. (This conditionis apparently not so generally true for lanthanide com-

pounds. ) It then follows that the (higher BE) satellites areassociated with states of the system which are not fully re-laxed. Core-hole screening (still a relaxation response)could occur by partial electron occupation of spatially ex-tended band states which lie above the localized 3d's. Theresult is a single, many-electron polarization state centeredat the impurity site. This simple model view, with gui-dance from atomic calculations and simulated local-cationpotentials, appears to provide substantial predictive capa-bility. Observed satellite separations for simple com-pounds are correlated with cation valence states and withanion and cation electronegativities.

To test these model ideas more quantitatively, the satel-lite separation from the main line will be calculated for amodel cluster using transition-state theory, by considering(1) the fully relaxed (core-hole) ion state to obtain the lo-cally screened main line and (2) by performing a secondSCF calculation, while preventing compensating popula-tion of localized 3d orbitals, to obtain the satellite. Inthis view, the dominant charge Aow response to core-electron ejection is electron migration from ligands to-ward the core hole, both for the main line and for the sa-tellite.

ACKNOWLEDGMENTS

The authors are grateful to numerous people for partici-pating in valuable and stimulating discussions pertainingto the work presented here. Deserving special mention arethe contributions of D. J. Lam, D. E. Ellis, A. J. Freeman,D. D. Koelling, M. Norman, and S. Bader. We are alsograteful to J. W. Stout for providing samples of FeC12 (in-got) and FeC13, and to N. L. Peterson for supplying an in-got of Cr203. This work was supported by the U.S.Department of- Energy.

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45See, for example, C. S. Fadley, in Electron Spectroscopy:Theory, Techniques, and Applications, edited by C. R. Brundleand A. D. Baker (Academic, New York, 1978), Vol. 2, p. 2.See Rashmi-Rekha, Satya Pal, and R. P. Gupta, Phys. Rev. 826, 35 (1982) and references therein.

47S. Larsson, Chem. Phys. Lett. 40, 362 (1976); S. Larsson andM. Braga, ibid. 48, 596 {1977).J. C. Fuggle, M. Campagna, Z. Zol'nierek, R. Lasser, and A.Platau, Phys. Rev. Lett. 45, 1597 (1980).

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OIn general, the wave-function composition of the charge corn-pensating or screening orbitals will not be identical to thenominally equivalent orbitals of the ground state atom.SCF calculations of transition-element molecules or clusterswhich include a 3d or deep core hole show that the hole be-comes screened by occupation of a 3d orbital. See, for exam-ple, J. A. Tossell, J. Electron Spectrosc. Relat. Phenom. 8, 1

(1976).O. Gunnarsson and K. Schonhammer, Phys. Rev. B 22, 3710(1980).

See, for example, M. Cardona and L. Ley, Photoemission inSolids I, Vol. 26 of Topics in Applied Physics, edited by M.Cardona and L. Ley (Springer, Berlin, 1978), p. 1.

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65Fuggle et al. (Ref. 48) have used the terminology "wellscreened" and "poorly screened" to describe these final-stateconditions. The well-screened state corresponds to occupancyof a localized charge-compensating electron orbital.

66M. A. Brisk and A. D. Baker, J. Electron Spectrosc. Relat.Phenom. 7, 197 (1975).G. Wendin, Struct. Bonding (Berlin) 45, 1 (1981).This code was originally developed by D. A. Liberman, D. T.Cromer, and J. T. Waber, Phys. Rev. 137, 27 {1965). Subse-quently, the code was extensively revised and simplified by D.D. Koelling. We are grateful to Dr. Koelling for making therevised code available to us. For all calculations reportedhere, const' p' exchange was used. p is the charge densityand the coefficient a was set equal to 3 .

69J. C. Slater, The Self Consistent Field for-Molecules andSolids, Vol. 4 of Quantum Theory of Molecules and Solids(McGraw-Hill, New York, 1974).

This point has been well recognized in the literature. See forexample, E. H. S. Burhop, The Auger Effect (CambridgeUniversity Press, Cambridge, 1952), and Ref. 59 for an exten-srve dlscusslon.The possibility of chemical sensitivity in satellite separationshas been considered by other researchers, usually within theframework of a model that associates the satellite with ashakeup process. For example, see Ref. 36.A peak appears in the Fe + spectra at 15—18 eV from the2p&&2 peak. However, we do not believe the peak results froma nonlocal screening relaxation response to photoejection andthus have not displayed the feature in Fig. 9.

73L. Pauling, The Nature of the Chemical Bond (Cornell Univer-

5416 B. %. VEAL AND A. P. PAULIKAS 31

sity Press, Ithaca, 1960).~4I. Ikemoto, K. Ishii, S. Kinoshita, T. Fujikawa, and H. Kuro-

da, Chem. Phys. Lett. 38, 467 (1976).I. Ikemoto, K. Ishii, S. Kinoshita, and H. Kuroda, J. ElectronSpectrosc. Relat. Phenom. 11, 251 (1977).

~6See, for example, D. E. Eastman and J. L. Freeouf, Phys. Rev.Lett. 34, 395 (1975).B. Ruscic, G. Goodman, and J. Berkowitz, J. Chem. Phys. 78,5443 (1983), and private communication.S. Sato, Y. Sakisaka, and T. Matsukawa, Vacuum UltravioletRadiation Physics, edited by E. Koch, R. Haensel, and C.Kunz (Pergamon, Vieweg, 1974), p. 414.J. M. Dyke, N. K. Fayad, A. Morris, I. R. Trickle, and G. C.Allen, J. Chem. Phys. 72, 3822 (1980).D. Adler, Insulating and Metallic States in Transition MetalOxides, Vol. 21 of Solid State Physics, edited by H. Ehren-reich, Frederick Seitz, and David Turnbull (Academic, NewYork, 1968), p. 1.

8 For example, the transition-state energy for removal of a Cr2p3/p electron that experiences nonlocal screening, from anenvironment where the Cr ground-state potential is represent-ed by Cr(3d 4p ), is obtained from the SCF calculation ofCr(2pq~q)(3d"4p )(3d ' 4p ). The removal energy E,„, isgiven by E„,= —E&~ +0.33E&q+0.67E4~, where E~~P g/p

Eqq, and E4p are eigenvalues from the atomic calculation (see

Sec. III).Reference 2 lists a binding energy of 576.6 eV for the 2p3/ppeak using conventional calibration procedures.Electron-removal energies for deep core levels are quite sensi-tive to the exchange coefficient a. A small adjustment of awould make these energy differences agree with experiment.

84K. D. Sevier, At. Data Nucl. Data Tables 24, 323 (1979).856-. K. Wertheim, in Electron Spectroscopy: Theory, Tech-

niques, and Applications, edited by C. R. Brundle and A. D.Baker (Academic, New York, 1978), Vol. 3, p. 259.

86M. Campagna, G. K. Vr'ertheim, and E. Bucher, Struct. Bond-ing (Berlin) 30, 99 (1976).J.-N. Chazalviel, M. Campagna, G. K. %'ertheim, and P. H.Schmidt, Solid State Commun. 19, 725 (1976).R. D. Shannon, Acta Crystallogr. Sect. A 32, 751 (1976).

89R. G. Hayes and N. Edelstein, in Electron Spectroscopy, editedby D. A. Shirley (North-Holland, Amsterdam, 1972), p. 771.This description of the main peak was also offered by A.Fujimori, F. Minami, and S. Sugano, Phys. Rev. B 29, 5255(1984).

9IS. Hufner and G. K. %'ertheim, Phys. Rev. 8 8, 4857 (1973).B. W. Veal, D. J. Lam, and D. E. Ellis (unpublished).M. Norman, D. D. Koelling, and A. J. Freeman (private com-munication).

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Final-State Screening and Chemical Shifts in Photoelectron Spectroscopy

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