Analysis of the Fe 2p XPS for hematite
Fe2O3: Consequences of covalent bonding
and orbital splittings on multiplet splittings
Cite as: J. Chem. Phys. 152, 014704 (2020); https://doi.org/10.1063/1.5135595
Submitted: 06 November 2019 . Accepted: 12 December 2019 . Published Online: 02 January 2020
Paul S. Bagus
, Connie J. Nelin, C. R. Brundle, N. Lahiri, Eugene S. Ilton, and Kevin M. Rosso
COLLECTIONS
Paper published as part of the special topic on Oxide Chemistry and Catalysis
Note: This article is part of the JCP Special Topic on Oxide Chemistry and Catalysis.
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Analysis of the Fe 2p XPS for hematite α Fe2O3:
Consequences of covalent bonding and orbital
splittings on multiplet splittings
Cite as: J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
Submitted: 6 November 2019 • Accepted: 12 December 2019 •
Published Online: 2 January 2020
Paul S. Bagus,1,a)
Connie J. Nelin,2 C. R. Brundle,3 N. Lahiri,4 Eugene S. Ilton,4 and Kevin M. Rosso4
AFFILIATIONS
1
Department of Chemistry, University of North Texas, Denton, Texas 76203-5017, USA
2
Consultant, Austin, Texas 78730, USA
C. R. Brundle and Associates, Soquel, California 95073, USA
3
4
Pacific Northwest National Laboratory, Richland, Washington 99352, USA
Note: This article is part of the JCP Special Topic on Oxide Chemistry and Catalysis.
a)
E-mail: bagus@unt.edu
ABSTRACT
The origins of the complex Fe 2p X-Ray Photoelectron Spectra (XPS) of hematite (α-Fe2 O3 ) are analyzed and related to the character of
the bonding in this compound. This analysis provides a new and novel view of the reasons for XPS binding energies (BEs) and BE shifts,
which deepens the current understanding and interpretation of the physical and chemical significance of the XPS. In particular, many-body
effects are considered for the initial and the final, 2p-hole configuration wavefunctions. It is shown that a one-body or one-configuration
analysis is not sufficient and that the many-body, many-determinantal, and many-configurational character of the wavefunctions must be
taken into account to describe and understand why the XPS intensity is spread over an extremely large number of final 2p-hole multiplets.
The focus is on the consequences of angular momentum coupling of the core and valence open shell electrons, the ligand field splittings of
the valence shell orbitals, and the degree of covalent mixing of the Fe(3d) electrons with the O(2p) electrons. Novel theoretical methods are
used to estimate the importance of these various terms. An important consequence of covalency is a reduction in the energy separation of the
multiplets. Although shake satellites are not considered explicitly, the total losses of intensity from the angular momentum multiplets to shake
satellites is determined and related to the covalent character of the Fe-O interaction. The losses are found to be the same for Fe 2p1/2 and 2p3/2
ionization.
Published under license by AIP Publishing. https://doi.org/10.1063/1.5135595., s
I. INTRODUCTION
It has been known since the early work of Gupta and Sen1,2 that
multiplets make important contributions to the X-Ray Photoelectron Spectra (XPS) of open shell systems. However, closely coupled
to multiplets, other factors contribute to the complexity of these
XPS. They are ligand field splittings, spin-orbit (SO) splittings, especially for the core orbitals, and the covalent mixing of metal cation
and ligand frontier orbitals. The lower symmetry found for the point
groups of many crystalline compounds of high-spin metal cations,
such as their oxides, leads to extremely large numbers of multiplets
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
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with energy splittings that are sometimes too small to be resolved
and other times easily resolved. Another effect that complicates the
XPS of high spin ionic crystals is that XPS-forbidden multiplets can
steal intensity from XPS-allowed multiplets (see, for example, Refs. 3
and 4). For these factors, there is a need to separate atomic effects
for multiplets and angular momentum coupling from the effects due
to the crystalline environment where this environment includes the
ligand field splittings.5 There are important aspects of these mechanisms for the XPS that have not received as much attention but are
essential for the proper interpretation of the XPS of ionic materials.
In particular, the extent of the covalency in the cation-ligand bond
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and the important role that it plays in multiplet splittings and even
in apparent spin-orbit splittings has not received the attention that
it merits. Furthermore, the change in covalency of core-hole ions is
a major mechanism for the screening of the core ions formed in an
XPS process.6
In this work, these effects will be considered and new, novel
measures to characterize covalency and the screening of core-holes
will be applied. In particular, the relationship of covalency to the
energy splittings of multiplets and how this splitting changes from an
isolated cation to a compound will be established. Another important topic is the losses from main XPS peaks to shake satellites.7–9
These losses reduce the intensity of the main peaks as well as lead
to satellites at higher apparent binding energies (BEs) than the main
peaks.
The intent in this paper is to collect the effects described above
together and to shed light on their interplay in modifying the energy
splittings and the XPS intensities of the ionic states. Quantitative
estimates of the importance of the various contributions to the complexity are made using theoretical methods for the analysis of wavefunctions, WFs. The WFs are obtained for cluster models that have
previously been successful for the analysis and physical interpretation of XPS (see, for example, Ref. 9). The XPS will be examined
in detail for the model system of Fe(III) in hematite, α-Fe2 O3 . It is
expected that the physical and chemical mechanisms explored and
demonstrated for hematite will be directly relevant to other open
shell cations. Furthermore, in order to focus on the open shell angular momentum coupling, the multiplet structure, and the importance of covalent bonding, we will restrict ourselves to the so-called
main XPS peaks and we will not explicitly consider shake satellites
and shake configurations.8,9 This work provides a complete theoretical foundation for the multiplet splittings and covalent interactions
and will make it possible to improve the quality of the chemical
information obtained from analyses of XPS. As well as the use for
the general understanding of the mechanisms responsible for features of XPS, the particular application to hematite is valuable in its
own right. X-Ray absorption spectroscopy (XAS) has been used to
distinguish different Fe oxidation states in a range of iron oxides.10
This work shows how theory coupled with XPS measurements can
be used to extract chemical information about the properties of iron
oxides.
In Sec. II, the theoretical and computational models and methods for the calculation and analysis of the WFs and the XPS are
reviewed. The emphasis is on the chemical and physical content of
these methods rather than on the numerical details, which are available in the cited references. In Sec. III, the theoretical predictions
for the Fe 2p XPS are presented for the isolated Fe3+ cation and
for the cluster model of Fe2 O3 . The physical origins of the spectra and the distribution of the XPS intensity over a range of final
states are examined and contrasted for these two models of Fe2 O3 .
This examination provides an understanding of the importance and
the consequences of (1) angular momentum coupling, (2) spin-orbit
and ligand field splittings, and (3) covalent mixing of Fe 3d and O
2p. The theoretical predictions of the Fe 2p XPS obtained only by
considering these multiplets are compared with experimental data
for of the XPS of Fe2 O3 , which also include shake satellites. However, the magnitudes of the losses of intensity to shake satellites will
be discussed. In Sec. IV, the consequences of multiplets and covalency for the interpretation of the XPS of Fe2 O3 are reviewed. It is
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
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suggested that the energetic separation of XPS features, including the Full Width at Half Maximum (FWHM) and the apparent spin-orbit splitting, should be examined since they may contain information on the extent of covalent mixing in different
compounds.
II. METHODOLOGY AND MODELS
Two models of Fe2 O3 are used to separate the different physical contributions to the XPS. They are an isolated Fe3+ cation
and a point charge (PC) embedded FeO6 cluster, which are shown
schematically in Fig. 1. Although there is considerable covalent character in the valence closed and open shell orbitals of the FeO6 cluster,
the embedding charges are chosen to have the formal ionicities, +3
and −2, of Fe cations and O anions. The atoms and embedding
charges are placed at their positions in the Fe2 O3 crystal.11 The cluster, including the embedding charges, has C3 point group symmetry.
The embedding charges used are within a sphere of ∼7 Å from the
central Fe cation, and the outermost point charges are adjusted to
have the net charge of the cluster approximately zero. The details of
the geometry of the atoms and the embedding charges are given in
the supplementary material.
The principle concern in this work for the FeO6 cluster embedding is to correctly represent the influence of the extended Fe2 O3
system on the Fe 2p XPS. In an earlier study,12 we have shown that
the predictions for the relative energies and intensities of features
in the core-level spectra depend only very weakly on the details of
the embedding. To provide further support for this weak dependence, the core-level spectra obtained with this embedded cluster
have been compared with a more realistic embedding where the +3
PCs nearest the six O anions are replaced with Sc3+ cations to form
an FeO6 Sc13 cluster. The logic is that the Sc3+ ions have a similar
spatial extent to the Fe3+ cations and, thus, exert a compressional
effect on the O ligands, which is absent with point charges, and,
thus, might influence the core-level features. Both the XAS13 and
the XPS have been examined for this extended cluster and found
to be virtually identical, as far as relative energies and relative intensities are concerned. In addition, for octahedral FeO, an embedded
FeO6 Mg18 cluster formed with a similar logic of replacing the +2 PCs
nearest the O anions with Mg2+ cations has been studied and shown
to give the same relative Fe 2p XPS BEs and intensities XPS as the
PC embedded FeO6 cluster.12 Thus, only the FeO6 results for the 2p
FIG. 1. Models for Fe2 O3 . Isolated Fe3+ and point charge embedded FeO6 where
the Fe cation is shown as a blue sphere and the O anions as green spheres; the
embedding point charges of +3 and −2 are shown as smaller spheres.
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XPS of Fe2 O3 will be presented. We do, however, in the supplementary material, briefly discuss embedding and cite representative studies of the use of embedding for other properties besides core-level
spectra.
The WFs that form the basis for the analysis of the XPS are the
mixtures of orbital configurations that are needed to ensure that the
angular momentum coupling of the open shell electrons is properly described. The number of states that arise from this coupling
is very large, and it will be shown that many of the states carry significant XPS intensity. The WFs are obtained with orbitals that are
solutions of the Dirac-Hartree-Fock equations for an average of configurations for the distribution of electrons over core and valence
open shells.14 These orbitals provide a balanced treatment of the
spin-orbit and, for the FeO6 cluster, ligand field splittings.9 The
Dirac Coulomb Hamiltonian with exact treatment of the integrals
over the large and small components and with Breit corrections is
used.15,16 These orbitals are then used to form configuration mixing or configuration interaction (CI), many-body WFs that involve,
with a constraint, all possible distributions of the open shell electrons over the open shell orbital sets. Thus, for the initial states of
Fe3+ and the Fe2 O3 cluster, five electrons are distributed in all possible ways over the 10 spin-orbitals that arise from the Fe 3d shell.
This distribution leads to 252 determinants. Although for the cluster,
these open shell orbitals are not pure Fe 3d but are covalent antibonding mixtures of Fe(3d) and O(2p).5,9 We shall refer to this set
of orbitals either as Fe 3d or as valence open shell orbitals. For the Fe
2p-hole states, 5 electrons are distributed in all possible ways over the
2 Fe 2p1/2 and 4 Fe 2p3/2 orbitals while the 5 valence shell electrons
are distributed over the 10 valence orbitals. This leads to 1512 = 6
× 252 determinants. The constraint is that there must always be
5 electrons in the Fe 2p shell. The many-body configuration mixing WFs determined in this way are eigenfunctions of the angular
coupling operators with J = L + S being the angular momentum
for the isolated Fe3+ cation and the irreducible representations of
the C3 double group,17,18 forming the basis for the angular momentum solutions for the FeO6 cluster model of Fe2 O3 . Because spin
orbit coupling is taken into account, the total spin, S, is not a good
quantum number. Although, as discussed for the XPS of Fe3+ , spin
selection rules can provide useful guides to the XPS intensity. These
many-body wavefunctions for the core-hole states take account of
spin-orbit and ligand field splittings and of the angular momentum coupling of the open shell electrons. The multiplet splittings
obtained with these many-body WFs are reasonably accurate but
do have a modest uncertainty because the distribution of electrons
over only the open shells neglects certain many-body effects.19,20
The possible extents of such errors in the multiplet splittings will
be discussed in Sec. III.
The relative intensity, Irel , of the individual XPS final states is
obtained from the Sudden Approximation (SA),8,9,21 which is accurate for Irel at ∼100 to 200 eV above photoionization threshold.22
The SA assumes that at the instant of photoionization, the WF of
the ionic state is the same as the neutral system, except that one of
the orbitals is unoccupied; this is often called Koopmans’ Theorem
(KT) WF.23 The KT WF is not an eigenfunction of the Hamiltonian because it neglects the orbital relaxation due to the presence
of the core-hole; thus, it does not have a well-defined energy. However, the KT WF can be expanded in terms of eigenfunctions of the
Hamiltonian for the ionized states, and the SA Irel to a given final
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
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state is simply the square of the overlap integral between the KT WF
and the eigenstate WF for the ion, i.e., the many-body configuration mixing WF. It is necessary to sum the SA Irel over degenerate
or nearly degenerate initial states using a Boltzmann distribution
for the occupation of the initial states. The ground state of Fe3+
is a 6 fold degenerate J = 5/2 level, and the ground state WFs of
the cluster model of Fe2 O3 have 6 states with energy splittings less
than 0.02 meV or three orders of magnitude smaller than KT at
room temperature. A second sum for contributions to the Irel is
taken is over the KT WFs for removal of different degenerate or
nearly degenerate core-orbitals. In principle, photoionization of an
Fe 2p1/2 and of an Fe 2p3/2 electron may both contribute to the SA
Irel of a given final state. However, it is found (see Sec. III) that ionization of only one of the 2p1/2 or 2p3/2 is dominant for a given
2p-hole state. The calculated Irel are broadened by a Voigt convolution of a Gaussian and a Lorentzian,24 where the Gaussian represents experimental resolution and vibrational broadening25 and
the Lorentzian represents core-hole lifetimes.26 The FWHM of the
Gaussian and Lorentzian broadenings is chosen from physical considerations. For the Gaussian, a FWHM of 1.0 eV is a reasonable
estimate for the experimental resolution of laboratory XPS.27 However, in order to account for additional broadening due to vibrational excitations,25,28,29 a somewhat larger Gaussian FWHM may
be required. When we compared our calculations with experimental
XPS, we found that a slightly increased Gaussian of 1.2 eV FWHM
better described the experimental width of the leading, Fe 2p3/2 ,
feature and this is the FWHM used in the broadening of all our theoretical results. For the Lorentzian FWHM, we use the recommended
lifetime broadenings given by Campbell and Papp30 of 0.41 eV for
Fe 2p3/2 and 1.14 eV for Fe 2p1/2. Since the lifetimes are quite different for the 2p1/2 and 2p3/2 ,30 a dual Lorentzian broadening is
used with the larger 2p1/2 FWHM for the higher BE features and
the lower 2p3/2 FWHM for the lower BE features. The energy where
the Lorentzian broadening is changed is at Erel = 8.0 eV, roughly
midway between the two main XPS features. This energy is chosen because the XPS intensity below Erel = 8 eV arises mainly from
ionization of 2p3/2 , while the XPS intensity for Erel greater than
8 eV arises mainly from ionization of 2p1/2 (see the discussions in
Sec. III B describing Fig. 3). This simple model takes the differential
broadening of these peaks into account using the known30 different
lifetimes of 2p3/2 and 2p1/2 . Indeed, when a complete set of manybody effects is used, including shake excitations, it is possible to
use the theory to obtain accurate values for these lifetimes.31 However, for the present case, the simple model is sufficient to allow a
meaningful comparison with experiment. A brief discussion of more
sophisticated treatment of lifetimes is given in the supplementary
material.
A final consideration is the intensity that is found for satellites
that are not included in the many-body WFs that we have considered
for the angular moment coupling terms. These satellites involve core
ionization and simultaneous excitation of a valence electron into an
unoccupied orbital, typically described as shake excitations.7,8,32 It
is possible with the SA8 to determine the intensity that is lost to
these excitations by making suitable sums over final states and initial
states. The total SA intensity for the multiplets that we have considered is denoted I(Mult) and the total SA intensity into all final
2p-hole many body states is denoted I(Total); rigorous definitions of
I(Mult) and I(Total) are given in the supplementary material. The
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intensity lost to the shake satellites is I(Total) − I(Mult), and it is
represented as a percent loss, I(loss),
I(loss) = [1 − (I(Mult)/I(Total))] × 100.
(1)
The I(loss) can be restricted to either 2p1/2 or 2p3/2 ionization.
In order to understand the physical origins of the XPS features, different methods of analysis of the orbitals and the WFs are
used. One objective is to obtain quantitative measures of the covalent character of the orbital and WFs.6 The covalent character of the
cluster orbitals can be written schematically as
φbond = Bψ[Fe(3d)] + Aψ[O(2p)] with A > B and
φanti-bond = Aψ[Fe(3d)] − Bψ[O(2p)].
(2a)
(2b)
The ψ are orbitals of the separated Fe and O fragments; φbond is an
orbital of the filled, closed, dominantly O(2p) shells and φanti-bond is
an orbital of the open, dominantly Fe(3d) shells. The signs of the
coefficients A and B are chosen to highlight that the closed shell
orbitals are bonding, while the open shell orbitals are antibonding.
The objective is to obtain information about the magnitudes of the
coefficients A and B. The first method is to examine the size of the
orbitals, reff (i) for the i-th orbital, defined as
reff (i) = [⟨φi ∣r2 ∣φi ⟩]
1/2
,
(3)
where the origin for r is the Fe nucleus and the concern is primarily
for the open shell orbitals of Eq. (2b). If the differential overlap of
the fragment orbitals is neglected, then from Eq. (2b),
reff (i) = [A2 ⟨ψ[Fe(3d)]∣r2 ∣ψ[Fe(3d)]⟩
1/2,
+ B2 ⟨ψ[O(2p)]∣r2 ∣ψ[O(2p)]⟩]
(4)
where the first term is the size of the Fe(3d) orbital and the second term is approximately R(Fe-O), the distance between Fe and O.
Clearly, R(Fe-O) is considerably greater than the size of the Fe(3d)
orbital. Thus, the increase in reff (3d) over the value for the isolated
Fe3+ cation indicates that there is a covalent contribution to the
valence open shell orbital of Fe2 O3 with larger values of reff indicating greater covalency. A second method to quantify the covalent
character of an orbital is to use projection operators6,33,34 of the
Fe 3d orbitals, ψ[Fe(3d)]ψ[Fe(3d)]† , to provide a projected occupation, NP , for the 3d character of the orbital. For the NP , it is common to make suitable sums over the components of the 3d shell
and sums over the occupied orbitals of the cluster model of the
crystal.6,33
The many-body WFs can be analyzed in terms of the occupation numbers, ni ,35 of the orbitals, φi , used to form the determinants in the expansion of the many-body CI WFs. The ni are
simply sums over the φi occupation in a given determinant times the
weight of that determinant in the WF.36 These occupation numbers
provide considerable information about the many-configurational,
many-determinantal character of the WF. In particular, summing
the orbital occupation times the orbital size [Eq. (3)], ni × reff (i),
over the valence open shell orbitals, one obtains an effective size
of this shell for each CI WF. This is a measure of the covalency
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for the many-electron WFs. Furthermore, if the WF can be represented almost entirely by a single configuration, the ni will be very
nearly integer. Departures of the ni from integer indicate that the
many-body WF is a sum over several different configurations. A
third method for the analysis of the relativistic many-body WFs is
to examine how different Russel-Saunders (RS) multiplets, where
the spin and orbital angular momentum are both good quantum
numbers that contribute to this WF.36–39 This is done by calculating the RS multiplets, denoted for an isolated atom as 2S+1 L, where
the spin-orbit coupling is turned off. These RS multiplets are then
projected on the relativistic WFs, where only the sum of the spin
and orbital angular momenta is a good quantum number, to determine a %(2S+1 L) RS multiplet character of the many-body relativistic
WF. This is valuable because many selection rules for XPS and XAS
depend on the RS coupling. This decomposition will be made for the
Fe 2p XPS of Fe3+ to demonstrate how the small number of allowed
XPS intensities become distributed over many final 2p-hole states.
The 4-component relativistic orbitals and many-body CI WFs
were obtained as solutions of the Dirac-Coulomb Hamiltonian with
the DIRAC program system.16 The orbitals were expanded in terms
of uncontracted Gaussian basis functions, where the O basis set was
taken as used in previous calculations40 and the Fe basis set is a
modified Wachters basis taken from the Environmental Molecular Sciences Laboratory (EMSL) tabulation.41 These basis sets are
sufficiently large to describe the initial and 2p-hole multiplet WFs.
The basis function exponents and the coordinates of the Fe and O
nuclei and the PCs are given in the supplementary material. The
results of the Dirac calculations were interfaced to the core level
ionization potential spectroscopy (CLIPS) program system42 for the
calculation of the dipole transition matrix elements and intensities. The full many electron dipole transition matrix elements have
been computed using programs that calculate the cofactors of the
matrices of the overlap integrals between the orbitals optimized for
the initial and the 2p-hole configurations.43 The Voigt convolution
for the broadening and the plotting of the broadened spectra were
performed using PC software that we have developed.
III. Fe 2p XPS FOR Fe2 O3
A. XPS for Fe3+
The case of the 2p XPS of the isolated Fe3+ cation is considered
first because the relatively high symmetry has multiplets with relatively large degeneracies and, thus, limits the number of multiplets.
The reduced number of multiplets makes it possible to examine
individual terms in order to understand how the intensities are distributed. The initial state is J = 5/2 with six degenerate states and very
strongly dominated by the high spin RS 6 S5/2 multiplet.37 This multiplet is well separated from the next excited multiplet, which is higher
in energy by >3 eV.44 Two extremes are described for the 2p XPS.
First, the spin-orbit coupling of the 2p shell is neglected, leading to
the configuration 2p5 3d5 where the only XPS-allowed coupling is
2p5 (2 P)3d5 (6 S).3,4,9 The coupling of 2p5 (2 P) with 3d(6 S) leads to two
XPS-allowed multiplets, 7 P and 5 P. There are two other couplings
of 3d5 that lead to a coupling with 2p5 (2 P) to give a total 5 P multiplet.4 These alternative 3d5 couplings can mix with the XPS-allowed
2p5 (2 P)3d5 (6 S); 5 P coupling leads to multiplets that have an XPS
intensity proportional to the weight of the XPS-allowed coupling.
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Thus, the RS coupling would lead to at most 4 XPS peaks. The other
extreme is to assume that either a 2p3/2 or a 2p1/2 electron is ionized
to couple with the J = 5/2 coupling of the 3d5 open shell. The ionizations of these two shells will be separated by ∼15 eV, the 2p spin-orbit
splitting. From the rules of angular momentum addition,9,45 the
J = 3/2 coupling of the 2p shell when a 2p3/2 electron is ionized can
couple with the 3d5 shell J = 5/2 to give 4 XPS-allowed configurations with J = 4, 3, 2, and 1, which will be split by ∼1 eV.40 For
the J = 1/2 coupling, when a 2p1/2 electron is ionized, the coupling
with the 3d shell J = 5/2 will give 2 XPS-allowed configurations with
J = 3 and 2, again with a splitting of ∼1 eV. Thus, neglecting mixing
of these XPS-allowed configurations with XPS-forbidden configurations having the same value of total J but different couplings of 3d5 ,
a group of 4 peaks, perhaps not fully resolved separated by ∼15 eV
from a group of two peaks, would be expected.
The theoretical 2p XPS for Fe3+ is shown in Fig. 2(a), where the
large solid black curve is the intensity from all of the final states,
FIG. 2. (a) The 2p XPS for Fe3+ where the calculated intensities are broadened
with a Voigt convolution. The full curve, which is the sum of all individual contributions, is shown as a bold curve, while the largest individual contributions are
shown below the full curve as light lines (see text for details). (b) The 2p3/2 XPS
for Fe3+ [see panel (a) description and text]. (c) The 2p1/2 XPS for Fe3+ [see panel
(a) description and text].
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
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suitably broadened, and the largest individual contributions are
shown as light curves below the total curve (see the supplementary
material for details). The energy scale is for relative energies, where
Erel = 0 is for the lowest energy 2p-hole multiplet. We use Erel rather
than the absolute values of the XPS BEs because of the uncertainty in
defining the BE with respect to the vacuum energy as 027 and because
the theory is most accurate for the Erel .9,12 When we compare theory with experiment, we make a rigid shift to align the two spectra.
The units of relative intensity, Irel , are arbitrary. The contribution
of each final state multiplet is the SA relative intensity8 broadened
with a Voigt convolution24 of a Gaussian and a Lorentzian with
FWHM, as described in Sec. II. It is clear from Fig. 2(a) that the
intensity is distributed over many final state multiplets, much more
than would be expected based on either of the models described
above. Figures 2(b) and 2(c) parallel Fig. 2(a), but they give the SA
intensity for only 2p3/2 and 2p1/2 , respectively; the plot of Fig. 2(a)
is the sum of the plots of Figs. 2(b) and 2(c). While most of the
intensity for the energy range of 0 < Erel < 5 eV comes from 2p3/2
ionization and most of the intensity for the features at Erel ∼ 8 eV
and Erel ∼ 16 eV comes from 2p1/2 ionization, there are small contributions from 2p1/2 in the dominantly 2p3/2 feature and from the
2p3/2 in the dominantly 2p1/2 features. This is a first indication that
different configurations with the same value of J mix to determine
the final multiplets that carry XPS intensity. It is also interesting
that the ∼8 eV feature, which is observed in the 2p XPS of Fe2 O3 46
and in the 2p XPS of MnO,40,47 which is also 3d5 , is present in our
theoretical XPS, albeit with smaller intensity than in the XPS measurements. The contribution of angular momentum coupled multiplets compared to shake satellites to this feature is considered in
Subsection III B where comparison of our theory with experiment is
made.
A final consideration concerns the energy separation of the
lower Erel main features associated with 2p3/2 ionization and the
main higher Erel feature associated with 2p1/2 ionization, especially
because this might be taken as a measure of the spin orbit splitting.
The best measure of the spin-orbit splitting is the difference of the
Dirac-Fock spinor energies, Δε, for the 2p1/2 and 2p3/2 spinors. This
difference for the configuration 2p5 . . . 3d5 is Δε = 12.6 eV, and the
difference for the ground state configuration . . . 3d5 is very similar
at Δε = 12.3 eV. However, the energy differences between the three
maxima at low Erel , associated with 2p3/2 ionization, and the maxima at Erel = 17.04 eV, associated with 2p1/2 ionization, 17.0, 15.3,
and 13.9 eV, respectively, are significantly larger than Δε between
2p1/2 and 2p3/2 . This is another strong indication that the multiplets
are not described by a single configuration with either a 2p1/2 or a
2p3/2 hole but have substantial multiconfigurational character where
configurations with each of these holes are mixed. The increase in
splitting between the dominantly 2p1/2 and 2p3/2 multiplets is exactly
as expected because the trace of the diagonal elements of the Hamiltonian matrix must be constant.48 The energies of the lower, 2p3/2
hole, multiplets are lowered and the energies of the higher, 2p1/2
hole, multiplets are raised, thus increasing the separation of the two
sets from Δε.
The multiconfigurational character is examined quantitatively
in Table I where data for the 36 most intense multiplets are given;
these are the multiplets with 2p XPS SA intensity greater than or
equal to 1% of the first, most intense multiplet at Erel = 0. For each of
the 2p-hole multiplets, Erel , the J value, where only multiplets with
152, 014704-5
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TABLE I. Properties of the 2p XPS multiplets with Irel greater than 1% of maximum Irel , which is normalized to 1. The Erel , SA
Irel with separate contributions from P1/2 and p3/2 ionization, and the contributions from septet and quintet Russell-Saunders
multiplets (see text).
Multiplet
1
2
3
4
5
6
7
8
9
10
11
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Sum
Erel (eV)
J
Irel (1/2)
Irel (3/2)
Irel
%7 P
%5 P(1)
%5 P(2)
0
1.764
3.185
17.47
4.087
17.156
16.061
13.95
7.949
15.702
16.392
15.12
8.385
8.656
14.453
10.582
21.683
12.265
12.566
15.761
15.005
9.469
10.13
21.2
9.206
15.345
19.821
6.818
16.616
22.415
7.559
10.906
19.449
23.702
4
3
2
3
1
3
2
2
3
2
3
2
2
2
2
1
3
1
1
3
3
2
1
3
2
3
3
2
2
3
3
1
3
3
0.00
0.03
0.02
0.25
0.00
0.16
0.11
0.10
0.08
0.08
0.08
0.06
0.04
0.04
0.05
0.00
0.03
0.00
0.00
0.02
0.02
0.01
0.00
0.01
0.01
0.01
0.01
0.00
0.01
0.01
0.01
0.00
0.01
0.01
1.00
0.70
0.42
0.02
0.20
0.01
0.02
0.01
0.02
0.01
0.00
0.01
0.02
0.02
0.00
0.05
0.01
0.02
0.02
0.00
0.00
0.00
0.02
0.00
0.00
0.00
0.00
0.01
0.00
0.00
0.00
0.01
0.00
0.00
1.00
0.73
0.44
0.27
0.20
0.17
0.13
0.11
0.10
0.09
0.08
0.07
0.06
0.06
0.05
0.05
0.04
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
99.9
68.8
31.2
6.8
0.0
4.6
8.5
11.2
11.1
6.2
2.5
5.9
10.7
10.5
4.9
0.0
0.5
0.0
0.0
0.6
0.8
3.3
0.0
0.3
2.4
0.5
0.2
1.6
0.6
0.2
1.2
0.0
0.2
0.1
20.7
0.0
27.9
63.8
10.0
94.2
8.0
1.3
8.4
30.6
1.5
6.2
2.4
4.1
5.5
2.9
0.3
0.6
0.3
0.4
1.9
2.7
1.9
0.2
0.1
1.9
1.5
0.0
0.3
0.0
0.1
3.0
0.0
0.0
0.5
14.1
0.0
2.3
1.9
19.7
0.7
10.3
22.0
1.5
18.6
11.2
2.6
5.5
11.4
11.2
1.7
26.0
15.0
20.5
19.7
0.4
0.1
2.8
7.9
5.4
2.4
0.1
2.9
2.2
2.5
4.4
2.0
5.9
1.8
5.5
12.6
J = 4, 3, 2, or 1 are XPS-allowed, and the SA Irel are given. The Irel
are sums over ionization to all the degenerate states in the multiplet
and are normalized so that the multiplet at Erel = 0, which is most
intense, has Irel = 1. Note that this is different from the scaling of Irel
used in Fig. 2. Furthermore, the contributions to Irel from ionization
of the 2p3/2 and 2p1/2 are given separately as Irel (3/2) and Irel (1/2),
where Irel = Irel (3/2) + Irel (1/2). Also given in Table I are the composition of the relativistic 2p-hole wavefunctions, WFs, in terms of
the 7 P coupled and two of the 5 P coupled Russell-Saunders multiplets, denoted 5 P(1) and 5 P(2), for the open-shell configuration 2p5
. . . 3d5 . The third 5 P multiplet is not included since this multiplet
has only negligible XPS intensity (see the supplementary material
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
Published under license by AIP Publishing
where the division into XPS-allowed and XPS-forbidden couplings
is discussed).
The first multiplet, which is J = 4, gets all of its intensity from
Irel (3/2) because J = 4 can be formed only by coupling 2p3/2 with
3d5 (J = 5/2).45 Similarly, the J = 1 multiplets, which are numbers 5,
18, 20, 21, 25, and 34, get all their intensity from Irel (3/2) since J = 1
can be formed only by ionizing 2p3/2 . The J = 2 and J = 3 multiplets
can have intensity from both Irel (3/2) and Irel (1/2) although one of
the two contributions dominates (see Table I). However, it is usually
the case that a fraction of the intensity comes from the other contribution demonstrating the multiconfigurational character of the
2p-hole WFs. Another demonstration of the multiconfigurational
152, 014704-6
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character of the WFs is obtained from the compositions of the relativistic WFs in terms of the XPS-allowed RS 7 P, 5 P(1), and 5 P(2)
multiplets. The first J = 4 2p-hole multiplet is essentially a pure 7 P4
with only a very small contribution, 0.1%, from other XPS-forbidden
J = 4 multiplets. In a similar way, the first, and most intense,
J = 1 multiplet is dominated to 95% by the two XPS-allowed RS 5 P
multiplets. The other J level multiplets in Table I are significant combinations of the RS 7 P and 5 P. Moreover, the contributions of these
XPS-allowed RS multiplets are distributed over a great many relativistic multiplets. There is a sum rule for the projections, shown in
Table I as % contributions, of the RS multiplets on the J levels. The
sum of the projections on all the J levels, including their degeneracies, must be the total number of states in the RS multiplets, 21 for 7 P
and 15 for 5 P (see the supplementary material). The weighted sums
for only the states shown in Table I are 20.7 for the RS 7 P multiplet
and 14.1 and 12.6 for the 5 P(1) and 5 P(2) multiplets, respectively.
These sums are close to the values for summing over all final 2p-hole
states, showing that most of the intensity will be in the multiplets
shown in Table I. However, some intensity will be distributed over
the 2p-hole relativistic multiplets that have lower XPS intensity than
those shown in Table I.
Another way to characterize the multiconfigurational character
of the 2p-hole relativistic multiplets is from the orbital or shell occupations, denoted n(iλ) and defined in Sec. II, for the spin-orbit split
2p1/2 and 2p3/2 , and 3d3/2 and 3d5/2 , open shells. The n(iλ) are given
in Table II for the same 2p-hole multiplets as in Table I. Table II also
includes the excitation energy, ΔE, the J value, and the 2p XPS SA Irel
so that the n(iλ) can be related to the XPS energies and intensities.
The occupation numbers are also given for the initial state, denoted
GS, before Fe 2p ionization. It is recalled that if the wavefunction
can be represented by a single configuration, then the occupation
numbers will be integer; significant departures from integer values
indicate that more than one configuration makes significant contributions to the WF. For the relativistic GS, the occupations of the 3d
shell for the GS depart only slightly from the values of n(3d3/2 ) = 2.0
and n(3d5/2 ) = 3.0 for the ideal RS 6 S5/2 multiplet37 shown as ideal
RS(6 S5/2 ). This shows that contributions from other RS J = 5/2 multiplets, besides the 6 S5/2 multiplet, to the relativistic GS multiplet are
negligible. The lowest energy 2p-hole multiplet with Erel = 0, which
is J = 4, has integral occupations for the 5 2p electrons with n(2p1/2 )
= 2.00 and n(2p3/2 ) = 3.00, indicating that only configurations where
a 2p3/2 electron is ionized contribute significantly. The 3d occupations are also close to the ideal RS limit for 3d5 (6 S5/2 ), showing that
this J = 4 multiplet is essentially the coupling of a j = 3/2 2p hole,
n(2p3/2 ) = 3, with the 3d5 shell coupled to j = 5/2. The next higher
energy multiplets at Erel = 1.8, 3.2, and 4.1 eV are J = 3, 2, and 1
multiplets, which can also arise from the coupling of (2p3/2 )3 with
3d5 (6 S5/2 ), but the n(iλ) show that the departures from a single configuration are larger than for the J = 4 multiplet. The n(3d3/2 ) and
n(3d5/2 ) for these multiplets show that other J = 5/2 levels besides
the 6 S coupling contribute to the multiplet. The mixing of these XPSforbidden couplings means that the Irel of these J = 3, 2, and 1 multiplets will be reduced from that expected from their multiplicities, as
discussed in the supplementary material. A small fraction of configurations with occupation (2p1/2 )1 (2p3/2 )4 contribute to the J = 3, 2,
and 1 multiplets, leading to n(2p1/2 ) slightly less than 2.0. Figure 2(c)
shows that there is a small intensity for 2p1/2 ionization for the J = 3
and J = 2 multiplets at Erel = 1.8 and 3.2, respectively. For the J = 1
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
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multiplet, all the XPS Irel is from the 2p3/2 ionization (see Table I).
This means that the 2p shell (2p1/2 )1 (2p3/2 )4 occupation couples with
an XPS-forbidden 3d5 shell coupling, which is not 6 S5/2 ; the need for
this recoupling is explained in the supplementary material.
None of the multiplets given in Table II have n(2p1/2 ) ≈ 1.0,
which would be the case for a WF that is close to pure ionization
of a 2p1/2 electron. The smallest value of n(2p1/2 ) = 1.2 occurs for
multiplets 19, 26, and 36. This means that the XPS intensity for
these multiplets may contain contributions from ionization of 2p3/2 ,
Irel (2p3/2 ), as well as from 2p1/2 , Irel (2p1/2 ). That is indeed the case
is clear from the data in Table I and from Fig. 2(b), where there is
clearly 2p3/2 XPS intensity in the regions normally considered to
be associated with 2p1/2 ionization. In sum, there is considerable
multiconfigurational character in the 2p-hole multiplets for the XPS
of Fe3+ .
B. XPS for the FeO6 cluster model of Fe2 O3
As described in Sec. II, this cluster models the rhombohedral
crystal structure of hematite where Fe is surrounded by six nearest neighbor O anions with embedding point charges (see Fig. 1).
Furthermore, it was shown in Sec. II that more sophisticated embedding will only lead to relatively minor changes in the XPS Erel
and Irel . It is important that the cluster includes ligand field splittings and covalent mixings of Fe(3d) with O(2p), which are not
present in the isolated cation. It will be shown that these effects
have major consequences for the XPS Erel and Irel and the physical
and chemical reasons for these consequences are identified. Given
the low, C3 , point group symmetry of the crystal, the high degeneracies found for the isolated atom are split into many states with
splittings ranging from <0.05 eV to ∼1 eV. Furthermore, the covalent mixing leads to open shell orbitals that may have significant
departures from the orbitals of the isolated Fe cation, which can
modify multiplet splittings. The effects of covalency, ligand field
splittings, and spin-orbit splittings will be analyzed both for individual orbitals and for individual many electron final states. However, first an overview of the 2p XPS multiplets of Fe2 O3 will be
considered.
In Fig. 3(a), the XPS contributions of both 2p3/2 and 2p1/2 ionization of the FeO6 cluster model are plotted, while in Figs. 3(b) and
3(c), only the XPS contributions of 2p3/2 and 2p1/2 , respectively, are
plotted. The same broadenings are used as for Fig. 2 so that the XPS
of the isolated cation and the FeO6 cluster can be directly compared.
There are significant differences, along the entire spectral region,
between Figs. 3(a) and 2(a). The broad leading edge, dominantly
from 2p3/2 ionization [see Figs. 2(b) and 3(b)], is much narrower
for the cluster model of Fe2 O3 than for Fe3+ . While only 4 multiplets
make a significant contribution for the XPS of Fe3+ with 3 of them
fully resolved, there are many individual contributions to the cluster
leading edge XPS but with smaller energy separations so that only
two features are resolved. Similar large changes appear for the high
BE feature at Erel ∼ 16 eV. The peak is narrowed from a FWHM of
3.9 eV for the cation to 3.1 eV for the cluster. An even more striking feature is that the separation of the main and the 2p1/2 peaks
is lowered by almost 2 eV from Fe3+ to the cluster. It is tempting
to assign this reduction to a change in the 2p spin-orbit splitting,
but it will be demonstrated that the splitting does not change significantly between cluster and cation. Another important difference is
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TABLE II. Occupations of the 2p and 3d open shells, n(2pj ) and n(3dj ), for the 2p XPS multiplets with Irel greater than 1%
of maximum Irel . The Erel , J, and SA Irel are given as well as the occupations for the initial multiplet are denoted as GS (see
text).
Multiplets
GS
Ideal RS(6 S5/2 )
2p_hole
1
Ideal RS(7 P4 )
2
3
4
5
6
7
8
9
10
11
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Erel (eV)
J
Irel
n(2p1/2 )
n(2p3/2 )
n(3d3/2 )
n(3d5/2 )
0.00
...
5/2
5/2
...
...
2.00
2.00
4.00
4.00
2.04
2.00
2.96
3.00
0.00
...
1.76
3.19
17.47
4.09
17.16
16.06
13.95
7.95
15.70
16.39
15.12
8.39
8.66
14.45
10.58
21.68
12.27
12.57
15.76
15.01
9.47
10.13
21.20
9.21
15.35
19.82
6.82
16.62
22.42
7.56
10.91
19.45
23.70
4
4
3
2
3
1
3
2
2
3
2
3
2
2
2
2
1
3
1
1
3
3
2
1
3
2
3
3
2
2
3
3
1
3
3
1.00
...
0.73
0.44
0.27
0.20
0.17
0.13
0.11
0.10
0.09
0.08
0.07
0.06
0.06
0.05
0.05
0.04
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
2.00
2.00
1.96
1.96
1.60
1.98
1.71
1.75
1.71
1.89
1.83
1.80
1.84
1.93
1.93
1.83
1.97
1.18
1.95
1.97
1.88
1.93
1.97
1.97
1.17
1.96
1.94
1.34
1.98
1.88
1.31
1.97
1.97
1.77
1.22
3.00
3.00
3.04
3.04
3.40
3.02
3.30
3.25
3.29
3.11
3.17
3.20
3.17
3.07
3.07
3.17
3.03
3.82
3.05
3.03
3.12
3.07
3.04
3.03
3.83
3.04
3.06
3.66
3.02
3.12
3.69
3.03
3.03
3.23
3.78
2.05
2.00
2.26
2.14
2.00
2.07
2.02
2.04
2.08
1.65
1.84
1.76
1.87
2.37
2.02
1.67
1.73
1.65
1.72
2.74
1.52
2.03
2.02
1.53
1.53
2.13
1.91
1.64
2.47
1.90
1.78
1.75
2.05
1.86
1.47
2.95
3.00
2.74
2.86
3.00
2.93
2.99
2.96
2.92
3.35
3.16
3.24
3.14
2.63
2.98
3.33
3.27
3.35
3.28
2.26
3.48
2.97
2.98
3.47
3.47
2.87
3.09
3.36
2.53
3.10
3.22
3.25
2.95
3.14
3.53
that the feature at Erel ∼ 8 eV, which is dominantly from 2p1/2 ionization for the cation [see Fig. 2(c)], moves to Erel ∼ 6 eV for the cluster
but now arises from mostly 2p3/2 ionization. This change shows that
the angular momentum coupling has become very complex due to
the additional ligand field splitting and assignments of the coupling
require detailed calculation. The differences of the positions of the
maxima for the cation and the cluster are quantified in Table III.
These large changes in the energy separation of the features can be
understood by considering the differences of the WFs between Fe3+
and the FeO6 cluster model of Fe2 O3 .
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
Published under license by AIP Publishing
The differences of the Fe 2p and the open shell, dominantly Fe
3d, orbitals are given in Tables IV–VI for the orbitals of both the
ground state and the 2p-hole configurations of Fe3+ and the FeO6
cluster model of Fe2 O3 . For Fe3+ , atomic labeling is used for the
orbitals. A different labeling is needed for the FeO6 orbitals since
the cluster has only rhombohedral, C3 , symmetry11 and a modified notation that shows the origins of differences is used rather
than the notation for the C3 double group.17,18 The FeO6 2p orbitals
are labeled 2p1/2 , 2p3/2 -a, and 2p3/2 -b, where the -a and -b denote
the C3 symmetry breaking of 2p3/2 . Since the rhombohedral crystal
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TABLE III. Positions of the maxima, Erel in eV, for the main peaks of the 2p XPS of
the isolated Fe cation, Fe3+ , and for the FeO6 cluster model of Fe2 O3 . Erel = 0 is the
energy of the lowest final state with a 2p electron ionized.
First feature
Second feature
Third feature
FIG. 3. (a) The 2p XPS for the FeO6 cluster model of Fe2 O3 where the calculated
intensities are broadened with a Voigt convolution as for the 2p XPS of Fe3+ [see
the caption of Fig. 2(a)]. (b) The 2p3/2 XPS for the FeO6 cluster model of Fe2 O3
where the calculated intensities are broadened with a Voigt convolution as for the
2p XPS of Fe3+ [see the caption of Fig. 2(a)]. (c) The 2p1/2 XPS for the FeO6
cluster model of Fe2 O3 where the calculated intensities are broadened with a Voigt
convolution as for the 2p XPS of Fe3+ [see the caption of Fig. 2(a)].
structure of Fe in Fe2 O3 is a distorted octahedral structure,11 a modification of the Bethe notation for the Oh double group is used17,18
with the notations γ7 (t2g ), and γ8 (t2g ) and γ8 (eg) where the γ8 representations also have the addition of either -a or -b to distinguish
the symmetry-broken γ8 pair. As shown in Tables IV–VI, the small
differences of the properties of the -a, -b pairs of orbitals show that
it is reasonable to view Fe in Fe2 O3 as having a distorted octahedral
geometry.
In Table IV, the Dirac-Fock orbital energies, ε, are given as differences, Δε, with the lowest Fe 2p or the lowest valence open shell ε.
The Δε are used because the absolute values of the ε change considerably between Fe3+ and FeO6 and because the Δε are the quantities
relevant for the Erel of the 2p XPS features.12 A first observation
from Table IV is that the 2p spin-orbit splitting is barely changed
between Fe3+ and FeO6 , not surprising since the spin-orbit interaction is largely an atomic effect.45,49,50 Clearly, the different separation
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
Published under license by AIP Publishing
Fe3+
Fe2 O3
First maximum
Second maximum
Third maximum
0.0
1.8
3.2
0.0
1.4
...
Maximum
Maximum
8.3
17.1
6.2
15.3
of the 2p3/2 and 2p1/2 XPS features (Figs. 2 and 3 and Table III)
between Fe3+ and FeO6 does not arise from a change in the 2p spinorbit splitting. For the Fe3+ 3d shells, the spin-orbit splitting is small
and slightly larger for the 2p-hole configuration. This increase arises
(as shown in Table V) because the optimized 3d orbital for the 2phole is contracted with respect to the ground configuration 3d orbital
and this increases the spin-orbit splitting.45,49 The ligand field splitting of the t2g and the more strongly antibonding eg orbitals is ∼1 eV
for the ground configuration, which is a typical value for this splitting.5,51 The t2g -eg splitting is almost twice as large for the 2p-hole
configuration. As shown from the data in Tables V and VI, this
increase is because the covalent character of the eg orbitals increases
significantly when there is a core-hole.
The sizes of the 2p and open shell 3d orbitals, reff defined in
Eq. (3), are shown in Table V. For comparison, the Fe distances to
the nearest O anions are 1.9 Å and 2.1 Å, respectively, for the nearer
and more distant set of three O atoms.11 The 2p orbitals are quite
contracted and have the same size for both initial and 2p-hole configurations and for both the isolated Fe3+ cation and the FeO6 cluster.
Clearly, they are true core orbitals. The 3d orbitals of Fe3+ are somewhat larger but are still, with reff ∼ 0.5 Å, much smaller than the Fe-O
distances; furthermore, the reff are similar for both 3d3/2 and 3d5/2 .
In addition, the reff for the 2p-hole configuration is more than 10%
TABLE IV. Orbital energy differences, Δe in electron volts, for the 2p and 3d orbitals
of the Fe3+ and FeO6 cluster models of Fe2 O3 ; data for both initial and 2p-hole final
state configurations are shown. The notation for the 3d orbitals combines a modified
Bethe notation for the octahedral double group, g7 and g8 , with the octahedral ligand
field split t2g and eg (see text).
Fe3+
Fe3+ -2p
2p1/2
0.00
0.00
2p3/2
12.31
3d3/2
3d5/2
FeO6
FeO6 -2p
2p1/2
0.00
0.00
12.56
2p3/2 -a
2p3/2 -b
12.31
12.31
12.59
12.62
0.00
0.00
γ8 (t2g )-a
γ8 (t2g )-b
0.00
0.01
0.00
0.06
0.14
0.20
γ7 (t2g )
γ8 (eg )-a
γ8 (eg )-b
0.08
1.35
1.36
0.20
2.28
2.29
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TABLE V. Effective sizes, reff in Å, of the 2p and 3d orbitals of the Fe3+ and FeO6
cluster models of Fe2 O3 ; data for both initial and 2p-hole final state configurations are
shown. The notation follows that of Table IV (see also text).
Fe3+
Fe3+ -2p
2p1/2
0.14 Å
0.14
2p3/2
0.14
3d3/2
3d5/2
FeO6
FeO6 -2p
2p1/2
0.14
0.14
0.14
2p3/2 -a
2p3/2 -b
0.14
0.14
0.14
0.14
0.58
0.51
γ8 (t2g )-a
γ8 (t2g )-b
0.70
0.69
0.76
0.78
0.58
0.51
γ7 (t2g )
γ8 (eg )-a
γ8 (eg )-b
0.70
0.90
0.90
0.79
1.52
1.53
smaller than for the ground configuration since the effective nuclear
charge seen by the 3d shell electrons in the hole state is larger by ∼1
electron.52,53 The situation for the 3d cluster orbitals is different in
important ways. The reff of the spin-orbit and ligand field split initial state 3d FeO6 orbitals are significantly larger than the sizes of the
Fe3+ 3d orbitals, by ∼20% for the t2g derived orbitals and ∼55% for
the eg derived orbitals. Furthermore, the size of the orbitals becomes
larger when there is a 2p-hole, which is opposite to the case of the
isolated Fe3+ where the orbitals in the presence of a 2p hole became
smaller. These increases in size are consistent with a small to modest
covalency [see Eq. (4) and related discussion]. From the increase in
reff , it is clear that the covalent mixing between Fe(3d) and O(2p) is
greater for the eg derived orbitals than for the t2g derived orbitals.
This is because of the different directional character of these orbitals
(see the discussion in Refs. 9 and 54). Furthermore, the covalency of
the 3d orbitals in the presence of 2p-hole is larger than for the initial
state 3d orbitals.
In Table VI, a direct measure of the covalency of Fe2 O3 is presented by using projection operators of the isolated Fe3+ 3d orbitals
TABLE VI. Projections of the orbitals of isolated Fe3+ on the orbitals for the initial and
2p-hole configurations of Fe2 O3 are given for the individual open shell cluster orbitals
of dominantly d character and for sums over open and closed shells of Fe2 O3 (see
text for further details). The same notation for the open shell orbitals is used as in
Tables IV and V. The units of the projections are electrons.
3d orbitals
Totals
FeO6
FeO6 -2p
γ8 (t2g )-a
γ8 (t2g )-b
γ7 (t2g )
γ8 (eg )-a
γ8 (eg )-b
0.96
0.97
0.96
0.84
0.84
0.93
0.92
0.91
0.51
0.50
Open
Closed
Open + closed
4.57
0.85
5.40
3.78
2.37
6.15
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on the orbitals of the FeO6 embedded cluster. The projection operators have been reviewed briefly in Sec. II. The 3d occupations, given
in Table VI, are appropriate sums of the expectation values of the 3d
projection operators taken over the occupied orbitals of hematite.
The deviation of these sums, denoted NP (3d), from the nominal
values neglecting covalency provides a quantitative measure of the
covalent mixing for individual orbitals as well as within subsets of
the orbitals. The projections considered are as follows: (1) The five
individual 3d Kramers pairs (see, for example, Ref. 14); for these five
orbitals, the nominal Np (3d) = 1. (2) The sum over the closed shell
orbitals, where the nominal NP (3d; closed) = 0. (3) Totals of NP over
the open shell orbitals with an average occupation of 1 for each of the
Kramers’ pairs, where the nominal NP (3d; open) = 5. The sum of the
projection over both the open and closed shells, NP (3d; total), where
the nominal value is 5, is also given. In order to take account of the
contraction of the atomic 3d orbitals when a 2p-hole is present, different atomic 3d orbitals are projected for the initial and final state
orbitals of the FeO6 . For projection on the initial state Fe2 O3 orbitals,
the Fe orbitals of the ground state configuration of Fe3+ are used,
while for the 2p-hole state of Fe2 O3 , the Fe orbitals for the 2p-hole
state configuration are used.
The projections on the Fe2 O3 open shell orbitals arising from
the octahedral t2g symmetry are only slightly reduced from the nominal value of 1 for a pure 3d orbital. The reduction is slightly larger
for the 2p-hole state Fe2 O3 orbitals, but the projections are much
smaller than for the open shell orbitals derived from eg symmetry.
Indeed, the NP (3d) for the 2p-hole eg orbitals show that they have
almost equal Fe 3d and O 2p character. The origin of the larger
covalency for the eg orbitals is the directionality of the orbitals as discussed when the sizes of the orbitals were considered. The amounts
of covalency for the orbitals are consistent with the changes in the
orbital sizes. The increase in covalency for the 2p-hole configuration
orbitals is because the Fe with a 2p-hole appears, as far as the valence
electrons are concerned, to be Co4+ .52,53 The increase in covalency
for hole states in many oxides has been identified as a major origin for the screening of the core-hole.9,33 The covalency of these
open shell electrons also has significant consequences for the multiplet splitting,9,54 as will be discussed below. The closed shells have
a significant 3d character although the nominal NP (3d) = 0. The loss
of 3d character in the valence open shell is less than the gain of d
character in the closed shells by approximately half. The difference
between the amount of loss of 3d character in the open shells compared to the gain in the closed shells is because the open shell orbitals
are only half occupied, while the closed shell orbitals are fully occupied. Thus, the net charge on the Fe cation is less than the nominal
charge. The increase in total 3d character over the nominal value of
5 is especially large, by more than a full electron, when a 2p-hole is
present (see Table VI).
In Table VII, we examine the many-body 2p-hole states that
carry significant XPS intensity. Because of the low degeneracy of
the Fe2 O3 multiplets, the information is more compressed than in
Tables I and II. First, only the 50 individual final states that carry the
largest intensity are included. Because the intensities of individual
final states decrease slowly from the states with the lowest intensity in Table VII, this means that the intensity of weaker XPS features, as shown in Fig. 3, may not be fully represented in Table VII.
However, the intensities of the main peaks, especially the low BE
features, will be properly included. Second, the nearly degenerate
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TABLE VII. Properties of the states with the largest 2p XPS SA Irel for Fe2 O3 where nearly degenerate final states are
grouped together. The relative energies, Erel , of the states in the group, the number of these states, in the column labeled
Number, and the SA Irel are given. The groups of states are characterized with many-body occupation numbers, n(2p1/2 ),
n(2p3/2 ), n(t2g ), and n(eg ), and with the effective size of the set of 5 open shell 3d-like electrons. See text for further
details.
Group
Erel (eV)
Number
Irel
n(2p1/2 )
n(2p3/2 )
n(t2g )
n(eg )
3d(size)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
0.00
1.35–1.36
2.32–2.33
14.07
2.83–2.86
15.56
15.51
14.10
15.57
15.58
15.46
14.23
15.45
14.21
15.34
14.06
15.41
14.41
2.92
3.01
15.39
9
7
5
2
3
2
2
2
1
1
1
1
2
2
2
1
1
2
2
1
1
1.00
0.70
0.38
0.15
0.13
0.13
0.12
0.09
0.08
0.07
0.06
0.05
0.04
0.04
0.03
0.02
0.02
0.02
0.02
0.01
0.01
2.00
1.98
1.98
1.32
1.99
1.32
1.36
1.60
1.19
1.32
1.40
1.57
1.73
1.79
1.81
1.80
1.75
1.88
2.00
2.00
1.83
3.00
3.02
3.02
3.68
3.01
3.68
3.64
3.40
3.81
3.68
3.61
3.43
3.27
3.21
3.20
3.21
3.25
3.12
3.00
3.01
3.17
3.01
3.07
3.17
2.86
3.29
2.94
2.79
2.74
2.98
2.83
2.87
2.69
2.60
2.60
2.32
2.60
2.62
2.33
3.69
3.46
2.31
1.99
1.93
1.83
2.14
1.71
2.06
2.21
2.26
2.02
2.17
2.13
2.32
2.40
2.40
2.68
2.40
2.38
2.67
1.31
1.54
2.69
5.38
5.33
5.26
5.50
5.17
5.44
5.55
5.58
5.41
5.52
5.49
5.63
5.69
5.69
5.90
5.69
5.67
5.90
4.87
5.04
5.90
final states with very similar energies and other similar properties are
grouped together. The small energy splittings of the many-electron
final states arises, in large part, from small ligand field splittings of
the distorted octahedral geometry of Fe2 O3 ; these small splittings
are seen in the orbital energies shown in Table IV. The range of
energies grouped together are within 0.01 eV with one exception at
Erel = 2.8 eV where the states grouped together are within 0.03 eV.
For the lower Erel states, the number of states in a grouping follows the J values of the Fe3+ final 2p-hole states (see Table I); for
the higher Erel states, the number of states in a grouping follows the
degeneracies of the octahedral double group with 1, 2, or 3 states
in a grouping. The data given in Table VII are as follows: The relative energy, Erel in electron volts, of the states in a group is given
as a single number, if the energy range is <0.005 eV, or a pair of
numbers when the energy range is larger. This is followed by the
number of states in the group. The Irel , summed over the states in
the group, is given and normalized so that the Irel of the first group is
1.00; this is done so that the 2p XPS Irel of Fe2 O3 in Table VII can be
directly compared to the Irel of Fe3+ in Tables I and II. For the manybody states, the occupations of the spin-orbit split 2p shells, n(2p1/2 )
and n(2p3/2 ), and the occupations of the open 3d shell are given. For
the 3d shells, the occupations are given for sums over the orbitals
that arise, dominantly, from the octahedral t2g and eg orbitals, n(t2g )
and n(eg ) (see Tables IV–VI). The n(t2g ) and n(eg ) occupations are
averaged over the states in the group. Finally, the effective sizes of
the open shell 3d electrons, denoted 3d(size) and defined in Sec. II
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
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in terms of the orbital reff , is given. The values of 3d(size) provide
a further indication of the different occupations of the covalent 3d
orbitals with larger values of 3d(size) indicating a larger occupation
of the eg orbitals that have a greater covalent mixing with the O(2p)
(see Table V).
The first group of 9 states has essentially each of the Kramers’
pairs singly occupied since the t2g and eg are half occupied. With its
2p and 3d occupations and its 9-fold degeneracy, this group is close
to the first, J = 4, 2p-hole level of Fe3+ . The second group with a
degeneracy of 7 and an Irel = 0.70 is close to the second Fe3+ 2p-hole
level with J = 3 and a similar Irel = 0.73. The third group with a degeneracy of 5 and an Irel = 0.38 can be associated with the third, J = 2,
level of Fe3+ with a somewhat larger Irel = 0.44. The major difference
between these Fe2 O3 groups and the Fe3+ levels is the energy splittings, which are 1.4 and 2.3 eV compared to 1.8 and 3.2 eV for the
Fe3+ splittings. It is difficult to associate the other Fe2 O3 groups with
levels of Fe3+ , indicating that the configuration mixing and angular momentum coupling are different between the two systems. The
groups at Erel = 14.1, 15.5, and 15.6 eV that are dominantly 2p1/2
holes, with n(2p1/2 ) = 1.32 and 1.36, get most of their SA Irel from
2p1/2 ionization [see Fig. 3(c)]. These groups have a center of intensity at lower energy than the multiplets numbered 4, 6, 7, and 8 of
Fe3+ at Erel = 14.0–17.5 eV that also get most of their SA Irel from
2p1/2 ionization. The same shifts have been noted in Table III for the
features of the total XPS intensity curves rather than for individual
states. In other words, the ligand field splittings and covalency for a
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realistic FeO6 cluster model of Fe2 O3 lead to significant changes in
the theoretical Fe 2p XPS. This is a strong caution about the quantitative limitations of using atomic models of XPS, as presented, for
example, in the work of Gupta and Sen,1,2 to interpret the XPS of
metal oxides.
A major origin of the lowering of the energy separations of
the Fe2 O3 multiplets arises from the covalency of the open shell,
dominantly 3d, orbitals, which, especially for the eg derived orbitals,
have considerable O(2p) character (see Tables V and VI). An important driving force for the splittings for different angular momentum couplings comes from the exchange integral between the Fe
2p orbitals and the valence open shell orbitals (see, for example,
Refs. 45 and 55). These integrals depend on an exchange distribution, ρex , which is a product of the 2p and valence open shell
orbitals,
ρex = φ[Fe(2p)]φ[val],
(5)
where φ[val] is a combination of Fe(3d) and O(2p) orbitals [see
Eq. (2b)]. Since the φ[Fe(2p)] is purely localized on Fe (see the rreff
in Table IV), the product ρex will be nonzero only for the part of
φ[val] arising from the φ[Fe(3d)] contribution and will, hence, be
smaller than the ρex for an isolated Fe3+ cation. For the case of MnO,
the differences between the MnO and the Mn2+ exchange integrals
have been specifically examined.40 Furthermore, since the Fe cation
in Fe2 O3 is 3+ rather than 2+ for the Mn cation in MnO, the covalent mixing with O(2p) is larger for Fe2 O3 .54 Thus, the reduction in
the multiplet splitting for the compound from the isolated cation is
greater for Fe2 O3 than for MnO. Using the schematic expression of
Eq. (2b), we have for the cluster exchange density [Eq. (5)] between
Fe(2p) and the valence open shell, φanti-bond ,
ρex = φ[Fe(2p)]φanti-bond = Aφ[Fe(2p)]φ[Fe(3d)].
Since the exchange integrals are quadratic in ρex , the exchange integrals for Fe2 O3 will be reduced by A2 from the values for the isolated
Fe3+ cation. An estimate of this reduction can be made from the projections of Fe(3d) on the cluster orbitals given in Table VI where the
projections for the 2p-hole configuration, FeO6 -2p, are used. While
the reduction of the cluster exchange integrals for the t2g derived
orbitals is less than 10%, it is 50% for the eg derived orbitals. The
reduction of the cluster exchange integrals from the atomic values
averaged over the t2g and eg orbitals is 75%. This is much larger
than the average reduction of the MnO exchange integrals of only
7% from the atomic Mn2+ values.40
In Tables I, II, and VII, the SA XPS intensity has been normalized to 1 for the first, most intense, 2p-hole final state for both isolated Fe3+ and Fe2 O3 . It is possible to examine the total SA intensity
from the sum over final states and the average over the six degenerate initial states. Note that for Fe2 O3 , the initial states are separated
by less than 0.02 meV and can still be viewed as degenerate. For the
Fe3+ isolated cation, this intensity is 1.35, while for Fe2 O3 , it is 0.90.
This indicates that there is a much greater loss from the main peaks
to shake satellites7,8,32 for Fe2 O3 than for Fe3+ . The shake losses from
the final many-body 2p-hole multiplets where only angular momentum coupling and spin-orbit and ligand field splittings are taken into
account is given by Eq. (1). The losses to shake satellites of the 2p
XPS for Fe3+ are 10.2%, while the losses for the 2p XPS of the FeO6
cluster model of Fe2 O3 are 40.0%. These losses are almost identical
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
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for Fe 2p3/2 and Fe 2p1/2 ionization. The additional shake losses arise
because the added covalency, when there is a 2p-hole (see Table VI),
acts to provide additional screening of the core hole in the oxide
(see also Refs. 54 and 56). Since losses to shake satellites may be
different between the metal cations and the O anions, theoretical
values for these losses could provide useful data that would allow
more accurate estimates of stoichiometry to be obtained from XPS
data.
Finally, we compare our predictions for the Fe 2p XPS for
Fe2 O3 using the FeO6 cluster with measurements. The experimental
spectrum shown in Fig. 4 is the XPS for Fe2 O3 nanoparticles using
an Al Kα x-ray source with a Shirley background subtracted; details
of the measurements are given in the supplementary material. Our
results are similar to other XPS studies of Fe2 O3 .46,57,58 While the
BE positions of all the features are consistent in all of these studies,
the relative intensities of these features vary in a systematic manner. It involves a gradual decrease or increase in intensity across
the spectrum caused by the different background removal procedures used (e.g., Shirley, iterated Shirley, and Tougaard).59 Although
this may be a significant issue when trying to establish accurate stoichiometry from the Fe 2p/O1s intensity ratio, it has little impact
on a comparison to theoretical predictions for the peak structure
assignments.
Based on our analysis of the embedding,12 we do not expect
cluster size to be a significant limitation in our representation of
the observed XPS. The major limitation is that the calculations do
not include many-body excitations to model the shake structure,
whereas prominent features in the experimental spectrum have long
been associated with shake.60 In Fig. 4, these features are at ∼9 and
∼23 eV above the zero and are labeled A and B. The parentage of the
9 eV feature (peak A) is assigned to the 2p3/2 manifold and that of the
23 eV feature (peak B) to the 2p1/2 manifold. Supporting this assignment is the fact that peaks A and B have identical separations from
the two parent manifolds and roughly the same intensities relative
to their respective parent manifolds, as is often the case for 2p shake
structure. The intensity in A and B is about 20%–40% the total signal intensity, depending on how one fits the peaks. The theoretical
total loss to shakes is ∼40% (see earlier). This suggests at least half
the shake intensity is captured in the spectrum, but that up to half
may be somewhere else beyond the 28 eV cut off. In fact, we know57
that a small feature occurs at about 743 eV BE and there may be
more at higher BE, which would be lost in the background and the
interfering Fe Auger structure in that region.
FIG. 4. The 2p XPS for the FeO6 cluster model of Fe2 O3 compared with experiment shown as a dotted line. Specific features of the experiment, labeled A and B,
and of the theory, labeled C and D, are discussed in the text.
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The theoretical Fe2 O3 2p XPS are plotted compared to the
experimental results in Fig. 4 where the experiment is a dotted
curve and the theoretical results are from use of the FeO6 cluster
model. There is a rigid shift so that the experiment and theory are
aligned, but no changes are made for the relative energies. The same
Voigt broadening as in Fig. 3 was used. For the first, mostly 2p3/2
originated manifold, spreading from −2 eV to ∼4 eV, the agreement with experiment is quite good, as it is for the 2p1/2 originated manifold spreading from ∼12 to ∼20 eV. Discrepancies are as
follows:
(1)
(2)
(3)
a roughly 1 eV too great apparent SO splitting,
excess intensity in the theory at ∼6 eV (peak C in Fig. 4) and
at ∼19 eV (peak D),
missing intensity in the theory at ∼4 eV and ∼17 eV.
These discrepancies must arise from many-body effects not included
in our current theoretical treatment, which only treats the angular momentum coupling of the open shell electrons and does not
take shake satellites into account. A possible and likely explanation for these discrepancies is that there are additional low-lying
shake contributions at ∼4 eV and ∼17 eV. In particular, the excitations from occupied bonding to unoccupied antibonding orbitals
may be responsible. Support for this possibility is provided from the
study of the 2p XPS of Ti(IV)31 where such low-lying excitations did
lead to a broadening, albeit only of the lower-lying Ti 2p1/2 XPS
peak.
It is important to stress that despite the relatively minor discrepancies discussed above between theory and experiment, our theory describes the two main manifolds in the spectrum correctly.
This is a clear indication that the many-body angular momentum
coupling, including intermediate coupling,37,49,50 combined with the
ligand field and spin-orbit orbital splittings is dominantly responsible for these XPS features. Furthermore, as shown by the data in
Tables II and VII, a one-electron, one-determinant view of the XPS
process is, at best, of only qualitative value.
IV. CONCLUSIONS
A detailed discussion of the contributions of the angular
momentum coupling of the open-shell electrons for nominally
Fe(III) in hematite α-Fe2 O3 has been presented. This included analysis of the theoretical Fe 2p XPS for an isolated Fe3+ cation and for
an embedded FeO6 cluster model of Fe2 O3 . The origin of the differences in the XPS predictions of these two models of Fe2 O3 has been
identified as arising from the covalent character of the valence level
orbitals where the Fe(3d) and O(2p) orbitals mix to form molecular
orbitals. Novel methods have been used to characterize this covalency and to provide quantitative measures of its importance for
orbitals as well as for different many-electron 2p-hole states. One
method to quantify the covalency involved calculations of the effective orbital sizes, reff , as measured by the square root of the expectation value of r2 taken with respect to the Fe nucleus. A second
method for characterizing the covalency is to project the 3d orbitals
of the isolated Fe3+ onto the orbitals of Fe2 O3 ; for ideal orbitals
where covalency is not present, the projections would be either 0
or 1. It has been shown that there are significant departures from
these ideal limits. Furthermore, the extent of the covalency is greater
J. Chem. Phys. 152, 014704 (2020); doi: 10.1063/1.5135595
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for the 2p-hole orbitals than for the initial state orbitals. The physical origin of the increased covalency in the 2p-hole orbitals is the
larger nuclear charge, as seen by the valence electrons, for Fe with a
2p-hole. This additional charge draws electrons from the O anions
to the partly occupied Fe 3d shell through an increase in the covalent
character of both the closed and open shell orbitals.
Strong evidence is given that the wavefunctions, especially for
the 2p-hole states, cannot be described by a single configuration but
involve sums over many determinants with different occupations of
the spin-orbit and ligand field split core and valence open shells.
This is directly shown by computing the occupation numbers of the
open shell orbitals for the many-body, many-determinantal, wavefunctions. If these wavefunctions were single configurations or were
dominated by one configuration or one determinant, the occupation
numbers would be integer or nearly integer. While wavefunctions
of the lowest Fe 2p-hole multiplets, corresponding to ionization of
the 2p3/2 orbitals, do have integer or nearly integer occupations,
the occupation numbers for the wavefunctions of the other 2p-hole
multiplets are far from integer. For example, the smallest 2p1/2 occupation numbers of the multiplets with the largest XPS Irel are much
larger than 1.0 (see Tables II and VII for the Fe3+ and FeO6 models
of Fe2 O3 , respectively). In other words, the XPS-allowed determinants are distributed over the wavefunctions for many states instead
of having a single or a few multiplet coupled final states that carry
all the XPS intensity. An important consequence is that XPS features
are broadened far beyond the experimental resolution because there
are many unresolved final states with XPS intensity. This is an inherent broadening that cannot be reduced through higher experimental
resolution.
The differences between the XPS of the ideal isolated Fe3+
cation and the more realistic embedded FeO6 model of Fe2 O3
involve major reductions in the spacing of the multiplets. This is seen
for the leading XPS peak primarily due to 2p3/2 ionization where the
peak is less broad for the cluster model than for Fe3+ . The reduction of the 2p-hole multiplet spacings is also seen in the splitting of
the two main peaks between Fe3+ and FeO6 (see Figs. 2 and 3 and
Table III). Because these two features are associated with ionization
of 2p3/2 and 2p1/2 , respectively, it is tempting to assign this to a reduction of the 2p spin-orbit splitting between the isolated cation and
the oxide. However, our calculations show that the true spin-orbit
splitting given by the Dirac Hartree-Fock orbital energies is essentially unchanged between the Fe cation and cluster. This is physically
reasonable since the 2p spin-orbit splitting is largely an effect arising from the distribution of the 2p core orbital, which is largely
unchanged between the cation and cluster. Another possible explanation for the reduction of the splitting of the two main XPS peaks
is that there is a different, larger, loss to shake satellites for the 2p1/2
ionization than for the 2p3/2 ionization. If this were the case, then
from the sum rule for shake satellites,32 the main 2p1/2 peak would
be shifted to lower BE and hence closer to the main 2p3/2 peak. Our
direct calculation of the losses to shake satellites shows that the losses
for 2p1/2 and 2p3/2 are essentially identical. In other words, there are
no differential losses to satellites from the spin-orbit split levels and
this cannot be the origin of a shift in the apparent spin-orbit splitting
between the cation and cluster. This result is physically reasonable
considering that the origin of shake losses is the orbital relaxation
to screen the core-hole.8,9,21,32 The largest part of this orbital relaxation is from the valence electrons, and for these valence electrons,
152, 014704-13
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the potential of a core-hole in 2p1/2 is equivalent to the potential of a
core-hole in 2p3/2 .
Not only have we been able to show that two explanations for
the change in the apparent spin-orbit splitting are incorrect but,
more importantly, we have identified the correct reason for the difference in this splitting. Indeed, the reduction of the width of the
leading, Fe 2p3/2 , XPS peak has a common origin with the reduction of the separation of the two main XPS peaks. This origin is the
change of the exchange integrals between the Fe 2p and the valence
open shell, purely Fe 3d for Fe3+ and covalent mixing of Fe 3d and
O 2p for FeO6 . These exchange integrals make major contributions
to the multiplet splitting and are reduced for FeO6 from their values for Fe3+ because of the covalent mixing. Thus, the spacing of
the multiplets of the cluster will be reduced from the spacing of
the Fe3+ multiplets, exactly as obtained in our calculations. Furthermore, the larger the covalent character in an oxide, the larger will be
the difference between the isolated cation XPS and the XPS for the
oxide.
A reduction of the theoretical separation of the energies of the
XPS features has also been found for the Mn 2p XPS between an isolated Mn2+ cation and an embedded MnO6 cluster model of MnO.40
However, the difference between the 2p XPS for an isolated Mn2+
cation and the XPS for an MnO6 cluster model is smaller than we
found between Fe3+ and the Fe2 O3 cluster model. This is because the
covalent mixing between the cation and O(2p) is larger for Fe2 O3 ,
where the nominal charge is +3, than for MnO where the nominal
charge of the cation is only +2. It has been observed that the XPS
apparent 2p3/2 –2p1/2 spin-orbital splitting for a given 3d cation is
different for different compounds with that cation (see Fig. 14.2 of
Ref. 61). Our work provides an explanation for these changes in the
apparent spin-orbital splitting as arising from different covalency in
the different compounds. In other words, changes in the apparent
spin-orbit splitting may indicate changes in the covalent character
in different compounds; combining theory with experiment to identify this contribution to the splitting could be a new and novel use of
XPS to identify material properties.
SUPPLEMENTARY MATERIAL
See the supplementary material for specific details of the XPS
measurements and to support several applications of methodology
and for details of plotting parameters.
ACKNOWLEDGMENTS
This material is based on work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences,
Chemical Sciences, Geosciences, and Biosciences (CSGB) Division
through its Geosciences program at the Pacific Northwest National
Laboratory (PNNL). We thank Xin Zhang and Meirong Zong at
PNNL for providing us with Fe2 O3 nanoparticle samples for XPS
analysis.
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