A New Mechanism For XPS Line Broadening: The 2p-XPS of Ti(IV

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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A New Mechanism For XPS Line Broadening: The 2p-XPS of Ti(IV) Paul S. Bagus,*,† Connie J. Nelin,‡ C. R. Brundle,§ and Scott A. Chambers∥ †

Department of Chemistry, University of North Texas, Denton, Texas 76203-5017, United States Consultant, 6008 Maurys Trail, Austin, Texas 78730, United States § C. R. Brundle and Associates, Soquel, California 95073, United States ∥ Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States J. Phys. Chem. C Downloaded from pubs.acs.org by KAOHSIUNG MEDICAL UNIV on 08/10/18. For personal use only.

‡

S Supporting Information *

ABSTRACT: There is almost a factor of 2 increase in the full width at half maximum (FWHM) of the main Ti 2p1/2 XPS peak compared to the 2p3/2 in the closed-shell Ti(IV) compounds TiO2 and strontium titanate, STO. Although the spectra of anatase and rutile forms of TiO2 differ slightly from STO, the 2p1/2 broadening over 2p3/2 is very similar. For STO, we show that ascribing this differential broadening to a short 2p1/2 lifetime is unphysical. For STO, rigorous and fully relativistic electronic structure calculations have been carried out for both the initial state and the 2p core-hole states; these calculations include many-body effects as well as the one-body effects of spin−orbit and ligand field splittings. The agreement of the theoretical and measured XPS data for the main 2p1/2 and 2p3/2 peaks indicate that the necessary one- and many-body effects have been included. They show that the broadening is due to the presence of XPS intensity distributed over many unresolved final states for a 2p1/2 core-hole, whereas the 2p3/2 core-hole has the expected single symmetric peak. The many-body effects for the corehole states involve mixing of the normal, single-hole, configurations with shake up configurations where valence electrons are promoted from filled orbitals into empty orbitals. This configuration mixing allows configurations with a 2p1/2 core-hole to mix with those that have a 2p3/2 core-hole, an effect which, to our knowledge, has not been previously considered. It is the mixing of XPS allowed 2p1/2 excitations with XPS forbidden 2p3/2 shake configurations that leads to the distribution of the 2p1/2 XPS intensity over several final states, and the 2p1/2 XPS broadening is reproduced using a realistic lifetime for the 2p1/2 core-hole. This novel mechanism for the broadening of XPS features might be more general than solely for the 2p XPS of Ti(IV) oxides. The calculations also show the presence of major covalency for the STO orbitals, which is larger for the 2p core-hole configuration than for the ground state, proving that the change in covalency is a major contribution to the core-hole screening. 2p1/2 will have a shorter lifetime and, hence, a larger broadening4 than the 2p3/2. This follows because there are more decay channels for the 2p1/2. The assignment of the differential broadening to a shorter lifetime for the Ti(2p1/2) core-hole was investigated and was found to require a lifetime broadening that is larger than expected based on known values of the core-

I. INTRODUCTION The present combined experimental and theoretical study of the 2p XPS of Ti(IV) in strontium titanate, SrTiO3 and denoted STO, shows that the spin−orbit split Ti(2p1/2) and Ti(2p3/2) peaks have significantly different broadening. Experimental data show that there is a similar differential 2p1/2 and 2p3/2 broadening also for TiO2. For closed-shell Ti(IV), each of the main XPS peaks should correspond to one of the shells of the system with satellites of lower intensity, see for example refs 1 and 2. Thus, it is tempting to assign the differential Ti(2p) broadening to different lifetimes of the 2p1/2 and 2p3/2 coreholes.3 In particular, it is known that the more strongly bound © XXXX American Chemical Society

Special Issue: C: Hans-Joachim Freund and Joachim Sauer Festschrift Received: June 12, 2018 Revised: July 17, 2018 Published: July 23, 2018 A

DOI: 10.1021/acs.jpcc.8b05576 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C lifetimes.4 In order to resolve the apparent need to use an unrealistically short lifetime for the Ti(2p1/2) level, the possible role of satellites involving determinants formed by a shake process was investigated. The Ti 2p XPS has been predicted from wave functions (WFs) for the initial (filled core) and final (2p ionized) configurations of models of STO. The models considered are the isolated Ti4+ ion and an embedded cluster model of STO where a central Ti cation is surrounded by its nearest O anion and Sr cation neighbors. The satellites for the STO cluster model are treated using a theoretical framework based on shake excitations within the valence space in addition to the ionization from a core level. This approach is somewhat different from the commonly used semiempirical Anderson model Hamiltonian treatment of the main and satellite XPS peaks. For a discussion of the Anderson model theoretical approach see, for example, refs 3, 5, and 6 and for a comparison of the Anderson model with ab initio wave function methods see ref 1. The present work relies on a detailed analysis of the WFs that represent the XPS final state multiplets, especially for the structure of the WFs in terms of Koopmans-like and shake-like configurations and on how these multiplets obtain their XPS intensity. The intensity is determined with the Sudden Approximation (SA),7 where it is assumed that the WF, at the instant of ionization, involves only the removal of a core electron with the other, passive, orbitals frozen as they are in the initial, un-ionized, configuration. This “frozen orbital” WF is then expanded in stationary states of the Hamiltonian for the final states, and the SA intensity is the square of the expansion coefficients for the final state WFs. An important and novel feature of the current work is that it shows that the XPS intensity of the Ti(2p1/2) ionization is distributed over a very large number of states, all of which are dominated by shake character. It is the unexpected distribution of intensity over a large number of final states, which are many-body mixtures of different configurations, that changes the one-body view for the main XPS Ti(2p1/2) peak for ionization of closedshell Ti(IV). The origin of the distribution of the Ti(2p1/2) XPS intensity is shown to arise from symmetry flip shake configurations which violate the usual monopole selection rules for shake excitations.8 Such symmetry flip configurations have not been considered previously. The covalent character of the orbitals of STO is investigated using novel methods of the projection of fragment orbitals to estimate the extent of the covalent mixing, primarily of the O(2p) with the Ti(3d) orbitals. It is shown that this covalent mixing is quite large for both the ground state and 2p-hole state configurations. For the ground state configuration, there is a Ti(3d) occupation of 1.9 electrons while the nominal 3d occupation, which neglects the covalent mixing, is zero. For the 2p-hole configuration, the Ti(3d) occupation is significantly larger at 3.1 3d electrons for an increase over the ground state configuration of 1.2 electrons. In other words, the core-hole is over-screened by the change in the covalent character of the orbitals between the initial and final, core ionized, configurations. The variational many-body WFs for the core-hole final states are determined with the covalent orbitals for the Ti 2phole configuration, thus directly and explicitly taking account of the screening of the core-hole. The paper is organized as follows. In Section II, the theoretical procedures to determine the WFs and XPS intensities are reviewed and the experimental procedures are described. For the comparison of theory and experiment, the broadening of the theoretical results with a convolution of a Lorentzian broadening

for the core-hole lifetime and a Gaussian for resolution and for other broadenings is described in this section. In Section III, the properties of the orbitals are analyzed and the extent of the covalent mixing is determined. In Section IV, the origin of the differential broadening in terms of the electronic structure of many-body, unresolved shake final states is determined. A progression of theoretical models is used to determine the importance of different one-body and many-body effects for the Ti(2p) XPS. Unless the symmetry flip shake configurations are included in the many-body treatment, unphysical values of the Ti(2p1/2) lifetime are required to describe the Ti(2p1/2) broadening. Finally, in the conclusions (Section IV), the arguments for the importance of shake many-body effects for the Ti(2p1/2) XPS are reviewed and it is suggested that analysis of measured broadening of XPS features may be a new way to obtain chemical information from XPS spectra.

II. THEORETICAL METHODS AND XPS MEASUREMENTS For the theoretical analysis, we have modeled the XPS of SrTiO3, STO, although we expect the results to be valid as well for TiO2 since, as discussed below, the differential broadening of the Ti(2p1/2) and Ti(2p3/2) of STO and TiO2, in both rutile and anatase forms, is similar. The STO crystal has cubic symmetry and has been modeled with a cluster that contains a central Ti cation surrounded by its 6 oxygen anion nearest neighbors and by the nearest shell of Sr cations. The TiO6Sr8 cluster is embedded in several shells of point charges at lattice sites with the nominal ionic charges of +4 for Ti, −2 for O, and +2 for Sr to represent the Madelung potential. The experimental geometry9 is used for the positions of the atoms and point charges. A schematic of the cluster is shown in Figure 1. The use of a cluster

Figure 1. Schematic view of the embedded TiO6Sr8 cluster used to model STO. The Ti is shown as the central sphere with 6 O atoms and 8 Sr atoms. The embedding charges are shown as small spheres.

to model the local XPS process allows us to interpret the oneand many-body effects in terms of the orbitals involved and in terms of the chemical bonding and interactions between Ti and O.1 We have also examined the XPS for the isolated Ti4+ cation; this is done in order to distinguish the effects of the crystalline environment of STO from the effects arising for the Ti4+ cation. Four component spinors were obtained as variational solutions of the Dirac−Hartree−Fock, DHF, equations with the Dirac−Coulomb Hamiltonian10 for the closed-shell configuration derived from the configurations of the Ti4+, O2−, B


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The Journal of Physical Chemistry C and Sr2+ closed-shell fragments. These orbitals include the effects of spin−orbit and ligand field splittings. They transform according to the irreducible representations of the Oh double group, Oh*.11 Two sets of orbitals are determined for the TiO6Sr8 and Ti4+ systems studied. The first set of orbitals is for the initial configuration, where the Ti 2p-shell is filled, and the second set is for the final configuration, where the Ti 2p-shell has a hole. Thus, the screening of the core-hole after ionization is explicitly taken into account.1 This screening is particularly important for the condensed phase STO where there are major changes in the covalent character of the orbitals when a corehole is created. While the occupied orbitals for both the initial and final configurations are nominally the Ti Ar core (Ti4+) and O orbitals (O2−), this is changed considerably by the covalent mixing of O(2p) and Ti(3d) orbitals. These orbitals are used to form N and N-1 electron determinants for the initial and final states of the cluster. The initial, ground state WF is represented by a single determinant. The final state WFs may be represented by a single determinant or by many determinants. When only one-body effects are taken into account, there are six final states where each is represented by a single determinant. There are two degenerate final states where one of the Ti(2p1/2) electrons is removed and four degenerate spin−orbit split final states where one of the Ti(2p3/2) electrons is removed. When many-body effects are taken into account, the states of the ionized N-1 electron system are represented by a sum over many determinants. Besides the six determinants for the ionization of a Ti (2p1/2) or a Ti(2p3/2) electron, there are determinants that are formed by these ionizations and, in addition, by exciting one or more electrons from occupied orbitals into unoccupied orbitals. In particular, the occupied orbitals, from which electrons are excited, are dominantly O(2p) orbitals. The unoccupied orbitals, into which the electrons are excited, are dominantly Ti(3d) and are antibonding between Ti(3d) and O(2p). In Section IV, the logic of the choices of these additional determinants or configurations is discussed. It is natural to regard these excited configurations as shake configurations, in which one electron is ionized and one or more valence electrons are promoted into unoccupied orbitals.1,2,7 The many-body WFs, Ψk, for the states that can be represented by this set of determinants, denoted Φi, are ψk =

∑ Ck ,iΦi i

WFs, the output of DIRAC was interfaced to the CLIPS programs,17 extended as required for the relativistic WFs. The visualization of the spectra were carried out with programs written for this purpose. If a single set of orbitals is used to construct the determinants that describe the initial and final state WFs, then the shake determinants have no intensity. This is because they are forbidden transitions which, by construction, differ from the determinants for the initial state WFs in the occupation of at least two spin−orbitals.18 The shake determinants can gain intensity because they are formed from a different set of orbitals from those used for the initial state WF and the non-zero overlaps between the orbitals of the two different sets can lead to a non-zero SA Irel.1,7,19 However, there is another mechanism by which the states with WFs that have major contributions from the shake determinants may gain intensity. This is because these WFs also have contributions from one of the allowed six determinants where only a Ti 2p electron is ionized and none of the other orbital occupations change. Then, the SA Irel for this WF will have a contribution proportional to the square of the coefficient of this allowed determinant in the final state CI WF, eq 1. It will be shown in Section IV that this latter mechanism is the way that states dominated by XPS forbidden symmetry flip configurations gain intensity in the broadened Ti(2p1/2) XPS peak. In order to compare with experiments, it is necessary to broaden the calculated final state intensities to account for experimental resolution, core-hole lifetime, and any other effects, see for example ref 1. This is done by using a Voigt convolution20 of a Lorentzian to represent lifetime and a Gaussian to represent other broadening effects. Indeed, the choice of suitable full width at half maximum, FWHM, parameters for the Gaussian and Lorentzian functions is one of the important subjects of this paper. A special advantage of the Voigt convolution is that the appropriate FWHM can be separately identified for the contributions from lifetime and experimental resolution. An important criterion is that the FWHM parameters chosen be consistent with the widths that are believed to be appropriate based on other evidence, e.g., measurements of core-hole lifetimes.4 In addition to the calculation of the XPS spectra, the properties of the orbitals and the WFs must be analyzed in order to identify the character of the bonding and the interaction between Ti and O and to relate these properties to the observed features of the XPS. The orbitals are analyzed with projection operators in order to identify their covalent character, and the WFs are analyzed with number operators to characterize their composition in terms of shake configurations. While these two methods of analysis have been described elsewhere, they are reviewed briefly here. The projection operator for the DHF 3d orbital of isolated Ti4+ is φ(3d)φ(3d)† and the 3d occupation of the ith DHF orbital of the cluster model of STO, φi(STO), is

(1)

and are conventionally described as configuration interaction, CI, WFs.1,12 The Ψk are determined by solving the relativistic Hamiltonian over the space of the determinants used for the descriptions of the excited states.10 Typically, the Hamiltonian is solved for all the states that can be formed from the determinants in the space, and the solutions with large intensity correspond to main XPS peaks, while solutions with lower intensity correspond to satellite peaks.1 The choice of determinants is crucial for the determination of the energy and intensity of the XPS peaks, see Section IV. The XPS relative intensities, Irel, for the main and satellite XPS peaks are determined with the Sudden Approximation, SA,7 see also ref 1. The SA Irel are exact in the limit of very high photon energy but have been shown to be accurate for photon energies ∼200 eV above threshold.13 The basis sets and parameters used for the calculation of the WFs are described in ref 1 and references therein; for Ti, the basis set of Wachters14 supplemented by the diffuse d function of Hay15 was used. The DIRAC program system16 was used to determine the relativistic WFs. For the analysis of the relativistic

Np(3d,i) = =

∑

∑ ||2

(2)

where the sum is taken over the 5 different degenerate 3d orbitals of Ti4+. These projections provide reliable guides to the occupations of the Ti 3d orbitals and especially for changes of occupations for different configurations.1,21,22 Suitable sums of the projections for the occupied and the virtual STO orbitals can be taken to obtain total Ti(3d) occupations. For the CI WFs, Ψk in eq 1, the concern is to determine the fractional occupation of a C


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The Journal of Physical Chemistry C

other two, possibly indicating unique spectral weight at these energies. The FWHM of the 2p3/2 and 2p1/2 peaks at Erel = 0 and 5.8 eV have been obtained from a linear interpolation of the experimental data points with intensity nearest the halfmaximum intensity. These FWHM are in Table 1, where two

particular orbital, or combination of orbitals, in these WFs. Formally, this is simply the expectation value for Ψk of the number operator for the orbitals,23−25 denoted N(i) for the occupation of the ith orbital. Of particular concern will be the occupations, or more precisely, the changes in the occupations of the covalent bonding, dominantly O(2p) orbitals, ΔN(O 2p), and the antibonding, dominantly Ti(3d) orbitals, ΔN(Ti 3d). Ti 2p spectra were measured for single crystals of Nb-doped STO(001) and rutile TiO2(110), as well as for epitaxial films of anatase TiO2(001) deposited on LaAlO3(001) substrates. The STO crystals were prepared by etching them in buffered HF, followed by rinsing them in deionized water and annealing them in a tube furnace with flowing air at 1000 °C to achieve a TiO2terminated (001) surface. Rutile single crystals were cleaned by sonication in acetone and isopropyl alcohol on the bench, followed by annealing them in activated oxygen from an electron cyclotron plasma source in the oxygen plasma-assisted molecular beam epitaxy (OPAMBE) deposition chamber (appended to the XPS chamber) at an oxygen partial pressure and temperature of 2 × 10−5 Torr and 600 °C, respectively. Anatase(001) films were grown by OPAMBE as described elsewhere.26 All spectra were excited with monochromatic Al Kα X-rays and measured using either a Scienta SES-200 or R3000 hemispherical analyzer with a pass energy and slit width that yield an energy resolution of ∼0.5 eV, based on fitting the Fermi level of polycrystalline Ag at ambient temperature to a Fermi function. We show, in Figure 2, Ti 2p spectra for these three oxides measured under identical instrument conditions after Shirley

Table 1. Differential XPS Broadening of the Main Ti(2p3/2) and Ti(2p1/2) Peaks of Anatase and Rutile TiO2 and of STO As Given by Their FWHM FWHM (eV) anatase rutile STO

2p3/2

2p1/2

0.99 0.92 1.07

1.96 1.91 1.94

things are immediately clear. First, the FWHM are similar for all three compounds, differing by ≲0.1 eV. Second, the 2p1/2 FWHM are close to twice as large as the 2p3/2 FWHM. The quite different FWHM are easier to see in Figure 3 where the

Figure 3. Same as Figure 2 but with the Shirley background subtraction done such that only the more intense j = 3/2 and j = 1/2 features are included. The larger FWHM of the 2p1/2 peak compared to the 2p3/2 peak is clear.

spectra are presented over a narrower energy range. This very large difference is surprising, and its origin in terms of manybody effects will be shown. We do not consider the weaker higher energy satellites in this paper.

Figure 2. Ti(2p) spectra for anatase TiO2(001), rutile TiO2(110), and STO(001). The binding energy scale is relative, with the main 2p3/2 peak at Erel = 0 eV.

III. COVALENT CHARACTER OF THE STO ORBITALS The covalent character of the closed-shell ground state and the Ti 2p-hole configurations is obtained by taking sums of the orbital projections of eq 2, denoted NP(3d) in Table 2. For the occupied orbitals, the sums are over the dominantly O(2p) orbitals that have (i) eg symmetry, denoted O2p(eg); (ii) t2g symmetry, denoted O2p(t2g); (iii) the sum of the O2p(eg) + O2p(t2g), denoted Sum O2p; and (iv) the sum of the projections over all occupied DHF orbitals, denoted Sum All. None of these sums take into account the closed-shell double occupation of these orbitals; this is taken into account with the Np(3d), denoted Total, in Table 2. For the unoccupied orbitals, the NP(3d) are given separately for the eg and t2g orbitals that have dominant Ti(3d) character but contain some antibonding O(2p) character, denoted Ti3d(eg) and Ti3d(t2g), respectively.

background subtraction. The nominally Ti(IV) cations in these three lattices have in common an octahedral or distorted octahedral coordination to oxygen, as seen in the three local structures shown in the figure. The spectra consist of four distinct features, including the j = 3/2 and j = 1/2 spin−orbit peaks at relative binding energies, Erel, of 0 and 5.8 eV, respectively, as well as weaker shake satellites at energies of 13.5 and 19.7 eV. The Nb doping level in the STO crystal is sufficiently low that the Ti3+ tail on the low binding energy side of the j = 3/2 peak resulting from donor electrons in the conduction band is not detectable.27 With the exception of the valleys at ∼3 and ∼9 eV, the spectra are very similar despite the substantial differences in lattice structure for the three oxides. Within these valleys, the rutile spectrum is more filled in than the D


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The unoccupied t2g and eg orbitals that have dominant Ti(3d) character are also listed in Table 2. The Ti3d(t2g) have lost some of their 3d character because they have an antibonding covalent mixing with the O(2p), and the loss is larger for the Ti 2p-hole configuration than for the ground state configuration. The losses of 3d character are greater for the unoccupied, dominantly 3d, Ti3d(eg) orbitals, which have lost almost half of their nominal 3d character. The losses for eg orbitals are larger than those for the t2g orbitals for the same reason that the gain of 3d character for the nominal O2p(eg) is larger than that for the O2p(t2g) (see above). However, since the gains and losses of 3d character are distributed over several occupied and unoccupied orbitals, one should not expect an exact agreement of gains and losses for the pairs of O2p and Ti3d orbitals of t2g and eg symmetry. The sum of the projected 3d character in the occupied and in the unoccupied, dominantly Ti3d, orbitals, given as Total in Table 2, is less than 5 for the 5 3d orbitals that are projected onto the TiO6Sr8 space. This means that some Ti 3d character will be found in other unoccupied orbitals. A final comment for the data in Table 2 concerns the Δε for these orbitals, which can be taken as very approximate indications of the excitation energy for moving an electron from an occupied covalent orbital, labeled O2p, into an unoccupied, antibonding covalent orbital, labeled Ti3d.12 These Δε show that such excitations will raise the diagonal energy of the excited determinant by ∼15 eV. While this may seem large, the excitation energy needs to be considered in terms of the off-diagonal matrix elements. These off-diagonal elements depend, in part, on the magnitude of the 3d−3d exchange integrals for the Ti atom. The Slater Fν integrals31 for the Ti atom, which contribute to this 3d−3d exchange are reasonably large, ∼10 eV. Thus, the off-diagonal matrix elements could be a significant fraction of the excitation energy, and these excitations could, and in fact do, lead to significant changes in the predicted 2p XPS.

Table 2. Covalent Character of the Ground State, GS, and 2pHole State Configuration Orbitals for STO Modelled with the TiO6Sr8 Clustera final 2p-hole configuration

initial GS configuration O2p(eg) O2p(t2g) Sum O2p only Sum All Total unoccupied Ti3d(t2g) Ti3d(eg) Sum All occupied + Ti3d occupied

Δε

NP(3d)

Δε

NP(change)

0 2.0

0.21 0.12 0.77 0.93 1.86 0.86 0.52 4.54

0 2.4

0.34(+0.13) 0.22(+0.10) 1.35(+0.58) 1.55(+0.61) 3.09(+1.23) 0.77(−0.09) 0.55(−0. 03) 4.94

19.8 20.9

16.1 17.3

a

The projected 3d character, NP(3d), normalized as described in the text, together with the changes in orbital energy, Δε in electron volts, are given for the highest occupied and lowest unoccupied orbitals of t2g and eg symmetry, labeled respectively, O2p and Ti3d. .The Total NP(3d) include an additional factor of 2 to reflect occupation of the shells.

The symmetry notation of eg and t2g is for the cubic Oh group without spin−orbit splitting.11 When spin−orbit splitting is taken into account, the t2g orbitals go to double and singly degenerate representations.28 Since, for the orbitals considered in this table, the spin−orbit splitting is small and not of concern, the t2g orbital values of NP are averaged over this pair of spin− orbit split orbitals. The relative orbital energies, Δε, in electron volts, of the O2p and Ti3d orbitals of eg and t2g symmetry are also given in Table 2 with respect to the lowest energy O2p(eg) taken as Δε = 0. As for the NP, the t2g Δε are averaged over the spin− orbit split DHF orbitals. For the ground state configuration, there is significant Ti 3d character in the dominantly O2p orbitals where the nominal 3d character, neglecting covalency, is zero, i.e., Ti is formally Ti(IV). The covalent character is significantly larger for the O2p(eg) orbitals than for the O2p(t2g) orbitals; NP(3d) is almost twice as large for the 2 eg orbitals than for the 3 t2g orbitals. This difference in covalent character is expected from the orientation of the Ti 3d orbitals; the Ti3d(eg) orbitals are directed toward the O atoms while the Ti3d(t2g) are directed between the O atoms, which is an orientation less favorable to forming covalent bonds.1 The sum of NP(3d) for the O2p(eg) and O2p(t2g) orbitals is 0.77 electrons. Summing the projections over all the occupied orbitals increases the sum of NP(3d) to 0.93 primarily because the dominantly O(2s) orbitals have a small covalent character. With the orbital occupation taken into account a total 3d projected occupation of 1.9 electrons compared to the nominal occupation of zero is obtained. There is a significant increase of d character when a 2p-hole is created, with the total occupation of NP(3d) increasing by more than 50% to 3.1 electrons. Clearly, the change in covalency makes a major contribution to the screening of the core-hole.1 It is possible to understand the increase of covalency for the core-hole configuration by considering the Jolly equivalent core model,29,30 see also refs 1 and 2. For the valence electrons, Ti with a 2p-hole is equivalent to V+. Since the charge of V is larger than that of Ti, it is reasonable to expect that there will be a greater covalency for the core-hole configuration than for the ground state. Indeed, this is a general observation and covalency is a major contribution to the screening of core-holes in compounds.1,2

IV. ANALYSIS OF THE TI 2P XPS OF STO In this section, our concern is for the different apparent broadening of the Ti 2p3/2 and Ti 2p3/2 spin−orbit split XPS peaks. Thus, we restrict ourselves to the energy region within the first 10 eV of the leading edge Ti 2p3/2 XPS peak. The plots that are shown in this section are all in the relative energy range of −4 ≤ Erel ≤ 10 eV, where Erel = 0 is taken as the maximum of the leading, Ti 2p3/2, peak and the splitting of the 2p3/2 and 2p1/2 XPS peaks is ∼6 eV. A. XPS from Wave Functions with Angular Momentum Coupling Only. The TiO6Sr8 model of STO and Ti4+ are closed-shell systems. If only the configurations and multiplets are considered where a 2p electron is ionized, there will be only two final state multiplets where each of the 6 possible final states, two states for a 2p1/2-hole and four for a 2p3/2-hole, is described by a single Slater determinant. Furthermore, given these degeneracies, the ratio of the intensities of the two XPS peaks should be approximately 2:1, see for example ref 1. This level of theory, where only the spin−orbit (SO) splitting of Ti 2p is taken into account, is denoted as SO only. In Figure 4(a), the Voigt broadened two 2p-hole peaks for the isolated Ti4+ cation, SO only, are shown as a solid curve and are compared with the experiment taken from Figure 2, shown as a dotted curve. There has been a rigid shift and scaling so that the experimental and theoretical 2p3/2 XPS peaks are at the same energy and have the same maximum intensity; the same adjustment is made for all other comparisons of theory and experiment shown in Figure 4 E


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Figure 4. Theoretical 2p XPS for STO, assuming only angular momentum coupling (SO splitting), in the energy range of the most intense 2p3/2 and 2p1/2 XPS peaks: (a) Ti4+ with a single set of broadening parameters; (b) embedded TiO6Sr8 cluster with a single set of broadening parameters; and (c) embedded TiO6Sr8 cluster with dual broadening parameters. The 2p1/2 Lorentzian broadening parameters, FWHM in electron volts, are (a) 0.25, (b) 0.25, and (c) 1.2. Experiment, shown as a dotted line, compared to theory, shown as a solid line; given the dense points for experimental data, theory and experiment are identified in the figure.

and Figure 5. There have been no other adjustments to the directly calculated Erel and the theoretical SA Irel. The Voigt broadening uses a convolution of a 0.25 eV FWHM Lorentzian for the 2p-hole lifetime and a 0.92 eV FWHM Gaussian for experimental resolution. These values have been chosen for the following reasons. The Lorentzian FWHM of 0.25 eV is the recommended Ti(2p3/2) lifetime taken from Campbell and Papp.4 The Gaussian FWHM represents the experimental resolution and other effects, including surface inhomogeneity, vibrational excitations, and surface core level shifts, see for example ref 1. The FWHM of 0.92 eV was chosen because it gave an excellent visual match with the experimental data, see Figure 4(a). The Voigt convolution for these Gaussian and Lorentzian FWHM also leads to a total FWHM of 1.08 eV, which is very close to the Ti(2p3/2) FWHM of 1.07 eV obtained

Figure 5. Progression of final state WFs for the 2p XPS for STO with the embedded TiO6Sr8 cluster; experiment and theory are shown as in Figure 2. A dual broadening has been used and the Lorentzian for the 2p1/2 lifetime has been optimized to give the best fit to the experimental data. (a) WFs with only spin−orbit splitting. (b) Step 2 CI WFs (1.1 eV). (c) Step 3 CI WFs (1.0 eV). (d) Step 3 CI WFs (0.5 eV). The numbers in parentheses are the Lorentzian lifetime broadening FWHM.

from the experimental data, see Table 1. This excellent agreement of the theoretical and experimental Ti(2p3/2) FWHM is further confirmation that these choices of Gaussian and Lorentzian FWHM are suitable. Since the Gaussian F


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shell with an occupation denoted as (Ti 2p)5; this hole can be created in any one of six ways. The orbital written as αO(2p) + βTi(3d) represents, schematically, a covalent mixing of O(2p) with Ti(3d). This occupied orbital is a bonding combination of Ti(3d) and O(2p) where the coefficient of the O(2p) contribution, α, is larger than the coefficient of the Ti(3d) contribution, β, and the signs are chosen to indicate a bonding orbital. Reference 22 presents the contribution of such bonding orbitals to the energy of representative oxides. The occupation of this orbital in the Koopmans configuration is 6 to indicate that it is fully occupied. The orbital written as βO(2p) − αTi(3d) represents, again schematically, the antibonding orbitals between O(2p) and Ti(3d) that are not occupied in the Koopmans configurations and are shown with an occupation of 0. The choice of the same coefficients, with changed signs, neglects the overlap of the Ti(3d) and O(2p), as well as the changes between the optimized bonding and antibonding orbitals. It is meant only to distinguish the bonding character of the fully occupied orbitals from the antibonding character of the empty antibonding orbitals. The configurations, or determinants labeled as Shake 1 and Shake 2 in eq 3, involve excitation from the filled bonding orbitals into the empty antibonding orbitals, as well as ionization from the Ti 2p. For Shake 1 only one electron is excited, or promoted, and for Shake 2, two electrons are promoted. Beyond the configurations shown in eq 3, there are higher order shake excitations where 3, or more, electrons are promoted from the bonding orbitals into the antibonding orbitals. Configurations constructed with the logic of eq 3 are those that must be included in the many-body CI WFs for a many-body treatment in order to represent the shake satellites that may make major contributions to the Ti 2p XPS spectra. In order to construct these CI WFs, it is necessary to define the active space of orbitals that are used to construct the determinants in the CI and the active space of determinants included in the CI. The orbitals used in eq 3 are schematic. The actual orbitals used for the CI WFs of STO are the orbitals with Oh, rigorously spin−orbit split double group Oh*, symmetry, as shown in Table 2. The orbitals used to represent the occupied space are O2p(eg) and O2p(t2g), which have significant Ti(3d) character, as well as the other orbitals of dominantly O(2p) character of symmetries, a1g and t1g (not shown in Table 2), that cannot, by symmetry, have covalent mixing with the Ti(3d). The orbitals into which excitations are made are the Ti3d(eg) and Ti3d(t2g) which, as shown in Table 2, have significant O2p character. These orbitals, or a subset, are used for the different CI WFs. The total amount of the Ti3d occupation, for the 2p-hole configuration, recovered with this group of orbitals is not the full 5, and for very accurate WFs, a larger active orbital should be used; however, as will be shown, the space described above is adequate to reproduce and to show the origin of the differential broadening of the Ti(2p1/2) XPS peak. With the orbitals described above, it is necessary to select configurations to be included in the CI WFs of the embedded TiO6Sr8 cluster to represent many-body effects for the final ionic states. The WFs are considered in four steps, generally in the order of their expected importance for the descriptions of the electronic structure. The first step is the minimal description where the 6 Koopmans determinants are used to describe the final states; these results have already been discussed in the previous subsection and are denoted as Step 1. The second step involves the occupied and unoccupied orbitals that have a major covalent mixing of Ti3d and O2p character. These orbitals are the

broadening represents physical effects that should be the same for Ti(2p1/2), we use the same Gaussian FWHM for the Ti(2p1/2) Voigt broadening. For the broadening of the Ti(2p1/2) XPS peak in Figure 4(a), we also use the same Lorentzian FWHM of 0.25 eV as for the Ti(2p3/2) peak. However, the Voigt convolution of these FWHM does not provide a good fit to the 2p1/2 XPS peak. While the positions of the maximum of the experimental and theoretical 2p1/2 XPS peaks have essentially the same 2p spin−orbit splitting, the maximum theoretical Irel is about twice as large as the experimental value and the theory is considerably narrower than that found experimentally. Clearly something is missing from the theory. It is reasonable to expect that the more realistic model of STO, given by the embedded TiO6Sr8 cluster, where the 2p-hole configurations are also single determinants with only a single hole in the ground state configuration, would give an XPS similar to that obtained for Ti4+ in Figure 4(a). This expectation follows from the fact that the spin−orbit splitting is dominated by atomic effects;32 however, it is important to confirm this expectation. The Ti 2p XPS for the TiO6Sr8 cluster model of STO is shown in Figure 4(b) where the same Lorentzian and Gaussian broadening FWHM are used as in Figure 4(a). The spectra for Ti4+ and the TiO6Sr8 cluster are essentially identical, and the spin−orbit splitting differs for these two models by only 1 meV. The next thing to consider is that there should be different lifetimes for the 2p1/2- and 2p3/2-holes; since there are additional decay channels open for the 2p1/2-hole, the lifetime for this hole should be shorter than that of the 2p3/2-hole corresponding to a larger 2p1/2 Lorentzian FWHM for the Voigt convolution. This different lifetime is taken into account using a dual Voigt broadening, where now the Lorentzian FWHM for the Ti(2p1/2) is adjusted to give a good empirical fit to the height and width of the 2p1/2 XPS peak. The best fit, found for a 1.2 eV FWHM Lorentzian broadening, is shown in Figure 4(c). This is an almost perfect fit to the experimental XPS data, but a 1.2 eV FWHM Lorentzian broadening for the 2p1/2 level cannot be justified. The available data for these lifetimes, based on theory as well as a variety of experimental measurements, is given in a compendium by Campbell and Papp.4 This compendium gives a wide range of lifetime broadenings for Ti 2p, where the Ti(2p1/2) FWHM is 0.25 ≤ FWHM ≤ 0.86 eV with a recommended value of 0.52 eV. While the uncertainties in the lifetimes are large, the available data strongly suggests that the Γ(1/2) = 1.2 eV, which was empirically determined to match experiment, neglecting the possible contribution of shake satellites, is likely to be incorrect. B. Shake Contributions to the 2p Ti XPS of STO. For condensed systems including oxides and other ionic crystals, satellites are often found at energies of less than ∼10 eV above the main peaks, see for example refs 1, 6, 33−35. These are satellites that involve the configurations that we have described, see Section III, as shake configurations or shake determinants. A schematic representation of the normal, or Koopmans, and the shake configurations is given as Koopmans: (Ti2p)5 [αO(2p) + βTi(3d)]6 [βO(2p) − αTi(3d)]0 Shake 1:

(Ti2p)5 [αO(2p) + βTi(3d)]5 [βO(2p) − αTi(3d)]1

Shake 2:

(Ti2p)5 [αO(2p) + βTi(3d)]4 [βO(2p) − αTi(3d)]2

(3)

There may be several determinants represented by each of the three configurations in eq 3, depending on how the open-shells are formed. All of the configurations have a hole in the Ti 2pG


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as light curves under the solid curve for the sum of the contributions of all final, ionic states to the SA Irel. The contributions from individual final states is most relevant for Steps 3 and 4 of the many body CI WFs. The XPS for the WFs of Step 1, the same as in Figure 4(c) since only the 2p spin−orbit splitting is considered, is repeated in Figure 5(a) to show the progression of the predicted XPS for the different WF steps. The XPS for Step 2, where the static electron correlation effects for the covalent bonding are included, is rather similar to that for Step 1, and the empirically optimized Lorentzian broadening for the 2p1/2 states is only slightly changed at 1.1 eV FWHM, see Figure 5(b). Furthermore, the spectrum is still dominated by two sets of degenerate states, and there are only very low intensity satellites between 8 and 10 eV that are not present in the experimental XPS spectrum. These satellites appear because we have a limited representation of the higher BE 2p shake satellites which are not of interest in the present paper. These small changes exist even though the total energy of the lowest energy 2p3/2-hole state is lowered by 0.9 eV. Clearly the dominantly 2p1/2 states are also lowered by a similar amount. Indeed, the Ti 2p spin−orbit splitting is slightly less than that of the angular momentum coupling only and is in slightly poorer agreement with experiment. However, the difference in the spin−orbit splitting is very minor, 0 because, in each determinant, an equal number of electrons are removed from the dominantly O2p orbitals as are placed in the dominantly Ti3d orbitals. The values of both occupations are given to demonstrate that the expected relationship between them is found. The intense peak at Erel = 0 eV gets all of its intensity from ionization of the Ti(2p3/2) as indicated by the occupations in Table 3. On the other hand, the multiplets shown for Erel > 5 eV get all their intensity from Ti(2p1/2) ionization and none at all from Ti(2p3/2). This explains why the SA intensity of these multiplets scales almost as the occupation of the (2p1/2)1(2p3/2)4 distribution, see Table 3. The separation of the 2p3/2 and 2p1/2 intensities can also be seen from Figure 6, where the XPS intensities for the accurate XPS of Figure 5(d), obtained with the CI Step 4 WFS, are plotted separately for 2p3/2, Figure 6(a), and 2p1/2, Figure 6(b), with the same broadening as in Figure 5(d). For the 2p3/2, there is a single main peak centered at Erel = 0 eV and very weak satellites around 9 eV. For 2p1/2, almost all the intensity is distributed over several broadened, unresolved final states for Erel in the range of ∼4 to ∼8 eV, where there is no intensity from 2p3/2 ionization, exactly as shown in Table 4. There is also a weak 2p1/2 intensity around ∼9 eV. Both the 2p3/2 and 2p1/2 intensities at ∼9 eV are poor approximations to the higher energy shake satellites seen in the experiment, Figure 2, for Erel > 14 eV. We have not included the shake configurations

include the many-body effects that result in a correct value of the Ti(2p1/2) lifetime broadening. This analysis allows us to understand how and why the XPS intensity of Ti(2p1/2) is distributed over several, unresolved final 2p-hole states. In Tables 3 and 4, information is given for the 8 most intense Table 3. Properties of the 8 Ti 2p-Hole Multiplets with the Largest SA Irel, including the Ti(2p1/2) and Ti(2p3/2) Occupations Erel (eV)

Irel (a.u.)a

N(2p1/2)

N(2p3/2)

%[occ(2,3)]

%[occ(1,4)]

0 5.79 4.98 6.48 5.16 5.48 6.08 5.36

2.31 0.24 0.19 0.12 0.10 0.06 0.05 0.05

2.00 1.79 1.83 1.89 1.91 1.94 1.95 1.95

3.00 3.21 3.17 3.11 3.09 1.06 1.05 1.05

100 79 83 89 91 94 95 95

0 21 17 11 9 6 5 5

a

In arbitrary units.

Table 4. Valuesa for Erel, Irel(2p1/2) and Irel(2p3/2),b and N(O2p) and N(Ti3d)c,d Erel (eV)

Irel(2p1/2) (a.u.)e

Irel(2p3/2) (a.u.)e

ΔN(O2p)

ΔN(Ti3d)

0 5.79 4.98 6.48 5.16 5.48 6.08 5.36

0 0.24 0.19 0.12 0.10 0.06 0.05 0.05

2.31 0 0 0 0 0 0 0

−0.17 −0.90 −0.94 −1.00 −1.01 −1.05 −1.05 −1.05

+0.17 +0.90 +0.90 +1.00 +1.01 +1.05 +1.05 +1.05

a For the multiplets with the largest SA Irel. bIntensity for ionization of the Ti(2p1/2) and Ti(2p3/2). cO2p and Ti3d occupations. dSee text and caption to Table 3. eIn arbitrary units.

multiplets which are in the energy range of Erel = 0−7 eV, where the multiplets are ordered with the most intense Irel given first. In Table 3, the Erel, in electron volts, and the SA Irel, in arbitrary units, are given together with information about the occupations of the Ti(2p1/2) and Ti(2p3/2) orbitals in the CI WFs of these 8 multiplets, see Section II. The occupation numbers of the Ti(2p1/2) and Ti(2p3/2) spin orbitals, N(2p1/2) and N(2p3/2), respectively, are given for these multiplets. These occupations are also recast in a form more directly related to the composition of the WFs, where the percentage character of the 2p electrons as having holes in either 2p1/2 or 2p3/2 are given. The determinants that make up the CI WFs either have Ti 2p occupations of (2p1/2)2(2p3/2)3, denoted as occ(2,3), or (2p1/2)1(2p3/2)4, denoted as occ(1,4). From the occupations N(2p1/2) and N(2p3/2), it is straightforward to determine the fraction of a CI WF with %[occ(2,3)] and %[occ(1,4)], and these percentages, which must sum to 100, are also given in Table 3. Clearly, the first multiplet is, as intuitively expected, essentially the ionization of a Ti 2p3/2 electron. The next multiplet, not shown in Table 3, that has any intensity, albeit a low intensity of Irel = 0.004, is at Erel = 4.5 eV. The multiplets with the largest SA Irel are between Erel of 5.0 and 6.5 eV. The intensity of these multiplets drops from Irel = 0.24 at Erel = 5.8 eV to Irel = 0.06 at Erel = 5.4 eV. All these Irel are very low compared to the expected half of the 2p3/2 Irel which is 1.2. In fact, the Irel of the multiplets in Table 3 scale very closely with the %[occ(1,4)]. If one sums the I


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the shake excitations important for the broadening of the Ti(2p1/2) XPS are not the usual monopole shake excitations where the symmetry of the orbitals in the valence excitation does not change.8 These shake excitations have a symmetry flip character that has not been previously recognized as being able to contribute to shake excitations. There is a reason that these symmetry flip shake excitations are especially important. The core electron transition which changes the excitation from being a 2p1/2-hole to a 2p3/2-hole lowers the diagonal energy of the shake configuration by ∼6 eV, the Ti(2p) spin−orbit splitting. This energy lowering offsets the energetic cost of the excitation in the valence space and makes possible the strong mixing of the 2p1/2-hole configuration with the 2p3/2-hole configurations. There are also the traditional monopole shake excitations present, and these are likely to account for the Erel ∼9 eV satellite features. Finally, it is noted that the centroid of the theoretical 2p1/2 XPS peak obtained with the CI Step 4 WFs, where the symmetry flip shake excitations have been included, is shifted to lower BE with respect to experiment by ∼0.3 eV. It is quite possible that this small error would be corrected with larger orbital and configuration active spaces; however, higher accuracy is not needed to demonstrate the new and novel importance of the symmetry flip shake excitations.

V. CONCLUSIONS The XPS for closed-shell systems are generally believed to be particularly simple and especially easy to interpret. This is not the case for the Ti(2p1/2) XPS of Ti(IV) in STO and TiO2. While there are two main peaks, corresponding to the ionization of the spin−orbit split Ti(2p3/2) and Ti(2p1/2), the Ti(2p1/2) peak is almost a factor of 2 broader than the Ti(2p3/2) peak. Ascribing the broadening of the 2p1/2 feature to a shorter 2p1/2 lifetime would require an unphysically short 2p1/2 lifetime. Thus, one should use care in assigning an unusual broadening of the XPS of certain levels to lifetime broadening. The importance of many-body effects for the Ti(2p) XPS is examined using a theoretical formulation of the final 2p-hole wave functions that involves the mixing of Koopmans configurations with shake configurations. For the shake configurations, there is, in addition to core ionization, excitation of valence electrons from occupied into unoccupied orbitals. The use of appropriate sets of orbitals for the shake excitations leads to a broadening of the Ti(2p1/2) XPS peak through the distribution of the 2p1/2 over a large number of unresolved final states over a range of ∼3 eV. With these many-body wave functions, the lifetime broadening of the 2p multiplets, especially for 2p1/2, needed to closely fit the observed broadenings is now fully consistent with other information regarding the 2p lifetimes.4 This is an important alert that before core-hole lifetimes are assigned as the origin of the broadening of XPS peaks, it should be checked that the proposed lifetimes are consistent with other data for the lifetimes.4 While the main 2p3/2 peak is dominated by the Koopmans ionization, which has an intensity much greater than the satellite peaks, there is substantial loss of the Ti(2p1/2) intensity into several, unresolved final states. The analysis of the 2p-hole wave functions reveals an unexpected, and previously unidentified, feature of the shake character of the final 2p1/2-hole states. While shake satellites are normally understood in the framework of monopole excitations in the valence space,8 the shake excitations which dominate the wave functions for the states in the broadened main Ti(2p1/2) XPS peak involve symmetry flip valence excitations. These symmetry flip excitations involve a

Figure 6. Separation of the XPS for STO from the theory with Step 4 CI WFs, Figure 5(d), into (a) contributions from ionization of Ti(2p3/2) and (b) Ti(2p1/2). The same broadening parameters are used as in Figure 5(d).

needed to properly describe these higher energy satellites33 since they are not the focus of the present paper. The information for the extent of shake excitations in the valence space, ΔN(O2p) and ΔN(Ti3d) in Table 4, helps us to understand the broadening and the character of the final Ti(2p) XPS states. For the 2p3/2 ionization, there is only a small contribution of shake determinants leading to an occupation of less than 0.2 electrons in the covalent antibonding Ti3d orbitals. It is this loss of bonding O2p character from the main peak that leads to the weak 2p3/2 satellite at Erel = ∼9 eV. The importance of the shake excitations is very different for the multiplets with Erel ≳ 4.5 eV, where the promotion from the nominally filled dominantly O2p orbital to the antibonding Ti3d is about 1 electron. Furthermore, the XPS SA intensity for these multiplets comes entirely from ionization of the Ti(2p1/2) orbital and not at all from ionization of the Ti(2p3/2) orbital even though the composition of the CI WFs for these multiplets is overwhelmingly from determinants with 2p occupation of (2p1/2)2(2p3/2)3. Both of these features can be understood by recognizing the character of the shake configurations with the occupation in the 2p-shell of (2p1/2)2(2p3/2)3. The symmetry of the 2p-shell with this configuration is 4-fold degenerate while the total state which carries 2p1/2 intensity is 2-fold degenerate. For this to be possible, there must also be a symmetry change in the valence excitation that takes the total symmetry of the shake configuration back to the correct 2-fold degeneracy. For the specific case at hand, the main contribution to this symmetry flip is the excitation of an electron from the O2p(eg) orbital to the Ti3d(t2g) orbital; see Table2. Because the symmetries of two orbitals have changed, one a core orbital and one a valence orbital, this shake excitation cannot receive any intensity. Thus, J


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The Journal of Physical Chemistry C change of the 2p-hole from j = 1/2 to j = 3/2, which changes the symmetry of the 2p electrons and requires that there be a symmetry flip in the valence excitation to return the total configuration to the proper symmetry for a 2p1/2-hole. Since the symmetry flip shake excitations cannot carry intensity, all the intensity in the states comes from the extent of the j = 1/2 2phole in these final states. Transferring the 2p-hole from a j = 1/2 orbital to a j = 3/2 orbital lowers the energy of the shake configuration by the spin−orbit splitting energy, which allows a larger mixing with the symmetry allowed 2p1/2-hole Koopmans configuration. If the generality of the role of symmetry flip shake excitations could be established for the XPS of other oxides, this may present a step forward in the goal of extracting chemical information from the XPS. The covalent character of the frontier orbitals of STO have also been examined, and it has been found to be rather large, especially for the frontier orbitals of eg symmetry. Indeed, a major contribution to the screening of the Ti(2p) core-hole is shown to be the change in covalency where the 3d occupation of the closed-shell configuration of STO is 1.9 electrons, but it grows to 3.1 electrons for the Koopmans’ configuration of the Ti 2p core-hole. In effect, this large change in the covalency in the presence of a core-hole over screens the core-hole. It may be that this large screening contributes to the large role paid by the symmetry flip shake determinants for the final states of the Ti(2p) XPS.

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Department of Energy’s Office of Biological and Environmental Research and located at PNNL.

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DEDICATION It is our pleasure and our honor to contribute this paper to the special issue for Profs. Freund and Sauer. We hope that the paper will reflect the importance that we place on their contributions to the understanding of core-level processes.

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(1) Bagus, P. S.; Ilton, E. S.; Nelin, C. J. The Interpretation of XPS Spectra: Insights into Materials Properties. Surf. Sci. Rep. 2013, 68, 273. (2) Bagus, P. S.; Ilton, E. S.; Nelin, C. J. Extracting Chemical Information from XPS Spectra: A Perspective. Catal. Lett. 2018, 148, 1785−1802. (3) Taguchi, M.; Uozumi, T.; Kotani, A. Theory of X-Ray Photoemission and X-Ray Emission Spectra in Mn Compounds. J. Phys. Soc. Jpn. 1997, 66, 247−256. (4) Campbell, J. L.; Papp, T. Widths of the Atomic K - N7 Levels. At. Data Nucl. Data Tables 2001, 77, 1−56. (5) de Groot, F. High-Resolution X-Ray Emission and X-Ray Absorption Spectroscopy. Chem. Rev. 2001, 101, 1779−1808. (6) Okada, K.; Kotani, A.; Thole, B. T. Charge Transfer Satellites and Multiplet Splitting in X-Ray Photoemission Spectra of Late Transition Metal Halides. J. Electron Spectrosc. Relat. Phenom. 1992, 58, 325−343. (7) Aberg, T. Theory of X-Ray Satellites. Phys. Rev. 1967, 156, 35. (8) Fadley, C. S. Basic Concepts of X-Ray Photoelectron Spectroscopy. In Electron Spectroscopy: Theory, Techniques and Applications; Brundle, C. R., Baker, A. D., Eds.; Academic Press: 1978; Vol. 2, pp 2− 145. (9) Schmidbauer, M.; Kwasniewski, A.; Schwarzkopf, J. HighPrecision Absolute Lattice Parameter Determination of SrTiO3, DyScO3 and NdGaO3 Single Crystals. Acta Crystallogr., Sect. B: Struct. Sci. 2012, 68, 8−14. (10) Visscher, L.; Visser, O.; Aerts, P. J. C.; Merenga, H.; Nieuwpoort, W. C. Relativistic Quantum Chemistry: The MOLFDIR Program Package. Comput. Phys. Commun. 1994, 81, 120−144. (11) Burns, G. Introduction to Group Theory with Applications; Academic Press: New York, 1977. (12) Levine, I. N. Quantum Chemistry; Prentice-Hall: Upper Saddle River, NJ, 2000. (13) Hermsmeier, B. D.; Fadley, C. S.; Sinkovic, B.; Krause, M. O.; Jimenez-Mier, J.; Gerard, P.; Carlson, T. A.; Manson, S. T.; Bhattacharya, S. K. Energy Dependence of the Outer Core-Level Multiplet Structures in Atomic Mn and Mn-Containing Compounds. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 48, 12425−12437. (14) Wachters, A. J. H. Gaussian Basis Set for Molecular Wavefunctions Containing Third-Row Atoms. J. Chem. Phys. 1970, 52, 1033−1036. (15) Hay, P. J. Gaussian Basis Sets for Molecular Calculations. The Representation of 3d Orbitals in Transition-Metal Atoms. J. Chem. Phys. 1977, 66, 4377−4384. (16) DIRAC, a relativistic ab initio electronic structure program, Release DIRAC08 (2008), written by L. Visscher, H. J. Aa. Jensen, and T. Saue, with new contributions from R. Bast, S. Dubillard, K. G. Dyall, U. Ekström, E. Eliav, T. Fleig, A. S. P. Gomes, T. U. Helgaker, J. Henriksson, M, Iliaš, Ch. R. Jacob, S. Knecht, P. Norman, J. Olsen, M. Pernpointner, K. Ruud, P. Sałek, and J. Sikkema (see http://dirac.chem. sdu.dk). (17) CLIPS is a program system that can be used to compute ab initio scf and correlated wavefunctions for polyatomic systems. It has been developed based on the publicly available programs in the ALCHEMY package from the IBM San Jose Research Laboratory by P. S. Bagus, B. Liu, A. D. Mclean, and M. Yoshimine. (18) Bethe, H. A.; Salpeter, E. W. Quantum Mechanics of One- and Two-Electron Atoms; Academic Press: 1957.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.8b05576.

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REFERENCES

The influence of the choice of the FWHM of the Gaussian broadening to represent experimental resolution and other physical effects common for both the 2p3/2 and 2p1/2 XPS has on the value of the FWHM of Lorentzian lifetime broadening is examined; in particular, it is shown that our conclusions about the importance of many-body effects to reduce the unphysically large lifetime broadening required when these many-body effects are neglected do not depend on the choice of the Gaussian FWHM of 0.92 eV (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Paul S. Bagus: 0000-0002-5791-1820 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon 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 the Geosciences program at Pacific Northwest National Laboratory, and by the U.S. Department of Energy, Office of Science, Division of Materials Sciences and Engineering (award no. 10122). The experimental work was performed in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the K


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