Chemical Physics Letters 394 (2004) 150–154
www.elsevier.com/locate/cplett
A new near degeneracy effect for photoemission in transition metals
Paul S. Bagus
a,*
, R. Broer b, Eugene S. Ilton
c
a
b
Department of Chemistry, University of North Texas, P.O. Box 30012, Denton, TX 76203-5070, USA
Department of Chemical Physics and Materials Science Centre, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
c
Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, Richland, WA 99352, USA
Received 3 April 2004; in final form 18 June 2004
Available online 20 July 2004
Abstract
A previously neglected intra-atomic many-body effect has important consequences for the X-ray photoelectron spectra (XPS) of
transition metal atoms and cations. This effect involves configurations where one elctron is promoted to a 4f orbital and another is
dropped to fill the XPS hole; this can be viewed as a frustrated Auger configuration (FAC). The identification of this FAC is a major
advance in the understanding of many-body effects in XPS. Its use affects the multiplet splitting and the absolute binding energy; it
can also lead to new satellite structure. Furthermore, it is expected to be generally important.
Ó 2004 Elsevier B.V. All rights reserved.
The physical origins of the features observed with Xray photoelectron spectroscopy (XPS), and the significance of these features for understanding materials
properties are relevant and important for both practical
technological and basic scientific considerations. The
better our understanding of the one-body and the
many-body physics that underlies XPS, especially for
transition metal (TM) systems [1–14], then the better
our ability to correctly relate the XPS to materials properties. Two types of intra-atomic many-body, or electron
correlation, effects are important for the XPS of TM cations [1–4]; one type is important for the 3s XPS [1,2]
and the other is important for the 2p, and 3p XPS
[3,4]. Since the initial work [1–4] was published in the
early 1970s, these atomic effects have been extensively
used to help interpret the XPS of TM systems; see, for
example, [5–16]. In this Letter, we show the importance
of a new intra-atomic many-body effect that involves excitation of an M shell electron into a 4f orbital; this type
of atomic excitation has not been considered previously
for the interpretation of TM XPS. The importance of
this excitation is proven specifically for Mn. However,
*
Corresponding author.
E-mail address: [email protected] (P.S. Bagus).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2004.06.120
based, in part, on the fact that the previously identified
atomic effects are important for a range of TM cations
[2–16], we believe that our newly identified atomic
many-body effect will be important for the XPS of other
TMs as well.
Fig. 1, reproduced from [14a], shows the Mn 3s XPS
for gas phase Mn atoms and the compounds MnF2 and
MnO. The spectra for atomic Mn and for the compounds are very similar and this is strong evidence that
the many-body effects that lead to the rich XPS spectra
for the atom are also of major importance for the condensed phase [14]. There is strong evidence that atomic
many-body effects are also of dominant importance for
the 2p and 3p XPS from Mn in compounds [6,14]. The
solid vertical bars shown in Fig. 1 are from the original
atomic many-body theory [1] and the figure clearly indicates limitations of this theory. We draw attention to the
relative energy of the leading two peaks, where the first
peak is a high spin, 7S, and the second peak is a low spin,
5
S, multiplet [1,14,15]. While the relative intensities of
these multiplets are predicted quite accurately [14,15],
the multiplet splitting of the 7S and 5S peaks is too small
by 2 eV, an error of 30%. Okada and Kotani [9a] point
out that they can reproduce the experimental splitting,
using the many-body formalism of [1] that has a 30% er-
P.S. Bagus et al. / Chemical Physics Letters 394 (2004) 150–154
Fig. 1. Experimental Mn 3s XPS from [14] for (a) MnO, (b) MnF2,
and (c) gas-phase atomic Mn, labeled Mn(g); the arrow at 27 eV
shows the position of a weak unassigned satellite for Mn(g). The solid
bars for theory (d) are from the CI of [1]; the dotted bar indicates the
new theoretical prediction for the relative position of the 5S(1) peak;
see Table 1.
ror, by reducing a key interaction integral to 75% of its
ab initio value. In the present work, we show that such
an ad hoc scaling is unnecessary. When a new atomic
many-body effect that involves the excitation of an electron into a 4f orbital is included in the theoretical treatment, the alignment of theory and experiment for these
first two XPS peaks is almost perfect; see the dashed vertical line in Fig. 1. Moreover, this new 4f many-body effect allows us to identify a previously unassigned feature
at 27 eV from the leading edge as an atomic manybody satellite. We have calculated the XPS for the neutral Mn atom so that we can compare our predictions to
the gas phase XPS without the need to account for a
condensed phase environment. In particular, studying
the atom allows us to examine the absolute value of
the 3s binding energy (BE), a test of the completeness
of the many-body theory that, to our knowledge, has
never before been made. However, given the data shown
in Fig. 1, it is clear that our atomic results are relevant
for condensed phase systems.
We use an ab initio theoretical framework that provides direct physical insight into the nature of the complex TM XPS and that provides a clear criterion for the
importance of many-body effects. This framework is
151
configuration interaction (CI) where the mixing of
XPS forbidden configurations with the XPS allowed
configurations can lead to complex spectra with intense
satellites [1–3,6,7,12,13,16]. The criterion for this CI
mixing to be important is that a forbidden configuration
is low-lying in energy, or nearly degenerate, with an XPS
allowed configuration [6,16]. One way to form a nearly
degenerate configuration with the proper total symmetry
for the CI mixing to be possible is to recouple the open
shell d electrons. This recoupling of the open d shell is
quite important for the XPS of p levels [2,4,6,7,16] but
not for the XPS of s levels because the proper total symmetry cannot be recovered [17]. However, for the XPS
of s levels, nearly degenerate configurations can be
formed by promoting one electron into a higher energy
level and dropping a second electron to occupy the core–
hole. This excited configuration is similar to an Auger
excitation but the excited electron remains in a bound level. This is necessary in order for the excited configuration to have a large off-diagonal matrix element with the
XPS allowed, Hartree–Fock configuration [17]. For this
reason, it is appropriate to call the configuration [18] a
frustrated Auger configuration or FAC. The FAC identified in the present work involves a 3p3d ! 3s4f excitation and can be viewed as a 3p filling the 3s hole and a
3d promoted to 4f. It is important to recognize that
these FACs can make different contributions to the energies and wavefunctions of different multiplets. One
reason for this differential importance arises because of
the possible angular momentum coupling of the FACs
[1–3]. In particular, a FAC may be able to couple only
to the low spin final states [1–3]; this occurs for the 3s
XPS of several TMs [3]. A second reason for a differential effect from a FAC is that the magnitude of the offdiagonal matrix elements depends on the details of the
angular momentum coupling algebra.; see [17] and references therein. The important point, as shall be shown
below, is that the differential importance of the FACs
can lead to major changes for the multiplet splitting of
the 3s-hole final states and for the absolute value of
the 3s BE.
We have calculated non-relativistic Hartree–Fock
(HF) and CI wavefunctions and also Dirac–Fock (DF)
and DF–CI relativistic wavefunctions [19]. The orbitals
for the CI calculations are those optimized for the HF
and DF wavefunctions [20]. The states of the Mn atom
considered are the ground state, . . . 3s23p63d54s2(6S5/2),
and the 3s-hole states, . . .3s13p63d54s2, coupled to 7S3
and 5S2 where, in the relativistic case, only the J values
are rigorously good quantum numbers.
We now describe the configurations included in the
two types of CIs that we performed. The first type of
CIs, a complete CI [6,19] within the space of the M shell,
parallels the original work [1] on the Mn 3s XPS. For
the ground 6S state of Mn, the CI included configurations where the 13 electrons from 3s23p63d5 were
152
P.S. Bagus et al. / Chemical Physics Letters 394 (2004) 150–154
distributed in all possible ways over the 18 3s, 3p, and 3d
orbitals. For the 3s-hole states, coupled to either 5S or
7
S, the CI included configurations where the 12 electrons
from 3s13p63d5 were distributed over the 18 M shell orbitals. For both ground and ionic states, the occupation
of the 4s orbital was fixed as 4s2 in all configurations.
The 4s is a passive orbital because it is not expected to
participate in the many-body effects that influence the
3s XPS; furthermore, treating 4s as passive makes our
results directly applicable for the XPS of Mn2+ cations.
The use of this restriction is strongly supported by the
experimental evidence that the 3s and 3p XPS of Mn0
are very similar to those for MnF2 and MnO [14]. These
CIs, denoted (3spd), include the 3p2 ! 3s3d FAC as well
as other configurations that are not nearly degenerate
with the HF configuration and, thus, are essentially perturbations. The second type of CIs, which include the
new 3p3d ! 3s4f FAC, combine the (3spd) CI with a
new class of configurations that involve promotion of
one electron from the M shell into a 4f orbital while
the remaining n 1 M shell electrons are distributed in
all ways over the 3s, 3p, and 3d orbitals. These are called
Ôsemi-internalÕ configurations [21]; the CIs, denoted
(3spd) + 4f, were only calculated as non-relativistic
wavefunctions. Relativistic corrections to the (3spd) + 4f
CI energy differences were estimated by using the changes between the non-relativistic (3spd) CI and the relativistic (3spd) DF–CI energies. The 4f orbitals used in these
CIs were virtual HF orbitals optimized separately for
the ground and 3s-hole states to give the lowest energies
for the first roots of each of the (3spd) + 4f CIs. These
correlating 4f orbitals are strongly contracted over the
orbitals appropriate for optically excited states. We
should note that, in addition to the 3p3d ! 3s4f FAC,
there is also a 3p3d ! 3s4p FAC that has the proper
symmetry and parity to mix with the XPS allowed configurations. However, the 4p orbital has two radial
nodes while the 4f orbital is nodeless. The nodes in the
4p orbital will lead to additional changes in the sign of
the integrand for the integral that determines the off-diagonal matrix element connecting the 3p3d ! 3s4p FAC
with the XPS allowed configuration. We expect that
these additional changes in sign of the integrand will reduce the magnitude of the off-diagonal matrix element
for the 3p3d ! 3s4p FAC compared to that for the
3p3d ! 3s4f FAC. Since there are smaller off-diagonal
matrix elements, the importance of this FAC is reduced.
Thus, although including the 3p3d ! 3s4p FAC would
lead to a larger CI wavefunction, it is not expected to
significantly change the XPS relative energies, Erel, and
intensities, Irel.
The 7S–5S multiplet splittings (MS) for the non-relativistic HF and CI wavefunctions are given in Table 1
where the energy improvements, DE(CI), of the CI over
the HF energies are also included. The HF MS is over
twice as large as the observed XPS splitting [14,15].
Table 1
Non-relativistic HF and CI multiplet splittings, MS, of the lowest 7S
and 5S 3s-hole states of Mn and energy lowerings, DE(CI), from the
HF; all energies in eV
MS(7S–5S)
DE(CI)
7
HF
(3spd) CI
(3spd) + 4f CI
Experimenta
a
b
S
–
0.8
6.0
–
5
S
–
10.4
13.1
–
14.1
4.5
6.9(6.3b)
6.5
See [14].
Value including relativistic corrections, see text.
However, with the (3spd) CI, which includes the
3p2 ! 3s3d FAC, the MS is decreased by 10 eV from
the HF value to 4.5 eV. While the many-body effects included in the (3spd) CI are a perturbation for the high
spin 7S, state, they are major for the low spin, 5S, state.
The differential effect is because the 3p2 ! 3s3d FAC
can only couple to 5S, not to 7S [1]. However, the
(3spd) CI, gives a splitting that is 30% smaller than experiment. A large portion of this error is accounted for
with the (3spd) + 4f CI. Including the 3p3d ! 3s4f FAC
gives an additional lowering of the 7S energy of more
than 5 eV but only of less than 3 eV for the 5S state. This
differential correlation increases the splitting to 6.9 eV,
only slightly larger than experiment. The relativistic correction taken from the (3spd) CI and DF–CI splittings is
0.6 eV; this correction reduces the non-relativistic
(3spd) + 4f value for the splitting to 6.3 eV, within 0.2
eV of the measured splitting for the Mn atom [14].
The results in Table 1 clearly show that including a
new form of near degeneracy arising from the
3p3d ! 3s4f FAC leads to a correct value for the 3s-hole
MS. In particular, there is no need to invoke an arbitrary reduction of the Slater integrals connecting 3s
and 3d orbitals as has been done by others [9,10].
Another measure of the importance of the
3p3d ! 3s4f FAC is its affect on the absolute value of
the lowest 7S 3s-hole state BE. In Table 2, relativistic
and non-relativistic BE(3s), obtained with HF, CI,
DF, and DF–CI energies, are given; the energy improvements, DE(CI), are also given for both the CI and DF–
CI. The non-relativistic HF and (3spd) CI values for the
BE(3s) are reasonably close to experiment while the
BE(3s) from the (3spd) + 4f CI is over 3 eV smaller than
experiment. The large reduction in the BE(3s) with the
(3spd) + 4f CI is because the CI lowering of the energy
of the initial 6S state is much smaller than the energy
lowering of the 3s-hole state; see Table 2. While the
3p3d ! 3s4f FAC is present for the 3s-hole state, it is absent for the initial state of Mn where the 3s orbital is
doubly occupied. The puzzle that the (3spd) + 4f CIs
yield a better MS but appear to give a poorer BE(3s)
is resolved when relativistic effects are taken into account. When the relativistic correction determined for
P.S. Bagus et al. / Chemical Physics Letters 394 (2004) 150–154
Table 2
Relativistic, Rel, and non-relativistic, Non-Rel, BE(3s) for Mn and
energy lowerings, DE(CI); all energies in eV
BE(3s)
DE(CI)
Non-Rel
HF
(3spd) CI
(3spd) + 4f CI
Rel
DF
(3spd) DF–CI
Experimenta
a
b
Mn0
Mn+ (3s-hole)
–
0.6
2.9
–
0.8
6.0
92.7
92.5
89.5(91.2b)
–
0.6
–
–
0.7
–
94.4
94.2
92.8
See [14].
Value including relativistic corrections, see text.
the DF and (3spd) DF–CI calculations is applied to the
(3spd) + 4f CI, the BE is 91.2 eV or 1.5 eV less than experiment. On the other hand, when the relativistic correction is applied to the HF and (3spd) CI values,
these BEs are no longer in good agreement with experiment but are 1.5 eV too large. Unless very long CI expansions for the wavefunction that include long range,
so-called dynamic, correlation effects [22] are used, the
BE are expected to be too small, compared to experiment, by 1 eV because ions have fewer electron pairs
than neutral atoms. Thus, including dynamic correlation
effects will further increase the error of the HF and
(3spd) CI BEs while it will reduce the error of the
(3spd) + 4f CI BE. The apparently good agreement of
the (3spd) CI BE with experiment, see Table 2, is due
to the fortuitous cancellation of large errors due to the
neglect of relativistic effects and to the neglect of the important many-body effects contributed by the
3p3d ! 3s4f FAC.
It is important to have a simple and direct measure of
the magnitude of the contribution of the 4f orbital to the
wavefunctions. Such a measure of the importance of the
FACs in a CI wavefunction is given by the occupations
[23] of the various orbitals; these occupations are, in effect, a count of the number of electrons in each orbital.
The occupations of the 3s, 3p, 3d, 4s, and 4f orbitals
of the HF and CI wavefunctions are given in Table 3
for the representative 7S 3s-hole state. In particular,
the comparison of these occupations for the different
wavefunctions indicates the contribution of the
3p3d ! 3s4f FAC to the (3spd) + 4f CI wavefunction.
For the (3spd) CI wavefunction, the orbital occupations
153
are almost the same as for the HF wavefunction; the
changes are small because the 3p2 ! 3s3d FAC cannot
couple to 7S [1]. However for the (3spd) + 4f CI, there
are significant changes from the (3spd) CI occupations;
the 3s and 4f occupations each increase by 0.07 while
the 3p and 3d occupations each decrease by 0.07 electrons. These changes show the contribution of the
3p3d ! 3s4f FAC to the CI wavefunction and they are
consistent with the energy lowering for the (3spd) + 4f
CI of over 5eV; see Table 2.
Finally, we show that a previously unexplained satellite feature in the Mn0 3s XPS may be a product of the
4f FAC. For the assignment of the Irel of the satellite
peaks, we follow common practice, see for example
[1–14,24], and use the sudden approximation [25]. The
strong mixing of FACs into the wavefunctions for the
ÔmainÕ XPS peaks can lead to intense satellite structure
at the expense of the main peaks [1–4,6,24]. Fig. 1
clearly shows two reasonably intense satellites at 23
and 43 eV above the main 7S peak. These peaks are
satellites of the 5S, low spin, main 3s XPS peak and
they are predicted by including the 3p2 ! 3s3d FAC
in the (3spd) CI [1–3,14,15]. With the (3spd) + 4f CI
wavefunctions, there are modest changes in the relative
energies and intensities of these 5S satellites; the differences of these 5S satellites will be analyzed in detail in a
future paper. In the present work, we focus on a prediction of an XPS satellite of 7S, high spin, symmetry. The
3p3d ! 3s4f FAC, which is reasonably important for
the energy of the lowest 7S 3s-hole state, also leads to
a satellite at 25.1 eV higher BE and with Irel = 6.0% relative to the first, 7S, 3s-hole XPS peak. Indeed, there is
an unassigned feature in the 3s XPS of gas phase Mn0
[14] at 27 eV higher BE than the first 7S peak, see the
arrow in Fig. 1, and, depending on the choice of background, this feature could have 6% of the intensity of
the leading 3s-hole XPS peak. This may be the manybody satellite predicted with the (3spd) + 4f CI. Additional evidence for a high spin satellite comes from
the spin polarization of the photoelectrons since photoelectrons leaving the ion in a high spin state are spin
polarized differently from photoelectrons that leave
the ion in a low spin state [24,26,27]. Lademann and
Klebanoff [26] measured the spin resolved XPS of ferromagnetic Fe and, for the 3s XPS, they found a satellite
polarized anti-parallel to the direction of the Fe magnetization at a relative BE of 28 eV. This minority spin
Table 3
Orbital occupations, Occ(n‘), for the non-relativistic HF and CI wavefunctions for the lowest energy 7S 3s-hole state of Mn
Mn+(7S)
HF
ND(3spd)
ND(3spd) + 4f
Occ(3s)
Occ(3p)
Occ(3d)
Occ(4s)
Occ(4f)
1
1.00
1.07
6
5.99
5.91
5
5.01
4.94
2
2
2
0
0
0.07
The 4s occupation is 2 in all cases because this passive orbital is doubly occupied in all configurations.
154
P.S. Bagus et al. / Chemical Physics Letters 394 (2004) 150–154
satellite is between two majority spin satellites whose
presence had been predicted on the basis of a (3spd)
CI for the Fe+1 atomic cation [24]. However, the minority spin satellite was not predicted. In future theoretical
work, it would be useful to test if inclusion of the
3p3d ! 3s4f FAC predicts the minority spin satellite
found in [26].
In summary, we have identified a new atomic manybody effect arising from the introduction of the
3p3d ! 3s4f FAC into the CIs for 3s-hole states. The
use of this FAC removes the 2 eV error found for
the 7S–5S multiplet splitting without the need to use an
ad hoc and non-physical scaling of two electron interaction integrals [9,10]. Further, the (3spd) + 4f CIs lead to
an absolute value of the BE(3s) that is consistent with
XPS measurements. Finally, we predict a new high spin
satellite feature that appears to be present in both Mn
and Fe 3s XPS. Although the present use of the
3p3d ! 3s4f FAC is restricted to the 3s XPS of atomic
Mn, there is strong reason to believe that similar FACs,
involving a 4f orbital, will be important for other TMs
and for the XPS from other shells. The inclusion of
the 3p2 ! 3s3d FAC in (3spd) CIs leads, for almost all
3d TM cations, to large changes from the HF values
for the multiplet splittings and for the relative intensities
[3]. It is likely that the 3p3d ! 3s4f FAC will also make
important contributions for other TM atoms and cations besides Mn. For the 3p XPS, the 3d2 ! 3p4f
FAC, in close analogy to the 3p3d ! 3s4f FAC for the
3s XPS, can be expected to play a major role in the CI
wavefunctions. Thus, configurations involving excitations to a 4f orbital may need to be taken into account
in addition to the configurations used so far [2,6,7,16]
that treat only the angular momentum recoupling
among the 3p and 3d shells. On the other hand for the
2p XPS, the FACs for the 2p-hole involve moving an
electron from the M shell to fill the 2p-hole. These FACs
will not be nearly degenerate with the HF configuration;
thus, excitations to the 4f orbital will probably play a
minor role; this is in sharp contrast to the 3s and 3p
XPS spectra. Our identification of the 4f FACs and
our demonstration of their importance for the Mn 3shole XPS is a major advance in the understanding of
many-body effects for the XPS of transition metal atoms
and cations.
Acknowledgements
This research was supported, in part, by the Geosciences Research Program, Office of Basic Energy Sciences, US Department of Energy (DOE). A portion of
the research was performed at the W.R. Wiley Environmental Molecular Sciences Laboratory, a national scien-
tific user facility sponsored by the US DOE and located
at PNNL, operated for the DOE by Battelle. One of us
(P.S.B.) is pleased to acknowledge partial computer support from the National Center for Supercomputing
Applications, Urbana–Champaign, Illinois.
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