Cluster Core-Level Binding-Energy Shifts: The Role of Lattice Strain
B. Richter,
1
H. Kuhlenbeck,
1
H.-J. Freund,
1
and P. S. Bagus
2
1
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195, Berlin, Germany
2
Department of Chemistry, University of North Texas, Denton, Texas 76203-5070, USA
(Received 30 April 2003; published 8 July 2004)
Our combined experimental and theoretical analysis of the shifts, with particle size, of core-level
binding energies (BE’s) of metal nanoparticles on insulating supports, shows that these shifts have an
important initial state contribution arising, in large part, because of lattice strain. This contribution of
BE shifts has not been recognized previously. Lattice strain changes the chemical bonding between the
metal atoms and this change induces BE shifts.
DOI: 10.1103/PhysRevLett.93.026805 PACS numbers: 73.22.–f, 79.60.–i
Photoelectron spectroscopy (PES) is often used to de-
duce information on the electronic structure of molecules,
solids, and at surfaces [1]. There is increasing interest in
nanostructured materials, especially in clusters grown on
inert surfaces since they may have high catalytic activity
[2]. Thus, the question of how the PES of deposited
nanoparticles reflects their electronic and geometric
structures is quite important. It is known that the core-
level BE’s of metal clusters on insulating supports [3–12]
shift to lower BE with increasing size by BE 1eV
from small clusters to bulk metal. However, there is
substantial disagreement over the assignment of these
shifts to initial or final state effects; see Ref. [13] for a
rigorous definition of these two contributions. Mason [7]
argued that changes in the electron configuration of the
atoms in smaller clusters, not relaxation energies, were
primarily responsible for the shift. On the other hand,
Wertheim and collaborators [4,5] assigned the shift as due
to final state screening effects and related the magnitude
of BE to an effective cluster radius. For Cu clusters
grown on thin Al
2
O
3
films, Wu et al. [11] concluded from
an Auger parameter analysis that initial state contribu-
tions are small and may be significant only for very small
clusters. This separation is quite important since the
initial state BE reflect changes in the electronic struc-
ture before ionization of a core level and, hence, are of
direct interest for materials properties. In the present
work, we show that the initial and final state contributions
to the BE are of comparable magnitude. Further, we
relate the initial state BE to a lattice strain that exists
because the average bond distances in small clusters are
shorter than in the bulk [14,15]. The chemical bonding
is different at the shorter bond distances and this, in
turn, leads to changes in the core-level BE’s. The
chemical changes important for the BE involve an
increased d to sp promotion, or hybridization, for shorter
bond distances.
Our work is based on a combination of experimental
and theoretical methods that allow us to decompose the
BE into initial and final state contributions. Our theo-
retical approach involves the calculation of electronic
wave functions (WF’s) for clusters and the determination
of the BE’s where relaxation in response to ionization is
excluded, a pure initial state BE, and where this relaxa-
tion is allowed [13]. Our experimental approach involves
use of an Auger parameter obtained from measured
Auger kinetic energies and core-level BE’s. The Auger
parameter concept, developed by Wagner [16], has been
discussed by several authors [3,17–21]. We use the exten-
sion proposed by Hohlneicher et al. [21], where the two
Auger final state core holes are in the same shell; this
extension puts the Auger parameter analysis on a sound
foundation. Previous applications of Auger parameter
analysis to the BE of supported clusters [11,22] have
not used these refinements [21]. Both the Auger parameter
analysis and the WF based separation of initial and final
state contributions to the BE with cluster size show that
these two terms have large magnitudes.
The experiments were performed at the BESSY II
synchrotron facility in Berlin. We studied Co, rather
than Cu [11], clusters on Al
2
O
3
films for two reasons.
First, it is easier to control particle size for Co since it is
less mobile than Cu [23]. Second, it is possible to study
the Co L
3
M
2;3
M
2;3
Auger transition where all holes are
in the core, while for Cu the best results reported [11]
used the L
3
M
4;5
M
4;5
Auger lines where the Cu 3d, M
4;5
,
electrons participate in the chemical bonding. However,
we expect that the results for Co=Al
2
O
3
are representative
for metal nanoparticles on relatively inert substrates [7].
The ultrahigh vacuum system consists of two chambers,
one used for preparation purposes, the other analysis
chamber carries a SCIENTA electron spectrometer as
well as detectors to perform x-ray fluorescence measure-
ments [24]. The analysis chamber is connected to an
undulator beam line (U 49) equipped with a plane grating
monochromator, yielding a resolution of approximately
10
4
, and a photon flux near 10
11
photons=s. The sample, a
NiAl(110) single crystal, is mounted on a manipulator
which allows for translation between the chambers. The
sample can be heated and cooled. The preparation of
the alumina film uses established recipes [25]. Co is
evaporated from an electron beam evaporator (focus
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EFM4) at a rate of 0.5 A
˚
per minute. In separate STM
experiments, the film morphology has been determined.
By combining the island density as determined by STM
and the deposited mass from the quartz balance, the
average number of Co atoms per cluster is obtained [26].
Figure 1 shows photoelectron and Auger spectra of
deposited Co aggregates for several coverages. With the
data for the shifts of the Co 3p and 2p
3=2
BE’s and the
L
3
M
2;3
M
2;3
Auger energies, we perform an Auger pa-
rameter analysis. The initial and final state contributions
to the BE obtained from this analysis are plotted in
Fig. 2 as a function of particle size. The initial state shift
is represented by ", the change in an effective orbital
energy. From Koopmans’ Theorem, the initial state BE
" [3,13]; thus "<0 indicates a shift to higher BE. The
final state, relaxation energy, contribution to the BE is
denoted R,andR<0 indicates a shift to higher BE. In
Fig. 2, " and R, measured with respect to bulk BE’s,
are both negative. The mean particle radius is obtained
assuming the particles are half spheres, consistent with
our STM profiles [24]. For the shift between the smallest
clusters, 4:7
A radius, and thick Co films, the Auger
parameter analysis gives an initial state contribution that
is 31% of the total BE 0:98 eV. Clearly, initial state
effects make a major contribution.
The goal of our theoretical studies of the BE is to
obtain an understanding of the physical mechanisms
responsible for the trend of the decrease of BE with
increasing particle size, observed for a variety of metals
[7]. Since we do not intend to simulate the explicit de-
pendence of the BE on particle size, we are able to make
approximations to simplify these studies: (i) We study
isolated clusters and neglect the weak interaction of the
particles with the oxide substrate [7]. (ii) We study Cu
clusters in order to avoid computational difficulties re-
lated to open d shells. For a variety of noble and transition
metal particles, the BE shift with particle size is 1eV
[3–12]; thus, it seems appropriate to study the BE for
Cu. However, we also study BE for small Ni clusters to
confirm the generality, for open d-shell metals, of our
results for Cu. (iii) The geometric structure of all Cu and
Ni clusters studied was taken as that of the fcc crystal
structure and the lattice strain is modeled by uniform
changes in the lattice constant, a
0
. This model does not
explicitly treat the specific shapes of the supported par-
ticles. (iv) Given our idealized cluster geometries, we
consider only BE’s for cluster atoms that have the bulk
coordination. Although core-level BE’s do depend on the
coordination of the ionized atom [13], this dependence,
especially for transition and noble metal atoms, is rela-
tively weak; for example, the BE shifts between surface
and bulk atoms of metal crystals are not large, 0:25 eV
[3]. Based on our results for the BE shifts with lattice
strain for (100) surface atoms compared to the BE for
bulk atoms, we expect the contributions of differently
coordinated atoms in supported particles to lead, domi-
nantly, to broadening of the PES peaks.
Initial and final state contributions to the BE were
determined for a series of clusters chosen to model both
particle size and lattice strain effects. The initial state
BE’s are obtained with Hartree-Fock self-consistent-field
(SCF) molecular orbitals for the ground state of the
cluster before ionization. These orbitals are used to form
a frozen orbital (FO) WF for the ionic states where
relaxation to screen the core hole is not allowed. The
difference between the energies of the ground state and
the FO ionic state WF’s is BE(initial). The difference
between the energies of the ground state and the SCF
WF for the ionized state [BE(SCF)] is the total BE.
The SCF orbitals for the ionic state WF’s, optimized for
the presence of the core hole, fully include electronic
relaxation in response to the hole [27]. The change
between the initial and total BE’s is the relaxation
energy, E
R
, associated with the final state effects;
56 58 60 62 64
Binding energy [eV]
776 778 780 782
Binding energy [eV]
600 620 640 660
Kinetic energy [eV]
Co L M M
3 2,3 2,3
Co 3p
h = 1100 eVν
Co 2p
3/2
0.05
0.1
0.2
0.4
0.8
6ML
FIG. 1. The Co 3p and the Co 2p
3=2
core-level BE’s and the
Co L
3
M
2;3
M
2;3
Auger transitions for Co clusters deposited onto
Al
2
O
3
=NiAl110 as a function of coverage; lines are drawn to
show shifts with coverage
5678910
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
Mean cluster radius [Å]
∆ε ∆ , R [eV]
Co/Al O /NiAl(110)
Co3p initial and final state shift
23
∆ R
∆ε
FIG. 2. Co 3p initial (e) and final state (R)shiftsasa
function of the mean cluster radius.
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E
R
BEinitialBESCF. The shifts are:
BESCF for the changes due to both initial and final
state effects; BE(initial) for the initial state changes;
and E
R
. Their relationship to the quantities obtained in
the Auger parameter analysis is BEinitial" and
E
R
R. However, the quantities obtained from the
SCF WF’s rigorously separate initial and final state con-
tributions [13], while the Auger parameter separation
involves assumptions about the intra- and extra-atomic
relaxation [16–21]. Furthermore, the SCF energies of
double-hole Auger states can be used to calculate the
Auger parameter [21] and the Auger relationship that
E
R
=2 can be compared to the E
R
calculated
directly from BE(initial) and BE(SCF).
The clusters used to study the progression of BE’s
toward the bulk value are shown in Fig. 3. The largest,
Cu
115
, cluster has seven layers parallel to the (100) sur-
face; the numbers of atoms in each layer are
Cu
115
(4,25,16,25,16,25,4). We use the BE’s for Cu
115
to
represent the limit of a large cluster although the BE’s for
clusters of this size are not fully converged to the bulk
[24]. The next smaller cluster, Cu
55
(9,12,12,12,9), has
four layers and the smallest cluster, Cu
18
(5,4,5,4), has
four layers. For Cu
115
and Cu
55
, we consider BE’s for
ionization of the central atom; for Cu
18
, the BE’s are for
ionization of the central atom of the third layer. In order
to study only the effect of cluster size on the BE’s, we
have used the bulk a
0
3:59
A. However, there is evi-
dence from transmission electron microscopy of Pd and
Pt on Al
2
O
3
that the effective a
0
for small clusters is
reduced by 5%–7% [14,15]; these contractions are
much larger than those found for matrix isolated Cu
clusters [28]. The much larger lattice strain for supported
clusters may be due to their weak interaction with the
support. The effect of this lattice strain on the core-level
BE’s is studied by determining the BE’s for Cu
18
with
three reductions of a
0
to 3.52, 3.44, and 3.37 A
˚
. For atoms
where core level BE’s may be studied, all the 29 Cu
electrons are explicitly included in the cluster WF’s; for
the other atoms, the core electrons are represented by a
pseudopotential [13]. For the open shell Cu
55
and Cu
115
clusters, we consider BE’s to the weighted averages of the
ionic states. To avoid the distraction of spin-orbit split-
tings in the 2p shell, we report here shifts of the 2s BE’s;
the BE’s calculated for 1s and 3s holes are very similar
to the BE2s. For the theoretical determination of
2s [21], we use SCF WF’s for the 2s and 3s hole states
and for the 3s double hole Auger state. We also report
BE2s for Ni
18
clusters constructed in an analogous
way to the Cu
18
clusters; the lattice strain for Ni is
examined by using contracted a
0
of 3.45, 3.37, and
3.30 A
˚
as well as bulk a
0
3:52
A.
In Table I, we give BESCF, BE(initial), and E
R
at the bulk a
0
and, for Cu
18
, also at a representative
contracted a
0
3:44
A. We also give shifts of the
Auger parameter, =2. The sequence from Cu
18
a
0
3:44
A to Cu
115
a
0
3:59
A models the progression of
BE from small clusters to bulk; the shift to lower BE of
1eV is consistent with the measured values for BE
shifts in supported clusters and indicates that our cluster
models correctly describe the physics of this shift. Note
that the total shift has approximately equal contributions
from initial and final state shifts.
Although the increase of the bond distance from small
to large clusters is not a step function, we use the step
from Cu
18
a
0
3:44
A to Cu
18
a
0
3:59
A to separate
the increase of the bond distance from the change of the
number of atoms. The increase of a
0
leads to a shift of
0.5 eV to lower BE, 50% of the total BE between small
clusters and bulk; this shift is almost entirely an initial
state effect (see Table I). There is a further large BE
decrease of 0.67 eV when the cluster size is increased
from Cu
18
to Cu
115
with bulk a
0
that is 2=3 due to
an increase in final state relaxation and 1=3 to an
initial state BE shift. In other words, the final state
relaxation dominates the shift to lower BE with increas-
ing cluster size for a constant a
0
; this is consistent with a
monotonic dependence of E
R
on system size [3,6,13]. The
BE(initial) do not vary monotonically with cluster size
suggesting that there is a dependence of the initial state
BE on the cluster morphology. However, the dependence
of BE(initial) on the details of the cluster morphology is
not particularly large and is not investigated further.
For Ni
18
and Cu
18
, the dependence of the 2s BE’s on a
0
is shown in Table II. For both metals, the BESCF,
and BE(initial) are almost the same and vary nearly
linearly with a
0
; these changes of BE with a
0
show
FIG. 3 (color online). Size progression of Cu
18
to Cu
55
to
Cu
115
clusters. The ionized atom is shaded.
TABLE I. The 2s BE shifts for Cu
n
at bulk a
0
with respect to
BECu
115
0; for Cu
18
, a reduced a
0
is also used. E
R
and
=2 are shown. All energies are in eV.
Cu
18
Cu
18
Cu
55
Cu
115
a
0
-A
˚
3.4 4 3.59 3.59 3.59
BESCF1:21 0:67 0:34 0
BE(initial) 0:73 0:22 0:27 0
E
R
0:47 0:45 0:07 0
=2 0:67 0:66 0:21 0
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the generality of the dependence of the BE’s on lattice
strain. The near equality of the initial and SCF values
show that the increase of the BE’s due to lattice contrac-
tion is a dominantly initial state effect. The origin of the
large BE(initial) is found by separating, using con-
strained variations [13], the contributions due to the
4sp conduction band electrons from those due to the 3d
electrons. This decomposition is given only for Cu but it
is similar for Ni. For the frozen core WF, the orbitals of
the electrons in the 1s to 3d shells are fixed to be the same
as in the isolated atom. With this constraint, the
BE(initial) depend on a
0
only because of changes in the
conduction band, 4sp electrons. For the frozen Ar core
WF, only the 18 Ar core electrons are constrained to be
atomic. Now, 3d hybridization and bonding is allowed. It
is clear that the 3d chemistry is the main reason for the
large BE as a
0
is reduced. The hybridization and pro-
motion of a fraction of an electron from the contracted 3d
shell into a more diffuse orbital leads to a large increase
in the core-level BE’s [13]. The d hybridization increases
strongly for shorter a
0
since shorter bond distances favor
an increased bonding participation of the compact d
orbitals.
The changes of the Auger parameter, =2, roughly
follow those of the E
R
; see Table I. The values of =2
are essentially equal for Cu
18
with a
0
3:44 and3.59A
˚
;
the same near equality is also found for E
R
. From Cu
18
with bulk a
0
to Cu
115
, the increases of =2 parallel the
increases of E
R
; however, the increases of =2 are
larger than those of E
R
. While the trend of E
R
is
correctly described by the trend of =2, the Auger
parameter analysis appears to indicate a larger contribu-
tion from final state effects than given by the ab initio
decomposition of the BE’s. This problem may be related
to assumptions about the intra- and extra-atomic contri-
butions to E
R
made in the derivation of the Auger pa-
rameter relationship.
A large initial state contribution to the cluster size
dependent BE shifts has been shown from both Auger
parameter analysis of the experimental data and from
calculation of the BE with ab initio cluster WF’s leaving
no doubt that initial state contributions are significant.
Further, we have shown that the origin of the initial state
effect is a lattice contraction that is part of the cluster
growth morphology [14,15]. In particular, the BE shift is
related to the d hybridization being larger for shorter
bond distances. These are important extensions of our
understanding of the origin and the physical significance
of the cluster BE shifts.
We acknowledge partial computer support from the
National Center for Supercomputing Applications,
Urbana-Champaign, Illinois.
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TA BL E II. BESCF and BE(initial), in eV, for the Cu
and Ni 2s BE’s in 18 atom clusters. The changes in the lattice
constants are given as a
0
in percent change from bulk a
0
.
BE 0 for a
0
0. For Cu, frozen core and frozen Ar core
values of BE(initial) are given (see text).
a
0
6% 4% 2% 0 (bulk)
Cu
BESCF0:84 0:54 0:26 0
BE(initial) 0:79 0:51 0:250
Frozen core 0:12 0:05 0:01 0
Frozen Ar core 0:78 0:51 0:24 0
Ni
BESCF0:72 0:45 0:21 0
BE(initial) 0:73 0:47 0:22 0
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