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Phil. Trans. R. Soc. A (2010) 368, 1211–1243
doi:10.1098/rsta.2009.0269
REVIEW
Determining the size-dependent structure
of ligand-free gold-cluster ions
B Y D ETLEF S CHOOSS1,2,3 , P ATRICK W EIS1,3 , O LIVER H AMPE1,2,3
AND M ANFRED M. K APPES1,2,3, *
1 Institute
of Physical Chemistry, 2 Institute of Nanotechnology, and 3Center
for Functional Nanostructures, Karlsruhe Institute of Technology (KIT ),
Karlsruhe, Germany
Ligand-free metal clusters can be prepared over a wide size range, but only in
comparatively small amounts. Determining their size-dependent properties has therefore
required the development of experimental methods that allow characterization of sample
sizes comprising only a few thousand mass-selected particles under well-defined collisionfree conditions. In this review, we describe the application of these methods to the
−
geometric structural determination of Au+
n and Aun with n = 3–20. Geometries were
assigned by comparing experimental data, primarily from ion-mobility spectrometry
and trapped ion electron diffraction, to structural models from quantum chemical
calculations.
Keywords: gold clusters; structure; electron diffraction; ion mobility; optical properties
1. Introduction
Gold nanoparticles, with sizes much below the wavelength of visible light,
were first inferred in aqueous colloidal gold suspensions (Faraday 1857). More
recently, monodispersed gold clusters with less than 1000 gold atoms have
become a focus of attention in fields ranging from synthetic chemistry to solidstate physics and nanotechnology. A significant part of this work has concerned
ligand-stabilized clusters (Schmid et al. 1981). These have been prepared and
structurally characterized by X-ray diffraction methods with core sizes of up to
102 gold atoms (Jadzinsky et al. 2007). While inorganic chemistry can access
molar quantities of such substances, not all atom counts or charge states are
available. Furthermore, even the largest gold-cluster cores synthesized so far
are still significantly modified by the ligand shell (Lopez-Acevedo et al. 2009).
*Author for correspondence ([email protected]).
Electronic supplementary material is available at http://dx.doi.org/10.1098/rsta.2009.0269 or via
http://rsta.royalsocietypublishing.org.
One contribution of 13 to a Theme Issue ‘Metal clusters and nanoparticles’.
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This journal is © 2010 The Royal Society
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D. Schooss et al.
Corresponding changes to electronic and geometric structures are still only poorly
understood—in part because of missing information concerning the ‘reference
state’: ligand-free clusters.
In contrast to their ligand-stabilized congeners, bare gold clusters can be made
in all sizes and many charge states (from multiply positive through neutral to
(multiply) negative), but typically in very small quantities. Over the last 20
years, physical characterization methods have however been developed, which
are sensitive enough to allow detailed studies, even on such small sample sizes.
As a result, two old questions can now be experimentally addressed: (i) how and
why do ligand-free gold-cluster properties (such as structure and colour) change
with the number of cluster atoms and (ii) what happens when the charge on a
cluster of a given size is varied.
In order to determine the size- and charge-dependent properties of ligand-free
clusters, they must first be generated in the form of atomically monodispersed
samples. This typically involves production of a cluster size distribution within
a collision-free molecular/ion beam (Foster et al. 1969), as well as some
form of mass selection. Furthermore, these monodispersed clusters must then
be characterized under conditions ensuring minimal (or at least uniform)
environmental perturbation of the inherent electronic and geometric structure.
This is done either: (i) directly in the gas phase (typically within the molecular
beam itself or after electrostatic extraction and trapping of cluster ions from
the beam), (ii) within a cryogenic inert gas matrix after cluster co-deposition
(Harbich & Felix 2002), or (iii) on a clean, single-crystal surface also after
fragment-free cluster deposition from a low kinetic energy ion beam (Dicenzo
et al. 1988). In particular, the first approach has been extensively pursued and
has yielded results for a wide range of monodispersed gold-cluster sizes. This
review primarily concerns such gas-phase studies.
The first molecular-beam experiments on gold clusters were performed using a
liquid metal ion source to generate small singly (and doubly) charged cluster
cations, which were detected mass spectrometrically (Sudraud et al. 1979).
Significantly larger Au+
n clusters were found some years later in experiments using
a sputter ion cluster source (Katakuse et al. 1985). The ion-intensity distributions
that were recorded showed a size-dependent structure, which was interpreted in
terms of the spherical jellium model (Knight et al. 1984). This model was put
forward to rationalize observations originally made for sodium clusters (Kappes
et al. 1982b). It approximates the electronic structure of simple s1 -electron
metal clusters in terms of the quantum mechanics of uncorrelated electrons
moving in a spherical uniformly positively charged potential box (one valence
electron per constituent atom). The model predicts a series of ‘magic numbers’,
stability islands at specific valence-electron counts corresponding to successive
electronic-shell closings. Many of these magic numbers were also observed
in the gold experiment—as discontinuities in the ion-abundance distributions
(offset by one atom because of the overall positive charge). Following these
pioneering mass spectrometric studies (also for singly charged anions: Katakuse
et al. 1986), ionization energies and adiabatic/vertical electron affinities were
acquired for a whole range of gold-cluster sizes (Ho et al. 1990; Jackschath
et al. 1992). By 1992, more detailed electronic structure information had
become available from anion photoelectron spectroscopy—notably from a study
using a magnetic-bottle spectrometer for cluster monoanions up to 223 atoms
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Review. Structures of gold-cluster ions
1213
(Taylor et al. 1992). Near-predictive-level quantum chemical calculations were
not yet possible, and consequently spectra were interpreted in terms of the
spherical jellium model. In particular, characteristic structure in the ‘valence’
regions of the spectra was interpreted in terms of the jellium energy-level sequence
and corresponding degeneracies. In addition, an ‘s–d band-splitting’ feature was
assigned in the spectra at higher binding energies, and its size-dependence
mapped. In one case (planar hexamer anions; Taylor et al. 1990; Ganteför
et al. 1992), vibrational fine structure was resolved allowing tentative geometric
inferences. Beyond photoelectron spectroscopy, other spectroscopic methods were
also brought to bear on characterizing free gold clusters. Resonant two-photon
ionization spectroscopy was applied to Au3 (triangular) (Bishea & Morse 1991).
Additionally, visible-near UV photodepletion spectra were recorded for various
neutral and cationic gold clusters up to 13 atoms—complexed to one or two xenon
atoms (Collings et al. 1994). The latter were thought to act as weakly bound
(and hopefully non-perturbing) tracers for the absorption of single photons.
Again, the implementation status of theory (particularly for electronically excited
states) precluded detailed structural inferences. Infrared multi-photon depletion
spectroscopy was also used to study gold clusters complexed to one or more
methanol molecules (Knickelbein & Koretsky 1998). In particular, the pioneering
study on Au+
n CH3 OH, n ≤ 15, (Rousseau et al. 1998) provided the complete
experimental size-dependence of the methanol C–O stretching frequency, as
well as Car–Parrinello calculations of vibrational frequencies and structures (for
specific cluster sizes). From these, it was inferred that Au+
n CH3 OH has a planar
gold-cluster core for n ≤ 7, whereas larger clusters are three-dimensional.
In parallel to probes of physical properties, studies of chemical reactivity
quickly followed the first cluster beam mass spectra. These ranged from
Penning-trap measurements of the reactivity of small cluster cations with N2 O
(Dietrich et al. 1994), through flow-tube studies of the uptake of diatomic
molecules onto clusters of various charge states (Cox et al. 1991; Salisbury
et al. 2000) to probes of unimolecular dissociation following collisional excitation
(Becker et al. 1994). Generally, these experiments uncovered strongly particlesize-dependent phenomena, which were interpreted either in terms of the
spherical jellium model, electron spin-pairing phenomena (‘even–odd effects’)
and/or size-dependent variations in electron affinities and ionization potentials.
However, detailed understanding was limited by the lack of knowledge concerning
structural details.
By about 2000, when we began our own work on gold clusters (which is to
be the focus of this review), this situation had begun to change, due in part to
observations that led to a surge of interest in these systems. First, it was shown
that small supported gold particles were surprisingly active oxidation catalysts
(Haruta 1997). This inspired work to explore the (strongly size-dependent)
reactivity of mass-selected gold clusters deposited onto single crystal surfaces
under ultrahigh-vacuum (UHV) conditions (Sanchez et al. 1999). Following up
on earlier synthetic work (Brust et al. 1994), it became possible to prepare,
separate and then physically characterize a wide size range of thiol-terminated
gold-cluster compounds (Whetten et al. 1996). These ligand-stabilized species
were shown to have interesting potential applications in nanoscience (Chen et al.
1998). At the same time, quantum chemistry was making great strides towards
accurately describing the ground states of both bare and ligand-stabilized clusters
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D. Schooss et al.
(Pyykkö 2004, 2005, 2008; Häkkinen 2008). Consequently, the time appeared
ripe for us to attempt more detailed structural probes of the bare goldcluster reference states. Below we describe the results, focusing primarily on the
structures of singly positively and negatively charged gold clusters ranging in size
of up to 20 atoms (Furche et al. 2002; Gilb et al. 2002, 2004; Weis et al. 2002b;
Schweizer et al. 2003; Neumaier et al. 2005; Lechtken et al. 2007, 2008, 2009;
Gloess et al. 2008; Johansson et al. 2008). At the same time, several other groups
also worked on structural determination of gold clusters (in various charge states)
using complementary/identical experimental methods. In particular, structures
were assigned via comparison of quantum chemical calculations to: (i) highresolution photoelectron spectra of cluster anions (Häkkinen et al. 2003; Li et al.
2003; Bulusu et al. 2006; Yoon et al. 2007), (ii) infrared multi-photon-dissociation
spectra of neutral gold clusters complexed to one or two krypton atoms (Gruene
et al. 2008), and (iii) trapped ion electron diffraction (TIED) measurements on
mass-selected gold-cluster anions (Xing et al. 2006). We compare our results to
these experiments as necessary.
2. Methods
We begin by describing experimental and theoretical methods used in
Karlsruhe for structural determination. Resulting structural assignments are
discussed in §3.
(a) Cluster-ion sources
The field of refractory element clusters can be traced back to the development
of suitable cluster-ion sources. Critical issues that needed to be tackled
were sufficient cluster intensity, variable size distributions, low vibrational
temperatures and long-term stability. Two types of cluster (ion) sources were
found to be most suitable and were systematically developed. We used both source
types and our findings were independent of cluster source type.
(i) Laser-vaporization cluster source
The laser-vaporization cluster-ion source dates back to the early 1980s (Smalley
1983). It combines the generation of a metal vapour/plasma by pulsed laser
heating and the subsequent rapid quenching by a pulsed supersonic expansion of
an inert gas (Bondybey & English 1981; Dietz et al. 1981). In the original design,
the output of a ns-pulsed laser (Nd:YAG laser or excimer laser) was directed
onto a target rod that rotated and translated through the laser (focus) to ensure
smooth surface ablation and stable conditions for cluster formation. The metal
vapour is entrained in a pulse of helium, and the mixture undergoes a nozzle
expansion. The associated rapid adiabatic cooling causes the (mostly atomic)
vapour to form clusters by multiple collisions. This design was later improved to
remedy the shortcomings such as coating of laser windows, gas leakage through
the motional feedthrough and unstable motion of the target rod (de Heer &
Milani 1991). The laser-vaporization cluster source used for our studies was based
on a further improved design (Heiz et al. 1997). It has a disc target (O’Brien
et al. 1986) of approximately 50 mm diameter and a planetary gear motion
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Review. Structures of gold-cluster ions
1215
(Gangopadhyay & Lisy 1991), which yields an increased usable surface of
approximately 15 cm2 . The counter-propagating vaporization laser (20–
40 mJ pulse−1 at 532 nm) enters the expansion nozzle along the primary beam axis
and is focussed onto the perpendicularly oriented disc target. The source yields
stable ion currents for metal clusters of up to approximately 1 nA for a massselected cluster size at a repetition rate of 100 Hz. For a typical mass spectrum,
see figure 1.
(ii) Magnetron cluster source
The magnetron cluster source (MCS; Haberland et al. 1994) is a variant
of an inert gas aggregation cluster source (Sattler et al. 1980) and is based
on a DC magnetron sputtering device (Cuomo & Rossnagel 1986; Hahn &
Averback 1990). The source comprises a DC sputter head in a liquid-nitrogencooled aggregation tube filled with a mixture of Ar and He (approx. 1 : 10)
to a pressure of approximately 1 mbar. Energetic argon ions generated in the
plasma, which is confined in front of the magnetron head, sputter atoms from
the gold target. These atoms are subsequently cooled by collisions with He,
leading to nucleation and growth of clusters along their route to the exit of the
aggregation tube. A considerable fraction of the clusters generated are positively
or negatively charged. The size distribution can be tuned (e.g. by the gas pressures
or aggregation length) from the monomer to several thousands of atoms per
cluster. A more detailed description of the MCS can be found in Xirouchaki &
Palmer (2004) and Kamalou et al. (2008).
The MCS is a continuous cluster source. However, in the TIED application
described below, the source is only switched on for several seconds per
measurement cycle to minimize material consumption and deposition along the
ion path. This ‘quasi-pulsed’ operation allows stable cluster-ion intensities for up
to several days.
(b) Direct structural-determination methods
We distinguish between ‘direct’ and ‘indirect’ structural-determination
methods. Here, direct refers to collision cross section or diffraction pattern
measurements that require comparison with structural models for geometry
assignment. Indirect methods rely on thermochemical or spectroscopic data.
(i) Collision cross sections from ion-mobility spectrometry
Ion-mobility spectrometry (IMS) is a method to obtain structural information
for cluster ions in gas phase via their reduced mobility K0 in a buffer gas (often
helium). The mobility can be obtained by measuring the drift time tD of the ions
pulled by an electrical field ED through a cell that is filled with the buffer gas at
a pressure p and temperature T ,
K0 =
Phil. Trans. R. Soc. A (2010)
273.2 K
p
L
.
tD ED 1013 mbar T
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D. Schooss et al.
0
10
20
30
40
cluster size (n)
50 60 70
80
90
100 110
1.0
Au n+
ion signal (arbitrary units)
0.8
0.6
0.4
0.2
0
5000
10 000
mass/charge
15 000
20 000
Figure 1. Typical gold-cluster cation mass spectra obtained using the laser-vaporization disc source
as interfaced to a 7T-FT-ICR mass spectrometer. The data shown were assembled from partial
mass spectra for which cluster source, ion optics and Penning trap were optimized for maximal
signals around cluster sizes n ∼ 12, 35, 60 and 90.
From the mobility, the experimental collision cross section Ωexp can be easily
calculated (Mason & McDaniel 1988) by
2π
3q
,
Ωexp =
16N0 K0 μkB T
where q is the ion charge, N0 the number density of the buffer gas and μ the
reduced mass of helium and the ion. The interaction between a neutral molecule
and an ion comprises two parts: the attractive (1/r 4 ) charge-induced dipole interaction, which scales with the polarizability of the neutral, and the repulsive
interaction owing to the van der Waals radii of the ion and neutral. When using
helium with its extremely small polarizability as the buffer gas, the attractive
interaction can be neglected, and the measured collision cross section essentially
corresponds to the geometrical (hard sphere) cross section. This significantly
facilitates comparison with theory. For a calculated candidate structure (obtained
by geometry optimization at density functional theory (DFT) level, see below),
a theoretical cross section Ωtheo can be calculated either by the projection
approximation (PA; Von Helden et al. 1993b) or the exact hard-spheres scattering
(EHSS; Shvartsburg & Jarrold 1996) model, which both treat the cluster ion
as comprised of hard-sphere atoms with element (and charge) specific radii. If
experimental and theoretical cross sections differ by more than the combined
uncertainty (typically 2%, see below), a candidate structure can be ruled out.
Note, however, that the method cannot strictly ‘prove’ a candidate structure.
The instrument used to determine the ion mobilities has been described
in detail elsewhere (Weis et al. 2002c). Briefly, the setup comprises a
laser-vaporization source (see above), a time-of-flight mass spectrometer with
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Review. Structures of gold-cluster ions
drift cell
ion source
quadrupole
mass filter
time-of-flight
mass spectrometer
gold target
ion beam
laser
mass gate
detector 1
deceleration
lens
detector 2
Figure 2. Schematic of the ion-mobility instrument. The setup comprises a laser-vaporization
cluster source, a time-of-flight mass spectrometer with a mass gate, a helium-filled, temperaturevariable drift cell and a quadrupole mass filter (see text).
a pulsed mass gate to select a specific cluster mass, a deceleration lens,
the helium-filled drift cell and a quadrupole mass filter to remove possible
fragmentation products (figure 2). The deceleration lens allows us to adjust the
injection energy, i.e. the energy of the ions entering the drift cell (typically
100–300 eV laboratory frame).
The drift cell is 110 mm long, it has 0.5 mm entrance and exit orifices and is
filled with typically 8 mbar helium. The gas temperature in the cell can be varied
between 77 and 400 K. The guiding electrical field is varied in the range between
0.5 and 3 V mm−1 . After leaving the cell, the ions pass the quadrupole mass filter
and are detected by a channeltron electron multiplier. The detector signal is fed
into a multi-channel scaler and recorded as a function of time. The maximum of
the arrival-time distribution is directly connected to the drift time tD plus a small
offset owing to the time the ions spend in the quadrupole mass filter and therefore
to the reduced mobility K0 and cross section Ωexp (see above). The resolution
of the instrument is between 25 and 40, dependent on applied drift voltage,
pressure and temperature. For all ions, the arrival-time measurements have been
reproduced several times to within 2 per cent. For the absolute error, we estimate
5 per cent, mainly owing to errors in temperature, pressure and voltage readings.
Note that recently the drift cell has been modified and an electrodynamic ion
funnel has been installed, which increased the transmission roughly by a factor
of five without significantly reducing the resolution.
(ii) Trapped ion electron diffraction
Gas-phase electron diffraction is a well-established method to obtain the
structure of neutral molecules (Brockway 1936). Ten years ago, a variant of this
approach was developed for measurements on >105 mass-selected ions stored
in a variable temperature quadrupole ion (Paul) trap (Maier-Borst et al. 1999;
Krückeberg et al. 2000). The Karlsruhe TIED setup is based on this design.
A schematic is shown in figure 3. Preformed ions are injected into the Paul
trap, which is contained in a UHV (diffraction) chamber. Within this UHV
chamber, all components (ion detector, ion trap and electron detector) are
mounted on a three-rod system centred on the exit of a collinear electron gun
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D. Schooss et al.
phosphor screen
Paul trap
electron gun
CCD
bender
magnetron cluster source
Figure 3. Schematic of the trapped ion electron diffraction setup. CCD is charge-coupled device.
to maintain cylindrical symmetry. Ions from an MCS are guided by electrostatic
steering and focussing elements into the radio-frequency (RF) quadrupole ion
trap. The ion trap (300 kHz RF, up to 7000 Vpp ) is used for ion capturing,
mass selection, ion storage and detection. The trap temperature can be regulated
between 100 and 650 K; for the experiments described here, it was set to
approximately 100 K. High-energy electrons (40 keV, approx. 2 μA) from a longfocal-length electron gun cross the trapped ion cloud. Scattered electrons are
detected on a phosphor-screen assembly, optimized to detect electrons in this
energy range. The (unscattered) main electron beam is captured by an on-axis
Faraday cup.
The TIED experimental cycle comprises a sequence of individual steps. A TIED
sequence starts with capturing cluster ions from the ion beam. To maximize the
capture rate, the ion trap is simultaneously filled with several 10−3 mbar He.
About 105 –106 cluster ions are then trapped, size-selected by applying a stored
wave inverse Fourier transformation (SWIFT) waveform dipolar to the end caps
of the ion trap, and cooled by (>106 ) He collisions to the trap temperature. After
pumping down to UHV conditions, the electron beam is switched on, and the
diffraction pattern as imaged by the phosphor screen is integrated by an external
charge-coupled device camera for approximately 30 s. After camera readout,
the remaining clusters in the trap are detected. To remove the experimental
background, exactly the same sequence is repeated without cluster ions in the
trap. This generates a reference measurement. This cycle is then repeated several
hundred times, until a sufficient signal to noise ratio is achieved. The overall
measurement time is typically 14–16 h.
For data reduction, the reference-corrected difference picture is centred
and radially averaged yielding the total scattering intensity as a function of
the electron momentum transfer s = 4π/λ sin(θ/2). λ denotes the electron de
Broglie wavelength (0.0602 pm) and θ the scattering angle. The experimental
molecular scattering function is calculated as sM exp = s(Itot /(Iback Iat ) − 1). Iat
is the atomic scattering function (Prince 2004) and Iback an unspecific, flat
and a priori unknown additional background that is determined within the
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Review. Structures of gold-cluster ions
1219
fitting procedure described below. Iback has the form Iback (s) = A exp(−αs) +
4 i
modified scattering function is approximated by sM theo =
i ai s . The theoretical
N
N
Sc /N exp(−L2 s 2 /2) i
j=i sin(rij s )/rij , with s = ks s. N is the number of gold
atoms in the cluster, Sc and ks are scaling factors and rij is the distance between
two atoms. L is the mean vibrational amplitude averaged over all distances in the
cluster and accounts for thermal vibrations. To include the finite sizes of electron
beam and ion cloud, the theoretical molecular scattering function is smoothed
by a running average over s = 0.39 Å−1 . Comparison of the experimental and
theoretical scattering function is achieved by a χ 2 -fit minimizing the differences
of experimental and theoretical scattering function by variation of Sc , ks , L and
the parameters of the background function. The quality of the fit, i.e. the level
expt
and sM theo , is characterized by a weighted R-value
of agreement between
sM
expt
expt
theo
of the form Rw =
− sMi )2 / i wi (sMi )2 . The sums go over
i wi (sMi
all experimental and corresponding theory data points. The weighting factors wi
are calculated from the (error-propagated) standard deviation of Itot . Because of
this dependence on the experimental data, comparisons of different Rw are only
meaningful within a single experimental dataset.
For a given material, the cluster size range accessible to TIED is limited
at its lower end by the atomic scattering intensity. This scales (in a crude
approximation) with the square of the atomic number (Hargittai & Hargitta 1988)
and increases linearly with N , the number of atoms in the cluster. The upper
cluster size limit is determined by the maximum mass-to-charge ratio detectable
in the ion trap (approx. 40 000 atomic mass units for singly charged species). In
the current configuration, this translates to an accessible size range of n = 10–200
for gold-cluster ions.
The good reproducibility of the TIED data has been demonstrated by a study
of clusters of very similar structure but different charge states (i.e. Ag+
55 and
Ag−
),
where
fitting
parameters
were
found
to
be
identical
within
experimental
55
error (Schooss et al. 2005).
In fitting the diffraction data to a theoretical model, the only structural
variation that is carried out is a uniform compression (or expansion) of the
calculated coordinates via the s-scaling factor ks . In effect, this allows an
experimental verification of the mean bond length of a model structure (Blom
et al. 2006). In cases where a single isomer describes the TIED data very well,
deviation of ks from unity can be mapped onto mean bond-length deviations of
the model structures. The maximum systematic error in ks is estimated to be
1–2 per cent. For gold-cluster ions using TPSS/7s5p3d1f, a consistent value of
ks ≈ 1.03–1.04 was found. Hence, TPSS/7s5p3d1f leads to a weak overestimation
of the mean bond lengths by 1–2 per cent, in good agreement with benchmark
calculations for smaller gold clusters (Johansson et al. 2008).
As the molecular scattering function is the Fourier transformation of the
(modified) radial distribution function (Hargittai & Hargitta 1988), TIED is a
sensitive measure of the atomic distance distribution. Consequently, in the case of
an isomer mixture, the TIED experiment measures the mean distance distribution
averaged over all isomers. Distinguishing different isomers can therefore be
difficult, if the isomers constituting the mixture belong to the same structure
family. Additionally, the s-range accessible to our TIED apparatus in its current
configuration is restricted to smax ∼ 12 Å−1 . This leads to limited contrast in
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D. Schooss et al.
distinguishing similar isomers. Nevertheless, in cases where isomeric structures
−
+
in a mixture belong to different motifs (e.g. Au−
12 , Au18 , Au20 , see below)
contributions from different isomers can be clearly identified, as indicated by
a significant reduction of the profile factor in a mixture fit compared with fitting
just one structure.
(c) Model structures from theory for comparison to experiment
Extensive surveys of the previous quantum chemical literature for gold clusters
and related systems can be found in reviews by Pyykkö (2004, 2005, 2008). All
quantum chemical calculations carried out for the gold-cluster ions of interest here
were performed with the T URBOMOLE program package (Ahlrichs et al. 1989)
using the DFT level of theory with the resolution of identity RI-J (Eichkorn
et al. 1995, 1997). Ground-state cluster geometries were optimized using either
the Becke–Perdew-86 functional BP86 (Becke 1988; Perdew et al. 1996) or
the meta-generalized gradient approximation of Tao, Perdew, Staroverov and
Scuseria (TPSS; Tao et al. 2003) in combination with the ‘7s5p3d1f’ basis set
((9s7p5d1f)/[7s5p3d1f]), which was specifically devised for gold clusters (Gilb
et al. 2002). This basis set includes a scalar relativistic effective core potential
that leaves 19 electrons per atom in the valence space.
The performance of ‘TPSS/7s5p3d1f’ has been validated for small gold-cluster
anions in a large-scale benchmark study including coupled cluster (CC) methods
up to CCSD(T), a Møller-Plesset (MP) perturbation series up to MP4, as
well as different variants of DFT (Johansson et al. 2008). For Au−
7 , TPSS
predicts the same energy ordering as CCSD(T) and performs better than MP2,
MP4 or the traditional generalized gradient functionals (GGAs). For the two−
dimensional–three-dimensional transition region (Au−
11 to Au13 ), the same study
showed that GGAs such as B3LYP, BP86 or PBE are significantly biased towards
two-dimensional structures (see §4 below).
For the larger gold-cluster cations Au+
n , n = 14–19, a DFT-based genetic
algorithm (GA) has been employed to help find the global minima (Sierka et al.
2007). Given the large number of geometry optimizations inherent in such a
procedure, a more modest basis set [def-SV(P)] had to be used. For Au+
14 and
+
Au15 , TPSS was used together with this basis. For the larger clusters, the BP86
functional was applied. While geometries are expected to be well described by this
approach, it is associated with energy errors of several tenths of an electronvolt.
In order to take this into account without loss of speed, we evaluated the ‘fitness’
of a cluster structure based not only on its energy, but also on agreement with
the experimental diffraction data (in terms of its profile factor Rw ). Further tests
and detailed calculations show that experimental structures can be found very
efficiently using such a modified GA (Neiss & Schooss in preparation). The final
output structure of the GA procedure, i.e. lowest energy structures and/or isomers
that optimally fit the diffraction data were re-optimized using TPSS/7s5p3d1f.
Independent of the structure search method, a vibrational frequency analysis
was conducted in each case to verify true (local) minimum structures for the
assigned isomers.
To illustrate the procedure of structure assignment using TIED, figure 4 shows
simulated scattering functions obtained for the lowest energy isomers of Au−
20 in
−
comparison with the experimental data. The structure of Au20 has been inferred
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Review. Structures of gold-cluster ions
(1) fcc D2d
0 eV
0.48 eV
2.3%
3.7%
sM (Å–1)
(2) d-fcc Cs
(b)
(3) distico C1
(4) dist-fcc C2
(5) deca Cs
0.59 eV
0.61 eV
0.57 eV
14%
10%
15%
2
1
0
–1
–2
–3
2
1
0
–1
–2
–3
2
1
0
–1
–2
–3
2
1
0
–1
–2
–3
(1)
2
1
0
–1
–2
–3
(5)
0.5
0
– 0.5
(2)
0.5
0
– 0.5
(3)
0.5
0
– 0.5
DsM (Å–1)
(a)
(4)
0.5
0
– 0.5
0.5
0
– 0.5
2
3
4
5
6
7
8
9
10
11
s (Å–1)
◦
Figure 4. (a) Minimum energy structures of Au−
20 (two views rotated by 90 ), together with
structural motif, point-group symmetry, relative energy and profile factor Rw . The lighter atoms are
visual aids to indicate the relative positions of the two views. (b) Comparison of the experimental
(open circles) and simulated (red lines) reduced molecular scattering function sM from DFT
structures (1)–(5) for Au−
20 . The blue traces show the residuals.
to be a slightly distorted tetrahedron (D2d ) by photoelectron spectroscopy (PES)
(Li et al. 2003). This was later confirmed in a TIED study (Xing et al. 2006).
Our results are fully consistent with these findings: the slightly (Jahn–Teller)
distorted tetrahedron, a segment of the gold face-centred cubic (fcc) structure,
is the ground-state structure according to TPSS/7s5p3d1f. The best agreement
with our experimental data (Rw = 2.3%) is found for this tetrahedral structure
(1). The remaining differences between experimental and simulated scattering
function (figure 4) are probably owing to incomplete consideration of vibrational
effects such as (bond-dependent) vibrational amplitudes and anharmonicities. As
indicated by their high(er) Rw -values, other structural motifs such as icosahedral
(3), or decahedral (5) can be clearly ruled out. Even the singly defective
tetrahedral isomer (2) or the distorted fcc structure (4) shows significantly
higher profile factors and are unlikely to contribute considerably to the cluster
ensemble probed.
Phil. Trans. R. Soc. A (2010)
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1222
D. Schooss et al.
(d) Indirect structural-determination methods
(i) Radiative association kinetics and adsorption equilibria
Ion cyclotron resonance (ICR) mass spectrometry makes use of a Penning
ion trap to probe near-thermal energy ion-molecule reactions at pressures well
below 10−6 mbar. Concomitantly, long trapping times of >1 ms are routinely
attained. ICR work on atomic metal cation chemistry under such single collision
conditions dates back more than 30 years (Staley & Beauchamp 1975). For
example, complete cycles of metal ion-catalysed oxidation reactions have been
studied (Kappes & Staley 1981) or thermochemical information like gasphase acidities/basicties or relative ligand-binding energies (‘thermochemical
ladder’) has been obtained by way of quantifying exchange equilibria
(Kappes et al. 1982a).
More recently, it was recognized that absolute binding energies of metalion/ligand systems may be obtained by modelling the low-pressure kinetics of the
corresponding bimolecular association reactions (Kofel & McMahon 1988; Dunbar
et al. 1996). This radiative association kinetics model is based on a mechanism
that can be written as
+
kf
M + L M(L)
kb
k
+
r
∗ −−→
M(L)+ + hv
kc [L]
−−→
M(L)+ ,
wherein the initially formed energized complex [ML+ ]∗ releases its excess
energy by photon emission (with a rate constant kr ) rather than by collisional
relaxation. By making further assumptions concerning the [ML+ ]∗ formation rate,
kf (=Langevin capture cross section) and by modelling the transition state and its
dissociation rate kb (Rice–Ramsperger–Kassel–Marcus (RRKM) theory or phasespace theory), an expression can be derived that may, in turn, be used to fit the
kinetic data of ML+ formation with the M+ -L binding energy as the sole free-fit
parameter (for more details, see Wu & McMahon 2009).
Apart from providing thermochemical information (which can then be
compared with predictions from structural models), adsorption/desorption
experiments can, in principle, also be used to obtain more direct information on
isomer content. For monodispersed cluster ions with two (or more) coexisting
isomers having significantly different chemical properties, there are several
consequences (assuming slow interconversion rate): (i) the adsorption kinetics will
deviate from the single-exponential decay behaviour expected for a single-isomer
parent species. Note, that such isomer-specificity has often been observed for the
‘inverse’ process of radiatively induced dissociation/depletion ‘BIRD’ (Dunbar
2004), e.g. for electron autodetachment (Arnold et al. 2003) and for radiatively
induced dissociation (Schnier & Williams 1998). In order to obtain reliable results,
such experiments and their kinetic modelling have to be performed at several
temperatures owing to the generally rather poor robustness of the corresponding
multi-parameter fits (ii) Two different saturation coverages may be observable:
under certain conditions of pressure and temperature it is possible to follow
physi- and/or chemisorption kinetics to a steady state (‘saturation’), e.g. allowing
‘titration’ of strongly binding apex sites and thus structural inferences. This
Phil. Trans. R. Soc. A (2010)
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Review. Structures of gold-cluster ions
1223
latter methodology was extensively employed in flow-tube studies on neutral Nin
(n ≤ 60) with N2 , CO and H2 , in the group of Riley at Argonne (Kerns et al.
2000; Parks et al. 2000).
In our experiments, a Fourier-transform ICR (FT-ICR) mass spectrometer
(Bruker Daltonics, APEX II) equipped with a 7 T magnet and a laser-vaporization
source was used. Ions are trapped using a homogenous magnetostatic and
superimposed quadrupolar electrostatic field inside an ICR cell under UHV
conditions. Ion-molecule reactions can be studied under few collision conditions
at reactive gas pressures of 10−7 to 10−8 mbar. Under these conditions, radiative
processes, e.g. spontaneous photon emission, may have to be taken into account
when analysing kinetic data (radiative association model, see above).
(ii) Electronic photodissociation spectroscopy
Measurements of the energies of electronically excited states, as well as
corresponding absorption cross sections, can be directly related to cluster
structures if: (i) excitation energies can be calculated to sufficient accuracy
(typically to within 0.1 eV) and (ii) possible structural isomers can be clearly
distinguished on the basis of predicted spectra (Schweizer et al. 2003).
Owing to the low particle densities, direct absorption measurements cannot
normally be performed on mass-selected cluster beams. One solution is to couple
photoabsorption to a change in cluster-ion intensity. The simplest version of this
is photodissociation as detected by parent ion intensity depletion. Unfortunately,
dissociation energies of gold-cluster ions are comparable with visible photon
energies (Becker et al. 1994; Spasov et al. 2000). Therefore, even if the (one)
photon energy is rapidly and completely converted into ground-state vibrational
excitation, unimolecular dissociation rates are often too slow for complete
fragmentation on the experimental time scale—particularly for larger clusters.
Consequently, depletion cross sections can be significantly smaller than the onephoton absorption cross sections (further complicated by unknown fluorescence
quantum yields). The inert-gas-tracer method offers (a partial) solution. Instead
are photodissociated. The
of bare gold-cluster ions, inert-gas adducts Aux Rg+/−
y
method presupposes that the inert-gas binding energy is small enough to yield
complete one-photon dissociation on the experimental time scale and that the
optical properties of the bare cluster are essentially unperturbed by complexation.
Both assumptions were tested in our experiments.
The experimental setup used has been previously described (Schooss et al.
(Rg = Ar or Xe) were generated using a Smalley/Heiz2000). Briefly, Aux Rg+/−
y
type pulsed laser-vaporization source. The gold vapour was expanded together
with a helium/inert gas mixture to yield a seeded supersonic beam. Cluster ions
were extracted from this primary beam into a perpendicularly oriented reflectron
time-of-flight mass spectrometer. For several experiments, this mass spectrometer
was equipped with custom ion-extraction optics that allowed setting the first
space focus to a comparatively small distance of ca 1 cm from the primary
beam axis. This allowed essentially simultaneous irradiation of a wide range of
extracted ion masses, while at the same time ensuring mass-specific detection
of depletions and ensuing fragment ions (Schooss et al. 2000). As a result, it
was possible to carry out spectroscopic measurements on several cluster ions
at once, thus enhancing the throughput of the experiment. Cluster ions were
Phil. Trans. R. Soc. A (2010)
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1224
D. Schooss et al.
photodissociated using a Nd-YAG-pumped, tuneable, pulsed optical parametric
oscillator (OPO) laser. One-photon dissociation conditions were ensured by also
determining depletions as functions of laser fluence. Details concerning laser/ion
beam overlap and the relations used to determine cross sections from measured
depletions can be found in Schweizer et al. (2003) and Gloess et al. (2008).
3. Structures
(a) Singly charged cluster ions
IMS was the first direct method used to obtain information on gold-cluster
structures (see figure 5). It was applied to singly charged cations and anions
ranging in size up to 13 atoms. Subsequently, cluster sizes from 11 atoms to
beyond 20 were studied by TIED. We discuss these efforts in sequence. The
resulting geometries are shown in figures 6 and 7. The corresponding atomic
coordinates are given in the electronic supplementary material.
(i) Ion-mobility measurements
A summary of the collision cross sections as determined by IMS is shown
in figure 5. Anions generally have larger cross sections than cations of the
same nuclearity—due essentially to electron spillout. For structural assignments,
individual cross sections were analysed in terms of model calculations as
described below.
+/−
Au3 : according to the DFT calculations, the lowest energy structure for the
trimeric cation is triangular (D3h symmetry, bond length 2.640 Å), while the anion
is linear (bond length 2.587 Å; figure 6). These assignments can be confirmed by
ion-mobility data (for details see Furche et al. 2002; Gilb et al. 2002).
+/−
Au4 : the DFT global minimum for the tetrameric cation is a planar rhombic
D2h structure, in agreement with the ion-mobility data. For the anion, a zig-zag
chain is lowest in energy, a Y-shaped structure is however only 0.02 eV higher
in energy. On the basis of our ion-mobility measurements (Ωexp = 58.6 Å2 ), we
can rule out the zig-zag structure (Ωtheo = 62.0 Å2 ) and confirm the Y-shaped
structure (Ωtheo = 58.5 Å2 ).
+/−
Au5 : DFT predicts the cation to be a planar, X-shaped (D2h ) structure
symmetry. The anion is planar as well; however, the symmetry is reduced to
a W-like (C2v ) structure.
+/−
Au6 : the lowest energy structure for both charge states is planar triangular.
For the anion, it is an isosceles triangle (D3h symmetry), the cation is slightly
Jahn–Teller-distorted (C2v symmetry).
+/−
Au7 : the DFT global minimum for the cation is a highly symmetric hexagon
with one central atom (D6h symmetry). The anion is planar as well; however, it is
lower in symmetry. It can be thought of as a square with three of its edges bridged
by additional gold atoms (C2v ; figure 5). All of these structures are confirmed by
ion-mobility data.
Phil. Trans. R. Soc. A (2010)
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1225
Review. Structures of gold-cluster ions
120
cross section (Å2)
100
80
60
40
Au–12
20
arrival time
0
5
10
15
number of atoms
20
25
Figure 5. Ion-mobility measurements: experimental cross sections for gold-cluster cations (black
circles) and anions (grey circles) at 300 K. Note that the small gold-cluster anions have significantly
larger cross sections than the corresponding cations. For Au−
12 , a bimodal arrival-time distribution
is obtained, indicative of two different isomers. This is the only cluster size where we observe two
peaks of comparable intensities in the room-temperature measurements.
Au7– C2v
Au–11 Cs
Au–14 C2
0.22 eV Au–18 C2v(1)
Au8– D4h
Au–12 D3h
Au–15 C2v
–
0.04 eV Au18 C2v (2) 0.17 eV
Au5– C2v
Au–9 C2v
Au–12 C2v
Au6– D3h
Au–10 D2h
Au3– D•h
Au4– C2v
0.02 eV
0.15 eV
Au–13 C2v
0.27 eV
Au–16 D2d
Au–19 C3v
Au–17 C2v
Au–20 D2d
Figure 6. Structures of gold-cluster anions Au−
n (n = 3–20). Shown are the isomers fitting the
experimental data best, together with their corresponding point-group symmetry. In cases where
the experimentally assigned structure is different from the calculated global minimum, the relative
−
energy is given. For Au−
12 and Au18 , two isomers are shown in each case, as here a two-component
isomer mixture has been identified.
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1226
D. Schooss et al.
Au+3 D3h
Au7+ D6h
Au+4 D2h
Au+8 Cs
Au+5 D2h
Au+9 C2v
Au+12 C2v
Au+6 C2v
Au+9 C3v
+
0.21 eV Au13 C2v
Au+10 C3v
0.06 eV Au+11 D3h
0.11 eV
Au+14 C1
0.12 eV Au+18 Cs
0.01 eV
Au+15 C1
Au+19 C1
0.30 eV
Au+16 C2v
Au+20 D2d
Au+17 Cs
+
0.36 eV Au 20 C3
0.27 eV
Figure 7. Structures of gold-cluster cations Au+
n (n = 3–20). Only the isomers that optimally fit
the experimental data are shown, together with their point-group symmetries. In cases where the
experimentally assigned structure is different from the calculated global minimum, the relative
+
energies are given. For Au+
9 and Au20 , two isomers are shown in each case, as two-component
isomer mixtures have been identified for these sizes.
+/−
Au8 : for the cation, DFT predicts a planar structure to be lowest in
energy (basically the Au+
7 hexagon with one additional bridging atom, C2v ).
A three-dimensional structure with completely different topology is found only
0.06 eV higher in energy. Based on the ion-mobility data, we can rule out the
planar global minimum structure and confirm the isomeric three-dimensional
structure (Cs symmetry). The anion on the other hand turns out to be planar and
highly symmetric (D4h ), its structure consists of a square with all edges bridged.
This structure can be confirmed experimentally—the energetically closest threedimensional structure is almost 1 eV higher and has a cross section that is 10 per
cent below the experimental value and can therefore be ruled out.
+/−
Au9 : the cation has a three-dimensional structure (C2v ) that basically
represents a segment of the gold-crystal lattice. In our ion-mobility measurements
at room temperature, we observe one single peak in the arrival-time distribution,
low-temperature studies reveal however the coexistence of isomer (C3v ; figure 5).
Both structures interconvert at room temperature (see below). Planar structures
can be ruled out both on the basis of cross section and relative energies. The
favoured structure for the anion, however, is planar, in agreement with the
ion-mobility data.
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Review. Structures of gold-cluster ions
+/−
+/−
+/−
1227
+/−
Au10 , Au11 , Au12 and Au13 : the cations are three-dimensional (figure 7).
For the anions, DFT predicts planar structures. This can be confirmed by ion
−
−
mobility only for Au−
10 and Au11 . For Au12 , we find a bimodal arrival-time
distribution (figure 5). The first peak can be identified as a three-dimensional
isomer, while the second corresponds to a planar structure. For Au−
13 , we find
only a three-dimensional structure, planar candidate structures can be ruled out
on the basis of the ion-mobility data.
(ii) Trapped ion electron diffraction measurements: Au−
n , n = 11–20
The smallest gold-cluster anion studied by TIED was Au−
11 (Johansson et al.
2008). It is a flat Cs structure in good agreement with theoretical prediction. For
Au−
12 , an isomer mixture was found: the three-dimensional C2v isomer together
with a smaller contribution (approx. 15%) of a planar D3h isomer. This is in
contrast to the theoretical prediction; the GGA functionals PBE and BP86
predict the planar structure to be the global minimum 0.4–0.6 eV lower than the
three-dimensional structure. Even TPSS predicts a slight bias towards the planar
structure (0.17 eV). Spin-orbit coupling (SOC) significantly affects the relative
energies. Incorporation of SOC into the calculations leads to a stabilization of
the three-dimensional structure by more than 0.1 eV. Contrary to previous PES
studies (Bulusu et al. 2006) and (Koskinen et al. 2007), which have suggested that
Au−
13 has a two-dimensional structure, we found it to have a flat three-dimensional
structure (C2v ). This is also in agreement with theory: at TPPS level, the twodimensional isomer is 0.2 eV higher in energy. The assignments based on TIED
−
for Au−
11 to Au13 are in perfect agreement with the room temperature IMS results
described above.
For Au−
14 , again a flat three-dimensional structure (C2 ) fits the experimental
data best. Interestingly, its energy is 0.22 eV above the two-dimensional groundstate structure suggested by TPSS/7s5p3d1f (Lechtken et al. 2009). To our
knowledge, neither the C2 nor the planar structure has been considered for Au−
14
before. In former TIED (Xing et al. 2006) and PES (Häkkinen et al. 2003; Bulusu
et al. 2006) studies, a C2v structure was assigned, which is a saddle-point rather
than a minimum-energy structure using TPSS/7s5p3d1f. For Au−
15 , a flat-layered
−
structure (C2v ) closely related to the Au14 structure is the best-fitting isomer, in
agreement with previous TIED measurements.
At Au−
16 , the structural motif changes: the ground state and also the bestfitting structure is now a slightly distorted tetrahedral (D2h ) cage structure. This
structure can be constructed from the tetrahedral Au−
20 by removing four corner
atoms and moving out each of the centre atoms of the four faces. This structure
comprises a sizeable hollow of 5.1 Å diameter, large enough to accommodate
a heteroatom, as was shown recently for Cu@Au−
16 (Wang et al. 2007) and
−
Fe/Co@Au−
(Wang
et
al.
2009).
Au
also
has
a
cage
structure (C2v ).
16
17
−
For Au18 , a mixture of structures was found. The dominating isomer (approx.
80%) is again a cage-like structure (C2v -2), while the minor component (C2v -1)
(TPSS/7s5p3d1f ground state) is an fcc-like structure. It can be derived from
−
−
the Au−
20 tetrahedron by removing two corner atoms. Finally for Au19 and Au20 ,
tetrahedral fcc-like structures have been found in good agreement with the former
TIED and PES measurements.
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1228
D. Schooss et al.
(iii) Trapped ion electron diffraction measurements: (Au+
n , n = 11–20 )
+
The structures of Au+
11 –Au13 (previously studied by IMS—see above) have
also been studied by TIED. For this, the three-dimensional structures found
by IMS were re-optimized using TPSS/7s5p3d1f, and the resulting simulated
scattering functions were found to be in close accordance to the TIED data
(Lechtken et al. in preparation).
For Au+
14 , the best agreement between experiment and theory is found
for a layered structure (C1 ) decorated with an additional atom. This motif
+
+
is continued for Au+
15 (C1 ) and Au16 (C2v ). Au17 is an interesting case.
Among the low-energy structures, only layered structures are able to explain
the experimental data. Neither the calculated high-symmetry ground state
(Lechtken et al. in preparation) nor structures based on the Au20 tetrahedron
are in agreement with the experimental data. Within the layered structure
family, the lowest-energy isomer we have found (figure 7) is 0.36 eV above the
TPSS/7s5p3d1f ground state. Additional support for this assignment results from
IMS measurements, as only flat-layered structures have simulated cross sections
close to the experimental value (Weis et al. 2002a).
At Au+
18 , the structural motif changes: a decorated cage that is isoenergetic with
the fcc-like ground-state structure is found to fit the TIED data best. The hollow
in this star-like configuration has a diameter of 5.9 Å and exceeds the hollow in
+
Au−
16 . Au19 is found in the experiment to again have a decorated cage structure,
while calculations predict a defected Au20 tetrahedron as the ground state.
For Au+
20 , a mixture of two isomers was found (Lechtken et al. 2008). The
predicted minimum-energy structure is similar to Au−
20 , a slightly distorted
(D2d ) tetrahedral structure. The next higher lying isomer (0.27 eV) is a
distorted icosahedral structure of C3 point-group symmetry. None of the
calculated structures alone is able to explain the experimental scattering function.
However, a 2 : 3 mixture of D2d and C3 structures fits the scattering data
very well.
(b) Comparison of experiment and theory and rationalization of structures
The overall agreement between TIED experiment and theoretical prediction
using TPSS/7s5p3d1s is remarkably good. For most clusters (anions and
cations) in this size range, the best-fitting structures correspond either to the
tentative ground states or to energetically close-lying isomers. However, there
−
−
+
+
+
are exceptions, most notably for Au−
12 , Au14 , Au18 , Au17 , Au19 and Au20 . This
discrepancy may be owing to (i) the possibility that the correct global minimumenergy isomer was not yet found/considered, (ii) significant changes in free-energy
ordering of isomers occurs at the experimental temperature (100 K) relative to
the sequence of vibration-less total energies, or (iii) systematic errors in theory
that yield the incorrect energy ordering of isomers (or perhaps even incorrect
structures). To rule out (i), we have conducted more extensive structure searches
−
+
(e.g. via ab initio molecular dynamics for Au−
11 to Au13 and GA for Aun ). However,
no lower-energy isomers were found. To test the finite-temperature effect, we have
calculated free-energy differences, i.e. differences in zero-point energies as well as
thermal corrections in the harmonic approximation. These corrections turn out
+
to be small (e.g. approx. 0.01 eV for Au−
12 and Au20 ) at 100 K, leaving the relative
energies virtually unchanged. Additionally, the TIED experiment probes clusters
Phil. Trans. R. Soc. A (2010)
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Review. Structures of gold-cluster ions
1229
thermalized in a He bath on second time scales. It is therefore unlikely that isomer
distributions are dominated by metastable species. This leaves (iii) as the likely
explanation.
−
The predicted ground-state structures for Au−
12 and Au14 are planar and tetra−
+
+
hedral for Au18 , Au18 to Au20 . Both comprise exclusively segments of the
gold (111) surface. Cluster geometries containing this structural element appear
to be overestimated in stability by the DFT calculations. Note, however, that this
systematic error in DFT can only be (experimentally) detected for those clusters
in which a different structural motif is comparable in energy to the (111) segment
geometries.
In order to rationalize the assigned structures, it is helpful to contrast these
structures to the ones of copper and silver clusters. In recent work, we have stud+/−
+/−
+/−
ied the structural properties of Cu20 , Ag20 and Au20 (Lechtken et al. 2008).
As already pointed out by Häkkinen et al. (2002) and Fernandez et al. (2006), Cu
and Ag are quite similar, whereas Au prefers different structures. It is well known
that relativistic contraction of the inner electronic shells of gold atoms stabilizes
the 6s valence electrons, while the lower-lying 5d electrons are raised in energy.
This leads to smaller s–d separation and significant s–d hybridization. In contrast,
for Cu and Ag, the corresponding effects are much smaller. The extent of s–d hybridization in gold clusters also depends on the actual structural motif/symmetry.
As a result, for some cluster sizes, notably at the two-dimensional/threedimensional structural transition, enhanced s–d hybridization can lead to relative
stabilization of planar structures and even compensate for decreased average
coordination numbers. Also, s–d hybridization is more pronounced for tetrahedral
than for icosahedral structures. Compact icosahedral structures in gold clusters
require stretching of interatomic distances compared with the (111) microfacets
in tetrahedral structures. Such deviations from optimal Au–Au bond distances
involve a large energy penalty, caused in part by the relativistic contraction of the
6s orbital. Altogether, these effects lead to non-compact, planar, flat or cage-like
structures instead of icosahedral structures as seen for copper and silver.
It is important to note that the minimum-energy structures determined for
a given cluster size depend strongly on the charge state. This might appear
surprising for a metallic cluster. In fact, calculations show that cations and anions
do have common structural isomer types with only minor charge state-dependent
geometry differences. However, the relative energies of different structural isomers
can change significantly upon changing charge, thus yielding different global
minima. This effect can be rationalized if one considers that the clusters
have structure-dependent highest occupied molecular orbital–lowest unoccupied
molecular orbital (HOMO–LUMO) gaps, which can be quite large (e.g. 1.81 eV for
Au20 ). Consequently, ionization energies and electron affinities are quite distinct
for different isomer geometries. Only for (larger) clusters for which band gaps
approach zero, would one expect that the energetic ordering of the isomers no
longer depends on the charge state.
(c) Isomer distributions, interconversion kinetics
and thermodynamic equilibrium
−
−
The IMS data resolved isomer mixtures for Au+
9 and Au12 . For Au12 , we
observed two well-separated peaks in the arrival-time distribution at room
temperature (figure 5). This indicates that any interconversion between the two
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1230
D. Schooss et al.
(c)
intensity
(a)
t1/2 > 50 ms
(b)
t1/2 ~~ 1 ms
intensity
(d)
t1/2 ~
~ 15 ms
arrival time
t1/2 < 0.1 ms
arrival time
Figure 8. Typical arrival-time distributions of Au+
9 for four different temperatures. Black trace:
measured arrival-time distributions (He pressure 5 mbar, drift voltage 200 V). Grey trace: simulated
arrival-time distributions obtained with the kinetic theory of ion mobility (Gatland 1974; Mason &
McDaniel 1988) based on two isomers interconverting with the indicated half-lives (Weis et al.
2002a). (a,b) 77 K and 120 K: the peaks corresponding to the two isomers are well separated for
time constants larger than the experimental time scale of 1 ms. (c) 140 K: the two peaks coalesce as
the conversion rate becomes comparable with or even faster ((d) 160 K) than the average drift time.
isomers is significantly slower than the drift time through the cell (1 ms), i.e.
the rate is smaller than 103 s−1 . Given an internal vibrational energy of ca
0.65 eV for Au−
12 at room temperature, this translates into an interconversion
barrier of >0.4 eV based on a RRKM calculation (Forst 1973) using DFTderived vibrational frequencies. For Au+
9 , we observed two peaks in the arrivaltime distribution only for T < 120 K. Near 140 K, one broad peak is seen.
Above 160 K, we observed one narrow peak. Its width corresponds to the
instrumental resolution (figure 8). These observations can be interpreted in terms
of two interconverting isomers—with a temperature-dependent half-life. This is
significantly larger than the average arrival time (1 ms) for temperatures below
120 K and significantly smaller above 160 K. The corresponding temperaturedependent rate translates into a barrier height of 0.1–0.2 eV (for details, see
Weis et al. 2002b). Based on their cross sections, we can assign structures
for the two isomers (figures 5 and 8). They differ basically by the position
of one atom and correspond to the DFT global minimum and the structure
closest in energy, respectively. These observations are independent of source
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Review. Structures of gold-cluster ions
1231
parameters such as vaporization laser intensity, timing and injection energy,
indicating that the experiment probes thermodynamically controlled isomer
distributions. Similar conclusions, i.e. near-thermal equilibrium conditions, can
be drawn for those TIED cases that require a mixture of lowest energy isomers
−
+
to optimally fit the measurements (Au−
12 , Au18 and Au20 ). Note however, that
equilibrium isomer distributions are not always observed in cluster experiments:
carbon clusters made by laser vaporization of graphite, for example, coexist
in several non-interconverting isomeric forms, such as chains, rings and cages,
and can be completely annealed into the most stable form upon injection
into the drift cell (Von Helden et al. 1993a). Carbon clusters have much
higher binding energies and interconversion barriers than gold clusters do.
Consequently, thermodynamically limited isomer distributions are more difficult
to achieve.
(d) Structural determinations for other cluster charge states
Experimental information on the structure of Auqn in charge states other than
q = ±1 is very scarce. So far, the only direct structure assignments for neutral
clusters were obtained in a messenger IR multi-photon dissociation study of
Aun Kr, n = 7, 19 and 20. The vibrational spectra showed a convincing consistency
with theoretical predictions (Gruene et al. 2008): Au07 is planar, but differs from
the highly symmetric D6h structure prevailing for the cation. Au019 and Au020
conform to tetrahedral structures with the 19-atom cluster being truncated at
one corner of the pyramid—both being closely related to the structures observed
for the respective anions.
Highly charged metal clusters have enjoyed considerable interest in cluster
science because of novel properties deriving primarily from competing cohesive
and repulsive Coulombic interactions (Näher et al. 1997). Stability criteria and
concomitant appearance cluster sizes have been predicted for many metallic
systems in pioneering theoretical work based in part on a liquid-drop model
(Yannouleas & Landman 1993, 2000).
(Sudraud et al. 1979) was the first multiply charged cluster to be
Au2+
3
experimentally observed. Subsequent more extensive studies of the properties of
Au2+
n (9 ≤ n ≤ 18) concerned their dissociation by fission (Saunders 1990, 1992).
(Herlert et al. 1999; Schweikhard et al. 1999) and Au3−
Generation of Au2−
n
n
(Yannouleas et al. 2001) was first achieved by electron attachment to trapped
gold-cluster anions for which appearance sizes of n ≥ 12 (dianions) and n ≥ 51
(trianions) were established (Herlert & Schweikhard 2003). Another source to
produce gold-cluster dianions was found to be UV laser ablation from a metal
target under high-vacuum conditions (Stoermer et al. 2001).
Essentially, the only information on the geometric structure of multiply charged
gold clusters derives from quantum chemical computations. Recently, the most
stable isomer of Au2−
6 has been calculated to have octahedral symmetry rather
than planar topology. The same authors have made structural predictions for
4−
2−
Au2+
10 (D4d symmetry) and Au14 (D2d symmetry; Chen et al. 2006). Au16 is
thought to have a hollow cage structure with full Td symmetry (similar to the
cage found for Au−
16 ). This structure was computed to be electronically stable
with a positive second electron affinity of 0.92 eV (Walter & Häkkinen 2006).
Phil. Trans. R. Soc. A (2010)
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1232
D. Schooss et al.
4. Consequences of structure for ion chemistry and electronic spectroscopy
(a) Carbon monoxide chemisorption
Knowledge of the geometric structures of gold clusters helps to rationalize their
ion chemistry. To illustrate this, we discuss the CO chemisorption (which is
also the most extensively studied chemisorption process on single-crystal gold
surfaces) and revisit some of the previous experimental results on clusters
‘in retrospect’. As outlined in §1, these were mostly analysed in terms of
electronic structure when first published. In the meantime, one can consider
these observations in terms of a more ‘holistic’ approach, which incorporates
interdependent electronic and geometric structure.
Absolute bimolecular rate constants for the adsorption of CO on gold-cluster
anions Au−
n were determined with a guided-ion-beam setup for n ≤ 7 (Lee & Ervin
1994). These rates increase with increasing cluster size and show a pronounced
step between n = 4 (a quasi-one-dimensional Y-shaped cluster with a singly
connected gold atom) and n = 5, which adopts a planar W-shaped structure. The
relative CO adsorption reactivities of Au−
n (n = 4–19) as determined in a flowtube study (Wallace & Whetten 2002) revealed local maxima at n = 11, 15 and 19.
These nuclearities mark the transition sizes for changes in structural motif (twodimensional → flat three-dimensional structures → hollow cages → tetrahedral).
Early accounts of CO reactivity with Au+
n included a preliminary FT-ICR
mass spectrometric study (Nygren et al. 1991) for n ≤ 21, which displayed local
reactivity maxima at n = 7 and n = 18/19. More recently, we have systematically
studied the chemisorption kinetics of CO reacting with Au+
n (n < 65) trapped in
an ICR cell at room temperature (Neumaier et al. 2005). Sequential CO uptake
of up to four carbon monoxide molecules is observed. The corresponding quasiunimolecular rate constants are summarized in figure 9a. The rate constants for
the first CO have been analysed by the radiative-association model to give the
binding energies (‘heats of adsorption’) that are shown in figure 9b. For some
of the larger cluster sizes (n > 20), this kinetic modelling was complemented
by measurements of the steady-state ion abundance equilibria resulting from
competing absorption and desorption kinetics. Analyses of equilibrium constants
yielded reaction enthalpies in excellent agreement with the binding energies from
the kinetic model. These decrease with cluster size from 1.09 eV for Au+
6 to below
0.65 eV for n > 26, with notable exceptions at n = 30, 31, 32 and 48, 49.
Note that experiments on gold surfaces (Lemire et al. 2004), as well as
quantum-chemical calculations (Neumaier et al. 2008), indicate μ1 -type bonding
of CO to (charged) gold clusters or gold surfaces, i.e. an atop Au–CO bond. Given
this information, can our observations from ion chemistry be used as a local
probe for the surface structure of a gold-cluster educt? As previously pointed
out, the simplest approach derives from saturation kinetics. Au+
20 is capable of
adsorbing four CO molecules with virtually identical efficiency (figure 9a). A
fifth CO is not observed to bind under experimental conditions. This behaviour
may be attributed to the four equivalent vertices of a tetrahedral cluster
structure. However, this simple picture fails as soon as the cluster significantly
restructures upon CO adsorption. Our quantum chemical calculations indicate
that lowest-energy structures for some gold carbonyl species deviate from
the structures of the bare cluster ions. In particular, the size range of the
Phil. Trans. R. Soc. A (2010)
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1233
Review. Structures of gold-cluster ions
Kapp 10–11 cm3 (molecule s)–1
(a) 100
15
10
7
19 21
31
1
5
0.1
0.01
(b)
1.6
binding energy (eV)
1.4
1.2
1.0
0.8
0.6
0
5
10
15
20
25
30
35
cluster size (n)
Figure 9. Quasi-unimolecular rate constants (k1 , . . . , k4 ) of sequential carbon monoxide (CO)
chemisorption on gold-cluster cations at room temperature versus cluster size (a) and binding
energy for Au+
n –CO, i.e. the first CO molecule (b), see text for details. (a) Dark green squares, k1 ;
red circles, k2 ; blue stars, k3 ; light green triangles, k4 . (b) Dark green squares, radiative association
model; black inverted triangles, B3LYP calculations.
two-dimensional–three-dimensional transition is affected: Au7 CO+ is calculated
to have a three-dimensional structure, whereas Au8 CO+ adopts a planar geometry
(Neumaier et al. 2005). This also means that the radiative association model is
too simple for these cluster sizes—an (activated) cluster core interconversion step
must be additionally invoked. Along the same lines, interpretation of adsorption
kinetics is complicated by significant reactant isomer interconversion. At room
temperature, Au+
9 reacts readily and sequentially with four CO molecules. This
is associated with single exponential kinetics (and virtually identical reaction
rates) in each case. One possible interpretation is that the cluster has a high
symmetry (four equivalent adsorption sites). This is not borne out by IMS
structural determination. Alternatively, the reactivity may reflect a fluxional
core—consistent isomer-interconversion at room temperature as observed in IMS.
Phil. Trans. R. Soc. A (2010)
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1234
D. Schooss et al.
Single adsorbate-induced restructuring (and large-scale isomer interconversion)
is expected to become less pronounced with increasing cluster size.
Correspondingly, interaction energies derived from radiative association kinetics
are more likely to reflect the strongest adsorption sites—which are in turn related
to those gold atoms with the lowest electron density, as our recent calculations
have shown (Neumaier et al. 2008). Then, our observations for Au+
20 indicate
a CO binding energy of 0.75 eV to the potentially tetrahedral apex sites, still
significantly higher than for a single-crystal gold surface—e.g. the surface binding
energy for a (reconstructed) Au(110)…CO amounts to 0.55 eV (Gottfried et al.
+
2003). Note that in contrast to Au+
20 , Au21 shows a pronounced affinity to the first
CO molecule—the rate constant for attaching a second one being two orders of
magnitude smaller. Here, it is tempting to postulate a closed-shell structure with
one additional reactive gold ad-atom. For this (still hypothetical) Au+
21 structure,
density-functional computations show that the atoms with the smallest electron
density, here the gold ad-atom, form the strongest CO bond.
In future, it will be of interest to rationalize local maxima in CO binding
energies at n = 30, 31, 32 and 48, 49 in terms of the actual cluster structures.
(b) Electronically excited states versus charge and topology
Three inert-gas-tracer depletion spectroscopic studies were performed in order
to obtain information on optically excited states and corresponding geometric
(Rg = Ar and Xe). First, depletion spectra were recorded
structures of Aux Rg+/−
y
for Au4 …Ar+
,
n
=
0–4,
in the photon energy range of 2.14–3.35 eV (Schweizer
n
et al. 2003). The molecule is small enough such that direct one-photon dissociation
is fast on the experimental time scale—throughout the experimental photon
energy range. This is consistent with the calculated dissociation energy (into
+
Au+
3 + Au) of ca 2.1 eV. Consequently, Au4 can be used as a reference to gauge
the spectral effect of inert-gas complexation (which can be regarded as upper
limits to analogous effects for larger clusters). Overall, the spectra recorded
for Au4 …Ar+
n , n = 0–2 had similar shapes. We found that argon-induced shifts
in the positions of electronic absorption bands were of the order of 0.1 eV
for adducts with one and two argon atoms, respectively. Component oscillator
strengths of the complexes were modified by at most ±50 per cent relative to
the corresponding transitions in the bare cluster ions. In contrast, complexation
of three or more argon atoms led to significant changes in the spectral shapes.
We modelled the experimental observations in terms of DFT-B3LYP (and RIMP2) calculations for ground and time-dependent density functional theory
(TDDFT) for excited states, respectively. Argon binding energies were 0.1–0.2 eV,
depending on computational method, adsorption isomer and argon coverage.
The geometric structure of the planar rhombic Au+
4 core remained essentially
unchanged upon complexation of one and two argon atoms. TDDFT calculations
for the lowest-energy-adsorption isomers can roughly describe the measured
spectral bands—although a systematic blue shift of features (by about 0.15 eV)
was observed superimposed on scatter of ±0.1 eV. Transition strengths were
typically not well-enough described to allow fingerprint assignments.
Next, we studied Aun Xe− , n = 7–11 (spectral range 2.1–3.4 eV; Gilb et al.
2004). Fluence dependencies showed the necessity for inert-gas-tracer
measurements at Au−
9 and by inference also at n = 7. Whereas the bare clusters
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Review. Structures of gold-cluster ions
1235
required two or more visible-region photons to dissociate on the experimental time
scale, Au9 Xe− showed a one-photon fluence dependence. Generally, agreement
between depletion spectra of monoxenon adducts and TDDFT predictions
for the corresponding bare-cluster anions using structures determined in our
IMS study was good but better for odd n species. Even n species have
lower vertical-detachment energies than their odd n neighbours, and direct
electron detachment is possible within the wavelength range probed (but not
taken into account in TDDFT calculations of dipolar allowed excitations). The
excitation energies predicted for odd n species were typically within 0.1–0.2 eV
of experimental features. Spectra were therefore consistent with planar cluster
cores. However, the level of agreement was not good enough to allow fingerprint
identification/differentiation of energetically close-lying planar isomers.
Finally, we have recorded the depletion spectra of Aum Ar+
n , m = 7; n = 0–3
and m = 8, 9; n = 0, 1 (Gloess et al. 2008). In the case of the bare clusters,
the spectra were deconvoluted under the assumption that two-photon absorption
(with identical cross sections for first and second photon) is required in order to
obtain dissociation on the experimental time scale. Spectral features recorded for
argon adducts can be described with TDDFT calculations for the most stable
adsorption isomers—to within ca 0.25 eV. They show a slight blue shift with
increasing argon complexation (smaller than that observed for Au+
4 ). Overall, for
n = 0 and 1, there is a change in the centroid of the spectral distributions between
m = 7 and m = 8. This can be rationalized on the basis of TDDFT calculations as
reflecting a corresponding change in topology from planar to three-dimensional.
DFT calculations indicate, as before, that the ground-state cluster core geometries
do not measurably change upon inert-gas complexation.
With regard to geometric structural determination, the direct tools previously
discussed are presently superior to electronic depletion spectroscopy. The corresponding spectra contain many comparatively weak electronic bands that cannot
yet be calculated routinely to predictive accuracies. Furthermore, several adsorption isomers differing slightly in optical spectra may be simultaneously probed.
For further advances in understanding electronic transitions, it is necessary to: (i)
obtain more highly resolved spectra (e.g. using low-temperature ion traps), as well
as (ii) more accurately calculate ground and excited states, e.g. by incorporation
of spin-orbit coupling as well as a better description of inert-gas bonding.
5. Outlook
(a) Determining the structures of larger clusters
This review has discussed gold clusters with up to 20 atoms. With the
experimental methods now available, significantly larger clusters can be
addressed. The present limitation lies in the ability of theory to rapidly and
accurately identify model structures. Whereas, we have acquired TIED data for
clusters with more than 90 atoms, the largest gold-cluster ion we have been
able to assign a structure to is Au−
34 (Lechtken et al. 2007). We find a chiral C3
structure, in agreement with the lowest energy structure predicted by theory. In
addition to the TIED data, photoelectron spectra were simulated and compared
with experimental PES data. In both experiments, the C3 structure gives best
agreement among the model structures considered—including different structural
Phil. Trans. R. Soc. A (2010)
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1236
D. Schooss et al.
(b)
2
(ii)
sM (Å–1)
(i)
1
0
–1
0.5
0
–0.5
–2
Au–34C3
2
4
6
8
10
12
DsM (Å–1)
(a)
s (Å–1)
Figure 10. (a) Minimum energy structure of Au−
34 ((i) side and (ii) top view). The lighter atoms
are internal atoms. (b) Comparison of the experimental (open circles) and simulated (red lines)
reduced molecular scattering function sM from DFT structures. The blue traces (right axis) show
the residuals.
motifs and morphologies. The C3 structure comprises a slightly distorted inner
tetrahedron, of which three faces are covered by a nearly planar arrangement of
six atoms, respectively. The chirality of the structure is most apparent in the
helical arrangement of the edge atoms, as shown in the top view of figure 10.
An intuitive way to rationalize this structure is to start with a 38-atom truncated octahedron, remove a seven-atom hexagonal plane from the bottom of
the truncated octahedron, and then add a triangle on the top, such that an
ABAC stacking results. The resulting C3v structure is then transformed into the
C3 structure by twisting the planes of the cluster with respect to each other
and by repositioning the surface atoms perpendicular to the planes (both steps
under maintaining the C3 symmetry). The transformation removes the (100)
facets of the truncated octahedron and leads to an increased surface density with
a higher coordination number. This ‘surface reconstruction’ leads to a substantial
energy gain (approx. 0.96 eV) and reveals another strategy to minimize the
(surface) energy of a gold cluster, while retaining a dense packing and an optimal
bond length.
(b) Structure-dependent properties: some open experimental questions
Experiments on Au−
10 have recently demonstrated that two non-interconverting
isomers simultaneously present can be separated by means of their widely different
reactivities—the more reactive isomer being in this case ‘titrated’ with O2 to
product (Huang & Wang 2009). Resolution of isomers by temperature-controlled
IMS is also feasible as we have demonstrated above. Recent improvements of ion
transmission through mobility cells suggest that IMS-based preparation of pure
isomers for further (e.g. spectroscopic) study is now possible. Among other things,
this will allow detailed studies of isomer interconversion, e.g. by means of selective
vibrational excitation (or rapid thermal heating). It will also facilitate TIED and
infrared multi-photon dissociation measurements (IR-MPD) on pure isomers—
leading to better structural data at specific sizes/charges. Along the same lines,
adsorbate positional isomers may also be separable by IMS—depending on
binding energies.
Related to structural determinations of adsorbate positional isomers is the
question of restructuring of the cluster core as a result of adsorbate binding. As
discussed above, restructuring has been inferred from calculations of Au7 CO+
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Review. Structures of gold-cluster ions
1237
and Au8 CO+ equilibrium geometries, cf. the bare clusters. It has also been
seen in IR-MPD probes of neutral gold-cluster carbonyls (Fielicke et al. 2005),
and is in fact expected to be quite common for strongly bound adsorbates.
Clearly, information on such structural changes, as well as the associated
thermochemistry and dynamics, are necessary in order to understand the
adsorption reactions/kinetics. Beyond the, as yet only partially understood
CO chemisorption system, adsorbate-induced cluster restructuring is of present
interest for: (i) oxidation catalysis involving supported gold clusters (which could
be modelled via structural characterization of possible intermediates in the gas
phase) and (ii) gold/thiol surface chemistry (structural probes of S–H cleavage
and H2 desorption upon reaction of gold-cluster ions with alkanethiols).
Most of the structural assignments in this paper refer to experiments at
temperatures between 100 and 300 K. In particular, measurements at higher
temperatures are also required, perhaps resolving the transition regime between
few isomer interconversion to more rapid transitions between many local minima.
So far, only neutral and singly charged clusters have been structurally
characterized. More highly charged species should also be looked at. Are
structural isomer types retained or does charge localization lead to dramatic
distortions? What are the global minima and does experiment still deliver them?
Dications are the most easily accessible higher charge-state clusters for the direct
structural-determination methods described above.
With regard to optical properties, apart from the general need for more highly
resolved electronic spectra, it is presently not known to what extent gold-cluster
ions luminesce. Fluorescence quantum yields and emission spectra need to be
acquired as functions of particle size, charge state and adsorbates. A recent
time-resolved pump-probe photoelectron spectroscopy study has shown that Au−
6
has a surprisingly long excited state lifetime—suggesting that fluorescence may,
in fact, be significant (Stanzel et al. 2007). Sufficiently sensitive trapped ion
laser-induced fluorescence (TLIF) setups have recently been developed to allow
analogous experiments on gold clusters (Iavarone et al. 2006).
This research would not have been possible without generous support by Deutsche Forschungsgemeinschaft (as administered by the Karlsruhe Centre for Functional Nanostructures), the
Bundesministerium für Bildung und Forschung (as administered by the Helmholtz-Research
Centre Karlsruhe) and by the State of Baden-Württemberg (as administered by the University
of Karlsruhe). We also thank a number of former collaborators who have contributed to the
work described: Martine Blom, Filipp Furche, Stefan Gilb, Alexia Gloess, Mikael Johansson, Anne
Lechtken, Christian Neiss, Marco Neumaier, Jason Stairs, J. Mathias Weber and Florian Weigend.
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