Communications: Tin cluster anions „Snn
comprise dimers of stable subunits
Anne Lechtken,1Nedko Drebov,2Reinhart Ahlrichs,1,2Manfred M. Kappes,1,2and
1Institut für Nanotechnologie, Karlsruher Institut für Technologie,
Postfach 3640, 76021 Karlsruhe, Germany
2Institut für Physikalische Chemie, Karlsruher Institut für Technologie,
Kaiserstrasse 12, 76128 Karlsruhe, Germany
−, n=18, 20, 23, and 25…
?Received 30 March 2010; accepted 10 May 2010; published online 7 June 2010?
The gas phase structures of tin cluster anions Snn
ion electron diffraction and density functional theory calculations. In the size range of n=18–25
these clusters comprise dimers of stable subunits. In particular Sn18
Sn9and Sn10subunits, respectively. In Sn23
atoms and Sn25
rationalized by the extraordinary stability of the building blocks Sn9, Sn10, and Sn15. © 2010
American Institute of Physics. ?doi:10.1063/1.3442411?
−have been studied by a combination of trapped
−are homodimers of
−two Sn10units are linked by three additional bridging
−is a heterodimer of Sn10and Sn15subunits. This rather unexpected growth mode is
Group 14 elements such as Si, Ge, and Sn show a large
variation in bulk-phase properties reflecting different struc-
tures and bonding characteristics. In contrast with semicon-
ducting silicon and germanium, bulk tin is metallic under
ambient conditions with a body centered tetragonal lattice
??-Sn?. However, the semiconducting covalently bound ?-Sn
?cubic diamond structure? is the thermodynamically most
stable allotrope below 286 K.
The question of whether ligand-free tin clusters can be
classified as metallic or semiconducting has motivated a
large number of experimental and theoretical studies.1,2
Shvartsburg and Jarrold3investigated the overall shapes of
small tin cluster cations Snn
spectrometry ?IMS?. A prolate growth pattern was inferred
up to ?Sn35
pologies in the size range between 35 and 65 atoms. A simi-
lar trend in shape versus size was observed for silicon and
germanium clusters.4The same group also studied the phase
behavior of tin cluster cations uncovering “melting points”
above the bulk value in the size range below 100 atoms.5
These unexpectedly high transition temperatures have be-
come the focus of further experimental5and theoretical
Only few experiments have so far yielded detailed struc-
tural information on tin cluster ions. Singly charged anions
have been investigated by photoelectron spectroscopy.7
Based on trends observed in such measurements, Wang and
co-workers8assigned a semiconductor to metal transition as
occurring between Sn41
inferred that Sn12
structure9by comparing experimental data to theoretical pre-
dictions for various possible geometries. In addition, several
other, purely theoretical investigations have focused on the
geometric structures of small tin cluster anions.10
+up to n=68 using ion mobility
+followed by a transition to quasispherical to-
−. The same group also
−has a slightly distorted empty icosahedral
Recently, we have studied the structural evolution of
small tin cluster anions up to n=15 by a combined experi-
mental and theoretical approach,11which applies IMS and
trapped ion electron diffraction ?TIED? together with density
functional theory ?DFT? calculations. We found compact,
quasispherical structures up to Sn12
icosahedron was confirmed. The larger clusters Sn13
were shown to have prolate structures. In particular, Sn15
was found to have a high-symmetry structure which can be
thought of as comprising two cluster subunits fused through
a common triangular face.
known. For other elements and even larger cluster sizes the
overall shapes can still change significantly with charge
state.12Consequently, it is not clear whether larger tin cluster
anions follow the same prolate shape trend as observed for
cations. By applying TIED and DFT to Sn18
mediate size range in fact have prolate shapes. Furthermore,
the assigned structures all conform to a common “segmented
cluster chain” motif comprising dimers of particularly stable
subunits. This appears to be prototypical for tin cluster an-
ions in this size regime.
TIED in combination with DFT has been extensively
used by us and others for structure determination of metal
clusters ions.13,14Structure assignment using TIED requires
?low-energy? candidate structures for comparison. These
were obtained here by a DFT-based genetic algorithm ap-
proach. Simulated scattering functions from candidate struc-
tures were compared to experimental scattering functions.
Assignments were based on optimal weighted profile factors
agreement between structural model and experimental
are theoretical and experimental modified molecular scatter-
ing functions. The weights wiare calculated from the stan-
−. For Sn12
−, the structures of tin cluster anions are not
−we demonstrate that anionic clusters in the inter-
expt?2. sMtheorand sMexpt
a?Author to whom correspondence should be addressed. Electronic mail:
THE JOURNAL OF CHEMICAL PHYSICS 132, 211102 ?2010?
0021-9606/2010/132?21?/211102/4/$30.00© 2010 American Institute of Physics
dard deviation of the experimental scattering function.14Ad-
ditional information about the experimental method and the
DFT calculation are given in the supplementary material.15
Figure 1 shows selected lowest-energy isomers obtained
from theory for Sn18
as many other higher lying candidate structures were each
compared to the respective TIED measurements. Figure 2
shows a comparison of simulated and experimental reduced
molecular scattering functions for three isomers of Sn23
Additional graphs for other cluster sizes as well as their co-
ordinates are provided in supporting information.15The cor-
responding relative energies and Rw-values are summarized
in Table I. We now briefly discuss each cluster size in turn.
The lowest-energy structure found for Sn18
prises two distinct, interlinked nine-atom tricapped trigonal
prism ?ttp? units ?shaded red in Fig. 1?. The next higher lying
isomer ?18-2? differs only in the relative orientation of its ttp
units. The lowest isomer with a differing structural motif
?18-3?—a ttp connected to a pentagonal bipyramid plus two
−, and Sn25
−. These as well
bridging atoms—is already 0.39 eV above the tentative
ground state ?18-1?. A structure similar to ?18-1? has previ-
ously been proposed for neutral Sn18.2Among the 20 lowest-
energy candidate structures considered, the best agreement of
simulated and experimental scattering functions was found
for ?18-1?, corresponding to a profile factor of Rw=3.1%.
The agreement of structure ?18-2? is poorer as indicated by a
higher profile factor ?Rw=5.3%?. A dominant contribution of
?18-2? to the experiment is unlikely, as a mixture with ?18-1?
does not improve the Rwvalue. Isomer ?18-3? has also a
relatively low profile factor ?Rw=3.8%?; however, a signifi-
cant contribution to the ensemble probed is improbable be-
cause of its high energy.
?0.22 eV? consist of two bicapped tetragonal ten-atom an-
tiprisms ?bta’s? ?blue in Fig. 1?. The lowest-energy structure
?20-1? has been proposed for neutral Sn20by DFT calcula-
tions in combination with electric deflection measurements.16
?20-2? is another isomer from this structure family. Both
structures are able to fit the experimental data well and a
mixture of several isomers with different orientations of the
two bta units cannot be ruled out, as their scattering func-
tions are virtually indistinguishable here. The lowest-energy
structure showing a different structural motif is ?20-3?. It is
composed of a 15-atom unit and a seven atom pentagonal
bipyramid. This isomer shows a large Rw-value and can
therefore be ruled out.
A structural motif consisting of interlinked subunits was
also found for Sn23
connected by three bridging atoms. The tentative ground
state is a C2visomer ?23-1?, which also shows the best agree-
ment with the TIED data ?Rw=2.6%?. Structure ?23-2? dif-
fers in the relative orientation of the two bta units and the
position of the bridging atoms. It is only slightly higher in
energy ?0.07 eV? but shows a significantly larger profile fac-
tor ?Rw=6.0%?. A mixture of ?23-1? and ?23-2? does not
considerably improve the Rw-value. Similarly, contributions
from isomers of other structural compositions e.g., ?23-3? are
−the lowest-energy structures ?within ?E
−. Here, the two compact bta units are
FIG. 1. Selected low-energy structures of Sn18
Note the common building blocks: tricapped trigonal prism ?red?, bicapped
tetragonal antiprism ?blue?, and pentagonal bipyramid ?green?. The cutoff
for drawing a connection between two atoms was chosen ?arbitrarily? to be
−, and Sn25
FIG. 2. Experimental and theoretical modified molecular scattering intensi-
ties sMexpt?black open circles? and sMtheor?red line? for isomers ?1?, ?2?, and
?3? of Sn23
with the experimental error for each isomer. Similar graphs for the other
cluster sizes are given in the supplementary material.
−. Also shown are the differences ?wsM ?blue lines? weighted
TABLE I. Properties and experimental Rw-values for the selected low-
energy isomers of Snn
the point group symmetry and ?E is the relative stability with respect to the
most stable isomer. Rwis the profile factor and defined in the text.?
−, n=18, 20, 23, and 25 shown in Fig. 1. ?G denotes
211102-2Lechtken et al.J. Chem. Phys. 132, 211102 ?2010?
atom bta and a 15-atom cluster. Interestingly, the 15-atom
subunit strongly resembles the ground state structure of
only the tentative ground state ?25-1? is shown in Fig. 1.
They differ only in the relative orientations of their compo-
nent clusters, which are very close in energy ??E
?0.12 eV? and indistinguishable within the error of the
TIED experiment. Similar mixtures of these isomers cannot
be ruled out. However, structures deviating from the 10
+15 motive, e.g., isomers ?25-2? and ?25-3?, show a much
larger profile factor together with a higher energy ?see Table
I? and consequently the probability that they contribute to the
ensemble probed is low.
The calculated next neighbor distances in the tin clusters
studied here span a range from 2.8 to 3.3 Å. Note that the
next neighbor distances within a subunit do not differ signifi-
cantly from the nearest neighbor separations of different sub-
units. The overall range of bond distances are similar to the
distances found in ?-Sn ?2.810 Å? and ?-Sn ?3.016 and
In summary, our results for anions are consistent with
the evolution of elongated prolate shapes as previously found
for tin cluster cations in this size regime by IMS. In addition
we observe a common structural motif: segmented chains of
discrete Snnsubunits. Sn18
of as homodimers whereas Sn25
of two different subunits ?Sn10and Sn15?. In contrast, Sn23
a dimer consisting of two bta units which are indirectly
linked via three additional bridging atoms.
We propose that these observations are related to the
enhanced relative stabilities of the common bta and ttp build-
ing blocks. Evidence for this comes from a closer inspection
of the cluster size dependence of the mean binding energies
per atom ?Eb? as well as the second differences ?SDs? of total
energies for adjacent nuclearities, as determined from DFT
Figure 3 shows the dependence of Ebon 1/n1/3. Furthermore,
in the inset in the same figure, SD is plotted as a function of
cluster nuclearity. Apparently, small tin cluster anions al-
ready have unusually high binding energies. The correspond-
ing values increase with size and reach about ?90% of the
bulk cohesive energy at the surprisingly small cluster nucle-
arity of ten atoms. Similar behavior was predicted by Ma-
jumder et al.2for neutral Sn-clusters. This is in stark contrast
to more typical metal clusters ?e.g., Mgx, Alx, or Pdx?, where
DFT calculations of Ebindicate that a similarly high fraction
of the bulk cohesion energy is only reached at much larger
cluster sizes—well beyond 100 atoms.18
Additionally, the SD plot indicates that the 7-, 10-, and
15-atom clusters have particularly high stabilities relative to
adjacent nuclearities. Similarly, the neutral clusters Sn7and
Sn10were found to be particularly stable.2Consequently, the
observed growth mode can be rationalized as due to a com-
bination of two effects: ?i? an only very gradual further in-
crease in Ebwith size beyond approximately ten atoms and
?ii? the extraordinary stability of the building blocks Sn9,
Sn10, and Sn15?as neutrals and/or anions?. Sn7is an apparent
−is composed of two discrete clusters: a 10-
−.11Several low-energy isomers were found, of which
−is a heterodimer consisting
−may then be thought
exception. Whereas Sn7is observed as a dominant fragment
in collision induced dissociation studies of smaller clusters,11
it was not found as a discrete structural element ?pentagonal
bipyramid? within the medium sized clusters considered
here. However, the Sn7unit is found as higher energy isomer.
This is presently not fully understood but may be due to the
fact that for steric reasons, the pentagonal bipyramid Sn7is
not able to interact strongly with a second subunit. In addi-
tion for the cluster sizes discussed here, only combinations
with less stable Snn
The ?multiply negatively charged? nine-atom subunit, as
ttp or single capped tretragonal antiprism, is well known as
Zintl-ion ?Sn9?−4in binary phases or as ligand stabilized
species.19Recently a 17-atom ligand stabilized cluster
?Sn17?4−was synthesized.20Interestingly, this cluster is com-
posed of two identical Sn9subunits sharing a common vertex
and resembling the structural motif suggested here.
We note in closing that ttp and bta based geometries as
assigned here cannot be directly related to segments of the
bulk tin lattice?s?. However, in the limit of large clusters,
eventually the bulk structure and quasispherical shapes have
to be recovered. IMS experiments have suggested a transi-
tion to quasispherical shapes for Sn-cluster cations beyond
35 atoms. This size range will be the subject of future TIED/
DFT investigations for both anions and cations.
In summary, we have studied and assigned the structures
of medium sized tin cluster anions Snn
25 by a combination of TIED measurements and DFT calcu-
lations, guided by a systematic genetic algorithm structure
search. In all cases, best agreement with the experimental
scattering function is found either for the lowest-energy iso-
mer identified or for an energetically close-lying species.
Clusters in this size range form prolate dimers of stable sub-
units comprising of nine-atom ttp’s and/or ten-atom bta’s.
−- units are possible ?e.g., with Sn13
−, n=18, 20, 23, and
This research was partially supported by DFG-CFN
?TP C4.6? and Helmholtz POF NanoMikro.
FIG. 3. Calculated binding energies Ebof the lowest-energy Snn
?3?n?25? as a function of n−1/3. The lines are to guide the eye only. The
inset shows second differences of total energies for adjacent nuclearities
?SD? as a function of n.
211102-3The structures of tin cluster anionsJ. Chem. Phys. 132, 211102 ?2010?
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−, and Sn25
−, and for atomic coordinates of the structures presented.
211102-4Lechtken et al.J. Chem. Phys. 132, 211102 ?2010?