Homoatomic Stella Quadrangula [Tl8]6 in Cs 18Tl8O6, Interplay of SpinOrbit Coupling, and JahnTeller Distortion

Article abstract of DOI:10.1021/ja1051022

Cs₁₈Tl₈O₆ was synthesized reacting the binary compounds CsTl and Cs₂O. According to single crystal X-ray analysis, the title compound crystallizes as a novel structure type in the cubic space group I23 and is diamagnetic. The electronic structure of the extended solid and of excised Cs₆Tl₈ clusters has been examined by relativistic density functional calculations including spin-orbit coupling. Cs₁₈Tl₈O₆ comprises a clusteranion [Tl ₈]^6- in the shape of a tetrahedral star. An isoelectronic cluster was found previously in Cs₈Tl₈O, however, with the shape of a parallelepiped. Both clusteranions can be derived from a homocubane unit by displacive distortions. It has been shown by quantum mechanical analyses that the closed-shell electronic structure of the parallelepiped is the result of a Jahn-Teller distortion, while in contrast the tetrahedral star in Cs ₁₈Tl₈O₆ would still exhibit an open-shell degenerate HOMO within a scalar relativistic approximation. Only if spin-orbit coupling is considered, a closed-shell electronic system is obtained in accordance with the diamagnetic behavior of Cs₁₈Tl₈O ₆.

Full text of DOI:10.1021/ja1051022

Published on Web 08/12/2010
Homoatomic Stella Quadrangula [Tl8]6- in Cs18Tl8O6, Interplay
of Spin-Orbit Coupling, and Jahn-Teller Distortion
Ulrich Wedig, Vyacheslav Saltykov, Ju¨rgen Nuss, and Martin Jansen*
Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
Received June 11, 2010; E-mail: M.Jansen@fkf.mpg.de
Abstract: Cs18Tl8O6 was synthesized reacting the binary compounds CsTl and Cs2O. According to single
crystal X-ray analysis, the title compound crystallizes as a novel structure type in the cubic space group
I23 and is diamagnetic. The electronic structure of the extended solid and of excised Cs6Tl8 clusters has
been examined by relativistic density functional calculations including spin-orbit coupling. Cs18Tl8O6
comprises a clusteranion [Tl8]6- in the shape of a tetrahedral star. An isoelectronic cluster was found
previously in Cs8Tl8O, however, with the shape of a parallelepiped. Both clusteranions can be derived
from a homocubane unit by displacive distortions. It has been shown by quantum mechanical analyses
that the closed-shell electronic structure of the parallelepiped is the result of a Jahn-Teller distortion, while
in contrast the tetrahedral star in Cs18Tl8O6 would still exhibit an open-shell degenerate HOMO within a
scalar relativistic approximation. Only if spin-orbit coupling is considered, a closed-shell electronic system
is obtained in accordance with the diamagnetic behavior of Cs18Tl8O6.
in an alkaline environment3 and Au- can function as an acceptor
in hydrogen bonds4 and displays a crystal chemistry quite
Introduction
The contraction of the electronic shell of the atoms with
growing nuclear charge is one of the basic factors causing the
periodicity in the properties of chemical elements. Evidently,
this effect, and its consequences for the electronic structure of
an atom, is most substantial for heavy atoms having nuclear
charges higher than ∼50, where the speeds at which the
electrons move in the vicinity of the nuclei are approaching
the velocity of light. At least starting at this point, it is
indispensable to consider the relativistic dependence of the
electron mass on its speed, in the context of electronic structure
calculations. The differences resulting between nonrelativistic
and relativistic quantum mechanical treatments have been
denoted as “relativistic effects”,1 distinguishing direct (contrac-
tion and stabilization of s and p shells, spin-orbit coupling)
and indirect (expansion and destabilization of d and f shells)
effects. Experimentally, significant respective peculiarities in
the chemical and physical properties of heavy elements have
indeed been identified. The most pronounced pertinent features
occur with gold and platinum,1 which can both exist as
monovalent and divalent anions, respectively, in fully charge
ordered bulk solids.2 Furthermore, gold as an anion has been
demonstrated to have a rich and diverse chemistry.1f It widely
resembles the halogens, in that elemental gold disproportionates
analogous to halides.5 However, these conspicuous experimental
findings cannot be straightforwardly attributed to “relativistic
effects”, since gold and platinum are unique in that they are
the first elements that have experienced the d and f contractions
in an immediate sequence. Thus, conventional orbital and
relativistic effects are superimposed.6
Spin-orbit coupling and its enhancement with growing
nuclear charge is of relativistic origin exclusively,7 in contrast
to the orbital contraction and expansion effects. Due to strong
relativistic spin-orbit coupling, the degeneracy of the Russel-
Saunders ground state of a 6p2 configuration is lifted and a
2
diamagnetic ground state (6p1/2
) results. The concomitant
0
lowering in energy is e.g. reflected by the first ionization
potential of lead exceeding the one of bismuth, which has a
half filled p-shell. For all corresponding pairs of lighter elements
the reverse sequence in ionization potentials is observed. We
2
regard Tl- as a candidate to express a closed shell (6p1/2
)
0
configuration in a solid state compound. For example a still
hypothetic solid like Cs3TlO being diamagnetic could only be
(3) (a) Mudring, A.-V.; Nuss, J.; Wedig, U.; Jansen, M. J. Solid State
Chem. 2000, 155, 29–36. (b) Mudring, A.-V.; Jansen, M. Angew.
Chem. 2000, 112, 3194–3196; Angew. Chem., Int. Ed. 2000, 39, 3066-
3067. (c) Nuss, J.; Jansen, M. Z. Anorg. Allg. Chem. 2009, 635, 1514–
1516.
(1) (a) Desclaux, J.-P. At. Data Nucl. Data Tables 1973, 12, 311–406.
(b) Pyykko¨, P. Chem. ReV. 1988, 88, 563–594. (c) Schwerdtfeger, P.,
Ed. RelatiVistic Electronic Structure Theory; Elsevier Science B.V.:
Amsterdam, The Netherlands, 2002. (d) Hess, B. A., Ed. RelatiVistic
Effects in HeaVy-Element Chemistry and Physics; John Wiley & Sons:
New York, 2003. (e) Jansen, M. Solid State Sci. 2005, 7, 1464–1474.
(f) Jansen, M. Chem. Soc. ReV. 2008, 37, 1824–1835.
(4) Nuss, H.; Jansen, M. Angew. Chem. 2006, 118, 4476–4479; Angew.
Chem., Int. Ed. 2006, 45, 4369-4371.
(5) (a) Feldmann, C.; Jansen, M. Z. Anorg. Allg. Chem. 1995, 621, 1907–
1912. (b) Nuss, J.; Jansen, M. Z. Kristallogr. New Cryst. Struct. 2002,
217, 313.
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U.; Jansen, M. Angew. Chem. 2003, 115, 4966–4969; Angew. Chem.,
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9
12458 J. AM. CHEM. SOC. 2010, 132, 12458–12463
10.1021/ja1051022  2010 American Chemical Society

Spin-Orbit Interaction in Thallium Clusters
A R T I C L E S
Jahn-Teller distortion and spin-orbit coupling as two compet-
ing mechanisms to obtain a closed-shell electronic system.
Experimental Method
Because both, educts and products, are very sensitive to air and
moisture, all operations were performed under dried argon (Schlenk
technique or glovebox with H2O, O2 < 0.1 ppm; MB 150B-G-II,
M. Braun GmbH, Mu¨nchen, Germany). Cs18Tl8O6 was prepared
by reaction of the binary compounds CsTl and Cs2O. Cesium
thallide was produced by reaction of cesium (synthesized from CsCl
by reduction with Ca and distilled twice in vacuum)12 with thallium
(ChemPur, Ju¨lich, 99.999%, dried before use at 393 K in dynamic
vacuum at 10-3 mbar during 12 h) in the molar ratio 2:1 (total
amount: 2-3 g) in a tantalum tube which was sealed under argon
with an arc-welder. The reaction mixture was heated with a rate of
50 K/h up to 773 K, annealed at this temperature for 2 days, and
then cooled to room temperature with a rate of 5 K/h. The excess
of cesium was distilled off at 373 K in a dynamic vacuum of 10-3
mbar. Cesium oxide was synthesized from Cs by oxidation with a
slight deficiency of oxygen followed by distillation of the excess
Cs.12 The mixture of CsTl and Cs2O in the molar ratio 1:1 (total
amount 0.5-1 g) was placed into a tantalum tube following the
packing procedure described above. The reaction mixture was
heated at a rate of 50 K/h up to 573 K, annealed at this temperature
for 1 week, and then cooled to room temperature at a rate of 5
K/h. The as-synthesized products were pure, sometimes containing
small amounts of Cs4Tl2O and Cs8Tl11 (1-4 wt %), according to
X-ray powder diffraction. The atom ratio of heavy elements in the
product was additionally confirmed by using a scanning electron
microscope (XL 30 TMP, Philips, Netherlands), equipped with an
integrated EDAX-EDX system.
Figure 1. Graphical presentation of the crystal structure of Cs18Tl8O6 (a)
(Tl8 clusters emphasized as blue polyhedra; OCs6 octahedra in red) and of
KSbO3 (b) (SbO6 octahedra in red; the K atoms are depicted as a corner-
connected array of K8 stellae quadrangulae). Green lines mark the unit cell
edges.
understood in terms of relativistic quantum mechanics. With
the objective of realizing solids containing isolated Tl- anions,
we have started to investigate the systems Rb/Tl/O and Cs/Tl/
O. A number of compounds featuring novel and interesting
structural properties have been obtained from these combinations
of elements;8 however, no evidence for the existence of
“isolated” thallium(-I) was gained. Instead, in each case
thallium cluster ions were identified, corroborating the well-
known propensity of thallium in negative oxidation states to
form homoatomic clusters.9,10 Here we report on Cs18Tl8O6
(Figure 1a) containing a homocubane-like clusteranion with the
shape of a double tetrahedron (stella quadrangula11 or tetra-
hedral star), not found before in compounds containing co-
valently bonded homoatomic clusters. An isoelectronic clus-
teranion was detected previously in Cs8Tl8O,8a however, with
the different shape of a parallelepiped. Both clusters can be
derived from an ideal cube by displacive distortions. In order
to investigate the mechanisms leading to the two different
shapes, scalar and fully relativistic density functional calculations
including spin-orbit coupling have been performed, opposing
Single-crystal X-ray diffraction data of Cs18Tl8O6 were collected
using a Bruker AXS APEX-SMART-diffractometer with a graphite
monochromator and corrected for absorption effects (SADABS).13
The structure was solved and refined with SHELXTL.14 Crystal
structure data of Cs18Tl8O6:15 cubic, I23 (no. 197), a ) 13.3724(3)
Å, V ) 2391.27(9) Å3, Fcalcd ) 5.727 g ·cm-3, Z ) 2, µ(Mo KR) )
40.366 mm-1, F(000) ) 3372, λ ) 0.710 73 Å, T ) 298(2) K,
ω-scan, 18 656 measured reflections, 1316 symmetry independent
reflections (2Θmax ) 69.84°), 27 refined parameters. Atom coor-
dinates: Tl1 (8c) 0.91059(2), x, x; Tl2 (8c) 0.13439(2), x, x; Cs1
(12d) 0.36483(5), 0, 0; Cs2 (24f) 0.21363(3), 0.4483(1), 0.17401(3);
O1 (12e) 0.3270(5), 1/2, 0; R1 ) 0.0248, wR2 ) 0.0519 (1570 F0
> 4σ(F0)); R1 ) 0.0299, wR2 ) 0.0536 (all). Residual electron
density: 1.253/-1.174 e ·Å-3
.
The thermal stability was studied using Differential Scanning
Calorimetry (DSC 404 C Pegasus, Netzsch GmbH, Selb,
Germany). The specimen (0.0184 g) was placed in an Al crucible
with a lid, cold-sealed to prevent access of air and heated to
673 K at a rate of 2 K/min, and then cooled down to room
temperature at the same rate. The whole process was run under
argon. Magnetization was measured using a SQUID magnetom-
eter (MPMS 5.5, Quantum Design, USA) in the temperature
range 5-300 K at H ) 0.001, 0.1, 1, 3, 5, and 7 T. The specimen
(8) (a) Karpov, A.; Jansen, M. Angew. Chem. 2005, 117, 7813–7816;
Angew. Chem., Int. Ed. 2005, 44, 7639-7643. (b) Karpov, A.; Jansen,
M. Chem. Commun. 2006, 1706–1708.
(9) (a) Corbett, J. D. In Structural And Electronic Paradigms In Cluster
Chemistry (Structure and Bonding, Vol. 87); Mingos, D. M. P., Ed.;
Springer-Verlag: Berlin, Germany, 1997; pp 157-193. (b) Corbett,
J. D. Angew. Chem. 2000, 112, 682–704; Angew. Chem., Int. Ed. 2000,
39, 670-690.
(10) (a) Hansen, D. A.; Smith, J. F. Acta Crystallogr. Sect. A: Found.
Crystallogr. 1967, 22, 836–845. (b) Dong, Z.-C.; Corbett, J. D. J. Am.
Chem. Soc. 1994, 116, 3429–3435. (c) Dong, Z.-C.; Corbett, J. D.
Angew. Chem. 1996, 108, 1073–1076; Angew. Chem., Int. Ed. Engl.
1996, 35, 1006-1009. (d) Dong, Z.-C.; Corbett, J. D. J. Am. Chem.
Soc. 1995, 117, 6447–6455. (e) Dong, Z.-C.; Corbett, J. D. J. Cluster
Sci. 1995, 6, 187–201. (f) Huang, D. P.; Dong, Z.-C.; Corbett, J. D.
Inorg. Chem. 1998, 37, 5881–5886. (g) Kaskel, S.; Corbett, J. D. Inorg.
Chem. 2000, 39, 778–782. (h) Dong, Z.-C.; Corbett, J. D. J. Am. Chem.
Soc. 1993, 115, 11299–11303. (i) Dong, Z.-C.; Corbett, J. D. Inorg.
Chem. 1996, 35, 2301–2306.
(12) Brauer, G. Handbuch der Pra¨paratiVen Anorganischen Chemie, Vol.
2; Ferdinand Enke: Stuttgart, Germany, 1978; pp 938-954.
(13) Sheldrick, G. M. SADABS - Bruker AXS area detector scaling and
absorption, version 2008/1; University of Go¨ttingen: Germany, 2008.
(14) Sheldrick, G. M. Acta Crystallogr. 2008, A64, 112–122.
(15) Further details of the crystal structure investigations may be obtained
from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein-
Leopoldshafen, Germany (fax: (+49)7247-808-666; e-mail: crys-
data(at)fiz-karlsruhe.de) on quoting the depository number CSD-
421376.
(11) Hyde, B. G.; Andersson, S. Inorganic Crystal Structures; John Wiley
& Sons: New York, 1989; pp 342-344.
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A R T I C L E S
Wedig et al.
(0.1309 g) was sealed in a quartz tube under helium. The raw
data were corrected for the holder contribution.
Theoretical Methods
DFT calculations using the PBE functional16 were performed
for the crystal structures as determined experimentally as well as
for isolated Cs6Tl8 clusters representing charge neutral cut-outs of
the crystal. The band structures of the periodic systems were
computed with the WIEN2k17 code, using the following compu-
tational parameters. Radii of the atomic spheres: 2.9 bohr (Tl), 2.7
bohr (Cs), and 2.7 bohr (O); cutoff parameter RKmax ) 7.0; Gmax
) 14.0. The Kohn-Sham equations were solved for 119 k-points
in the irreducible wedge of the Brillouin zone. The core-valence
separation was set to -6.0 Ry. Thus 13 electrons of Tl, 19 electrons
of Cs, and 6 electrons of O were taken as valence electrons, being
treated scalar relativistic. The APW+lo basis was applied, added
by local orbitals for l ) 2 (Tl, Cs) and l ) 0 (Cs, O). Spin-orbit
interaction was included by a second-variational method.18 The
isolated Cs6Tl8 clusters were computed with the TURBOMOLE19
program package, applying the RI-variant. The def2-TZVP basis
set was used. Scalar relativistic effects were included by the choice
of the proper pseudopotentials: Tl, 21 valence electrons;20 Cs, 9
valence electrons.21 In the two-component relativistic calculations,
the spin-orbit variant of the Tl pseudopotential was used. In the
scalar relativistic case the structures of the clusters were optimized
with (Oh, Td, and D3d) and without symmetry constraints. The energy
was converged to 10-9 a.u., the maximum norm of the Cartesian
gradient to 10-5 a.u. The existence of a minimum was verified by
a frequency analysis. As analytical gradients are not yet available
in the two component version of TURBOMOLE, the fully
relativistic structure optimizations were done numerically, presum-
ing Oh, Td, and D3d symmetry respectively. Effective charges of
the atoms in the crystals were calculated from the integrated electron
densities within the atomic basins, obtained by a topological analysis
of the electron density.22
Figure 2. Graphical presentation of the crystal structure of Cs8Tl8O:8a Tl8
clusters emphasized as blue polyhedra; Cs8 polyhedra in red, centered by
oxygen.
up to 573 K in an argon atmosphere. The magnetic susceptibility
is temperature independent in the range of 50 to 300 K (-6.84
× 10-4 emu/mol ( 2.5%) and approximates the sum of
diamagnetic core corrections (18ꢀ(Cs+) + 8ꢀ(Tl+) + 6ꢀ(O2-
)
) -9.02 × 10-4 emu/mol) and the Larmor susceptibility24 of
the cluster orbital electrons (-1.91 × 10-4 emu/mol), which
was calculated assuming the shape of an ideal cube with a side
length of 3.111 Å.
Structure. According to the results of an X-ray single-crystal
structure analysis, Cs18Tl8O6 crystallizes in a novel structure
type (Figure 1a) displaying isolated [Tl8]6- units with the shape
of a tetrahedral star, a so-called stella quadrangula,11 and is
the first example of a covalently bonded, homoatomic cluster
with such an arrangement. The oxygen atoms are surrounded
by six cesium atoms in the shape of a distorted octahedron.
The Cs-O distances of 2.936 Å (4×) and 2.862 Å (2×) comply
well with those in Cs2O (2.87 Å),25 which is indicative of a
full ionization of the Cs atoms. The electrons, which are released
from the Cs/O partial structure, are accommodated by the
isolated [Tl8]6- groups. Cesium and oxygen are constituting a
three-dimensional network of corner and edge sharing octahedra
3∞[OCs6/2]+ (Figure 1a). The resulting framework is providing
voids, sufficient in number and size, to accommodate the Tl8
clusters. A similar three-dimensional topology is realized in the
Results and Discussion
Synthesis and Properties. Cs18Tl8O6 was synthesized by
reacting binary CsTl and Cs2O at 573 K, followed by slow
cooling to room temperature in arc-welded tantalum ampules.
The product was obtained as black brittle crystals. The best
results were achieved by reacting the starting materials in a
molar ratio of 1:1, which implies evaporation of excess Cs2O
and Cs from the sample. The purity of the product sensitively
depends on purity, handling, and composition of the starting
mixtures as well as on precise control of the reaction conditions.
Cs18Tl8O6 can be obtained as a single phase. The most frequently
occurring admixtures (1-4 wt %) are Cs4Tl2O23 and Cs8Tl11.10e
Cs18Tl8O6 is extremely sensitive to moisture and air and is stable
(16) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77,
3865–3868.
(17) Blaha, P.; Schwarz, K.; Madsen, G. K. H.; Kvasnicka, D.; Luitz, J.
WIEN2k, An Augmented Plane WaVes + Local Orbitals Program for
Calculating Crystal Properties; Schwarz, K., Ed.; Techn. Universita¨t
Wien: Austria, 2001.
26
KSbO3 structure type (Figure 1b), where the Sb atoms are
surrounded by six O atoms.
The [Tl8]6- Clusteranion. Interestingly, the title compound
and the previously reported Cs8Tl8O8a contain Tl8-clusters
displaying the same number of valence electrons, however, of
different structures, a tetrahedral star (Figure 1a) or a paral-
lelepiped (Figure 2). Both clusters can be formally described
as [Tl8]6- clusteranions having 30 valence electrons available.
(18) Nova´k, P. http://www.wien2k.at/reg_user/textbooks/novak_lecture_
on_spinorbit.ps.
(19) (a) TURBOMOLE V6.1, University of Karlsruhe and Forschungszen-
trum Karlsruhe GmbH, TURBOMOLE GmbH, http://www.
turbomole.com, 2009. (b) Armbruster, M. K.; Weigend, F.; van
Wu¨llen, C.; Klopper, W. Phys. Chem. Chem. Phys. 2008, 10, 1748–
1756.
(20) Metz, B.; Schweizer, M.; Stoll, H.; Dolg, M.; Liu, W. Theor. Chem.
Acc. 2000, 104, 22–28.
(24) (a) Ashcroft, N. W.; Mermin, N. D. Solid State Physics; Holt, Rinehart
and Winston: Philadelphia, 1976; p 649. (b) Sevov, S. C.; Corbett,
J. D. Inorg. Chem. 1992, 31, 1895–1901.
(21) Leininger, T.; Nicklass, A.; Ku¨chle, W.; Stoll, H.; Dolg, M.; Bergner,
A. Chem. Phys. Lett. 1996, 255, 274–280.
(25) Tsai, K.-R.; Harris, P. M.; Lassettre, E. N. J. Phys. Chem. 1956, 60,
338–344.
(22) Bader, R. F. W. Atoms in Molecules: a Quantum Theory; Oxford
University Press: Oxford, 1990.
(26) Spiegelberg, P. ArkiV foer Kemi, Mineralogi och Geologi 1940, A14,
1–2.
(23) Saltykov, V.; Nuss, J.; Jansen, M. Unpublished results.
9
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Spin-Orbit Interaction in Thallium Clusters
A R T I C L E S
Figure 3. Optimized structures of Cs6Tl8 clusters. The shapes of the Tl8 units conform to the polyhedra found in Cs18Tl8O6 (left, tetrahedral star) and in
Cs8Tl8O (right, parallelepiped). The symmetry-unique computed (two component relativistic, PBE, def2-TZVP) Tl-Tl distances are given in Å. The
corresponding experimental values found for the crystal are added in parentheses.
Neither of them can be understood in terms of known qualitative
concepts. Within the Zintl-Klemm concept, which is based on
2e2c bonds, the number of valence electrons should be 40 (12
edges × 2e + 8 inert pairs) for both, the tetrahedral star and
the parallelepiped. Also applying Wade’s rules fails: a closo
cluster [Tl8]6- would require 34e (4 × 8 + 2, inert-electron
pairs included), which is in conflict with the 30e available. The
[Tl8]6- cluster can best be denoted as hypoelectronic9b with
2n-2 skeletal electrons (14e, disregarding 2 × 8e for the lone
pairs).
Electronic Structure Calculations. Topologically, both Tl8
units considered can be derived from an ideal cube by a
displacive distortion as sketched in Figure 3. Remarkably, in
either case the lattice symmetries would allow accommodation
of Tl8 units of cubic shape since the site symmetries are
subgroups of Oh. Moreover, the nearest neighbors (Cs+ ions)
do exert but a weak crystal field, and their positions could either
be easily reconciled with a high symmetric clusteranion by slight
displacive movements (Cs8Tl8O) or already display the higher
symmetry (Cs1 × 6: Oh) in comparison to the tetrahedral star
(Td) in Cs18Tl8O6. In order to understand the driving forces
behind the distortions, and thus to resolve these puzzling
inconsistencies, we have performed density functional (DFT)
calculations on the periodic crystals as well as on respective
isolated Cs6Tl8 clusters for both compounds. As both cluster-
anions derive from a cube, a hypothetical Cs18Tl8O6 crystal with
an ideal cubic Tl8 unit (side length: 3.11 Å) was also examined.
All the results discussed in the following are based on the PBE16
functional for exchange and correlation. Data obtained with a
hybrid functional, remarks on basis set effects, and further
details, especially on the scalar relativistic calculations, can be
found in the Supporting Information.
Figure 4. Total densities of states (DOS) near the Fermi level of Cs18Tl8O6
(a and b), hypothetical Cs18Tl8O6 with cubic Tl8 unit (c), and Cs8Tl8O (d
and e). Gray: without spin-orbit coupling (a and e); black: including
spin-orbit coupling (b, c, and d).
The periodic DFT calculations for the Cs18Tl8O6 crystal at
the scalar relativistic level result in a spin-polarized electronic
system with a finite density of states (DOS) of the majority
spin component at the Fermi level (Figure 4a), indicating half-
metallic properties of the crystal, which is in contrast to the
observed diamagnetism. This discrepancy is resolved, however,
if relativistic spin-orbit coupling is included in the calculations.
The spin polarization vanishes, and a gap (0.18 eV) between
valence and conduction bands in the crystal opens (Figure 4b
and first column in Figure 5). The band structure of Cs8Tl8O
looks similar. However, in contrast to Cs18Tl8O6, for this
compound no spin polarization but a band gap results already
at the scalar relativistic level (Figure 4e). Considering spin-orbit
coupling does not change the electronic structure of Cs8Tl8O
in principle (Figure 4d and columns 5-7 in Figure 5).
Calculations on the hypothetical Cs18Tl8O6 crystal with the ideal
cubic Tl8 unit yield a finite DOS at the Fermi level even with
spin-orbit coupling (Figure 4c).
The analysis of the charge distribution by a topological
analysis of the computed electron density22 does not provide
an explanation for the different shapes of the Tl8 units in either
compound Cs18Tl8O6 or Cs8Tl8O. The effective charges are quite
similar (Cs18Tl8O6: Tl1 -0.44, Tl2 -0.49, Cs1 +0.68, Cs2
+0.67, O -1.40; Cs8Tl8O: Tl1 -0.46, Tl2 -0.50, Cs1 +0.65,
Cs2 +0.64, O -1.39), revealing a charge transfer of comparable
size to the Tl8 unit (Cs18Tl8O6: -3.68; Cs8Tl8O: -3.78).
9
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A R T I C L E S
Wedig et al.
Figure 5. Density of states (DOS) of the crystals and MO diagrams of the Cs6Tl8 clusters. Left side: Cs18Tl8O6 and tetrahedral star; right side: Cs8Tl8O and
parallelepiped. The diagrams show scalar relativistic MOs (majority spin, column 3 and 5; occupied: black; partially occupied: gray; unoccupied: red), fully
relativistic spinors (column 2 and 6), and DOS including spin-orbit coupling (column 1 and 7; total DOS: gray; Tl-projected DOS: black). EF and ꢀHOMO
are shifted to 0 eV.
Effective charges derived from quantum chemical calculations
suffer in some respect from arbitrariness.27 Nevertheless, as
effective charges tend to be lower than formal charges,28 the
high cumulative negative charge in the Tl8 units justifies their
formal description as [Tl8]6-. Moreover, it suggests discussion
of the peculiarities of the clusteranions in a local picture,
comparing the electronic structures obtained on the various types
of excised, charge neutral Cs6Tl8 molecular units (clusters) with
those calculated for the extended solids.
Tl8-cube is 79 kJ/mol less stable than the tetrahedral star. It
will be worthwhile to analyze the ratio of electrostatic and
relativistic forces contributing to the Jahn-Teller coupling of
this cubic cluster according to the procedure as described in ref
29 for tetrahedral systems. This will be subject to future
investigations.
For comparison of the DOS of the extended structures with
the MO diagrams calculated for the isolated cluster types (Figure
5), the atom-projected DOS of the oxygen atoms (at -1 to -2
eV) can be disregarded. The spatial separation and the shielding
by the Cs atoms render any covalent interaction with the
clusteranions insignificant. Besides the O-projected DOS, only
contributions of the interstitial space and of the Tl atoms are
found at energies above -8.2 eV. The latter are highlighted in
Figure 5. The cluster MOs map very well onto the Tl-projected
DOS in both cases, Cs18Tl8O6 and Cs8Tl8O. The respective
partial DOS in the valence region split into two parts. Below
-4 eV, eight very narrow, partially degenerate bands appear
per Tl8 unit, which correspond to the lower MOs of the cluster
in the same energy region. This part of the electronic structure
can be attributed to the inert-electron pairs of the Tl atoms. The
marginal dispersion of these bands points to a high localization.
In the nonrelativistic limit, the corresponding energy levels are
shifted upward by more than 1 eV, indicating that these bands
are stabilized significantly by scalar relativistic effects. The
bands between -1 eV and EF (set to 0 eV) correspond to
the 14 skeletal electrons of the n-atomic cluster (2n-2). The
pronounced similarity of the MO patterns of the Cs6Tl8 clusters
and the densities of states of the extended crystals as well as
the analogies concerning the open- and closed-shell electronic
structures support the view of covalently bonded clusteranions.
The ideal cubic arrangement leads to an open shell system
at any level of theory applied in this work. Its stretching along
the body diagonal leading to the parallelepiped in Cs8Tl8O can
be regarded as a Jahn-Teller distortion, resulting in a closed-
The results for the molecular units are based on optimized
structures. When spin-orbit coupling is neglected, the lowest
minimum found on the potential energy surface with no
symmetry restrictions corresponds to a Tl8 unit with the shape
of a parallelepiped with D3d symmetry (Figure 3, right side),
comparable to the Tl8 unit found experimentally in Cs8Tl8O.
The Cs atoms take roughly the positions of Cs1 in the crystal.
This minimum is a closed-shell singlet state. If the symmetry
is constrained to Td, which is the symmetry of the tetrahedral
star in Cs18Tl8O6, the minimum corresponds to an open-shell
triplet state which is 13 kJ/mol lower than an open-shell singlet
of same symmetry. But even the triplet state is less stable by
24 kJ/mol than the parallelepiped. If, however, fully relativistic
calculations including spin-orbit coupling are performed, both
the parallelepiped and the tetrahedral star configuration are
closed-shell systems and, moreover, the energetic order of both
configurations is reversed: The tetrahedral star is now 13 kJ/
mol more stable than the parallelepiped. Thus the contribution
of spin-orbit coupling to the stabilization of the tetrahedral star
amounts to 37 kJ/mol. The optimized Tl-Tl distances in both
configurations are represented in Figure 3, together with the
corresponding distances measured in the crystals. If the sym-
metry is constrained to Oh, forcing a cubic arrangement of the
Tl atoms, the cluster remains an open-shell system (〈Sz〉 ) 0.54)
even with spin-orbit coupling. Such a cluster with an ideal
(27) Jansen, M.; Wedig, U. Angew. Chem. 2008, 120, 10176–10180; Angew.
Chem., Int. 2008, 47, 10026-10029.
(29) Opalka, D.; Segado, M.; Poluyanov, L. V.; Domcke, W. Phys. ReV. A
2010, 81, 042501.
(28) Meister, J.; Schwarz, W. H. E. J. Phys. Chem. 1994, 98, 8245–8252.
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12462 J. AM. CHEM. SOC. VOL. 132, NO. 35, 2010

Spin-Orbit Interaction in Thallium Clusters
A R T I C L E S
shell electronic system. In Cs18Tl8O6 the situation is more
complicated. The tetrahedral star results from moving the two
subsets of each of the four tetrahedrally arranged Tl atoms
constituting the cube inward and outward, respectively, and still
maintains a high symmetry (Td). In a scalar relativistic MO
picture, such an arrangement cannot be understood in terms of
the Jahn-Teller theorem, as in this case the compound would
still take a spin-polarized, open-shell electronic structure. Only
in a fully relativistic treatment, which includes spin-orbit
coupling, the tetrahedral star becomes a closed-shell electronic
system, in accordance with the experimental findings. At this
level of theory, the tetrahedral star can be regarded as a
Jahn-Teller distorted cube. The stabilization of the clusteranion
due to spin-orbit interaction has turned out to be much larger
for the tetrahedral star than for the parallelepiped. Thus both
shapes of [Tl8]6- become competitive local minima on the
potential energy surface, and both shapes are realized in
compounds of the Cs/Tl/O system, depending on the ratio of
the three constituents.
Cs8Tl8O, which has the same number of (valence) electrons but
a different structure compared to the one in Cs18Tl8O6, the
correct structure is already reproduced on the scalar relativistic
level. Since a regular cube [Tl8]6- would display an open-shell
degenerate ground state, the distortion encountered in Cs8Tl8O
can be completely understood in terms of the Jahn-Teller
theorem. Spin-orbit coupling does not yield in a qualitatively
different ground state, but results in a destabilization relative
to the tetrahedral star, thus making both cluster configurations
competitive. The discrimination between the kind of cluster
realized depends on the boundary conditions imposed on the
overall structures of the hosting extended solids. The higher
content of Cs2O in Cs18Tl8O6 ) Cs6Tl8 ·6Cs2O as compared to
Cs8Tl8O ) Cs6Tl8 ·Cs2O alone already enforces substantially
different crystal structures.
Furthermore, our analyses revealed traditional approaches
admissible to qualitatively addressing the causal relationship
between electron counts and structures of clusters, which like
e.g. the Zintl-Klemm concept or Wade’s rules are based on
considering isolated clusters, excised from the solid. Our
treatments regarding the [Tl8]6- clusters embedded in the solid
or as charge neutral Cs6Tl8 units have rendered rather consistent
results. In light of the new insights provided, it appears
worthwhile to revisit the extended family of homoatomic
thallium cluster ions, which have so far been eluding a coherent
and conclusive interpretation of their electronic structures, in
striking contrast to boron based clusters to which the classical
rules nicely apply.
Conclusions
Following a fundamental principle in chemistry, given
configurations tend to stabilize by opening a gap between the
highest occupied and the lowest unoccupied electronic states.
As a special manifestation of this principle, highly symmetric
species with degenerate frontier orbitals stabilize by geometric
distortion, thus lifting electronic degeneracy and arriving at a
closed-shell system (Jahn-Teller or Peierls distortion). In the
cluster chemistry of heavy main group elements, spin-orbit
coupling is an alternative mechanism leading to a nondegenerate
HOMO. Here, we present the first experimental evidence for
such a mechanism that was previously disclosed theoretically
e.g. for Pb clusters.19b Quantum chemical calculations, both for
the extended solid and for excised, charge neutral molecular
units, clearly show that a closed-shell electronic system in
accordance with the magnetic properties is achieved for the
highly symmetric tetrahedral star in Cs18Tl8O6 only if spin-orbit
coupling is taken into account.
Acknowledgment. The authors thank E. Bru¨cher for performing
the magnetic measurements.
Supporting Information Available: Crystallographic informa-
tion file (CIF); checkCIF report; coordinates file of various
structures of Cs6Tl8; further DOS diagrams; additional compu-
tational results concerning the molecular units, basis sets, and
functionals. This material is available free of charge via the
Internet at http://pubs.acs.org.
Moreover, spin-orbit interaction not only influences the
electronic state but also changes the relative energies of various
cluster configurations. For the [Tl8]6- cluster contained in
JA1051022
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J. AM. CHEM. SOC. VOL. 132, NO. 35, 2010 12463