Zn gen chemphys2007

Available online at www.sciencedirect.com

Chemical Physics 342 (2007) 253–259
www.elsevier.com/locate/chemphys

The growth behaviors of the Zn-doped different sized
germanium clusters: A density functional investigation
Jin Wang
b

a,1

, Ju-Guang Han

b,*

a
Department of Chemistry, University of Guelph, Guelph, Ontario, Canada N1G 2W1
National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230026, People’s Republic of China

Received 11 July 2007; accepted 17 October 2007
Available online 22 October 2007

Abstract
Growth behaviors of the Zinc doped germanium clusters are systematically investigated by using density functional method. The
growth-patterns, relative stabilities, charge-transfers, highest occupied molecular orbital–lowest unoccupied molecular orbital
(HOMO–LUMO) gaps and polarities of these clusters are discussed in detail. The threshold size of the Zn-encapsulated germanium clusters emerges as n = 10 while the icosahedral ZnGe12 cluster has stronger relative stability as compared to other sized clusters, which differs from the first-row unfilled d orbitals transition metal doped germanium clusters. The calculated fragmentation energies manifest that
the magic numbers of relative stabilities for the Zn-doped germanium clusters are 5, 9, and 12. Natural population analyses show that
charges transfer from the Zn to the germanium framework. It is worth pointing out that the HOMO–LUMO gap of the icosahedral
ZnGe12 is remarkably large (3.159 eV) in comparison with other sized caged ZnGen (n = 1–11, 13) clusters.
Ó 2007 Elsevier B.V. All rights reserved.

Keywords: Clusters; Geometry; Electronic structure; Computational investigation

1. Introduction
Currently, theoretical and experimental investigations
on the transition metal (TM) doped silicon and/or germanium clusters reveal a novel way contributing to strengthening clustered stability [1–8]. As for the semiconductor
germanium clusters, the TM-doped large-sized caged germanium clusters (n = 14–16) have been investigated by
using ab initio pesudopotential plane wave methods with
spin-polarized generalized gradient approximation [9] indicating that the growth behaviors of metal encapsulated
germanium clusters are different from those of metal

*

Corresponding author. Fax: +86 551 514107.
E-mail address: (J.-G. Han).
1
On leaving from National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230026, People’s
Republic of China.
0301-0104/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.chemphys.2007.10.008

encapsulated silicon clusters. The larger HOMO–LUMO
gaps and the weaker interactions between the clusters make
these species attractive for germanium clustered assembled
materials. In addition, the anion binary CoGeÀ
10 cluster
with high abundance in mass spectrum has been produced
by laser ablation and the bicapped tetragonal antiprism is
assigned as the most stable structure for these cluster series
[10]. Our previous investigations [11,12] on the first-row
TM (TM = Ni and Cu) with unfilled d subshell doped

germanium clusters indicate the threshold number at which
the endohedral coordination is favored at n = 10, which is
different from many TM-doped silicon clusters. However,
to our knowledge, there is no detailed investigation on
the growth behaviors of the TM (with filled d orbitals)
doped germanium clusters, e.g., the growth pattern, the
sized selectivity, the charge-transfer, etc. In this paper,
transition metal zinc doped germanium clusters with size
varying from the small-size clusters to the relative large-size
clusters are investigated.


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J. Wang, J.-G. Han / Chemical Physics 342 (2007) 253–259

2. Computational details
The geometry optimizations of the ZnGen (n = 1–13)
clusters are carried out by using density functional theory
(DFT) with the (U)B3LYP exchange-correlation potential
[13,14] and standard 6-31G basis sets. The polarization
basis sets are not considered in this work because our previous work showed that they are insignificant to our results
[6]. In order to test the reliability of our calculations, the
Zn2 dimer is calculated and Zn–Zn bond distance of
˚ , which is in good agreement with
ground state is 2.77 A
˚ [15,16] and some
ideal Zn–Zn bond distance of 2.70 A
˚
experimental values of 2.3–2.94 A in solid crystal structures

[17–20]. One can find that the calculated results of the Ge2
and Zn2 clusters are in good agreement with the reported
theoretical or experimental results that are available
[11,12,17–20]. It can be concluded that the calculated
results at the UB3LYP/6-31G level are accurate and reliable in the present work.
Equilibrium geometries of the Gen clusters were
optimized previously [12]. On the basis of the previous
optimized Gen geometries, different evolution patterns for
determining the different sized ZnGen isomers, i.e., Zn
capped, Zn substituted and Zn concaved patterns as well
as Ge-capped pattern, are taken into accounts. Furthermore, different spin states of ZnGen clusters are considered
and calculated by using the Gaussian-03 program package
[21] and the calculated results indicate that the ground
states of the ZnGen (n = 1–2) correspond to spin triplet
state; however, spin singlet state for each isomer is the lowest-energy state as compared to other spin states of this
unit when the size of the ZnGen clusters exceeds 2. The
detailed calculated results and discussions are followed.
3. Results and discussions
3.1. The Zn exohedral doped ZnGen (n = 1–9) clusters
As seen from the optimized small-sized ZnGen (n = 1–3)
geometries, the symmetric triangular ZnGe2 structure is
slightly weaker in stability than the non-symmetric triangular structure in that total energy of the former is higher
than that of the latter by 0.08 eV. Moreover, their triplet
states of the ZnGen (n = 1–2) clusters are obviously lower
in total energies than the singlet states, indicating that the
ground states for the ZnGe and ZnGe2 clusters are the triplet spin states, the correspondingPelectronic states for the
ZnGe and ZnGe2 clusters are 3
and 3A00 , respectively.
The singlet state of the rhombus Cs ZnGe3 3a isomer is
optimized to be a stable structure while the spin triplet state

of the bent rhombus 3b structure is a stable state; furthermore, the singlet spin state is the ground state and the corresponding electronic state is 1A 0 . Consequently, beginning
from the ZnGe3 clusters, the electronic spin state of the
lowest-energy structure varies from spin triplet state to spin
singlet state. As the size of clusters grows up to 4, the Zn
exohedral Gen clusters are formed. Two different ZnGe4

geometries are found as the stable structures; the 4a structure is described as the Zn atom being only bonded with
the planar rhombus Ge4 frame, and the 4b isomer is shown
as the Zn atom being face-capped on bent rhombus Ge4
framework and interacting with two germanium atoms
directly. Furthermore, on the basis of the calculated total
energy, the lowest-energy ZnGe4 structure is confirmed to
be the 4b isomer which is similar to those of the NiGe4
and CuGe4 molecules [11,12].
Two kinds of bi-pyramidal ZnGe5 geometries are found
as the stable structures. As seen from Fig. 1, difference
between 5a and 5b geometries lies in the Zn position in
the bi-pyramidal frames. It should be pointed out that
the 5a and 5b isomers are generated from different lowsized molecules. That is: the 5a is generated from rhombus
ZnGe3 3a structure when the two germanium atoms are
capped on top and bottom of the planar rhombus; for
the 5b isomer, it is obtained from the ZnGe4 4b above.
As illustrated in Table 1, the 5a is more stable than the
5b, reflecting that the 5a is the lowest-energy structure,
which is different from those of the CuGe5 and NiGe5
isomers [11,12]. However, the most stable 4b and 5a clusters are depicted as the Zn atom being face-capped on
the most stable Gen (n = 4 and 5) clusters [11] (Table 2).
On the base of the multi-rhombus Ge7 cluster [11], the
ZnGe6 6a isomer can be obtained when one Ge atom is
substituted by the Zn atom. Another stable 6b structure

can be formed if the bottom Ge atom in the tricapped
rhombic Ge7 cluster is replaced by the Zn atom. In addition, the stable 6c structure is yielded when the Zn atom
is directly capped on the boat-like Ge6 cluster. As compared to the calculated total energies of the 6a and 6c
isomers, the 6b isomer is selected as the lowest-energy
ZnGe6 cluster, the most stable 6b geometry is different
from those of the NiGe6 and CuGe6 clusters [11,12].
The exohedral ZnGen structures, however, are still dominant structures when the size of clusters increases to 7. The
7a is optimized to be the lowest-energy structure while two
multi-rhombus 7b and 7c isomers are found as the stable
structures as compared to the 7a isomer. As seen from all
optimized low-lying ZnGe7 structures, no stable Zn-concaved Ge7 structure appears at this size. It should be mentioned that the obvious divergence of the growth behaviors
for the TMGen (TM = Ni and Zn) clusters appears at n = 7
as compared to the previous investigation on the NiGen
clusters. The stable endohedral NiGen structures emerge
at n = 7 and gradually become dominant structures when
the size of n > 7 [12].
As far as the ZnGe8 clusters are concerned, the low-lying
stable geometries are different from those of the stable
NiGe8 structures [12]. The initial geometry obtained with
one Zn atom being capped on the multi-rhombic Ge8 frame
is finally optimized to be the Zn-convex 8a structure.
Another tetrahedral pyramidal 8b geometry is optimized
to be a stable isomer and its total energy is lower than that
of the 8a isomer; one stable 8d structure is generated when
one Ge atom is capped on the low-rhombus Ge4 unit of the


J. Wang, J.-G. Han / Chemical Physics 342 (2007) 253–259

255

Table 1
Geometries and total energies of the ZnGen (n = 1–13) Clustersa
Clusters

Sym.

Freq. (cmÀ1)

ZnGe

C1v

219.4

À3853.8951672

ZnGe2

Cs(a)
Cs(b)

154.5
39.5

À5928.7460122
À5928.7487606

ZnGe3

Cs(a)
Cs(b)

92.0
39.9

À8003.6857308
À8003.6462131

ZnGe4

C1(a)
C1(b)

48.1
19.9

À10078.5513132
À10078.5547701

ZnGe5

Cs(a)
C2v(b)

16.7
51.4

À12153.5067159
À12153.4944199

ZnGe6

C1(a)
C2v(b)
C1(c)

29.1
87.9
41.1

À14228.3883442
À14228.4097478
À14228.3645709

ZnGe7

C1(a)
C1(b)
Cs(c)

56.7
29.3
37.5

À16303.3033272
À16303.2917688
À16303.2839307

C1(a)

C1(b)
C1(c)
C1(d)
C1(e)

19.1
69.7
53.9
45.7
50.8

À18378.2097996
À18378.2111839
À18378.2018176
À18378.2047752
À18378.1662103

C1(a)
C1(b)
Cs(c)

65.0
56.2
60.7

À20453.1469357
À20453.1125729
À20453.1091569

0.94

1.03

C1(a)
C1(b)
C1(c)

31.1
58.1
53.3

À22528.0729217
À22528.0668902
À22528.0530808

0.16
0.54

C1(a)
C1(b)
C1(c)
C1(d)
C1(e)
C1(f)

49.8
60.4
65.8
45.9
27.9
38.7

À24602.9258323
À24602.9596197
À24602.9867675
À24602.9548540
À24602.9642856
À24602.9355404

1.66
0.74

ZnGe12

C1(a)
C1(b)
C1(c)
C1(d)
C1(e)

33.1
72.7
42.4
33.8
104.1

À26677.9023734
À26677.8444670
À26677.8789696
À26677.8704576
À26677.9289224

0.72
2.30
1.36
1.59

ZnGe13

C1(a)
C1(b)
C1(c)

29.1
31.2
40.9

À28752.7847589
À28752.7810418
À28752.7889657

0.11
0.22

ZnGe8

ZnGe9

ZnGe10

ZnGe11

ET (hartree)

DE (eV)

0.08

1.08
0.09

0.33
0.58
1.23
0.31
0.53
0.04
0.25
0.17
1.22

0.87
0.61
1.39

a
Sym. means point-group symmetry. Freq. represents the lowest
vibrational frequency. ET denotes the total energies of different ZnGen
structures. DE denotes relative energy of every conformer and the lowestenergy identical sized cluster.

Fig. 1. All the equilibrium geometries of ZnGen (n = 1–9) clusters, stars

show the lowest-energy ZnGen (n = 1–9) structures.

multi-rhombic ZnGe7 7c isomer. As for the ZnGe8 isomers,
the doped Zn is not concaved into the germanium frame.
However, the Ni-concaved NiGe8 geometry is the most stable isomer [12] indicating that the growth behavior of the
NiGe8 isomers is actually different from ZnGe8 isomer
and the doped Ni atom tends to form the Ni-encapsulated
Gen structure when the size of n P 8 (Fig. 2).
The stable Zn-absorbed 9a is generated when one Zn
atom is capped on the outside of the irregular polyhedron


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J. Wang, J.-G. Han / Chemical Physics 342 (2007) 253–259

Table 2
Natural charge population, HOMO–LUMO gap, and dipole moment of
the located-energy structures with the spin singlet state of different sized
ZnGen (n = 3–13) clusters
Clusters

Natural
population

HOMO–LUMO gap
(eV)

Dipole moment
(D)

ZnGe3
ZnGe4
ZnGe5
ZnGe6
ZnGe7
ZnGe8
ZnGe9
ZnGe10
ZnGe11
ZnGe12
ZnGe13

0.765
1.015
0.936
1.125
1.010
1.028
1.032
1.056
1.103
1.011
1.179

3.200
1.733
2.286
2.216
2.230

1.859
2.195
2.106
1.896
3.160
1.851

2.733
2.259
2.647
1.952
1.554
1.736
1.331
0.393
0.571
0.013
0.819

Ge9 cluster. Based upon the ZnGe8 8a structure, the Ge
edge-capped pattern gives rise to a stable ZnGe9 9b structure with the Zn atom being localized at outside of the
Ge9 polyhedron. On the basis of the optimized geometries
and calculated total energies of the ZnGe9 isomers, it
should be mentioned that the stability of the ZnGe9 isomers with Zn-absorbed on the germanium polyhedron is
relative weaker as compared to the Zn-convex Ge9 9c structure in that the total energy of 9c is higher than that of the
lowest-energy 9a structure by 1.03 eV.
3.2. Zn-encapsulated ZnGen (n = 10–13) clusters
Beginning from the ZnGe10 clusters, an obvious divergence of growth behaviors between small-sized ZnGen clusters and relatively large-sized ZnGen clusters is revealed.
When the number of Ge atoms in the Zn-doped Gen clusters is up to n = 10, the Zn-encapsulated Gen structures are
formed. Similar to the multi-rhombic or bicapped tetragonal antiprism TMGe10 (TM = Ni and Cu) isomers [11,12],

the analogous ZnGe10 10a geometry is also optimized to be
the most stable isomer. The stability of the 10a isomer is
stronger than that of the surface-substituted ZnGe10 10b
isomer because the 10a is lower in total energy than the
10b isomer. The previous investigation on the NiGen isomers is a guide, the Zn-convex 11a and 11b structures,
the Zn-concaved 11c, 11d, and 11e structures, and the Zn
surface-inserted 11f structure are optimized to be the stable
geometries. For the stable ZnGe11 clusters, the Ge-capped
pentagonal antiprism 11c geometry is found to be the lowest-energy structure. Furthermore, the most stable 11c isomer keeps the geometry that is analogous to that of the
most stable NiGe11 cluster [12].
As far as the ZnGe12 isomers are concerned, the
bicapped pentagonal prism, which is analogous to the most
stable NiGe12 geometry [12], is not optimized to be the lowest-energy structure. Among all the optimized stable isomers, the Zn capped basket-like 12b isomer is determined
to be the weakest structure in stability. Surprisingly, the
icosahedral stable 12e structure is much lower in total

Fig. 2. All the equilibrium geometries of the ZnGen (n = 10–13) clusters,
stars show the lowest-energy ZnGen (n = 10–13) geometries.

energy than those of other isomers and is selected as the
most stable isomer, which is in good agreement with the
previous icosahedral ZnGe12 isomer calculated by using
ab initio ultrasoft pesudopotential plane wave method
[22]. On the basis of the calculated results and the natural
charge analyses, it is found that the Zn atom in the most
stale 12e isomer acts the same behavior as the Cu atom
in the most stable CuSi12 isomer [23]; furthermore, the d
orbitals of the Zn atom in the most stable 12e act as core
without taking part in the chemical bonds. According to
the previous investigation on the TM-encapsulated silicon

clusters, the metal encapsulated hexagonal prism is proven
to be the lowest-energy geometry [23]; however, the analogous TM at Ge12 (TM = Ni, Cu, and Zn) geometries are


J. Wang, J.-G. Han / Chemical Physics 342 (2007) 253–259

not the most stable ones; furthermore, the growth behaviors of the TM-doped Gen clusters are obviously different
from those of the TM-doped Sin clusters [8,23]. In addition,
it should be mentioned that the icosahedral NiGe12 is proven to be an unstable structure which has one imaginary
vibrational frequency.
On the basis of the two typical ZnGe12 structures, i.e.,
the bicapped pentagonal prism and hexagonal prism, two
stable ZnGe13 13b and 13c isomers are considered and
optimized, the calculated results show that the 13c isomer
is the most stable geometry.
To sum up, in analogy to the TM with unfilled d orbitals
doped Gen clusters, the critical size of the Zn-encapsulated
caged germanium clusters emerges at n = 10. Different
from the TM at Ge12 (TM = Ni, Cu) clusters, the icosahedral ZnGe12 geometry is proved to be the lowest-energy
structure in comparison to the irregular basket-like or
bicapped pentagonal ZnGe12 structures.

257

Fig. 3. Sized dependence of the atomic averaged binding energies of
ZnGen (n = 3–13) clusters.

3.3. Sized selectivity of the ZnGen clusters
The sized selectivity of the Zn-doped germanium clusters can be reflected from the atomic averaged binding
energy and fragmentation energy. The atomic averaged

binding energies and fragmentation energies of the
Zn-doped germanium clusters can be calculated from the
following formula:
Eb ðnÞ ¼ ½ET ðZnÞ þ nET ðGeÞ À ET ðZnGen ފ=n þ 1
Dðn; n À 1Þ ¼ ET ðZnGenÀ1 Þ þ ET ðGeÞ À ET ðZnGen Þ
where ET(ZnGenÀ1), ET(Ge), ET(Zn), and ET(ZnGen) represent the total energies of the lowest-energy ZnGenÀ1,
Ge, Zn, and ZnGen clusters, respectively.
The calculated results of the atomic averaged binding
energies are plotted as the curves which show the sized
dependence of the atomic averaged binding energies of
the ZnGen clusters. Because the ground states of the
small-sized ZnGen (n = 1–2) correspond to triplet spin
state, the discussions on the atomic averaged binding energies of different sized clusters with the size n > 2 correspond
to spin singlet state. As shown in Fig. 3, the atomic averaged binding energy of the ZnGen clusters is monotonously
increased to the maximum when the size of the NiGen goes
from n = 1 to n = 12; then, the atomic averaged binding
energy of the ZnGen clusters begins to be decreased when
the size of the ZnGen exceeds 12.
On the other hand, the sized dependence of the fragmentation energies of the ZnGen clusters is also investigated.
As seen from Fig. 4, the local maxima of D(n, n À 1) of
the ZnGen clusters localize at n = 5, 9, and 12. As compared to the TM at Ge10 (TM = Co, Ni, and Cu), the
ZnGe10 does not show the stronger relative stability as
compared to the adjacent sized clusters although the
bicapped tetragonal antiprism is optimized to be the lowest-energy structure. On the contrary, the ZnGe12 shows
the strongest stability because of the special stable icosahe-

Fig. 4. Sized dependence of the fragmentation energies of ZnGen
(n = 4–13) clusters.

dral geometry which does not correspond to the minima

for the NiGe12 and CuGe12 clusters. On the basis of the calculated results above, one can concluded that the most stable geometry depends on the doped transition metal, which
is analogous to the transition metal doped silicon clusters
[8,25].
3.4. Electronic properties of the ZnGen clusters
Charge-transfer phenomena of the ZnGen clusters can
be obtained by natural population analyses. Different from
the Ni-doped germanium clusters [12] however, charges
transfer from the Zn to the Ge atoms in all sized ZnGen
clusters because the Zn atom with filled 3d occupied orbitals does not obtain the extra charge from the germanium


258

J. Wang, J.-G. Han / Chemical Physics 342 (2007) 253–259

frame. This finding is confirmed that the charge-transfer
direction in the TM-doped germanium clusters depends
on the doped transition metal.
The electronic property of the metal doped germanium
clusters can be reflected from the energy gap between the
highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO). Previous calculated results on the NiGen clusters indicated that the
HOMO–LUMO gap of NiGe10 cluster is much larger than
other sized clusters [12]. However, in the case of ZnGen
clusters, the most stable ZnGe12 has remarkably large
HOMO–LUMO gap (3.160 eV) with the weakest chemical
stability as compared to the ZnGe10 (2.106 eV) and other
sized clusters. As mentioned above, the ZnGe12 isomer
has the largest atomic averaged binding energy and biggest
fragmentation energy; implying that the icosahedral
ZnGe12 has the strongest stability and is appropriate for

building-block of novel cluster-based nanomaterials. Furthermore, in order to examine the special stable properties
of the icosahedral ZnGe12 cluster, the spatial distribution
of the highest occupied molecular orbitals are analyzed.
As shown in Fig. 5, the molecular orbitals in the icosahedral 12e structure are delocalized on the two pentagonal
planes and uniform distribution of electronic density can
be formed; furthermore, the HOMO of the 12e isomer is
indicative of covalent bonding between the metal Zn and
Ge12 frame. However, in the case of hexagonal prism, electronic density of four germanium atoms is much smaller
than other germanium atoms and the doped Zn atom does
not contribute to forming uniform distribution of electronic density in the caged germanium clusters. Similar to
the most stable stability of the TM at Si12 (TM = Ta, W,
and Cr) [3,24], the ZnGe12 is also more stable as compared
to other sized clusters. However, geometry is the essential

Fig. 5. Representations of the HOMO and LUMO orbitals of the
icosahedral and hexagonal prism ZnGe12 clusters. The different gray tones
of the orbitals denote the positive and the negative regions.

difference among them; the stability of the formers is due
to the stable hexagonal prism geometry while the stability
of the latter is because of the stable icosahedral geometry.
Previous investigation on the bicapped tetragonal antiprism TM at Ge10 (TM = Cu and Ni) clusters reveal that
their dipole moments are almost zero and appears nearly
to be non-polar molecule [11,12]. However, the dipole
moment of the bicapped tetragonal antiprism ZnGe10 isomer is 0.393 D and has obvious the polarity. As for as
the icosahedral ZnGe12 is concerned, its dipole moment is
quite small (0.013 D) and the weak electrostatic interactions between the encapsulated Zn and all germanium
atoms are balanced because of the higher symmetrical
geometry. Hence, it can be expected that the polarity and
distribution of electronic density in the frontier orbitals of

the Zn-encapsulated caged germanium Gen clusters are correlated with the spatial distribution of germanium atoms.
4. Conclusions
The geometries, stabilities, and electronic properties of
the ZnGen (n = 1–13) clusters are investigated at the
B3LYP/6-31G level. All the results are summarized as
follows:
1) The optimized geometries of the Zn-doped Gen clusters reveal that the Zn atom is encapsulated in caged
germanium clusters at n = 10. Moreover, the stable
bicapped tetragonal antiprism ZnGe10 cluster in term
of the investigated relative stability is not stronger
than its neighbors. Furthermore, the Zn capped pentagonal antiprism ZnGe11 is more stable than the Zn
capped pentagonal prism Ge11 isomer; however, the
Cu capped pentagonal prism CuGe11 is more stable
than the Cu capped pentagonal antiprism CuGe11
isomer. Interestingly, the lowest-energy TMGe12
geometries depend on the different kinds of the
encapsulated transition metals. For example, the
irregular basket-like CuGe12 structure, the bicapped
pentagonal prism NiGe12 structure, and the special
high-symmetry icosahedral ZnGe12 structure are
optimized to be the lowest-energy TMGe12 geometries. Consequently, the different sized and shaped
lowest-energy TM-encapsulated Gen building blocks
for mew cluster-based nanomaterials will lead to the
new material with the novel properties.
2) The natural population analyses indicate that different charge-transfer mechanisms depend on different
transition metal being doped into germanium clusters. Charges in the Zn-doped Gen clusters transfer
from the Zn atom to the Gen frame, which is different
from those of the NiGen clusters with the chargetransfer directions between the Ni and germanium
framework being changed at certain size of cluster.
3) The atomic averaged binding energy of the ZnGen is

increased to maxima at n = 12 when the size
increases. According to the calculated fragmentation


J. Wang, J.-G. Han / Chemical Physics 342 (2007) 253–259

energies, the magic numbers of the relative stabilities
are confirmed to be n = 5, 9, and 12. Furthermore,
the icosahedral ZnGe12 is stronger in stability as compared to the adjacent sized clusters. Simultaneously,
the polarity of the icosahedral ZnGe12 is obviously
weakened because of the symmetric distribution of
germanium atoms around Zn atom. Hence, it is quite
interesting that the Zn atom with filled d orbitals is
encapsulated into the Ge12 frame to forming highsymmetry icosahedral geometry.
Acknowledgement

[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]

This work is supported by Natural Science Foundation
of China (20173055) and starting fund(985029) of USTC.

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