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Structures and ionization energies of small lithium
doped germanium clusters†
Jorg De Haeck,a Truong Ba Tai,b Soumen Bhattacharyya,za Hai Thuy Le,a
Ewald Janssens,a Minh Tho Nguyenb and Peter Lievens*a
We present a combined theoretical and experimental investigation of neutral and cationic lithium
doped germanium clusters, GenLim (n = 5–10; m = 1–4). The vertical ionization energies and ionization
thresholds are derived from threshold photoionization efficiency curves in the 4.68–6.24 eV range and
are compared with calculated vertical and adiabatic ionization energies for the lowest energy isomers
obtained using DFT computations. The agreement between experimental and computed values
supports the identification of the ground state structures. Charge population analysis shows that
lithium transfers its valence electron to the Gen hosts to form GenmdÀ–mLid+ and Gen(md

À

+1)

–mLid+

Received 6th December 2012,

Accepted 13th February 2013

complexes. This is also illustrated by the strong correlation between the size dependent lithium

DOI: 10.1039/c3cp44395g

adsorbing lithium atoms on either triangular or rhombic faces of the Gen framework with the lithium

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atoms tending to avoid each other. The chemical bonding phenomena of clusters are analyzed in detail
using the densities of states and molecular orbitals.

adsorption energies in GenLi and the Gen electron affinities. Neutral GenLim clusters are formed by

A Introduction
Germanium-based clusters have attracted much attention, in part
due to important applications of germanium based materials in
the electronic industry. Germanium was commonly used in the
early generations of semiconductor devices. Together with silicon,
germanium is one of the most promising materials for dilute
magnetic semiconductors (DMS).1–3 Recently, self-assembled
dilute magnetic Mn0.05Ge0.95 quantum dots were successfully
synthesized by Wang et al.4 and demonstrated the electric field
control of ferromagnetism in metal–oxide–semiconductor ferromagnetism capacitors up to 100 K. To gain insights into the
fundamental properties of these intriguing materials, studies on
relevant atomic clusters have extensively been performed during
the past decades.5,6 However, while pure germanium clusters have
carefully been investigated in several combined experimental and
theoretical studies, less work has been done on binary germanium

clusters.7–24

a

Laboratory of Solid State Physics and Magnetism, KU Leuven,
Celestijnenlaan 200D, B-3001 Leuven, Belgium. E-mail:
b
Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium
† Electronic supplementary information (ESI) available. See DOI: 10.1039/
c3cp44395g
‡ Present address: Atomic & Molecular Physics Division, Bhabha Atomic Research
Centre, Mumbai 400085, India.

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Mixed lithium and group IVA element compounds are
intriguing subjects. Lithium has the lightest weight among
the metallic elements and possesses a simple electronic
configuration with one valence electron (1s22s1). It is frequently
used to investigate fundamental properties and theoretical
models for different classes of chemical compounds, and
attracts much attention as a good electron-donating dopant
in binary clusters.25–31
Both bulk and nanostructured germanium and silicon, such
as nanoparticle assemblies and nanowires,32,33 are ideal anode
materials for lithium ion batteries with a high theoretical

capacity of 1600 and 4200 mA h gÀ1, respectively,34–36 that are
much higher than the value of 372 mA h gÀ1 of classical Li–C
systems.
Recently, structures and properties of binary lithium–silicon
clusters SinLimx (with n = 1–11 and m = 1–3 at various charge
states x = +1, 0, À1) have extensively been investigated, both
experimentally and theoretically.29,30,37–42 These studies led to a
better understanding of the bonding and fundamental properties
of mixed lithium–silicon systems. Kishi et al. reported on
sodium doped silicon clusters.43 Investigations on binary
lithium germanium clusters GenLim are rather limited, despite
their potential use in applications that could be based on the
high diffusivity of lithium in germanium-anode material at
room temperature, which is 400 times higher than that in
silicon-anode material.44 Some of the authors of the present

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work reported earlier on small mixed GenLim clusters using both
mass spectrometry and quantum chemical computations.29,45 It
was shown that lithium doped germanium clusters are able to
form gas phase nanowires based on the Ge9 building blocks.45
Nevertheless, the identity of the lowest-energy structure for small

GenLim clusters could not firmly be established yet. In addition,
despite the observation in previous reports that lithium tends to
transfer its valence electron to the silicium or germanium hosts
in SinLim and GenLim clusters,37,39,40 a deep analysis of the
chemical bonding associated with interactions between lithium
atoms and the hosts is not available.
While ionization energies of small pure germanium clusters
are relatively high,14 doping them with alkali metal atoms
brings the photoionization threshold of several lithium doped
germanium clusters within the energy window of commercially
available dye lasers and optical parametric oscillators (typically
hn o 6.3 eV).
Motivated by the above reasons, we performed a combined
experimental and theoretical investigation on the binary
lithium–germanium clusters GenLim (n = 5–10 and m = 1–4) in
both neutral and cationic states. The experimental ionization
efficiency curves of the GenLim clusters are determined for the
first time, and comparison of the experimental ionization
energies with computational results using density functional
theory helped us to assign the structures of these clusters. An
analysis of densities of states (DOS) and canonical molecular
orbitals (CMO) of the GenLim species has been carried out to
analyze the interactions between the lithium atoms and the
germanium hosts. On the basis of the geometrical features and
the electron distributions, the growth pattern of the clusters
could be identified.

B Methods
B.1

Experimental method

The binary GenLim clusters are produced in a pulsed (10 Hz)
dual-target dual-laser vaporization source.46 Rectangular
germanium and lithium targets are ablated by two pulsed
Nd:YAG lasers (532 nm) with typical energy densities of 8
and 0.5 mJ mmÀ2 for germanium and lithium, respectively.
Condensation of the vaporized material takes place in a pulse
of helium gas. By optimizing the ablation energies and the
extraction timing, clusters with various amounts of lithium
doping can be sampled. For the current work, the source
parameters are optimized to produce GenLim with m = 1–4.
The cluster source is cooled by a regulated flow of liquid
nitrogen. The cluster source temperature is set to 140 K for
the ionization energy measurements. Following adiabatic
expansion into a vacuum a beam of clusters is formed. Charged
clusters are deflected and the neutral clusters are subject to
single photon ionization in the extraction region of a reflectron
time-of-flight mass spectrometer.
Due to the natural isotope distribution of lithium and
germanium, the mass spectra are dominated by broad peaks,
which reflect the coexistence of GenLim clusters with different
amounts of lithium (for a given n). The isotope patterns of

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different GenLim clusters overlap with each other and cannot
readily be resolved with our current instrumentation except
for the smallest sizes (n o 5). Therefore, a deconvolution

scheme is applied to extract information on the intensities of
the individual clusters (for details see ESI†).
To measure photoionization efficiency (PIE) curves a series
of mass spectra are recorded at photon energies in the 4.68–
5.72 eV and 5.84–6.24 eV ranges with a step size of 0.04 eV using a
dye laser (Sirah CSTR-LG-24). To compensate for source production fluctuations the mass spectra are normalized with reference
spectra taken at a fixed photon energy of 6.42 eV (ArF excimer
laser). Care was taken to ensure overlap between the tunable and
reference laser beam, so that they irradiated the same area of the
cluster beam. An analog controller switched alternatively between
both lasers and drove the recorded signal in two different
channels of the oscilloscope. The pulse energy of both the
reference laser and the dye laser was kept below 250 mJ cmÀ2 to
ensure measurements in the single photon absorption regime.
A drawback of the low photon fluence is a low detected signal,
which reduces the signal to noise ratio. Each measurement
consists of 3000 acquisitions to obtain a good accuracy.
B.2

Data evaluation

PIE curves of the GenLim clusters are obtained after integration
of the corresponding peaks in the mass spectra taken at each
photon energy. These integrated intensities are then divided by
the laser power and the photon wavelength to account for the
number of incident photons. In addition, the signal is normalized by the intensity of the reference signal to account for the
amount of clusters produced.
An experimental value for the vertical ionization energy (VIE)
is derived from the PIE curve using a displaced harmonic
oscillator model47 as discussed in our recent work.30,31 Basically

this model gives that the VIE coincides with the steepest increase
of the PIE curve if photoionization occurs via a single electronic
transition. The measurable property most closely related to the
AIE is the ionization threshold. However, the measured ionization threshold can differ from the adiabatic ionization energy
(AIE) if the Franck–Condon factor for the transition between the
neutral and cationic ground state is zero, in which case the
ionization threshold is an upper value for the AIE. On the other
hand, thermal occupation of excited states in the neutral clusters
can allow ionization at photon energies below the AIE, in which
case the measured ionization threshold is lower than the AIE.
Both the ionization threshold (experimental AIE) and the VIE are
derived from the PIE curve after fitting a smeared-out step
function to the data points.30,31 The lack of knowledge about
cluster temperatures, Franck–Condon factors and vibrational
frequencies leads to a model uncertainty on the ionization
energies of at least 0.1 eV. The statistical errors depend on the
quality of the fit and are generally in the order of 0.05 eV.
B.3

Computational method

Quantum chemical computations are carried out using
the Gaussian 03 (ref. 48) suite of programs. Geometries and
harmonic vibrational frequencies of the lower-lying isomers are

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determined with the hybrid B3LYP functional, which involves
the Becke three-parameter exchange49 and the Lee–Yang–Parr
correlation50 functional. The search for possible low-lying isomers of GenLim (n = 5–10; m = 1–4) is performed using a recently
developed stochastic search algorithm.15 Briefly, possible structures
for each GenLim cluster are generated by a kick-procedure and
optimized at the B3LYP/6-31G level.51 In this kick-procedure, the
minimum and maximum distances between atoms are random
and limited to B2 Å and B7 Å, respectively. Geometries of the
stationary points located are then re-optimized using the same
functional but in conjunction with the larger 6-311+G(d) basis set.52
This computational method has been effectively applied in our
recent studies to investigate pure germanium and lithium doped
silicon clusters.15,30,31
The VIE is defined as the total energy difference between the
neutral cluster and the cation having the same geometry as the
neutral. The AIE is calculated as the difference in the total
energies of a pair of relaxed neutral and cationic isomers
in which the shape of the cation is similar to that of the
corresponding neutral cluster. All AIE values are corrected by

zero-point energies.
Atomic charges are obtained using the natural population
analysis (NPA) at the B3LYP/6-311+G(d) level using the NBO
software.53 The chemical bonding features of clusters are
revealed from the total densities of states (DOS) and canonical
molecular orbitals (CMO). While the DOS is considered as an
energy spectrum of molecular orbitals, the partial density of
states (pDOS) allows evaluating the distribution of molecular
orbitals into separate atomic orbitals. Molecular orbitals are
plotted by using the GaussView program.54

C Results and discussion
C.1

Mass abundance spectrometry

Fig. 1 gives an overview of mass spectra of neutral GenLim
(n = 5–12) clusters after laser postionization. The spectra are
dominated by broad peaks, corresponding to GenLim clusters
for a given n but different amounts of lithium atoms m. The
vertical bars indicate the relative intensities of the different
stoichiometries (n,m) derived after deconvolution (see ESI† for
details).
Fig. 1a shows a mass spectrum obtained by postionization of
the clusters with 6.42 eV photons (ArF excimer laser) at a laser
fluence of 200 mJ cmÀ2. The preferred amount of lithium
dopant atoms seems to depend strongly on n. Species like
Ge6Li2, Ge7Li1 and Ge10Li1 are more abundant than other
clusters. These maxima, however, do not reflect the actual
abundances of the GenLim clusters as produced in the source

because ionization efficiencies depend on the cluster composition. It is known that bare Gen clusters with n o 18 cannot
efficiently be ionized by 6.42 eV photons.14 Hence, also certain
monolithiated species are expected not to show up in our
experiment due to a low ionization efficiency at 6.42 eV.
This is indeed confirmed by the mass spectrum of GenLim
postionized by 7.89 eV photons (F2 excimer laser), which is
shown in Fig. 1b. Bare as well as singly and doubly lithium

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Fig. 1 Typical mass spectra of neutral GenLim clusters after laser postionization
with (a) 6.42 eV photons and (b) 7.89 eV photons using a laser fluence of
200 mJ cmÀ2. The vertical bars indicate the relative intensities of the different
stoichiometries (n,m) after deconvolution of the isotope patterns. The arrows in
(b) indicate species with a significantly enhanced photoionization efficiency
compared to (a). Bold arrows in (b) indicate pure Gen clusters with reduced
photoionization efficiency at 7.89 eV (compared to ref. 14).

doped species gain intensity relative to Fig. 1a and new maxima
appear in the spectrum: all doubly doped species now have a
relatively high intensity. However, even at this photon energy,
the ionization efficiency of a number of species is still small.
Judged by the results of Yoshida and Fuke the abundance of
Ge7 in Fig. 1b is underestimated, as it is expected to be larger
than the abundance of Ge6.14 These observations underline the
importance of photoionization efficiency in the analysis of

GenLim mass spectra.
Comparing the photoionization spectrum at 6.24 eV (Fig. 1a)
and 7.89 eV (Fig. 1b) also reveals a remarkable decrease in the
abundance of photoionized Ge7Li1, at least compared to the
neighbouring sizes. Possible explanations are either a reduced
ionization efficiency with increasing photon energy or that the
incident 7.89 eV photon can, besides ionization, also lead to
fragmentation of the Ge7Li+ cluster.
C.2

Photoionization efficiency curves

PIE curves of the GenLim clusters are obtained by measuring
their ionization efficiency in the 4.68–5.72 eV and 5.84–6.24 eV
photon energy ranges and by normalization with respect to the
ionization efficiency using 6.42 eV photons. The results are
shown in Fig. 2. The open squares represent the experimental
data, while the solid lines are smeared-out step functions fitted
to the data. The experimental values for the VIE and the
ionization threshold are both indicated by a dot. The ionization
threshold is an upper value for the calculated value of the AIE.
The scatter at the baseline is mainly due to the low signal to
noise ratio.
Without saturation of the PIE curve at high photon energies,
the fitting is liable to large deviations and in certain cases

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Fig. 2 PIE curves of the GenLim clusters (n r 10, m r 4) that have an ionization threshold below 6.25 eV. The open squares represent the experimental data, while
the solid lines represent smeared-out step functions fitted to the data. The experimental VIE and the ionization threshold are indicated by dots. The positions of the
calculated AIE and VIE are indicated by dashed and solid arrows, respectively. A star (*) indicates data for an isomer, which is not the calculated lowest energy structure.

(Ge6Li3, Ge10Li1, Ge10Li3) no value for the VIE could be derived.
As observed in earlier ionization energy measurements a single
photoionization curve cannot always be described by a
single step function,31,55 and multiple steps or slopes might
be present as is the case for Ge8Li3. These post-threshold
features might reflect ionization from lower lying electronic
states.31 In this case the variation of the energy of the photons
probes the density of states (DOS).
A steep slope of the PIE curve indicates that the geometry of
the neutral and the cationic cluster is similar and thus little
geometric relaxation takes place following ionization. With the
exception of Ge7Li3 and Ge8Li3 all triply doped species show a
shallow step function suggesting a considerable change in the
geometry between the neutral and cationic ground state. The
GenLi4 (n = 5–9) species on the other hand have relatively high
VIE and show a sharp step function, implying less geometric
relaxation upon ionization.
C.3 The geometries of neutral and cationic GenLim0/+

(n = 5–10; m = 1–4)
The shapes, relative energies, and point group symmetries of
the lowest-lying GenLim0/+ (n = 5–10, m = 1–4) isomers are
displayed in Fig. 3–6. Due to the large number of identified
isomers, only the lower-lying isomers with relative energies
within a range of B0.1 eV are depicted. In addition, some
cationic GenLim+ species with higher relative energies, but with
structures related to those of the lowest-energy neutral isomers,
are given to facilitate the comparison of the neutral and
cationic states. More isomers are presented in Fig. S2–S7 of
the ESI.†
Conventionally, each structure described hereafter is
denoted by the label n.my.x, in which n and m stand for
the number of germanium and lithium atoms, respectively,

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Fig. 3 The shape, relative energies (eV), point groups and electronic states of
the lowest energy isomers of Ge5Lim0/+ (m = 1–4) and Ge6Lim0/+ (m = 1–4)
clusters.

y denotes the charge state (n for neutral and c for cation), and x
indicates the xth lowest-lying isomer located for that cluster.
The vertical (VIE) and adiabatic (AIE) ionization energies of the
lowest-energy isomers found for GenLim are summarized in
Table 1.
Ge5Li1–4. The lowest-energy isomers of Ge5Li1–30/+ found in
the present work have the same germanium framework as
those found in earlier work.45 The structure 5.1n.1 (C1, 2A) in
which lithium is adsorbed on a triangular face of the pure Ge5

is the global minimum of Ge5Li (Fig. 3). Two structures, 5.2n.1
and 5.2n.2, that only differ in the positions of the lithium
atoms are found to be almost degenerate in energy and are the
lowest-lying isomers found for Ge5Li2. For Ge5Li3 the total

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Fig. 4 The shape, relative energies (eV), point groups and electronic states of
the lowest-energy isomers of Ge7Lim0/+ (m = 1–4) clusters.

Fig. 5 The shape, relative energies (eV), point groups and electronic states of
the lowest-energy isomers of Ge8Lim0/+ (m = 1–4) clusters.

energies of 5.3n.1 and 5.3n.2 are basically the same. Consequently, these two structures are considered as the degenerate
global minima of Ge5Li3. The C2v structure 5.4n.1 that can be
formed by adsorbing one excess lithium atom on a triangular

face of 5.3n.1 is found to be the lowest energy isomer of the
neutral Ge5Li4. It can be seen that the Gen frameworks of these
global minima retain the bi-capped trigonal form that is
characteristic for the Ge5 cluster.16 Following ionization, the
geometries of the resulting cationic clusters Ge5Lim+ are only
slightly distorted as compared to those of their corresponding
neutral species. 5.1c.1, 5.2c.1, and 5.4c.1 are calculated to be

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Fig. 6 The shape, relative energies (eV), point groups and electronic states of
the lowest-energy isomers of Ge9Lim0/+ (m = 1–4) and Ge10Lim0/+ (m = 1–4)
clusters.

the most stable isomers of Ge5Li+, Ge5Li2+ and Ge5Li4+, respectively. For Ge5Li3+, isomers 5.3c.1 and 5.3c.2 are almost
degenerate.
Ge6Li1–4. Isomer 6.1n.1 (C2v, 2B2) in which the lithium atom
is adsorbed on a rhombic face of the pure Ge6 is the global
minimum of Ge6Li (see Fig. 3). The same isomer was found as
ground state in a previous report on GenLim.45 Isomer 6.2n.1
(Cs, 1A 0 ) in which the second lithium atom is added on a Ge–Ge
edge of Ge6Li is found to be the most stable isomer of Ge6Li2.
The C2v, 1A1 structure 6.2n.2 is located only 0.07 eV higher in
energy. The most stable isomers found for Ge6Li3 and Ge6Li4
are 6.3n.1 and 6.4n.1, respectively. These isomers are formed by
adding one and two lithium atoms on rhombic faces of 6.2n.4

(see Fig. S3 of the ESI†). Except for the cationic Ge6Li3+ cluster,
the Ge6Lim+ cations have geometries that are similar to
the corresponding neutral clusters. The most stable Ge6Li3+
isomer, 6.3c.1, is the cationic form of 6.3n.2 and the cationic
form corresponding to the lowest energy neutral isomer, 6.3c.2,
is much less stable with a relative energy of 0.81 eV. Structures
6.4c.1 and 6.4c.2 are found to be the degenerate global minima
of Ge6Li4+.
Ge7Li1–4. The shapes and relative energies of Ge7Lim0/+ are
shown in Fig. 4. The Ge7Li cluster 7.1n.1 is formed by adding a
lithium atom on one of the edges of the bicapped pentagonal
pyramid Ge7.16 For dilithiated Ge7, several isomers having close
relative energies are located. Accordingly, three isomers 7.2n.1,
7.2n.2, and 7.2n.3 are almost degenerate in energy. The maximum
difference in their total energies is only 0.06 eV. The Ge7Li3 and
Ge7Li4 clusters favor geometries with distorted Ge7 frameworks.
Three isomers with a maximum relative energy of 0.08 eV, namely
7.3n.1, 7.3n.2, and 7.3n.3, are found for the neutral Ge7Li3. For the
Ge7Li4 clusters, the structures 7.4n.1 and 7.4n.2 in each of which
two Ge3 moieties are connected together by a single germanium
atom and a few lithium atoms are the lowest-lying isomers. In the

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Table 1 Calculated adiabatic (AIE) and vertical (VIE) ionization energies for the lowest energy isomers of GenLim (n = 5–10; m = 1–4) obtained at the B3LYP/
6-311+G(d) level and the corresponding experimental ionization threshold and VIE values. The standard error from the fitting procedure is given between brackets.
The model uncertainty for the experimental values of at least 0.1 eV is not included

VIE (eV)

AIE (eV)

Cluster

Exp.

Transition

Ge5Li3

5.1n.1
5.2n.1
5.2n.2
5.3n.1

A- A
A - 2A
1
A - 2A
2
B2 - 1A1

7.02

6.63
6.61
5.80

Ge5Li4

5.3n.2 2A00 - 1A 0
5.4n.1 1A1 - 2B1

5.78
5.19

- A1
A - 2A 0
2 00
A - 1A 0
2
B2 - 1A1
1
A1 - 2A1

6.82
6.14
6.24
4.88
5.93

>6.24
6.21 (0.02)
—

B2 - 1A1
A - 2A
1
A - 2A
1
A1 - 2B1
2
B2 - 1A1
2 0
A - 1A 0
2 0
A - 1A 0
1
A - 2A

5.89
6.50
6.18
5.74
5.42
5.94
5.09
6.05

5.86 (0.02)
5.85 (0.02)

Ge5Li1
Ge5Li2

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Calc.
2
1

6.1n.1
6.2n.1
6.3n.1
6.3n.2
6.4n.1

2

7.1n.1
7.2n.1
7.2n.2
7.2n.3
7.3n.1
7.3n.2
7.3n.3
7.4n.1

2

2

Ge8Li3

Ge8Li4

8.1n.1
8.1n.2
8.2n.1
8.2n.2
8.3n.1
8.4n.1

Ge9Li1
Ge9Li2
Ge9Li3
Ge9Li4

9.1n.1
9.2n.1
9.3n.1
9.4n.1

2

Ge10Li1
Ge10Li2
Ge10Li3
Ge10Li4

10.1n.1
10.2n.1
10.3n.1
10.4n.1

Ge6Li1
Ge6Li2
Ge6Li3
Ge6Li4
Ge7Li1
Ge7Li2
Ge7Li3
Ge7Li4
Ge8Li1
Ge8Li2

1

1

B2
1 0

1

A
A
1
A
1
A
2
A
1

A
2

-

1

A
A
A
2
A
1
A
2
A
1
2

6.71
6.41
6.75
6.39
5.40
5.90

A1 - 1A1
A - 2A
2
A - 1A

1
A - 2A

6.79
6.63
5.92
5.78

- 1A 0
- 2A
- 1A
- 2A

6.20
6.38
5.45
5.39

1

2 0

A
A
2
A
1
A
1

Exp.

5.1n.1
5.2n.1
5.2n.2
5.3n.1
5.3n.1
5.3n.2
5.4n.1

-

5.1c.1
5.2c.1
5.2c.1
5.3c.1
5.3c.3
5.3c.3
5.4c.1

6.34
6.26
6.26
4.74
5.54
5.54
5.00

—
o6.42

6.1n.1
6.2n.1
6.3n.1
6.3n.2
6.4n.1

-

6.1c.1
6.2c.1
6.3c.2
6.3c.1
6.4c.1

6.11
5.96
5.58
4.77
5.71

—

7.1n.1
7.2n.1
7.2n.2
7.2n.3
7.3n.1
7.3n.2
7.3n.3

7.4n.1

-

7.1c.1
7.2c.4
7.2c.3
7.2c.1
7.3c.3
7.3c.4
7.3c.2
7.4c.1

5.57
6.19
5.94
5.36
5.32
5.57
4.89
5.63

-

8.1c.3
8.1c.1
8.2c.4
8.2c.3
8.3c.2
8.4c.6

6.26
5.84
6.39
6.17
5.08
5.58

o6.42

5.24 (0.02)
6.01 (0.03)

8.1n.1
8.1n.2
8.2n.1
8.2n.2
8.3n.1
8.4n.1

>6.42
>6.42
6.11 (0.12)
5.95 (0.02)

9.1n.1
9.2n.1
9.3n.1
9.4n.1

-

9.1c.2
9.2c.2
9.3c.1
9.4c.2

6.60
6.25
5.37
5.56

—
—

>6.42
>6.42
5.79 (0.03)
5.12 (0.03)

5.87 (0.02)

5.94 (0.02)
6.06 (0.02)
o7.89
o7.89

>6.05
>6.42
>5.5

—

cationic state the structures 7.1c.1 and 7.2c.1, which are derived
by detachment of one electron from 7.1n.1 and 7.2n.1, are found
as the lowest-lying isomers of Ge7Li+ and Ge7Li2+, respectively.
The energetic ordering of the neutral and cationic Ge7Li3 clusters
is reversed. The most stable Ge7Li3+ isomer is the Cs structure
7.3c.1 in which three lithium atoms are added on edges of the
pentagonal Ge7 framework. While 7.3c.2, corresponding to
the neutral structure 7.3n.3, has a relative energy of only
0.04 eV, the cationic clusters 7.3c.3 and 7.3c.4, corresponding
to the lowest-energy neutral states 7.3n.1 and 7.3n.2, are much
less stable. The cationic Ge7Li4+ cluster 7.4c.1 is found to have a
geometry similar to the neutral ground state. The next isomer is
a Cs structure 7.4c.2 with a relative energy of only 0.05 eV.
Ge8Li1–4. Due to the increase in the number of germanium
faces, many lower-lying isomers co-exist that are virtually
degenerate in energy on the potential energy surface. Four
structures, 8.1n.1 to 8.1n.4, are found to have small relative
energies (Fig. 5). 8.1n.1 in which lithium is adsorbed on a
rhombic face of the tetracapped tetrahedral Ge8 structure is the

Phys. Chem. Chem. Phys.

Calc.

10.1n.1
10.2n.1
10.3n.1
10.4n.1

-

10.1c.1
10.2c.1
10.3c.1
10.4c.1

5.52
6.17
4.85
5.01

5.26 (0.14)
4.98 (0.14)
6.03 (0.02)
o5.5
5.57 (0.05)
5.63 (0.08)
5.54 (0.08)
5.59 (0.08)
5.88 (0.06)

o6.42
5.20 (0.21)
5.73 (0.12)

5.36 (0.36)
5.72 (0.11)
5.65 (0.24)

—
5.25 (0.61)
o6.0

lowest-lying isomer,16 but it is only 0.04 eV more stable than the
next isomer 8.1n.2. The global minimum of Ge8Li2 is a C1
structure 8.2n.1 in which two lithium atoms are adsorbed on
rhombic faces of the tetrahedral Ge8 framework. The 8.2n.2
isomer bears the same Ge8 framework as 8.2n.1, but has the
lithium atoms adsorbed at different positions. Other isomers in
which the geometries of the Ge8 host are more distorted turn
out to be less stable (see Fig. S6 of the ESI†). The isomer 8.3n.1
in which the third lithium atom is added on a third rhombic
face of 8.2n.1 is the most stable isomer found for Ge8Li3. The
next isomer is a C1 structure 8.3n.2 whose Ge8 frame is strongly
distorted. For Ge8Li4 the most stable isomer has a C1 structure
8.4n.1 in which four lithium atoms are adsorbed on triangular
and rhombic faces of the antiprism Ge8 frame. Three other
isomers (8.4n.2, 8.4n.3, 8.4n.4) have relative energies of only
B0.05 eV. The cations Ge8Lim+ can be formed by removing one
electron from the lowest-lying neutrals Ge8Lim.
Ge9Li1–4 and Ge10Li1–4. The larger clusters Ge9,10Li1–4 are
formed by adsorbing lithium atoms on different triangular

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faces of the Ge9 and Ge10 parents.16 The shapes of the most
stable isomers are shown in Fig. 6 and reveal that all lowest-lying
isomers of Ge9,10Li1–4 retain the germanium framework of the
corresponding pure Gen clusters. Similar to the Ge8Lim series,
there are a large number of isomers with very small relative
energies located on the potential energy surfaces of Ge9Lim and
Ge10Lim (see Fig. S6 and S7 of the ESI†). These structures differ in
most cases from each other only by the positions of adsorbed
lithium atoms, whereas their Gen skeletons are similar. Structures of the cationic Ge9,10Lim+ clusters are only slightly distorted
as compared to the corresponding neutrals.
C.4 Comparison of the experimental and calculated
ionization energies
The VIE and AIE values of the lowest energy GenLim (n = 5–10
and m = 1–4) clusters obtained at the B3LYP/6-311+G(d) level
are given in Table 1. If significant amounts of a certain cluster
are found in the mass abundance spectra taken by postionization with 6.42 eV photons, but no VIE could be derived, the
ionization threshold is indicated by o6.42 eV. Comparing the
calculated VIE and AIE values with experimental values allows
us to challenge the computations, as certain isomers can
support the experiments and other isomers can be excluded

on the basis of the comparison.
Ge5Li1–4. Calculated VIEs of 5.1n.1 and 5.2.n1 are above
6.42 eV, while their AIE values are below 6.42 eV. This is
consistent with the experimental observation that Ge5Li and
Ge5Li2 show up in the abundance spectrum taken by postionization with 7.89 eV photons, but not or to a minor extent in the
spectra taken by postionization with 6.42 eV photon.
For Ge5Li3 the calculated VIEs of 5.3n.1 and 5.3n.2 amount
to 5.80 eV and 5.78 eV, respectively, which are both in good
agreement with the experimental value of 5.79 Æ 0.03 eV. Also
the AIEs corresponding to the 5.3n.1 - 5.3c.3 and 5.3n.2 5.3c.3 transitions of 5.54 eV are in agreement with the experimental value of 5.26 Æ 0.14 eV. The AIE value corresponding to
the transition from the neutral to the cationic lowest energy
states, 5.3n.1 - 5.3c.1, amounts to 4.74 eV only, which is
significantly lower than the experimental value. This probably
implies that this transition is not realized in the experiment.
On the other hand the PIE curve of Ge5Li3 (see Fig. 2) is quite
shallow, what indicates that geometric relaxation takes place
upon ionization.
The VIE value of the lowest energy structure found for
Ge5Li4, 5.4n.1, is equal to 5.19 eV, being in line with the
experimental value of 5.12 Æ 0.03 eV. The AIE for 5.4n.1 5.4c.1 of 5.00 eV also agrees perfectly with the experimental
value of 4.98 Æ 0.14 eV.
In general, the comparison of the experimental and computed values supports the lowest energy structures found for
Ge5Lim (m = 1–4).
Ge6Li1–4. No PIE curve could be recorded for Ge6Li, but the
mass spectral observations (Fig. 1) imply that the VIE is
between 6.24 eV and 7.89 eV, which is in line with the
computed result for 6.1n.1. The computations give a small
energy difference between the VIE and AIE of the lowest energy

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isomer of Ge6Li2, 6.2n.1. This is consistent with the experimental observation that Ge6Li2 has a steep PIE curve (Fig. 2).
Both the computed VIE of 6.14 eV and AIE for 6.2n.1 - 6.2c.1
of 5.96 eV agree well with the experimental values of 6.21 Æ 0.02 eV
and 6.03 Æ 0.02 eV, respectively. The experimental ionization
energy of Ge6Li3 is smaller than 5.50 eV and a large difference
between the ionization threshold and the VIE of Ge6Li3 can be
predicted on the basis of the shallow PIE curve (Fig. 2). These
experimental observations are in reasonable agreements with
the calculated AIE for 6.3n.1 - 6.3c.2 of 5.58 eV and a large
difference of 0.66 eV between the calculated VIE and AIE,
implying a considerable change in the geometry upon ionization. It should be noted that isomer 6.3n.2, being only 0.21 eV
higher in energy than 6.3n.1, cannot be excluded, since it has a
significantly lower AIE value (6.3n.2 - 6.3c.1) of 4.77 eV.
The computed VIE and AIE for the lowest energy isomer of
Ge6Li4 are 5.93 and 5.71 eV, respectively. These values are somewhat larger, though still in reasonable agreement with the experimental values of 5.87 Æ 0.02 eV and 5.57 Æ 0.05 eV, respectively.
Ge7Li1–4. Experimental ionization energies could be determined for Ge7Lim with m = 1–4. The experimental VIE (5.86 Æ
0.02 eV) and AIE (5.63 Æ 0.08 eV) agree perfectly with the
computed values for the obtained lowest energy isomer 7.1n.1
of 5.89 eV and 5.57 eV, respectively. For Ge7Li2 several isomers,
7.2n.1, 7.2n.2, and 7.2n.3, are found close in energy. The
experimental VIE of 5.85 Æ 0.02 eV clearly favors isomer
7.2n.3, which has a VIE of 5.74 eV. The VIE of 7.2n.1 (6.50 eV)
and 7.2n.2 (6.18 eV) is much larger than the experimental
prediction and therefore can be excluded as the isomers that
are present in the molecular beam.

Also for Ge7Li3 the measured ionization energies help us to
assign the structure that is present in the experiment. The
computed VIE and AIE for 7.3n.2 of 5.94 eV and 5.57 eV,
respectively, are in excellent agreement with the experimental
values of 5.94 Æ 0.02 eV and 5.59 Æ 0.08 eV. On the other hand,
the calculated ionization energies for 7.3n.1 and especially
7.3n.3 are far below the experimental values.
For 7.4n.1 a VIE of 6.05 eV is computed, in excellent
agreement with our experimental value of 6.06 Æ 0.02 eV
described above. The computed AIE for 7.4n.1 - 7.4c.1 of
5.63 eV is slightly below, but still in reasonable agreement with,
the experimental ionization threshold of 5.88 Æ 0.06 eV.
In summary, we can state that the ionization energies for
computed lowest energy isomers of Ge7Lim with m = 1,4 all
agree perfectly with the experimental values. For Ge7Lim with
m = 2,3 the ionization energies of the computed lowest energy
isomers do not agree with the experiment, and thus are not the
isomers present in the molecular beam. On the other hand a
good agreement between the computed and measured ionization energies is found for two isomers 7.2n.3 and 7.3n.2 at low
relative energies (within the computational accuracy).
Ge8Li1–4. Among the Ge8Lim with m = 1–4 series, PIE curves could
only be measured for Ge8Li3 and Ge8Li4. According to the mass
spectra shown in Fig. 1 the ionization threshold for Ge8Li and
Ge8Li2 is between 6.2 eV and 6.42 eV, in line with the computed
values for 8.1n.1 - 8.1c.3 (6.26 eV) and 8.2n.1 - 8.2c.4 (6.39 eV).

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The computed VIE and AIE for the lowest energy isomer found for
Ge8Li3, 8.3n.1, are 5.40 and 5.08 eV, respectively. While the VIE is
somewhat higher than the experimental value of 5.24 Æ 0.02 eV, the
AIE agrees well with the measured ionization threshold of 5.20 Æ
0.21 eV. For Ge8Li4 the computed VIE and AIE for 8.4n.1 are slightly
smaller but in reasonable agreement with the experimental values
(VIE = 5.90 eV, VIEexpt = 6.01 Æ 0.03 eV and AIE = 5.58 eV, AIEexpt =
5.73 Æ 0.12 eV).
Ge9Li1–4 and Ge10Li1–4. Additionally, Table 1 points out that
there is an overall good agreement between the computed VIE
and AIE values and those obtained from our experiments.
C.5

Charge population analysis

The NBO analysis shows that the net positive charges of the lithium
atoms in GenLim0/+ vary in a range of 0.84–0.93 electrons. This
observation indicates that lithium tends to transfer its valence
electron to the Gen framework to form GendmÀ–nLid+ complexes or
ion pairs. Such a bonding behavior was also seen in other lithium
doped clusters such as BnLi,17,26,27 AlnLi,28 and SinLim.30,31
Due to the fact that lithium atoms effectively donate their
valence electron to form the GendmÀ–nLid+ complexes, the
adsorbing energies of lithium on Gen are expected to show a

parallel trend to the Gen electron affinities. This correspondence was also found in lithium and sodium doped silicon
clusters.37–40 The average adsorption energy per lithium dopant
(Ed) is defined as Ed = [E(Gen) + mE(Li) À E(GenLim)]/m, where
E(Li), E(Gen), and E(GenLim) are total energies of the lithium
atom and the Gen and GenLim clusters, respectively. Ed is plotted
in Fig. 7 for GenLi (n = 5–10) and compared with the electron
affinities (EAs) of Gen, which is defined as EA = E(GenÀ) À
E(Gen). The values can be found in Table SII of the ESI.† The
curves in Fig. 7 reveal that there is indeed a parallelism between
the Ed of GenLi and the EA of Gen. Accordingly, two local
minimum peaks are observed at n = 7 and n = 10.
C.6

Growth mechanism of lithium doped germanium clusters

Based on the geometric and electronic structure of the GenLim0/+
clusters, the growth mechanism of these systems can be

Fig. 7 The average adsorption energy per lithium atom (Ed, eV) for GenLim
(n = 5–10; m = 1–4) and the electron affinities (EA, eV) for Gen (n = 5–10).

Phys. Chem. Chem. Phys.

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summarized as follows: there are no Li–Li bonds. The neutral
GenLim clusters can be formed by adsorbing lithium atoms on
either triangular or rhombic faces of the Gen framework.
A preference for the rhombic faces is found for small GenLim
(n r 8) clusters, whereas adsorbing on triangular faces
becomes predominant for larger clusters (n Z 9). Mono- and

di-lithiated clusters, GenLi1,2, invariably have the same Gen
framework as the pure germanium clusters. For lithium richer
clusters (m = 3,4), the smaller species Ge5–7Li3,4 favor structures
with germanium frameworks that are distorted compared to
the pure clusters. While Ge5Li3,4 retains the trigonal Ge5
geometry, although slightly distorted along the C3 axis, the
rhombic faces of the Gen frameworks of Ge6,7Li3,4 are considerably distorted. The Ge8–10 frameworks in Ge8–10Li3,4, on the
other hand, are close to the corresponding pure clusters.
The charge population analysis shows a strong positive
charge on the lithium atoms. The neutral GenLim and cationic
GenLim+ clusters can thus be considered as GenmdÀ–mLid+ and
À
Gen(md +1)–mLid+ complexes, respectively. This implies a strong
similarity between the cation GenLim+1+ and the neutral GenLim.
Similar behavior was previously found for SinLim and SinNam
clusters.30,31,43 The ground state of the cation GenLim+1+ has
often the same geometric shape as the ground state of the
neutral GenLim, rather than GenLim+1. The exceptions of this
growth mechanism are 7.4c.1 and 8.1c.1–8.4c.1. For n = 8, many
low lying isomers coexist, which can be an explanation for the
discrepancy.
To further investigate the strong electron donation character
of the lithium atoms we compared our results of lithium doped
germanium clusters with calculations from King et al. and Xu
et al. on negatively charged bare germanium clusters.16,56 In
general, a good correspondence is found between the germanium core in GenLim0,+ and the corresponding bare anionic
germanium cluster, GenmÀ,(mÀ1)À. The global minima of the
Ge52À dianion and the Ge5À anion are both a trigonal bipyramid of D3h symmetry,16 similar to the neutral ground state,
but stretched along its axis with increasing negative charge.
Fig. 3 shows the same trigonal bipyramid shape for the corresponding germanium frameworks of Ge5Li1 and Ge5Li2, as well

as for Ge5Li2+ and Ge5Li3+. The bipyramid is also stretched with
increasing lithium content. Analogously, the global minimum
of the Ge72À dianion is a pentagonal bipyramid of D5h symmetry, similar to the neutral ground state, but stretched along its
axis with increasing negative charge.16 Ge7Li1, Ge7Li2, Ge7Li2+,
and Ge7Li3+ all have similar structures (see Fig. 4). However,
there is disagreement for n = 6; while Ge6xÀ (x = 0–2) is built
around an octahedral motif, the lithium doped species Ge6Li1
and Ge6Li2, as well as Ge6Li2+ and Ge6Li3+, adopt a pentagonal
shape by capping a rhombic site. While Ge8 prefers a capped
pentagonal shape, the Ge82À dianion is expected to adopt a
tetracapped tetragonal shape, in agreement with the structure
of Ge8Li2.16 This structure opens up at one side in the case of
Ge8Li4, permitting a lithium atom to cap a pentagonal face.
This resembles, but is different from, the open structure Ge84À
which has a hexagonal face.16 Ge9xÀ (x = 2–4) clusters have
tricapped trigonal prism (TTP) structures, while the capped

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square antiprism (CSA) is an alternative for the ground state of
Ge94À.16 The TTP and the CSA are closely related by a single
diamond-square process involving rupture of an edge connecting
two degree 5 vertices of the TTP. For the lithium doped clusters
the CSA motif is the ground state for Ge9Li3, but in general the
structural agreement between Ge9xÀ and Ge9Lix is still very strong.
The anion and the dianion of Ge10 both have bicapped square
antiprism (BSA) structures.16 Also Ge10Li2 has a BSA structure,
while Ge10Li shows substitution of one capping atom by a
lithium atom.
C.7 Chemical bonding: densities of states and molecular
orbitals
Since GenLim clusters can electronically be regarded as GendmÀ–
nLid+ complexes, we examine the chemical bonding features of
GenLim in comparison to the bonding in pure Gen. Hereto a
combined density of states (DOS) and canonical molecular
orbital (CMO) analysis was performed. As a representative
example, Ge5Lim is considered in detail. Observations for larger
GenLim (n > 5) clusters are similar. The total DOS and partial
densities of states (pDOS) of Ge5Lim (m = 0–4) are shown in
Fig. 8, those of larger lithium doped germanium clusters are
depicted in Fig. S8 of the ESI.† Firstly, it can been seen in Fig. 8
that the energy levels for mixed Ge5Li1–4 clusters are split as
compared to those of the pure Ge5 species, which is due to
lowering of the symmetry. The energies of frontier orbitals of the
mixed Ge5Lim clusters tend to increase with increasing m.
Importantly, the pDOS plots indicate that the contribution of

lithium atomic orbitals (AOs) in the frontier MOs of Ge5Li and
Ge5Li2 is very small, whereas the lithium AOs have a more
important contribution in the frontier MOs of Ge5Li3 and Ge5Li4.

These results can be understood from their bonding motifs. For
Ge5Li and Ge5Li2, the lithium atoms are adsorbed on triangular
faces of the unchanged Ge5 frames. They transfer their valence
electron and do not take part in the bonding of the Ge5 moiety.
In Ge5Li3 and Ge5Li4, some lithium atoms are adsorbed on
rhombic faces of the distorted Ge5 frameworks. As a consequence
they make important contributions to the bond formation of the
mixed clusters, and thereby stabilize the inherently unstable Ge5
entity. Analysis of pDOS demonstrates that the largest contribution of the lithium AOs in Ge5Li3 and Ge5Li4 is found at deeper
frontier MOs (HOMO À 5 and HOMO À 6 for both Ge5Li3 and
Ge5Li4). These results are remarkable as earlier studies on the
SinLim and SinNan clusters showed that the lithium only interacts
with the highest frontier MOs.
The CMOs provide additional insight into the bonding
features. Fig. 9 points out the similarity of shapes and ordering
of MO energy levels between Ge5 and Ge5Li, with the exception
of a lifting of the degeneracy of the MO energy levels in Ge5Li.
The excess electron of the lithium dopant atom occupies the
LUMO of Ge5, which consequently becomes the SOMO of Ge5Li.
The same predictions are observed for the Ge5Li2 cluster where
two excess electrons of the lithium donors are now fully
occupying the LUMO of Ge5 (Fig. S9 of the ESI†).
However, a considerable change in the ordering of MO
energies occurs in Ge5Li4 as compared to those of the pure
Ge5 cluster (Fig. 9). The excess electrons transferred from
lithium atoms occupy the two degenerate MOs (LUMO + 1) of

the Ge5 instead of its LUMO. Additionally, the ordering of the
highest occupied MOs of Ge5Li4 is also changed considerably.
The CMO analysis reveals that MOs having a larger contribution from lithium AOs are more stable. For instance, the
degenerate HOMO À 1(1e00 ) MOs of Ge5 are split into HOMO À
2(1a2) and HOMO À 5(2b1) of Ge5Li4. While HOMO À 2 of
Ge5Li4 is mainly composed of p-AOs of germanium atoms
(lithium AOs: 5%, pxy-AOs of germanium: 44% and pz-AOs of
germanium: 50%), HOMO À 5 arises from a hybridization of
lithium AOs (36%), s-AOs of germanium (8%) and p-AOs of
germanium (60%). Consequently, the presence of lithium AOs
significantly stabilizes HOMO À 5 with respect to HOMO À 2.
Similarly, the degenerate HOMO(2e 0 ) levels of Ge5 are split in
Ge5Li4 into HOMO À 4 (Li-AOs: 18%) and HOMO À 6 (Li-AOs:
37%). Moreover, we find that while LUMO + 1 of Ge5 is mainly
composed of s-AOs and pxy-AOs of germanium atoms, the
pz-AOs considerably participate in its LUMO. Due to a stronger
interaction between s-AOs(Li) and the symmetry of s- and pxy-AOs,
the electrons from lithium are favored to occupy the LUMO + 1 of
Ge5 rather than its LUMO. The MO picture of Ge5Li3 is very similar
to that of Ge5Li4, except for the fact that the highest MO of Ge5Li3
is only singly occupied (see Fig. S9 of the ESI†).

D Conclusion

Fig. 8

Total and partial densities of states of Ge5Li0–4 clusters.

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We reported a combined experimental and theoretical study
of the binary lithium–germanium clusters GenLim (n = 5–10
and m = 1–4) in both neutral and cationic states. Based on
DFT calculations at the B3LYP/6-311+G(d) level we can make

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Fig. 9

Shapes of molecular orbitals of Ge5 (middle), Ge5Li (left) and Ge5Li4 (right).

three observations: (i) NBO population analysis shows large net
positive atomic charges on all lithium atoms of GenLim. (ii) The
cation GenLim+1+ has for most n and m the same geometric
shape as the lowest energy structure found for the neutral
GenLim. (iii) The neutral GenLim clusters can be formed by

adsorbing lithium atoms on either the triangular or rhombic
faces of the Gen framework. A preference for the rhombic faces
is observed for small GenLim (n r 8) clusters, whereas adsorbing on triangular faces becomes predominant for larger clusters
(n Z 9). For all sizes, the lithium atoms tend to avoid each
other. (iv) Mono- and di-lithiated germanium clusters GenLi1,2
hold the host Gen frameworks unchanged, while lithium richer
clusters have distorted Gen frameworks. In general the germanium core is similar to the corresponding bare anionic germanium cluster. The neutral GenLim and cationic GenLim+ clusters

Phys. Chem. Chem. Phys.

À

can thus be considered as GenmdÀ–mLid+ and Gen(md +1)–mLid+
complexes.
The experimental ionization efficiency curves of selected GenLim
clusters are determined for the first time, which allows for
experimental verification of the calculated structures. There is an
overall good agreement between the experimental and theoretical
VIE and AIE values, which supports the assignment of the
calculated lowest energy isomers as those that are produced in
the experiment. For a few sizes, such as Ge7Li2 and Ge7Li3, the
ionization energies of the computed lowest energy isomers do not
agree with the experiment. However, good agreement between the
computed and measured ionization energies is found with isomers
that are slightly higher in energy than the predicted ground states.
This result demonstrates the use of the ionization energy measurements as benchmark data for the computational approach.

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There is a parallelism between the average absorption
energy (Ed) for the lithium atom in GenLi and the electron
affinity of pure Gen species. Analysis of the density of states and
the shapes of the molecular orbitals demonstrated that the
Ge5Lim clusters with unchanged Gen frameworks have bonding
features similar to those of their corresponding Gen clusters
whose LUMO and LUMO + 1 receive electrons donated by
lithium atoms and the resulting complexes are stabilized
by electrostatic forces. The bonding patterns of the Ge5Li3,4
species with the distorted Gen frames differ from those of the
pure Gen species. The lithium atoms in these systems give
important contributions to deeper-lying molecular orbitals
rather than to their highest MOs.

17

18

19
20
21

Acknowledgements

22

This work is supported by the Research Foundation – Flanders
(FWO), the KU Leuven Research Council (BOF, GOA, and IDO
programs), and the Belgian Interuniversity Attraction Poles
(IAP) research program. T.B.T. thanks the Arenberg Doctoral
School of the KU Leuven for a scholarship and H.T.L. acknowledges
the Vietnamese Government (MOET program 322).

23

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