Cite this: DOI: 10.1039/c3cp44395gStructures and ionization energies of small lithium doped germanium clusters† Jorg De Haeck,aTruong Ba Tai,bSoumen Bhattacharyya,zaHai Thuy Le,a Ewald J
Trang 1Cite this: DOI: 10.1039/c3cp44395g
Structures and ionization energies of small lithium doped germanium clusters†
Jorg De Haeck,aTruong Ba Tai,bSoumen Bhattacharyya,zaHai Thuy Le,a Ewald Janssens,aMinh Tho Nguyenband Peter Lievens*a
We present a combined theoretical and experimental investigation of neutral and cationic lithium doped germanium clusters, Ge n Li m (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 Genmd –mLi d+ and Gen(md+1) –mLi d+
complexes This is also illustrated by the strong correlation between the size dependent lithium adsorption energies in Ge n Li and the Ge n electron affinities Neutral Ge n Li m clusters are formed by adsorbing lithium atoms on either triangular or rhombic faces of the Ge n framework with the lithium atoms tending to avoid each other The chemical bonding phenomena of clusters are analyzed in detail using the densities of states and molecular orbitals.
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.4and demonstrated the electric field
control of ferromagnetism in metal–oxide–semiconductor
ferro-magnetism 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.5,6However, 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
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,32,33are ideal anode materials for lithium ion batteries with a high theoretical capacity of 1600 and 4200 mA h g1, respectively,34–36that are much higher than the value of 372 mA h g1of 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, 0,1) have extensively been investigated, both experimentally and theoretically.29,30,37–42These 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 GenLimare 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
a Laboratory of Solid State Physics and Magnetism, KU Leuven,
Celestijnenlaan 200D, B-3001 Leuven, Belgium E-mail: peter.lievens@fys.kuleuven.be
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.
Received 6th December 2012,
Accepted 13th February 2013
DOI: 10.1039/c3cp44395g
www.rsc.org/pccp
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Trang 2work reported earlier on small mixed GenLimclusters using both
mass spectrometry and quantum chemical computations.29,45It
was shown that lithium doped germanium clusters are able to
form gas phase nanowires based on the Ge9building blocks.45
Nevertheless, the identity of the lowest-energy structure for small
GenLimclusters 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
hno 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 GenLimclusters 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 GenLimspecies 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 GenLimclusters 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 mm2 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 GenLimclusters with different
amounts of lithium (for a given n) The isotope patterns of
different GenLimclusters 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 produc-tion fluctuaproduc-tions 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 cm2to 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 GenLimclusters 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 normal-ized 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 model47as discussed in our recent work.30,31Basically 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 ioniza-tion threshold can differ from the adiabatic ionizaioniza-tion 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
Trang 3determined with the hybrid B3LYP functional, which involves
the Becke three-parameter exchange49and the Lee–Yang–Parr
correlation50functional The search for possible low-lying
iso-mers of GenLim(n = 5–10; m = 1–4) is performed using a recently
developed stochastic search algorithm.15Briefly, possible structures
for each GenLim cluster are generated by a kick-procedure and
optimized at the B3LYP/6-31G level.51In this kick-procedure, the
minimum and maximum distances between atoms are random
and limited toB2 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 GenLimclusters
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 cm2 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
composi-tion It is known that bare Gen clusters with no 18 cannot
efficiently be ionized by 6.42 eV photons.14Hence, 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
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
Ge7in Fig 1b is underestimated, as it is expected to be larger than the abundance of Ge6.14These observations underline the importance of photoionization efficiency in the analysis of
GenLimmass 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
Fig 1 Typical mass spectra of neutral GenLimclusters after laser postionization with (a) 6.42 eV photons and (b) 7.89 eV photons using a laser fluence of
200 mJ cm 2 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 Ge n clusters with reduced photoionization efficiency at 7.89 eV (compared to ref 14).
Trang 4(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,31,55and 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.31In 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 Ge7Li3and Ge8Li3all 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,
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
Fig 2 PIE curves of the Ge n Li m 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.
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.
Trang 5energies of 5.3n.1 and 5.3n.2 are basically the same
Conse-quently, these two structures are considered as the degenerate
global minima of Ge5Li3 The C2vstructure 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 Genframeworks 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
the most stable isomers of Ge5Li+, Ge5Li2 and Ge5Li4 , respec-tively 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,1A0) 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 Ge6Li3and 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 Ge7.16For 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 Ge7Li3and
Ge7Li4clusters favor geometries with distorted Ge7frameworks 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
Ge7Li4clusters, the structures 7.4n.1 and 7.4n.2 in each of which two Ge3moieties are connected together by a single germanium atom and a few lithium atoms are the lowest-lying isomers In the
Fig 4 The shape, relative energies (eV), point groups and electronic states of
the lowest-energy isomers of Ge 7 Li m0/+(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.
Fig 6 The shape, relative energies (eV), point groups and electronic states of the lowest-energy isomers of Ge 9 Li m0/+(m = 1–4) and Ge 10 Li m0/+(m = 1–4) clusters.
Trang 6cationic 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 Ge7Li3clusters
is reversed The most stable Ge7Li3 isomer is the Csstructure
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 Csstructure 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 Ge8structure is the
lowest-lying isomer,16but 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 Ge8host 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 C1structure 8.3n.2 whose Ge8frame is strongly distorted For Ge8Li4the most stable isomer has a C1structure 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
Table 1 Calculated adiabatic (AIE) and vertical (VIE) ionization energies for the lowest energy isomers of Ge n Li m (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
Cluster
5.3n.1 - 5.3c.3 5.54
Ge10Li1 10.1n.12A 0 - 1 A 0 6.20 >6.05 10.1n.1 - 10.1c.1 5.52 5.65 (0.24)
Trang 7faces 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 Ge9,10Li1–4retain the germanium framework of the
corresponding pure Gen clusters Similar to the Ge8Limseries,
there are a large number of isomers with very small relative
energies located on the potential energy surfaces of Ge9Limand
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
Struc-tures 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
postioniza-tion with 6.42 eV photons, but no VIE could be derived, the
ionization threshold is indicated byo6.42 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
Ge5Li2show up in the abundance spectrum taken by
postioni-zation with 7.89 eV photons, but not or to a minor extent in the
spectra taken by postionization with 6.42 eV photon
For Ge5Li3the 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 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
experi-mental value of 5.26 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 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 0.14 eV
In general, the comparison of the experimental and
com-puted 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
isomer of Ge6Li2, 6.2n.1 This is consistent with the experi-mental 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 0.02 eV and 6.03 0.02 eV, respectively The experimental ionization energy of Ge6Li3is smaller than 5.50 eV and a large difference between the ionization threshold and the VIE of Ge6Li3can 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 ioniza-tion 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
Ge6Li4are 5.93 and 5.71 eV, respectively These values are some-what larger, though still in reasonable agreement with the experi-mental values of 5.87 0.02 eV and 5.57 0.05 eV, respectively
Ge7Li1–4 Experimental ionization energies could be deter-mined for Ge7Limwith m = 1–4 The experimental VIE (5.86 0.02 eV) and AIE (5.63 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 Ge7Li2several isomers, 7.2n.1, 7.2n.2, and 7.2n.3, are found close in energy The experimental VIE of 5.85 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 Ge7Li3the 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 0.02 eV and 5.59 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 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 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 Ge7Limwith
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 ioniza-tion 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 Ge8Limwith 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
Ge8Li2is 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)
Trang 8The 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 0.02 eV, the
AIE agrees well with the measured ionization threshold of 5.20
0.21 eV For Ge8Li4the 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 0.03 eV and AIE = 5.58 eV, AIEexpt=
5.73 0.12 eV)
Ge9Li1–4and 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 Genframework to form Gendm–nLid+complexes or
ion pairs Such a bonding behavior was also seen in other lithium
doped clusters such as BnLi,17,26,27AlnLi,28and SinLim.30,31
Due to the fact that lithium atoms effectively donate their
valence electron to form the Gendm–nLid+ complexes, the
adsorbing energies of lithium on Gen are expected to show a
parallel trend to the Gen electron affinities This
correspon-dence was also found in lithium and sodium doped silicon
clusters.37–40The average adsorption energy per lithium dopant
(Ed) is defined as Ed= [E(Gen) + mE(Li) E(GenLim)]/m, where
E(Li), E(Gen), and E(GenLim) are total energies of the lithium
atom and the Genand GenLimclusters, respectively Edis plotted
in Fig 7 for GenLi (n = 5–10) and compared with the electron
affinities (EAs) of Gen, which is defined as EA = E(Gen)
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
summarized as follows: there are no Li–Li bonds The neutral
GenLimclusters 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 Ge5–7Li3,4favor 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 Genframeworks of Ge6,7Li3,4are consider-ably 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 GenLimand cationic
GenLim+clusters can thus be considered as Genmd–mLid+and
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.16,56In general, a good correspondence is found between the germa-nium core in GenLim0,+ and the corresponding bare anionic germanium cluster, Genm,(m1) The global minima of the
Ge5 dianion and the Ge5 anion are both a trigonal bipyr-amid 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 corre-sponding germanium frameworks of Ge5Li1and Ge5Li2, as well
as for Ge5Li2 and Ge5Li3 The bipyramid is also stretched with increasing lithium content Analogously, the global minimum
of the Ge7dianion is a pentagonal bipyramid of D5h symme-try, similar to the neutral ground state, but stretched along its axis with increasing negative charge.16Ge7Li1, Ge7Li2, Ge7Li2, and Ge7Li3 all have similar structures (see Fig 4) However, there is disagreement for n = 6; while Ge6(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 Ge8 dianion is expected to adopt a tetracapped tetragonal shape, in agreement with the structure
of Ge8Li2.16This 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 Ge8
which has a hexagonal face.16 Ge9 (x = 2–4) clusters have tricapped trigonal prism (TTP) structures, while the capped
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).
Trang 9square antiprism (CSA) is an alternative for the ground state of
Ge9.16 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 Ge9and Ge9Lixis still very strong
The anion and the dianion of Ge10both 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 GenLimclusters can electronically be regarded as Gendm–
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, Ge5Limis 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 Ge5Li1–4clusters 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 Ge5Li3and 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 Ge5frames They transfer their valence electron and do not take part in the bonding of the Ge5moiety
In Ge5Li3 and Ge5Li4, some lithium atoms are adsorbed on rhombic faces of the distorted Ge5frameworks 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 contribu-tion of the lithium AOs in Ge5Li3and Ge5Li4is found at deeper frontier MOs (HOMO 5 and HOMO 6 for both Ge5Li3and
Ge5Li4) These results are remarkable as earlier studies on the
SinLimand SinNanclusters 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 Ge5and 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 Ge5Li2cluster 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 Ge5instead of its LUMO Additionally, the ordering of the highest occupied MOs of Ge5Li4is also changed considerably The CMO analysis reveals that MOs having a larger contribu-tion from lithium AOs are more stable For instance, the degenerate HOMO 1(1e00) MOs of Ge5are split into HOMO 2(1a2) and HOMO 5(2b1) of Ge5Li4 While HOMO 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 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 5 with respect to HOMO 2 Similarly, the degenerate HOMO(2e0) levels of Ge5are split in
Ge5Li4into HOMO 4 (Li-AOs: 18%) and HOMO 6 (Li-AOs: 37%) Moreover, we find that while LUMO + 1 of Ge5is 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
Ge5rather than its LUMO The MO picture of Ge5Li3is 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
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
Fig 8 Total and partial densities of states of Ge5Li0–4clusters.
Trang 10three 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 Genframework A preference for the rhombic faces
is observed for small GenLim(nr 8) clusters, whereas
adsorb-ing 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 Genframeworks unchanged, while lithium richer
clusters have distorted Genframeworks In general the
nium core is similar to the corresponding bare anionic
germa-nium cluster The neutral GenLimand cationic GenLim+clusters
can thus be considered as Genmd–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 measure-ments as benchmark data for the computational approach
Fig 9 Shapes of molecular orbitals of Ge 5 (middle), Ge 5 Li (left) and Ge 5 Li 4 (right).