PCCP View Article Online PAPER View Journal Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G Cite this: DOI: 10.1039/c3cp44395g 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 www.rsc.org/pccp 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: 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 This journal is c the Owner Societies 2013 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 Phys Chem Chem Phys View Article Online Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G Paper 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 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 Phys Chem Chem Phys PCCP 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 This journal is c the Owner Societies 2013 View Article Online Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G PCCP Paper 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 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, 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 This journal is c the Owner Societies 2013 Fig 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 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 Phys Chem Chem Phys View Article Online Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G Paper PCCP Fig 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, Phys Chem Chem Phys Fig 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 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 This journal is c the Owner Societies 2013 View Article Online Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G PCCP Paper Fig The shape, relative energies (eV), point groups and electronic states of the lowest-energy isomers of Ge7Lim0/+ (m = 1–4) clusters Fig 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 This journal is c the Owner Societies 2013 Fig 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 ) 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 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 Phys Chem Chem Phys View Article Online Paper PCCP Table 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 A - 2A B2 - 1A1 7.02 6.63 6.61 5.80 Ge5Li4 5.3n.2 2A00 - 1A 5.4n.1 1A1 - 2B1 5.78 5.19 - A1 A - 2A 00 A - 1A B2 - 1A1 A1 - 2A1 6.82 6.14 6.24 4.88 5.93 >6.24 6.21 (0.02) — B2 - 1A1 A - 2A A - 2A A1 - 2B1 B2 - 1A1 A - 1A A - 1A 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 Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G Calc 6.1n.1 6.2n.1 6.3n.1 6.3n.2 6.4n.1 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 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 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 B2 1 A A A A A A - A A A A A A 6.71 6.41 6.75 6.39 5.40 5.90 A1 - 1A1 A - 2A A - 1A A - 2A 6.79 6.63 5.92 5.78 - 1A - 2A - 1A - 2A 6.20 6.38 5.45 5.39 A A A A 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 This journal is c the Owner Societies 2013 View Article Online PCCP Paper Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G faces of the Ge9 and Ge10 parents.16 The shapes of the most stable isomers are shown in Fig 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 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 Ỉ 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 Ỉ 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 Ỉ 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 This journal is c the Owner Societies 2013 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 Ỉ 0.02 eV and 6.03 Ỉ 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 Ỉ 0.02 eV and 5.57 Ỉ 0.05 eV, respectively Ge7Li1–4 Experimental ionization energies could be determined for Ge7Lim with m = 1–4 The experimental VIE (5.86 Ỉ 0.02 eV) and AIE (5.63 Ỉ 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 Ỉ 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 Ỉ 0.02 eV and 5.59 Ỉ 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 Ỉ 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 Ỉ 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 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 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) Phys Chem Chem Phys View Article Online Paper Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G 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 Ỉ 0.02 eV, the AIE agrees well with the measured ionization threshold of 5.20 Ỉ 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 Ỉ 0.03 eV and AIE = 5.58 eV, AIEexpt = 5.73 Ỉ 0.12 eV) Ge9Li1–4 and Ge10Li1–4 Additionally, Table 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 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 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 = 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 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 PCCP 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 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 This journal is c the Owner Societies 2013 View Article Online PCCP Paper Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G 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 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 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 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 and HOMO À 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 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 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 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 with respect to HOMO À Similarly, the degenerate HOMO(2e ) levels of Ge5 are split in Ge5Li4 into HOMO À (Li-AOs: 18%) and HOMO À (Li-AOs: 37%) Moreover, we find that while LUMO + 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 + 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 Total and partial densities of states of Ge5Li0–4 clusters This journal is c the Owner Societies 2013 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 Phys Chem Chem Phys View Article Online PCCP Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G Paper Fig 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 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 This journal is c the Owner Societies 2013 View Article Online Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G PCCP Paper 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 + 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 References 27 28 T Jungwirth, J Sinova, J Masek, J Kucera and A H MacDonald, Rev Mod Phys., 2006, 78, 809 H Akai, Phys Rev Lett., 1998, 81, 3002 S A Wolf, D D Awschalom, R A Buhrman, J M Daughton, S von Molnar, M L Roukes, A Y Chtchelkanova and D M Treger, Science, 2001, 294, 1488 F Xiu, Y Wang, J Kim, A Hong, J Tang, A P Jacob, J Zou and K L Wang, Nat Mater., 2010, 9, 337 M Moskovits, Annu Rev Phys Chem., 1991, 42, 465 K D Sattler, Handbook of Nanophysics: Clusters and Fullerenes, CRC Press, 2011 J M Hunter, J L Fye, M F Jarrold and J E Bower, Phys Rev Lett., 1994, 73, 2063 Q L Zhang, Y Liu, R F Curl, F K Tittel and R E Smalley, J Chem Phys., 1988, 88, 1670 Y Liu, Q L Zhang, F K Tittel, R F Curl and R E Smalley, J Chem Phys., 1986, 85, 7434 10 L Xu and S C Sevov, J Am Chem Soc., 1999, 121, 9245 11 A Ugrinov and S C Sevov, J Am Chem Soc., 2002, 124, 10990 12 C Downie, Z Tang and A M Guloy, Angew Chem., Int Ed., 2000, 39, 337 13 L Z Zhao, W C Lu, W Qin, Q J Zang, C Z Wang and K M Ho, Chem Phys Lett., 2008, 455, 225 14 (a) S Yoshida and K Fuke, J Chem Phys., 1999, 111, 3880; (b) K Fuke and S Yoshida, Eur Phys J D, 1999, 9, 123 15 T B Tai and M T Nguyen, J Chem Theory Comput., 2011, 7, 1119 16 (a) R B King, I Silaghi-Dumitrescu and A Kun, Dalton Trans., 2002, 3999; (b) R B King and I Silaghi-Dumitrescu, Inorg Chem., 2003, 42, 6701; (c) R B King, I Silaghi-Dumitrescu and This journal is c the Owner Societies 2013 24 25 26 29 30 31 32 33 34 35 36 37 38 39 40 41 42 A Lupan, Dalton Trans., 2005, 1858; (d) R B King, I SilaghiDumitrescu and A Lupan, Chem Phys., 2006, 327, 344; (e) R B King, I Silaghi-Dumitrescu and M M Uta, Inorg Chem., 2006, 45, 4974 (a) T B Tai and M T Nguyen, Chem Phys Lett., 2010, 492, 290; (b) T B Tai, H M T Nguyen and M T Nguyen, Chem Phys Lett., 2011, 502, 187; (c) T B Tai and M T Nguyen, J Phys Chem A, 2011, 115, 9993 J Wang, L Ma, J Zhao and G Wang, J Phys.: Condens Matter, 2008, 20, 335223 V Kumar and Y Kawazoe, Appl Phys Lett., 2002, 80, 859 J Wang and J G Han, Chem Phys., 2007, 342, 253 G Gopakumar, P Lievens and M T Nguyen, J Chem Phys., 2006, 124, 214312 G Gopakumar, P Lievens and M T Nguyen, J Phys Chem A, 2007, 111, 4355 G Gopakumar, V T Ngan, P Lievens and M T Nguyen, J Phys Chem A, 2008, 112, 12187 X J Hou, G Gopakumar, P Lievens and M T Nguyen, J Phys Chem A, 2007, 111, 13544 T B Tai and M T Nguyen, Chem Phys., 2010, 375, 35 A N Alexandrova, A I Boldyrev, H J Zhai and L S Wang, J Chem Phys., 2005, 122, 054313 Q S Li and Q Jin, J Phys Chem A, 2004, 108, 855 C Majumder, G P Das, S K Kulshrestha, V Shah and D G Kanhere, Chem Phys Lett., 1996, 261, 515 V T Ngan, J De Haeck, H T Le, G Gopakumar, P Lievens and M T Nguyen, J Phys Chem A, 2009, 113, 9080 N M Tam, V T Ngan, J de Haeck, S Bhattacharyya, H T Le, E Janssens, P Lievens and M T Nguyen, J Chem Phys., 2012, 136, 024301 J De Haeck, S Bhattacharyya, H T Le, D Debruyne, N M Tam, V T Ngan, E Janssens, M T Nguyen and P Lievens, Phys Chem Chem Phys., 2012, 14, 8542 M H Park, K Kim, J Kim and J Cho, Adv Mater., 2010, 22, 415 C K Chan, X F Zhang and Y Cui, Nano Lett., 2008, 8, 307 G L Cui, L Gu, L J Zhi, N Kaskhedikar, P A Aken, K Mullen and J Maier, Adv Mater., 2008, 20, 3079 W J Weydanz, M Wohlfahrt-Mehrens and R A Huggins, J Power Sources, 2003, 81, 237 H Lee, M G Kim, H H Choi, Y K Sun, C S Yoon and J Cho, J Phys Chem B, 2005, 109, 20719 H Wang, W C Lu, Z S Li and C C Sun, THEOCHEM, 2005, 730, 263 (a) C Sporea, F Rabilloud, X Cosson, A R Allouche and M Aubert-Frecon, J Phys Chem A, 2006, 110, 6032; (b) C Sporea, F Rabilloud and M Aubert-Frecon, THEOCHEM, 2007, 802, 85 D Hao, J Liu and J Yang, J Phys Chem A, 2008, 112, 10113 J C Yang, L Lin, Y Zhang and A F Jalbout, Theor Chem Acc., 2008, 121, 83 V T Ngan, P Gruene, P Claes, E Janssens, A Fielicke, M T Nguyen and P Lievens, J Am Chem Soc., 2010, 132, 15589 P Claes, E Janssens, V T Ngan, P Gruene, J T Lyon, D J Hardling, A Fielicke, M T Nguyen and P Lievens, Phys Rev Lett., 2011, 107, 173401 Phys Chem Chem Phys View Article Online Downloaded by KU Leuven University Library on 01 March 2013 Published on 14 February 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44395G Paper 43 R Kishi, S Iwata, A Nakajima and K Kaya, J Chem Phys., 1997, 107, 3056 44 J Graetz, C C Ahn, R Yazami and B Fultz, J Electrochem Soc., 2005, 151, A698 45 G Gopakumar, X Wang, L Lin, J De Haeck, P Lievens and M T Nguyen, J Phys Chem C, 2009, 113, 10858 46 W Bouwen, P Thoen, F Vanhoutte, S Bouckaert, F Despa, H Weidele, R E Silverans and P Lievens, Rev Sci Instrum., 2000, 71, 54 47 T Bergmann and T P Martin, J Chem Phys., 1989, 90, 2848 48 M J Frisch, et al., Gaussian 03, Revision D.02, Gaussian, Inc., Wallingford, CT, 2004 49 A D Becke, J Chem Phys., 1993, 98, 5648 Phys Chem Chem Phys PCCP 50 C Lee, W Yang and R G Parr, Phys Rev B: Condens Matter Mater Phys., 1988, 37, 785 51 W J Stevens, M Krauss, H Basch and P R Jasien, Can J Chem., 1992, 70, 612 52 R C Binning and L A Curtiss, J Comput Chem., 1990, 11, 1206 53 A E Reed and F Weinhold, J Chem Phys., 1983, 78, 4066 54 R Dennington, T Keith and J Millam, GaussView, Version 5, Semichem Inc., Shawnee Mission, KS, 2009 55 O Kostko, S R Leone, M A Duncan and M Ahmed, J Phys Chem A, 2010, 114, 3176 56 W Xu, Y Zhao, Q Li, Y Xie and H F Schaefer III, Mol Phys., 2004, 102, 579 This journal is c the Owner Societies 2013