Bismuth-Doped Tin Clusters: Experimental and Theoretical Studies of

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Bismuth-doped tin clusters: Experimental and theoretical studies of neutral Zintl analogues. Sven Heiles,∗,† Roy L. Johnston,‡ and Rolf Schäfer† Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Petersenstrasse 20, 64287 Darmstadt, Germany, and School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, U.K. E-mail: [email protected]

∗ To

whom correspondence should be addressed University of Darmstadt ‡ University of Birmingham † Technical

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Abstract

The electron count of gas phase clusters is increased gradually by element substitution in order to mimic the total number of electrons of known stable closo-clusters. A combination of elements from the 4th and 5th group of the periodic table such as Sn and Bi are well suited for this approach. Hence, these small Sn-Bi clusters are investigated employing the electric field deflection method. For clusters in the series SnM−N BiN (M = 5 − 13, N = 1 − 2) the beam profiles obtained in cryogenic experiments are dominated by beam broadening, indicating the presence of a permanent electric dipole moment which is sensitive to the (rigid) cluster structure. An intensive search for the global minimum structure employing a density functional theory/ genetic algorithm method is performed. Dielectric properties for the identified low energy isomers are computed. The structural and dielectric properties are used in beam profile simulations in order to discuss the observed beam profiles. Comparison of theoretical and experimental results enables identification of the growing pattern of these small bimetallic clusters. For multiply doped clusters it is concluded that the dopant atoms do not form direct Bi-Bi bonds but more interestingly a rearrangement of the cluster skeleton becomes apparent. The structural motifs are different from pure tin clusters but rather are rationalized using the corresponding structures of tin anions or are based on the Wade-Mingos concept. Further evidence for this idea is deduced from nuclear independent chemical shift calculations which show nearly identical behaviour for negatively charged pure and neutral bimetallic clusters. All these findings are consistent with the idea of neutral Zintl analogues in the gas phase.

Introduction The concept of Zintl ions and phases has a longstanding tradition in the chemistry of main group elements. 1,2 A general definition of the concept of Zintl ions and phases could be that elements be-



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yond the Zintl boundary 3 form isolated (poly)ions or (poly)anionic networks. While for most cases of Zintl phases the Zintl-Klemm-Busmann 4 rule holds, Zintl ions can be rationalized within the framework of the Wade-Mingos concept. 5 The last mentioned concept states that closo-polyhedra form stable entities if a valence electron count of 2n + 2, contributing to bonds within the cluster skeleton (with n vertices), is satisfied. Following this idea closo-clusters with ..., 22, 24, 26, 28, ... valence electrons can be regarded as stable and form characteristic structures. Other typical concepts of simple electron counting rules for clusters are the jellium model 6,7 (2, 8, 20, 40, ... ) and Hirsch’s electron counting rule 8,9 (2, 8, 18, 32, ...) which also predict enhanced stability for a well defined valence electron numbers. While the first concept results from molecular orbital considerations for bound electrons the later two hold if the valence electrons move freely in or on a sphere, respectively. For simple metal clusters enhanced stability and characteristic properties are often, to a first approximation, discussed within the jellium model. 7,10 Unfortunately, this concept fails for most main group elements for which the inorganic chemistry community discuss enhanced stability and "aromaticity", 9,11 using the prior stated Hirsch rule or the Wade-Mingos concept. The discovery of [KSn12 ]− 12 and [Al@Pb12 ]+ 13 triggered efforts to unify ideas for solid state and gas phase clusters in order to understand the observed properties in a simple model. 14 In the course of stressing this simple concept bimetallic clusters which still fulfill the required electron count were investigated in the gas 15–18 and bulk phase 19 showing that these simple concepts apply (at least partially) to anionic, bimetallic species. Following this idea several questions arise: What happens if the composition of the cluster is changed in a way that the required valence electron count is achieved leaving the cluster uncharged? Do these clusters mimic the structures of isovalent inorganic Zintl cages or does the model fail? Is the position of the dopant atom(s) in the bimetallic cluster specified or interchangeable? Therefore, here we present a combined experimental and theoretical investigation of small mono- and bi-doped Sn-Bi clusters. For the series of neutral SnM−1 Bi1 and SnM−2 Bi2 clusters the valence electron count is successively changed compared to pure tin species. The structural change of the clusters is investigated by applying the electric field deflection method. 10,20–22 Experimental


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results are compared to theoretically predicted isomers found using a recently developed density functional theory/genetic algorithm (DFT/GA) routine. 23 Structural implications for Sn-Bi clusters are discussed and the validity of simple electron counting rules is critically tested, in an attempt to answer the questions posed above.

Methods Experimental methods The experimental setup has previously been reported in the literature 24 and we only give a brief description here. The bimetallic clusters are produced by a laser vaporization source. A plasma is formed by irradiating pulsed light (1064 nm) of a Nd:YAG (yttrium aluminum garnet) laser on a composite tin-bismuth rod. The plasma is cooled by injection of a helium pulse whereby it condenses to form mixed Sn-Bi clusters. The helium-cluster mixture is then expanded through a nozzle into a high vacuum apparatus, thereby forming a supersonic beam of SnM−N BiN clusters. In order to control the supersonic beam expansion the leading 25 mm of the 61 mm long nozzle (2 mm diameter) can be cooled with the help of a helium refrigerator to ∼ 30 K. By reducing the nozzle temperature the kinetic energy of the clusters in the molecular beam is lowered, in addition to the fact that a cooling of the internal degrees of freedom of the clusters occurs. In the present work, experiments were performed with a nozzle temperature of (33.0 ± 0.1) K. After the supersonic expansion a double skimmer narrows the beam diameter before passing a homemade chopper for measuring the cluster velocities. 25 Behind two collimators, the molecular beam reaches the inhomogeneous electric "two-wire" field, which is oriented perpendicular to the molecular beam axis. The distance between the two electrodes is 1.5 mm and the maximum value of the electric field is 2 × 107 V/m at an applied deflection voltage U of 30 kV. After passing a field free drift region (about ∼ 1.6 m) the alloy clusters reach a movable slit having a width of 400 µ m and are subsequently ionized by a low fluence excimer laser (7.89 eV). The ionized clusters enter a timeof-flight mass spectrometer (TOF-MS), are deflected perpendicular to the molecular beam axis and 4 ACS Paragon Plus Environment


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are detected in an Even-cup/Photomultiplier assembly. By repeating this procedure for different slit positions p the molecular beam profile is obtained. In order to quantify the measured electric dipole moments and polarizabilities, the known polarizability of the Ba atom was used to re-calibrate the apparatus. Therefore the reported dielectric properties have an absolute uncertainty of about 8%. The additional experimental uncertainties are the fluctuations of the cluster intensity and the measurment of the velocity. The first gives a typical uncertainty of 10% for the intensity, the second an error of 3% for the velocity determination. Therefore, the determination of µ and α by comparison with simulation results are afflicted with a uncertainty of ∼ (10 − 15)%. Additionally, the limited mass resolution results in overlapping mass peak signals. Therefore, a contribution to the beam deflection profile of other sizes and compositions cannot be excluded but is regarded as minor effect because the beam profiles of clusters with comparible masses are often very different (see Supporting Information). The bimetallic target rods, necessary in order to produce SnM−N BiN clusters were synthesized by melting the two elements (Sn 99.99% Alfa-Aesar; Bi 99.997% GoodFellow) in a quartz tube at 520 K. The metal melt was carfully homogenized for several minutes and subsequentely cooled rapidly to room temperature (less than 5 min) in order to produce homogeneous, polycrystalline sample rods. The resulting samples had a bismuth mass content of 16% and were used after reducing the rod size to the required diameter. Only small mixed clusters (M = 5 − 13) are analyzed in the following sections for several reasons. Firstly, due to the fact that small pure tin clusters (M < 13) are known in the literature, these can be compared to the results presented in this investigation. Secondly, the limited mass resolution of the TOF-MS [m/∆m ≈ (100 − 150)] in addition to the broad isotope distrubtion of Sn complicate the interpretation of the mass spectrum for larger clusters.

Theoretical methods In order to generate a large number of isomers for the investigated clusters two approaches were used. Firstly, an unbiased global optimization was performed using the DFT/GA program. In 5 ACS Paragon Plus Environment

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a second approach the isomers were created from known structures of tin clusters, 20 tin cluster anions 26 and closo − boranes 27 by substituting tin or B-H fragments with bismuth atoms. For an unbiased global optimization the newly implemented DFT/GA 23 approach, combining the PWscf program within the Quantum Espresso 28 package with the Birmingham Cluster Genetic Algorithm (BCGA) 29 code, was used. Details of the method are described elsewhere 23 therefore only a brief description is given here. Each DFT/GA run is initialized by geometrically relaxing fifteen clusters. For the following generations the offspring (80% of the population size) is created by using the "cut-and-paste" phenotypic crossover operation introduced by Deaven and Ho. 30 Additionally, mutants (20% mutation rate), made up of 50% new random structures and 50% atom-exchange moves, are added to the offspring to increase the structural diversity in each generation. After local geometry optimization the lowest lying structures are added to the population, replacing high energy isomers. This procedure is repeated until the energy of the lowest lying isomer changes by less than 1 mRy (∼ 13.605 meV) for ten generations. For the GA/DFT calculations four and five electrons are treated explicitly and the remaining 46 and 78 electrons for Sn and Bi, respectively, are described by newly generated normconserving Rabe-Rappe-KaxirasJoannopoulos 31 pseudopotentials, taking scalar-relativistic effects into account. The local spin density approximation (LSDA) exchange-correlation functional 32 is employed in addition to an energy cutoff of 35 Ry. In the next step all possible homotops 33 created from pure tin cluster(s) (anions) and closo − boranes in addition to all structures from the DFT/GA runs which are 0.5 eV higher in energy than the lowest found isomer are reoptimized and a harmonic frequency analysis is performed with NWChem v6.0, 34 in order to verify that the structures are energy minima. For this purpose an effective core potential, 35 an aug-cc-pVDZ-PP basis set 36 and the PBE0 37 functional are employed. For all structures Lanl2DZ 38 /PBE0 calculations were performed in NWChem for singlet (doublet) and triplet (quartet) spin states resulting in an energetic stabilization of the lower spin state by at least 0.4 − 0.5 eV. Hence aug-cc-pVDZ-PP/PBE0 calculations are performed only for the lowest possible spin configuration. Additional test calculations for an aug-cc-pVTZ-PP 36 basis demon-



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strated that the structural results (characterized by the moment of inertia tensor) and dielectric properties (value of the dipole moment) give almost identical results with respect to the typical experimental uncertainty (see Supporting Information). The choice of the functional was motivated by investigations of Assadollahzadeh et al., comparing the polarizability of Sn at the DFT level of theory with relativistic coupled cluster calculations. 39 Therefore all calculations are performed at the aug-cc-pVDZ-PP/PBE0 level theory unless otherwise stated. Using the same level of theory the dipole moment, polarizability and nuclear-independent chemical shift (NICS) 40 using the gaugeindependent atomic orbital (GIAO) 41 method at the center of the cluster are computed with the Gaussian03 42 software package for the four lowest lying isomers or all isomers 0.5 eV higher in energy than the located ground state (GS). Additionally, NICS calculations for the corresponding 2− 3− GS’s of Sn− M , SnM and Sn9 are performed.

The resulting dielectric and structural parameters are used in classical beam deflection profile simulations introduced by Dugourd and coworkers. 43 Details of the method are described elsewhere 22 and only the main principles are discussed here. By Monte-Carlo (MC) sampling for a given rotational temperature, a set of rigid clusters 44 with various rotational energies and orientations is generated and for each cluster the classical equations of motion are solved in an electric field, resulting in a time average of the electric dipole moment hµ it . Using the cluster velocity v, cluster mass m, electric field and field gradient EZ and ∂ EZ /∂ Z, apparatus constant A and the isotropic electronic polarizability α the deflection of a cluster can be obtained as

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A ∂ EZ (hµ it + α EZ ). mv2 ∂ Z

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A rough approximation 20 shows that the dipole moment will lead to a broadening and the polarizability to a deflection of the beam profile. A convolution of all computed deflections d with the beam profile without electric field results in a simulated beam deflection profile if the statistical weight taken from the MC simulation is used. Therefore, the only free parameter, given that the dipole moment, polarizability and moment of inertia are available from quantum chemistry, is the


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rotational temperature. The influence of the rotational temperature on the molecular beam profile simulations is illustrated in Figure S2. The rotational temperature for which the best agreement between the simulations and data points for most clusters was obtained is likely to be the experimental temperature. Here this procedure yielded a rotational temperature of 6 K (with an estimated uncertainty of ±62 K) which is a reasonable choice for supersonic molecular beams with a nozzle temperature of 33 K (for further experimental evidence see the Supporting Information). This temperature was used for all presented simulations. 20,22,45 All calculations and simulations were performed on the University of Birmingham’s BlueBEAR high performance computer. 46

Results and Discussion Doping a tin cluster with bismuth atoms increases the valence electron number successively. Each Bi atom contributes one extra valence electron to the cluster cage resulting in a formally reduced − cluster species. Therefore, SnM−2 Bi2 (SnM−1 Bi1 ) can be identified as analogues of Sn2− M (SnM ).

Using this simple analogy directly gives insight into the structural motifs of these bimetallic species. While the location of the dopant atom(s) can not easily be predicted the structures of the cluster species should mimic the structures of the corresponding tin cluster (poly)anions. The aim of the experimental and theoretical investigations presented here is to test this hypothesis and to show that the structural motifs of the clusters are consistent with simple electron counting rules. Therefore, theoretical predictions and experimental findings for SnM−N BiN (M = 7 − 13, N = 1 and M = 5 − 11, N = 2) are compared in the following Subsection. Some results for nine-atom clusters have been presented elsewhere in detail and are incorporated here for completeness only. 47 Firstly, bimetallic clusters are discussed for which the theoretically located GS isomer fits the experimental beam profile. For some clusters it is not possible to describe the beam profile only using the GS. For these cluster sizes the best description of the experimental data using predicted structural and dielectric parameters of slightly excited isomers are presented. Hence, apparent



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differences are discussed by taking slightly higher lying isomers and multiple isomers into account. Possible theoretical and experimental effects are discussed which can be used to explain the need to incorporate high energy isomers in the beam profile simulations. Where possible the obtained beam profiles are used to discriminate structural motifs. All of this information is then used to discuss the influence of bismuth atom(s) on the cluster structure. Additionally, all SnM−N BiN clusters with M = 5 − 13, N = 1, 2 are compared to pure tin (di)anions of the same size. The previously stated questions are subsequently discussed in terms of structural, dielectric and theoretical findings for Sn-Bi clusters. Since the field induced change of the beam profiles primarily depend on α as well as the magnitude and orientation of ~µ the corresponding parameters for all clusters discussed in the text can be found in Table 1. For all experimental data sets blue dots (red squares) correspond to measurements without (with) an applied electric field and the solid blue line is the best Gaussian fit to the data points without deflection voltage. The theoretical parameters and simulated beam profiles for all cluster sizes and isomers are included in the Supporting Information. Table 1: Calculation results for SnM−N BiN at the aug-cc-pVDZ-PP/PBE0 level of theory. The polarizability per atom α /M is given in units of Å3 . Additionally, the dipole moment µi (in the molecular coordinate system) and |µ | in D are presented. Isomer Sn6 Bi1 -GS Sn7 Bi1 -GS Sn9 Bi1 -I Sn11 Bi1 -GS Sn12 Bi1 -GS Sn3 Bi2 -GS Sn4 Bi2 -GS Sn6 Bi2 -GS Sn7 Bi2 -GS Sn8 Bi2 -I Sn9 Bi2 -I

α /M 7.26 7.41 7.16 7.09 7.41 7.43 7.28 7.29 7.12 7.12 7.18

(µx , µy , µz ) (-0.71, 0.00, 0.00) (0.46, -0.29, -0.12) (-0.62, 0.00, 0.00) (1.06, 0.00, 0.69) (0.13, 0.00, 0.00) (0.00, 0.00, 0.05) (0.00, 0.00, 0.00) (0.41, 0.00, 0.00) (0.00, 0.89, 0.00) (0.00, 0.00, 0.74) (-0.18, -0.98, -0.66)

|µ | 0.71 0.56 0.62 1.27 0.13 0.05 0.00 0.41 0.89 0.74 1.19

Isomer α /M Sn6 Bi1 -I 7.27 Sn8 Bi1 -GS 7.16 Sn10 Bi1 -I 7.19 Sn11 Bi1 -III 7.44 Sn12 Bi1 -II 7.41 Sn3 Bi2 -I 7.47 Sn5 Bi2 -GS 7.29 Sn6 Bi2 -I 7.30 Sn7 Bi2 -I 7.13 Sn9 Bi2 -GS 7.17 Sn9 Bi2 -III 7.19


(µx , µy , µz ) (0.00, 0.00, -0.16) (-0.66, 0.16, -0.13) (-0.46, 0.00, 0.48) (0.84, -0.74, 0.37) (0.24, -0.14, 0.16) (0.00, -0.06, 0.53) (0.00, -0.60, 0.00) (0.64, 0.50, 0.00) (-0.01, 0.00, 0.45) (0.00, 0.00, 1.38) (0.00, 0.00, -0.11)

|µ | 0.16 0.69 0.67 1.18 0.32 0.53 0.60 0.81 0.45 1.38 0.11

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Beam profile simulations for GS isomers As described above, a large number of possible isomers were generated in order to locate the GS structure. Ideally a beam profile simulation using exclusively the GS should reproduce the experimental results. Here we present the clusters for which this procedure yields good results. Beam deflection profiles for various SnM−1 Bi1 clusters are shown in Figure 1. The GS isomer located for Sn7 Bi1 is a pentagonal bipyramid with an additional atom over one of the triangular faces. As the Bi atom is located within the pentagonal ring below the capping atom the Cs symmetry is lowered to C1 . While for pure Sn8 the capping atom binds to the cluster via an edge 20 and the corresponding dianion forms the borane-like D2d structure, 27 the structure found for Sn− 8 (Ref. 26) is closely related to the GS for Sn7 Bi1 . Simulation (Figure 1) of the beam deflection profile of Sn7 Bi1 using this GS isomer and its dipole moment of 0.56 D (Table 1) gives satisfying agreement between theory and experiment. For Sn8 Bi1 , containing one more tin atom, by far the most stable structural motif is the tricapped trigonal prism (TTP) which is not found for neutral tin clusters 20 but is the GS structure for the corresponding (poly)anionic nine-atom clusters (or slightly distorted structures). 26,48 In the bimetallic species one tin atom of the trigonal prism is replaced by Bi resulting in a Cs symmetric structure. Using this GS isomer the beam broadening is slightly overestimated if the theoretically predicted dipole moment of 0.69 D is taken into account whereas the beam deflection is well described. In order to reproduce the experimental data (this discrepancy can be caused by theoretical and experimental reasons as discussed below) the dipole moment has to be smaller by ∼ 15%, which is however within the uncertainty of the experiment. Nevertheless, no other isomer close enough in energy is able to describe the beam profile satifactorily. The icosahedral GS of Sn11 Bi1 depicted in Figure 1 does not have the expected C5v but only has Cs symmetry due to a distortion of the cage. Again the structural motif agrees with findings 26 and not with corresponding pure tin cluster structures. 20 Interestingly, the doping of for Sn− 12

a bismuth atom into the tin cluster alters the structural motif dramatically in contrast to doping isovalent Pb for which a substitutional alloy formation is predicted, maintaining the structural motif 10 ACS Paragon Plus Environment


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Figure 1: Beam deflection profiles for SnM−1 Bi1 clusters at 15 kV and 33 K nozzle temperature. The classical beam deflection simulations, only using the shown GS isomers (blue for Bi, grey for Sn), result in the red solid line. The GS isomer dipole moment in the molecular coordinate system is indicated by a blue arrow. of the pure cluster. 49,50 The simulated beam profile for the GS isomer somewhat overestimates the observed beam broadening but retains the GS as a possible candidate structure. In contrast to the other clusters the beam deflection of Sn12 Bi1 shows only minor beam broadening and the mean of the profile is just slightly deflected towards higher field strength. This observation is in good agreement with the profile simulated for the GS isomer. The Cs symmetric structure of the bimetallic cluster is based on a tetracapped trigonal prism (TeTP) additionally decorated with three atoms located around the triangle-face capping atom of the TeTP. This structural motif is known for neutral tin clusters 20 and tin anions. 26 For multiply doped SnM−N BiN clusters various beam profiles, simulations and GS isomers are depicted in Figure 2. The smallest investigated cluster Sn3 Bi2 is isovalent with Sn2− 5 and adopts a trigonal bipyramidal structure in which the doping atoms occupy equatorial sites resulting in a C2v symmetric arrangement of atoms. For the described GS the computed dipole moment of 0.05 D is almost negligible (see Table 1). Due to the fact that no significant beam broadening or intensity drop at the maximum appears the GS isomer nicely agrees with the experimental data. Only a minor high field feature is not described by the beam profile simulation. This perhaps indicates a small contribution of a second isomer with a large dipole moment to the beam profile.



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Figure 2: Beam deflection profiles for SnM−2 Bi2 clusters at 15 kV and 33 K nozzle temperature. The classical beam deflection simulations, only using the shown GS isomers (blue for Bi, grey for Sn), result in the red solid line. The GS isomer dipole moment in the molecular coordinate system is indicated by a blue arrow. A similar observation is made for Sn4 Bi2 . The predicted GS isomer, a doped D4h symmetric octahedral structure (with the Bi atoms trans to one another) which does not possess a dipole moment, agrees perfectly with the experimental findings. Here only a small drop in intensity at the maximum is apparent which is within the experimental error. For the seven atom cluster Sn5 Bi2 beam broadening is observed, i.e. the cluster possesses a permanent dipole moment. Therefore, the symmetrically doped pentagonal bipyramid can be ruled out. In the calculations the shown C2v structure is found as the lowest energy isomer and its dipole moment of 0.60 D is sufficient to describe the molecular beam profile, encouraging the conclusion that this structure is predominantly present in the molecular beam. The triangular dodecahedron is realized for the GS of Sn6 Bi2 . This structural motif is predicted 2− 27 for Sn2− Due to the bismuth 8 and experimentally and theoretically characterized for B8 H8 .

doping the symmetry of the structure is lowered to C2v giving rise to a dipole moment of 0.41 D. Again the predicted GS structure and its dielectric properties describe the experimental data points. 12 ACS Paragon Plus Environment


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Experimental results for Sn7 Bi2 are shown in Figure 2. This nine-atom cluster consists of a TTP GS-motif in which the bismuth atoms occupy sites within the TP resulting in a C2 symmetric structure. Due to the low symmetry of Sn7 Bi2 a dipole moment of 0.89 D is computed for this isomer (Table 1) resulting in a satisfying description of the data points by the beam profile simulation. It is not always possible to describe all clusters only using the GS isomer. Hence, for some cases higher lying isomers and multiple isomer simulations must be taken into account as presented in the next Subsection.

Beam profile simulations including other isomers For several reasons it is not expected to uniquely identify the structures of all clusters. Predictions of GS isomers by DFT methods are in general questionable since exchange and correlation energies are introduced semi-empirically. Therefore, the cluster GS isomer can change depending on the DFT method, especially if the energy differences between the isomers are small. This is the case for bimetallic clusters for which many homotops exist with typical energy differences between (0.01 − 0.10) eV. Furthermore, the semi-empirical exchange-correlation contribution and the neglected spin-orbit coupling introduces somewhat arbitrary results for the electric dipole moments. Unfortunately, a critical theoretical analysis is missing which accurately describes the influence of both mentioned aspects on the value of the electric dipole moment for comparable systems. Some of these issues will be addressed in future investigations. In the present work the DFT method was chosen in order to describe the dielectric properties of the clusters. A comparison of the performance of the method with respect to relative energies of wave function based methods or to predictions of dipole moments was not intended or is still not possible, respectively. From the experimental point of view it is clear that the beam deflection experiments are performed at finite temperatures, which are not reproduced by the calculations, introducing the possibility that multiple or kinetically stable isomers are present in the molecular beam. Furthermore, it was shown that excited vibrational modes can alter the dielectric response of a cluster. 51 There are several indica13 ACS Paragon Plus Environment

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Figure 3: Beam deflection profiles for SnM−1 Bi1 clusters at 15 kV using a nozzle temperature of 33 K are compared to classical beam deflection simulations. In red two component simulations and in black, green, cyan simulations using Iso-I, Iso-II and Iso-III are shown. The different isomers (blue for Bi, grey for Sn) used in the simulation are depicted, too, and the relative energy difference in eV (lower number) is given. For two component simulations the relative isomer population used is stated as the upper number. The dipole moment in the molecular coordinate system is indicated by a blue arrow.



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tions that the investigated clusters are rigid (see Supporting Information) but excited vibrations for a particular case cannot be excluded (especially for larger clusters). Therefore, here we present simulation results for higher energy isomers and multiple isomer simulations. In Figure 3 the results for SnM−1 Bi1 are depicted. For Sn6 Bi1 the beam broadening cannot be explained using only one isomer. While the calculated GS is a C2v symmetric structure with the Bi atom located in the equatorial plane of a pentagonal bipyramid, Iso-I (0.12 eV higher in energy) possess a Bi atom replacing an axial Sn atom resulting in C5v symmetry. If the isomers with a dipole moment of 0.71 D and 0.16 D, respectively, are included in the simulation with a relative population of 0.5 for each the experimental beam profile is reproduced. For Sn9 Bi1 no multiple isomer simulation is needed to reproduce the experimental results but Iso-I is used exclusively. The simulated beam profile is able to explain the experimentally obtained beam profile adequately. For this cluster the structural motif of a bicapped square antiprism is realized which is also found for Sn− 10 (Ref. 26). One of the capping atoms of the pure cluster is replaced by a Bi consequently creating a C2v symmetric structure. Sn9 Bi1 -Iso-I with a dipole moment of 0.62 D is only 0.06 eV higher in energy than the located GS which is the other possible homotop of Iso-I. Further increasing the cluster size to Sn10 Bi1 yields a Cs symmetric structure which is used in a beam profile simulation presented in Figure 3. This structure is derived from the C2v symmetric structural motif of a octadecahedron found for boranes 27 and tin anions. 26 A dipole moment of 0.67 D (see Table 1) is computed for this isomer and by additionally using structural parameters and polarizability in the beam profile simulation, as done in all calculations, the experimental data is reproduced. Since the GS is just a homotop of Iso-I and the energy difference is only 0.02 eV, using the higher lying isomer in the beam profile simulation seems reasonable. For Sn11 Bi1 the icosahedral structure, which is found as the GS isomer, was discussed in the previous Subsection. Here Iso-III, 0.16 eV higher in energy, is also taken into account. The structure of this isomer is of C1 symmetry and consists of a TeTP additionally capped with a Sn and Bi atom. With its dipole moment of 1.18 D a nearly perfect description of the beam profile is


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obtained. However, this structural motif is predicted to be a high energy isomer of Sn− 12 but was excluded by recent experiments of Kappes and co-workers. 26 Due to the fact that Iso-III agrees with the beam deflection profile best but the GS cannot be excluded both structures may be present in the molecular beam.

2

1

0


Sn3Bi2


The final single doped species is Sn12 Bi1 which was already discussed above. Though the intensity / arb. units

Sn6Bi2

2

-1

1

0

Sn7Bi2

2

-1

1

0 p / mm

p / mm

0.20 Iso-I 0.20

Sn8Bi2

2

1

0.40 Iso-I 0.09

0.60 GS 0.00

0 p / mm

0.60 GS 0.00


0.80 GS 0.00 intensity / arb. units

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1

0 p / mm

0.85 GS 0.00

Iso-I 0.01

0.40 Iso-I 0.15

Sn9Bi2

2

-1

-1

-1

0.15 Iso-III 0.21

Iso-I 0.07

Figure 4: The same comparison as shown in Figure 3 for SnM−2 Bi2 clusters. TeTP based GS structure is adequate to describe the molecular beam profile, even better agreement between theory and experiment is obtained when a second isomer, Iso-II (Cs ), is also used. The structure 0.10 eV higher in energy differs only from the GS by the location of one tin atom (see Figure 3) and possesses a dipole moment of 0.32 D (see Table 1). A simulation with a relative population of 0.5 for each isomer gives the best agreement with the experimental data points. The beam profile simulations for mixed clusters containing two bismuth atoms are depicted in Figure 4. A closer inspection of the beam profile for Sn3 Bi2 shows a minor high field feature which is not described by the GS isomer. Therefore, including the Cs symmetric homotop Iso-I (0.20 eV higher in energy) with a relative population of 0.2 and a dipole moment of 0.53 D results in an improved simulated beam profile. 16 ACS Paragon Plus Environment


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A similar observation is made for Sn6 Bi2 due to consideration of Iso-I. This isomer is a homotop of the GS wherein the atoms are arranged to give overall Cs symmetry. This isomer is characterized by an energetic separation of only 0.09 eV relative to the GS isomer and a dipole moment of 0.81 D. As a consequence of a two component simulation with a relative population of 0.4 for Iso-I the height of the beam profile is lowered and broadened resulting in an improved description of the experimental data points. In case of Sn7 Bi2 the GS isomer and Iso-I (0.15 eV higher in energy) are two possible homotops of a doubly doped TTP. While both isomers can be used individually in a beam profile simulation to give satisfying results, a two component calculation significantly improves the agreement between theory and experiment. The dipole moment of the GS isomer is 0.89 D (Table 1) producing a slightly overestimated beam broadening. On the other hand Iso-I with |µ | = 0.45 D underestimates the intensity drop. If the GS and Iso-I are mixed with a relative population of 0.6 and 0.4, respectively, the beam profile is described perfectly. For the largest experimentally investigated doubly doped clusters Sn8 Bi2 and Sn9 Bi2 the beam profile simulations are shown in Figure 4. A single isomer simulation is able to describe the experimental results if Iso-I is taken into account. In both cases Iso-I with C2 symmetry for Sn8 Bi2 and C1 for Sn9 Bi2 are homotops of the GS isomers only 0.01 eV and 0.07 eV higher in energy, respectively, showing that it is reasonable to use high energy isomers in the simulations. Additionally, a two component simulation for Sn9 Bi2 yields good results, if the GS and Iso-III (C2v ) are used with a relative population of 0.85 and 0.15. Due to the small difference in relative stability and dipole moment an identification of the isomer present in the molecular beam is not possible in all cases. However, an analysis of experimental findings assisted by theoretical results helped to determine structural motifs for the bimetallic clusters which will be discussed in the following Section.


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Structural trends and electronic properties We have assessed the structural motifs of small Sn-Bi clusters with the aid of the electric field deflection method and an extensive search for possible cluster structures. From these it becomes apparent that the growing pattern of the clusters change in comparison to pure tin clusters, behaviour which differs from findings for Sn-Pb. 49,50 As illustrated in Figure 5 a formal reduction

SnM

Analogues

(Di)anions

Sn9

Sn8Bi1

Sn9

Sn11

Sn10Bi1

Sn11

Sn6Bi2

Sn8

Sn8Bi2

Sn102-

2

2

Sn8

2-

2

2

Sn10

-

2

2

2

-

2

Figure 5: Structural rearrangement of cluster cages upon doping bismuth. The depicted Sn-Bi clusters (Sn in grey, Bi in blue) are the isomers most likely present in the molecular beam as discussed above. Blue arrows indicate the dipole moment in the molecular coordinate system. due to doping into the pure tin cluster drives the reorganization of the cluster skeleton. For example the doping of one Bi changes the structural motif for a nine atom cluster from a double capped pentagonal bipyramid to a TTP which is an analogue to the structure of Sn− 9 . Similar conclusions are corroborated by theoretical and experimental findings for Sn10 Bi1 as discussed above. On the other hand the location of the dopant atom is not positively identified by experiment. Figure 5 shows the isomers for which the best agreement between theory and experiment is observed but very often other homotops compete. The energetic separation of the different homotops is often marginal and the beam deflection profiles are comparable. Nevertheless, all homotops by definition 18 ACS Paragon Plus Environment


share the same structural motif. For Sn-Bi clusters containing two bismuth atoms a structural rearrangement upon doping is also observed. The triangular dodecahedron instead of a capped (distorted) pentagonal bipyramid is found for a eight atom cluster, whereas a ten atom species forms a bicapped square antiprism instead of a TeTP (see Figure 5). For these clusters the Wade-Mingos rules are formally fulfilled.

a) 20

NICS / ppm

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SnM-2Bi2 2SnM

0

b)

SnM-1Bi1 SnM

Sn9

2-

Sn7Bi2 HOMO

-20 HOMO-1

-40 -60

HOMO-9

5

6

7

8

9 10 11 12 13 M

Figure 6: a) Comparison of NICS values at the cluster center for GS of tin anions (triangles) and dianions (squares) with SnM−1 Bi1 (diamonds) and SnM−2 Bi2 (circles), respectively. b) Some molecular orbitals for Sn2− 9 and Sn7 Bi2 relative to the highest occupied molecular orbital (HOMO). The orbitals are viewed along the C3 or the pseudo C3 axis. The structural motifs found by experiment and theory support the speculation that the clusters can be understood as neutral closo-clusters. Additionally, it is observed - even if the unique homotop is not identified - that homotops with no direct Bi-Bi bonds are lower in energy and agree better with experimental findings. Therefore, it can be concluded that Sn-Bi interactions are favored in most cases compared to Bi-Bi interaction. Further evidence for the structural motifs discussed above is found by DFT calculations. Perhaps the most intriguing quantity is the NICS value. In Zintl ions the formed molecular orbitals give rise to a characteristic degree of electron delocalisation. This delocalisation can be quantified using the NICS value and interpreted in the context of "aromaticity". 9,40 Therefore, the NICS value is an indicator for the nature of the chemical bonding in the cluster. A comparison of NICS


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values at the cluster center for GS structures of pure tin (di)anions with SnM−1 Bi1 and SnM−2 Bi2 clusters is presented in Figure 6 a). Even if no experimental validation of the GS was possible for various compositions the lowest lying isomer is in all cases a homotop of isomers discussed above. The NICS value does not depend strongly on the location of the dopant atom but depends most critically on the structural motif (see Supporting Information). The evolution of the NICS values with cluster size for the tin (di)anions and the corresponding Sn-Bi clusters interestingly show the same trends. Even though, the symmetry of the clusters is lowered by the dopant atoms and further perturbations are introduced due to the nature of the added atom(s) the "aromaticity" of the clusters seem to be unchanged. Similar behaviour is found for the second differences, i.e. the relative stability for different cluster sizes, in agreement with these considerations (see Supporting Information). On the other hand simple molecular orbital (MO) considerations are not easily applied to bimetallic clusters. A comparison for Sn2− 9 with Sn7 Bi2 -GS of some MO’s relative to the highest occupied molecular orbital (HOMO) is presented in Figure 6 b) (see Supporting Information for complete comparison). It is obvious that the MO’s of Sn7 Bi2 -GS are deformed due to the presence of the Bi atoms compared to those of the pure dianion. However it is noticeable that the orbitals, even if the energetic ordering is changed [see HOMO and HOMO-1 in Figure 6 b)], keep the main characteristics supporting the previously mentioned NICS results and the idea of neutral Zintl analogues in the gas phase.

Conclusion In this study theoretically predicted isomers and their calculated dielectric properties were used to deduce structural motifs from electric beam deflection measurements. Cryogenic temperatures enable the experiments to be analyzed treating the clusters as rigid rotor. Various low lying isomers were found by the DFT/GA approach. Interestingly all isomers of a given size and composition show the same structural motif and only differ in the position of the dopant atom(s), i.e. they are homotops. The energy differences between the most stable isomers is only (0.01 − 0.10) eV and



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hence it is difficult to uniquely identify the GS by DFT calculations and beam deflection experiments. Even if the motifs of these isomers are identical the dielectric response is quite different. This allows us to describe the experimental results using one and in a few cases two isomers. The identified motifs consist of polyhedra derived from negative clusters, boranes and Zintl ions. An archetypal example of the structural influence of the dopant atom(s) [i.e. the additional electron(s)] is found for ten atom clusters. The pure, neutral species adopts a TeTP. Upon Bi doping the structure changes to a bicapped square antiprism consistent with findings for Sn− 10 . An additional Bi atoms only introduce small distortions due to bond elongations or a lowering in symmetry but the overall structural motif persists. The findings are particularly interesting for doubly doped bimetallic clusters. For these clusters the derived motifs are consistent with predictions based on the simple Wade-Mingos rules. Further support for this idea is given by a NICS analysis which reveals a similar trend for the doped and (poly)anionic clusters in addition to MO’s of the doped clusters which maintain the characteristics of the corresponding tin (di)anion obritals. Of course due to dopant induced symmetry breaking the simple molecular orbital picture which underpins the Wade-Mingos rule, breaks down for bimetallic clusters. Nevertheless, the total number of electrons in the cluster cage and the structural motif seem to be correlated in a similar way as previously deduced for boranes and related clusters. In the future it will be interesting to see if this simple rule can be applied to other cluster species (for example Pb-Sb, Ga-Te, Sn-Te and In-Bi only to mention a few) in order to validate if predictions of structural motifs for neutral, bimetallic clusters based on simple electron counting rules are possible.

Acknowledgement S.H. and R.S. acknowledge financial support from the Deutsche Forschungsgemeinschaft through Grant No. SCHA 885/10-1. S.H. is grateful to Fonds der Chemischen Industrie for a scholarship. Some of the authors (S.H. and R.S.) want to thank D.A.Götz and K. Hofmann for assistance with some DFT calculations and target material preparation, respectively. R.L.J. acknowledges financial support from COST Action MP0903: "Nanoalloys as Advanced Materials: From Structure to 21 ACS Paragon Plus Environment

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Properties and Applications". Neutral Cluster

Zintl-Ion Analogue?

Sn

210

Sn8Bi2

Electric Deflection Quantum Chemistry


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no field field simulation

2

1

0 p / mm

-1

Figure 7: Table of Contents picture.

Supporting Information Available Performance of the large core norm-conserving PPs for Sn and Bi; Basis set dependence of the dielectric and structural parameters; Comparison of beam profiles for pure and mixed clusters; Experimental estimation of the rotational temperature; All structures, structural and dielectric parameters in addition to all beam profiles for the lowest lying isomers of SnM−N BiN ; Structures 2− and NICS values for Sn− M and SnM ; Second differences for Sn-Bi clusters in comparison to tin

(di)anions and binding energies for SnM−1 Bi1 and SnM−2 Bi2 ; All MO’s for Sn7 Bi2 and Sn2− 9 ; Presentation of the re-calibration of the apparatus and the full list of authors for ref. 28,34,42. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Schäfer, H.; Eisenmann, B.; Müller, W. Angew. Chem. Int. Ed. Engl. 1973, 12, 694–712. (2) Scharfe, S.; Kraus, F.; Stegmaier, S.; Schier, A.; Fässler, T. F. Angew. Chem. Int. Ed. 2011, 50, 3630–3670. (3) Laves, F. Naturwissenschaften 1941, 29, 244–255. (4) Klemm, W.; Busmann, E. Z. anorg. allg. Chem. 1963, 319, 297–311. (5) Mingos, D. M. P. Acc. Chem. Res. 1984, 17, 311–319.



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(6) Knight, W. D.; Clemenger, K.; de Heer, W. A.; Saunders, W. A.; Chou, M. Y.; Cohen, M. L. Phys. Rev. Lett. 1984, 52, 2141–2143. (7) de Heer, W. A. Rev. Mod. Phys. 1993, 65, 611–676. (8) Hirsch, A.; Chen, Z.; Jiao, H. Angew. Chem. Int. Ed. 2000, 39, 3915–3917. (9) Hirsch, A.; Chen, Z.; Jiao, H. Angew. Chem. Int. Ed. 2001, 40, 2834–2838. (10) Bowlan, J.; Liang, A.; de Heer, W. A. Phys. Rev. Lett. 2011, 106, 043401. (11) King, R. B.; Heine, T.; Corminboeuf, C.; Schleyer, P. v. R. J. Am. Chem. Soc 2004, 126, 430–431. (12) Cui, L.-F.; Huang, X.; Wang, L.-M.; Zubarev, D. Y.; Boldyrev, A. I.; Li, J.; Wang, L.-S. J. Am. Chem. Soc. 2006, 128, 8390–8391. (13) Neukermans, S.; Janssens, E.; Chen, Z. F.; Silverans, R. E.; Schleyer, P. v. R.; Lievens, P. Phys. Rev. Lett. 2004, 92, 163401. (14) Chen, Z.; Neukermans, S.; Wang, X.; Janssens, E.; Zhou, Z.; Silverans, R. E.; King, R. B.; Schleyer, P. v. R.; Lievens, P. J. Am. Chem. Soc. 2006, 128, 12829–12834. (15) Gupta, U.; Reber, A. C.; Clayborne, P. A.; Melko, J. J.; Khanna, S. N.; Castleman, A. W. Inorg. Chem. 2008, 47, 10953–10958. (16) Zdetsis, A. D. J. Chem. Phys. 2009, 131, 224310–11. (17) Clayborne, P. A.; Gupta, U.; Reber, A. C.; Melko, J. J.; Khanna, S. N.; Castleman, A. W., Jr. J. Chem. Phys. 2010, 133, 134302–7. (18) Melko, J. J.; Werner, U.; Mitri´c, R.; Bonaˇci´c-Koutecký, V.; Castleman, A. W. J. Phys. Chem. A 2011, 115, 10276–10280. (19) Gillett-Kunnath, M. M.; Oliver, A. G.; Sevov, S. C. J. Am. Chem. Soc. 2011, 133, 6560–6562. 23 ACS Paragon Plus Environment

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(20) Schäfer, S.; Assadollahzadeh, B.; Mehring, M.; Schwerdtfeger, P.; Schäfer, R. J. Phys. Chem. A 2008, 112, 12312–12319. (21) Schäfer, S.; Schäfer, R. ChemPhysChem 2008, 9, 1925–1929. (22) Heiles, S.; Schäfer, S.; Schäfer, R. J. Chem. Phys. 2011, 135, 034303. (23) Heiles, S.; Logsdail, A. J.; Schäfer, R.; Johnston, R. L. Nanoscale 2012, 4, 1109–1115. (24) Schäfer, S.; Mehring, M.; Schäfer, R.; Schwerdtfeger, P. Phys. Rev. A 2007, 76, 052515. (25) Maguire, L. P.; Szilagyi, S.; Scholten, R. E. Rev. Sci. Instrum. 2004, 75, 3077–3079. (26) Oger, E.; Kelting, R.; Weis, P.; Lechtken, A.; Schooss, D.; Crawford, N. R. M.; Ahlrichs, R.; Kappes, M. M. J. Chem. Phys. 2009, 130, 124305–10. (27) McKee, M. L.; Wang, Z.-X.; Schleyer, P. v. R. J. Am. Chem. Soc. 2000, 122, 4781–4793. (28) Giannozzi, P.; et al., J. Phys.: Condens. Matter 2009, 21, 395502–395520. (29) Johnston, R. L. Dalton Trans. 2003, 4193–4207. (30) Deaven, D. M.; Ho, K. M. Phys. Rev. Lett. 1995, 75, 288. (31) Rappe, A. M.; Rabe, K. M.; Kaxiras, E.; Joannopoulos, J. D. Phys. Rev. B 1990, 41, 1227. (32) Perdew, J. P.; Zunger, A. Phys. Rev. B 1981, 23, 5048–5079. (33) Ferrando, R.; Jellinek, J.; Johnston, R. L. Chem. Rev. 2008, 108, 845–910. (34) Valiev, M.; et al., Comput. Phys. Commun. 2010, 181, 1477–1489. (35) Metz, B.; Stoll, H.; Dolg, M. J. Chem. Phys. 2000, 113, 2563–2569. (36) Peterson, K. A. J. Chem. Phys. 2003, 119, 11099–11112. (37) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158–6170.



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(38) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985, 82, 284–298. (39) Assadollahzadeh, B. A Systematic Search for the Global Minimum Structures of Cs, Sn and Au Clusters and Corresponding Electronic Properties. Ph.D. thesis, 2007. (40) Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Chem. Rev. 2005, 105, 3842–3888. (41) Ditchfield, R. Mol. Phys. 1974, 27, 789–807. (42) M. J. Frisch et al., Gaussian 03, Revision B.02, Gaussian, Inc., Pittsburgh PA, 2003. (43) Dugourd, P.; Antoine, R.; El Rahim, M. A.; Rayane, D.; Broyer, M.; Calvo, F. Chem. Phys. Lett. 2006, 423, 13–16. (44) The assumption of rigid clusters is to a very good approximation valid. Due to a lower nozzle temperature the agreement between theory and experiment for pure tin clusters is improved compared to previous results. 20 Therefore, mixed clusters are assumed to behave similarly. An example is given in the Supplementary Information. (45) Carrera, l.; Mobbili, M.; Moriena, G.; Marceca, E. Chem. Phys. Lett. 2008, 467, 14–17. (46) http://www.bear.bham.ac.uk/bluebear. (47) Heiles, S.; Hofmann, K.; Johnston, R. L.; Schäfer, R., ChemPlusChem 2012, doi:10.1002/cplu.201200085. (48) Fässler, T. F. Coord. Chem. Rev. 2001, 215, 347–377. (49) Barman, S.; Rajesh, C.; Das, P., G.; Majumder, C. Eur. Phys. J. D 2009, 55, 613–625. (50) Heiles, S.; Schäfer, S.; Schäfer, R. Phys. Chem. Chem. Phys. 2010, 12, 247–253. (51) Compagnon, I.; Antoine, R.; Rayane, D.; Broyer, M.; Dugourd, P. Phys. Rev. Lett. 2002, 89, 253001. 25 ACS Paragon Plus Environment

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Supporting information for: Bismuth-doped tin clusters: Experimental and theoretical studies of neutral Zintl analogues.. Sven Heiles,∗,† Roy L. Johnston,‡ and Rolf Schäfer† Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Petersenstrasse 20, 64287 Darmstadt, Germany, and School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, U.K. E-mail: [email protected]

∗ To

whom correspondence should be addressed University of Darmstadt ‡ University of Birmingham † Technical

S1 ACS Paragon Plus Environment


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Normconserving Pseudopotentials In order to obtain new pseudopotentials for Sn and Bi with only the valence electrons in active space, pseudo-wavefunctions were fitted to all electron DFT/LSDA calculations as implemented in the ATOMIC code in Quantum ESPRESSO v4.2.1 1 using the Rabe-Rappe-Kaxiras-Joannopoulos pseudization. 2 The new normconserving pseudopotentials take scalar relativistic but no spin-orbit effects into account. The structural parameters obtained with the pseudopotentials in a PWscf calculation using the LSDA are shown in Table S1. The dimers were calculated using an 40 Ry energy cutoff, unit cell size of 15 Å and the spin configuration was specified as shown in the table. For the solids the same energy cutoff was used in addition to a 12×12×12 integration grid varying all given structural parameters independently until the minimum energy was obtained. Table S1: Comparison of the structural parameters for the dimer and solid for tin and bismuth obtained within PWscf using the newly generated pseudopotentials with literature values. For the dimers the bond length d, for solid Sn and Bi cell parameters a and a0 , α and z (parameters for the rhombohedreal unit cell), respectively, are compared. The corresponding electronic configuration and phase of the solid are given in brackets. System parameter PWscf Lit. 3 − Sn2 ( Σg ) d 2.71 Å 2.75 Å 3 Sn (diamond) a 6.40 Å 6.49 Å 4 Bi2 (1 Σ+ d 2.57 Å 2.66 Å 5 g) α 59.93◦ 57.23◦ 6 Bi (A7) a0 4.53 Å 4.75 Å 6 z 0.248 0.234 6

Basis set dependence Results for SnM Bi1 and SnM Bi2 Shown below are the theoretical and experimental results for SnM Bi1 and SnM Bi2 . The theoretical and experimental procedure is described in more detail in the Method section. In Figure S1 a typical mass spectrum for bimetallic SnM−N BiN clusters is shown. Additionally the mass content S2 ACS Paragon Plus Environment

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Table S2: Basis set dependence of the structural and dielectric parameters. For some clusters the results for a DZ and TZ basis set are compared. The energy difference ∆E the moment of inertia Ii and all dipole moment components µi are given in units of eV, 10−44 kg·m2 and D, respectively. Isomer

method aug-cc-pVDZ-PP/PBE0 Sn3 Bi2 -GS aug-cc-pVTZ-PP/PBE0 aug-cc-pVDZ-PP/PBE0 Sn3 Bi2 -I aug-cc-pVTZ-PP/PBE0 aug-cc-pVDZ-PP/PBE0 Sn8 Bi1 -GS aug-cc-pVTZ-PP/PBE0 aug-cc-pVDZ-PP/PBE0 Sn8 Bi1 -I aug-cc-pVTZ-PP/PBE0

∆E (Ix , Iy , Iz ) (µx , µy , µz ) 0.00 (2.82, 3.39, 3.79) (0.00, 0.00, 0.05) 0.00 (2.77, 3.35, 3.75) (0.01, -0.01, 0.00) 0.20 (2.46, 3.81, 4.16) (0.00, -0.06, 0.53) 0.21 (2.41, 3.77, 4.12) (0.00, -0.03, 0.53) 0.00 (7.60, 8.28, 9.72) (-0.66, 0.16, -0.13) 0.00 (7.55, 8.23, 9.67) (-0.65, 0.16, -0.12) 0.13 (7.71, 8.27, 10.24) (-0.65, -0.19, 0.12) 0.14 (7.68, 8.21, 10.19) (-0.63, -0.19, 0.13)

of the target rod is given. Only a small quantity of Bi was used in the target material in order to produce mainly mixed clusters with small number of bismuth atoms (typically only 1 − 3 dopants). The limited mass resolution results in overlapping mass peak signals for some clusters. Beside the information gained by beam profile, which additionally indicates different electric deflection behaviour for different clusters (see Figure S3), the contribution of other clusters to the analysed mass peak is at maximum ∼ 10 %.

Sn6Bi1

Sn7Bi2

Target composition: 16% Bi, 84% Sn

intensity [arb. units]

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Target composition: 100% Sn

6

7

8

9

10 11 12 13 14

N Figure S1: Typical mass spectra for SnM−N BiN clusters in comparison to pure tin clusters. Some mixed species are highlighted.



In Figure S3 the results for pure and mixed clusters for the same experimental run are compared, showing that the beam deflection is changed due to Bi doping. In addition the beam profile simulation for Sn10 is shown in Figure S4 validating the assumption of a rigid cluster for typical experimental conditions. Typical vibrational frequencies for the investigated bimetallic clusters are between (40 − 50) cm−1 or ∼ (40 − 50) K. Consequently, it is expected that no vibrational modes are excited. Only for some larger (M = 12 − 13) cluster isomers vibrations of ∼ 30 cm−1 are computed. Furthermore, the rotational temperature can be estimated from a second order perturbation analysis. 7 From a perturbation theory analysis 8 an effective polarizability αe f f /M of (12.1 ± 1.2) Å3 is extracted from Figure S4. By taking account of the dipole contribution for a spherical rotor to the polarizability (αe f f − αe ) 1 2|µ |2 = M M 9kb Trot an increase of the experimentally observed polarizability by (5.8 − 19.3) Å3 is estimated for Trot between 10 K and 3 K. When the calculated electronic polarizability 8 αe /M is included in the calculation the rotational temperature of the cluster is between (9.0 − 15.0) K. This result is within the estimated error of the rotational temperature used in the simulation. In order to get an idea intensity / arb. units

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Sn9Bi2 15 kV 33 K

2

1

0 p / mm

3K 4K 5K 6K 7K 12 K

-1

Figure S2: Beam deflection profile of Sn9 Bi2 at 15 kV deflection voltage and 33 K nozzle temperature with the corresponding rotational temperature dependent beam profile simulations for Sn9 Bi2 -I. how the rotational temperature influences the simulation results an example is given in Figure S2 S4 ACS Paragon Plus Environment

Page 31 of 44

for Sn9 Bi2 -I (Figure S7). If the rotational temperature is too small the broadening is overestimated and the height of the profile is underestimated. In the case where the rotational temperature is too large the simulation overestimates the height of the profile. The overall best description of the data points is achieved with rotational temperatures in the range (5 − 7) K.

1.5

0 p / mm

1.5

-1.5

0 p / mm

0 p / mm


Sn6Bi1 25 kV 33 K

1.5

Sn10 25 kV 33 K



Sn7 25 kV 33 K


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Sn9Bi1 25 kV 33 K

1.5

-1.5

-1.5

0 p / mm

-1.5

Figure S3: Typical beam deflection profiles of pure Sn7 and Sn10 compared to the mixed species Sn6 Bi1 and Sn9 Bi1 at 25 kV and a nozzle temperature of 33 K. The profiles are compared for the same experimental run. The depicted Gaussian functions are only a guide to the eye. Given in Table S3 and Table S4 and shown in Figure S5 and Figure S7 are the theoretical results for SnM−N BiN (M = 5 − 13, N = 1, 2). At maximum the four lowest lying isomers are depicted. The isomers are taken from a pool of possible structures generated by the described DFT/GA approach and by doping SnM , Sn− M and closo-boranes. Shown in Figure S6 and Figure S8 are the measurements for 15 kV at 33 kV. Each data point is the average of 2 − 4 mass spectroscopic measurements which itself is the average of 100 single mass spectra. The blue data points describe the beam profile without electric field and red empty squares are measured with electric field. A Gaussian function was fitted to the data points without S5 ACS Paragon Plus Environment


Sn10 15 kV 33 K


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2

1

0 p / mm

-1

Figure S4: Beam deflection profile at a deflection voltage of 15 kV. The red curve is a beam deflection simulation using parameters from the work of Schäfer et al. 8 and a rotational temperature of 6 K. In the case of a symmetrical rotor (as found for the C3v symmetric isomer for Sn10 ) the rotational temperature does not critically influence the simulated beam profile. 9 electric field while all other curves are simulation results utilising the method described in the Method section. The red curve in all pictures is the beam profile simulation for the predicted ground state isomer. Analogously black (I), green (II) and cyan (III) curves are results for high energy isomers. Additionally, structures labeled GA, are presented in Table S5 and Figure S9. The located GS structures coincided for nearly all cluster sizes utilising the DFT/GA and doping approach. Only for the here presented clusters some discrepancies appeared. Therefore, these structures are presented separately. For Sn10 Bi2 and Sn11 Bi1 the lowest isomers produced by the GA are lower in energy at the DFT/GA level of theory. Using these structures in aug-cc-pVDZ-PP/PBE0 calculations result in the below presented parameters. Hence, the icosahedral structures for these cluster sizes sustain the lowest energy as expected. The situation is different for Sn11 Bi2 for which lower lying isomers are found by the DFT/GA routine considerably lower in energy than the boranlike structure. This is the only cluster size for which the simple model prediction for the cluster fails. The second difference

∆2 = −2 · E(M) + E(M + 1) + E(M − 1) S6 ACS Paragon Plus Environment

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Table S3: Calculation results for SnM Bi1 at the aug-cc-pVDZ-PP/PBE0 level of theory. The energy difference ∆E the moment of inertia Ii and the polarizability per atom α /M are given in units of eV, 10−44 kg·m2 and Å3 , respectively. Additionally dipole moment µi and |µ | in D and the NICS value at the center of the cluster in ppm are given. Isomer Sn4 Bi1 -GS Sn4 Bi1 -I Sn5 Bi1 -GS Sn5 Bi1 -I Sn5 Bi1 -II Sn5 Bi1 -III Sn6 Bi1 -GS Sn6 Bi1 -I Sn7 Bi1 -GS Sn7 Bi1 -I Sn7 Bi1 -II Sn7 Bi1 -III Sn8 Bi1 -GS Sn8 Bi1 -I Sn9 Bi1 -GS Sn9 Bi1 -I Sn9 Bi1 -II Sn9 Bi1 -III Sn10 Bi1 -GS Sn10 Bi1 -I Sn10 Bi1 -II Sn10 Bi1 -III Sn11 Bi1 -GS Sn11 Bi1 -I Sn11 Bi1 -II Sn11 Bi1 -III Sn12 Bi1 -GS Sn12 Bi1 -I Sn12 Bi1 -II Sn12 Bi1 -III

∆E 0.00 0.01 0.00 0.10 0.19 0.29 0.00 0.12 0.00 0.06 0.10 0.14 0.00 0.13 0.00 0.06 0.09 0.15 0.00 0.02 0.03 0.03 0.00 0.10 0.15 0.16 0.00 0.09 0.10 0.11

(Ix , Iy , Iz ) α /M (1.99, 3.72, 3.83) 7.57 (2.30, 3.18, 3.54) 7.61 (3.54, 4.11, 4.57) 7.28 (4.00, 4.00, 4.08) 7.32 (3.13, 4.53, 5.05) 7.54 (3.09, 4.61, 5.64) 7.49 (4.43, 5.21, 7.24) 7.26 (4.83, 4.83, 6.45) 7.27 (5.51, 7.46, 8.84) 7.41 (5.61, 7.47, 8.34) 7.38 (5.80, 7.25, 9.01) 7.41 (5.75, 7.61, 7.62) 7.32 (7.60, 8.28, 9.72) 7.16 (7.71, 8.27, 10.24) 7.17 (8.69, 11.06, 11.21) 7.14 (8.29, 11.45, 12.12) 7.16 (9.36, 10.48, 10.89) 7.15 (9.55, 10.37, 10.92) 7.17 (11.00, 12.52, 14.06) 7.18 (10.36, 13.21, 14.10) 7.19 (11.03, 12.66, 13.41) 7.16 (10.34, 13.39, 13.69) 7.17 (13.62, 14.58, 15.38) 7.09 (10.87, 18.28, 18.82) 7.42 (13.67, 14.64, 15.33) 7.11 (11.03, 17.41, 18.36) 7.44 (12.34, 20.63, 22.09) 7.41 (13.09, 19.61, 20.39) 7.44 (12.01, 20.80, 21.67) 7.41 (13.04, 19.96, 21.84) 7.46

(µx , µy , µz ) (0.29, 0.03, 0.09) (0.00, 0.06, 0.00) (0.32, -0.27, -0.13) (0.07, -0.15, 0.00) (0.09, -0.38, -0.10) (0.31, 0.31, 0.32) (-0.71, 0.00, 0.00) (0.00, 0.00, -0.16) (0.46, -0.29, -0.12) (0.46, 0.00, -0.09) (-0.51, -0.39, -0.31) (0.31, -0.21, 0.00) (-0.66, 0.16, -0.13) (-0.66, 0.00, 0.20) (-1.03, 0.00, -0.07) (-0.62, 0.00, 0.00) (0.32, 0.54, 0.00) (-0.61, -0.28, -0.43) (0.08, -0.79, 0.83) (-0.46, 0.00, 0.48) (0.00, -0.01, 0.70) (0.49, 0.80, 0.00) (1.06, 0.00, 0.69) (1.71, -0.35, 0.33) (1.24, 0.00, 1.17) (0.84, -0.74, 0.37) (0.13, 0.00, 0.00) (-0.39, 0.00, -0.53) (0.24, -0.14, 0.16) (-0.42, 0.66, -0.03)


|µ | 0.30 0.06 0.44 0.16 0.41 0.54 0.71 0.16 0.56 0.47 0.71 0.38 0.69 0.69 1.03 0.62 0.63 0.68 1.15 0.67 0.70 0.94 1.27 1.78 1.70 1.18 0.13 0.66 0.32 0.78

NICS -12.82 -9.27 -8.17 -11.38 -30.36 -27.76 -32.54 -28.99 -32.47 -26.43 -24.25 -14.01 -41.68 -38.61 -37.57 -35.35 -49.79 -51.73 -23.31 -17.49 -8.29 -14.53 0.45 -40.60 6.50 -38.07 -43.73 -47.83 -57.35 -45.89


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Sn4Bi1

GS

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Sn5Bi1

Iso-I

GS

Iso-I

Sn6Bi1

Iso-II Iso-III

GS Sn8Bi1

Sn7Bi1

GS

Iso-I

Iso-II

Iso-III

GS

Iso-I

Iso-II

GS

Iso-III

Iso-I

Iso-I

Iso-II

Iso-II

Iso-III

Sn12Bi1

Sn11Bi1

GS

Iso-I

Sn10Bi1

Sn9Bi1

GS

Iso-I

GS

Iso-III

Iso-I

Iso-II

Iso-III

Figure S5: Structures of the isomers presented in Table S3. In blue (grey) the bismuth (tin) atoms are depicted. The blue arrow represents the dipole moment in the molecular coordinate system.


0 p / mm

Sn9Bi1 15 kV 33 K

1

0 p / mm

1

0 p / mm

-1

2

1

0 p / mm


-1

Sn10Bi1 15 kV 33 K


2

2

-1

-1

Sn8Bi1 15 kV 33 K

2

1

0 p / mm


1

Sn7Bi1 15 kV 33 K


2


Sn6Bi1 15 kV 33 K


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Page 35 of 44

Sn11Bi1 15 kV 33 K

2

1

0 p / mm

Sn12Bi1 15 kV 33 K

2

1

0 p / mm

-1

Figure S6: Electric deflection profiles at 33 K and a deflection voltage of 15 kV.


-1

-1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 44

Table S4: Calculation results for SnM Bi2 at the aug-cc-pVDZ-PP/PBE0 level of theory. The energy difference ∆E the moment of inertia Ii and the polarizability per atom α /M are given in units of eV, 10−44 kg·m2 and Å3 , respectively. Additionally dipole moment µi and |µ | in D and the NICS value at the center of the cluster in ppm are given. Isomer Sn3 Bi2 -GS Sn3 Bi2 -I Sn4 Bi2 -GS Sn4 Bi2 -I Sn5 Bi2 -GS Sn5 Bi2 -I Sn5 Bi2 -II Sn6 Bi2 -GS Sn6 Bi2 -I Sn6 Bi2 -II Sn6 Bi2 -III Sn7 Bi2 -GS Sn7 Bi2 -I Sn7 Bi2 -II Sn7 Bi2 -III Sn8 Bi2 -GS Sn8 Bi2 -I Sn8 Bi2 -II Sn8 Bi2 -III Sn9 Bi2 -GS Sn9 Bi2 -I Sn9 Bi2 -II Sn9 Bi2 -III Sn10 Bi2 -GS Sn10 Bi2 -I Sn10 Bi2 -II Sn11 Bi2 -GS Sn11 Bi2 -I Sn11 Bi2 -II Sn11 Bi2 -III

∆E 0.00 0.20 0.00 0.23 0.00 0.03 0.22 0.00 0.09 0.20 0.21 0.00 0.15 0.19 0.26 0.00 0.01 0.15 0.16 0.00 0.07 0.09 0.21 0.00 0.03 0.25 0.00 0.12 0.18 0.19

(Ix , Iy , Iz ) α /M (2.82, 3.39, 3.79) 7.43 (2.46, 3.81, 4.16) 7.47 (3.84, 4.98, 4.98) 7.28 (4.31, 4.43, 4.88) 7.30 (4.84, 6.13, 7.94) 7.29 (5.69, 5.69, 6.19) 7.24 (5.15, 5.85, 7.03) 7.30 (6.67, 7.37, 8.66) 7.29 (6.20, 8.19, 8.92) 7.30 (5.99, 8.84, 9.15) 7.31 (6.53, 7.91, 8.06) 7.32 (8.26, 8.88, 10.35) 7.12 (8.04, 9.34, 10.73) 7.13 (8.44, 8.67, 10.19) 7.14 (8.39, 8.86, 9.99) 7.15 (9.73, 11.05, 12.23) 7.11 (9.52, 11.44, 12.09) 7.12 (9.61, 11.56, 11.70) 7.13 (9.18, 12.05, 12.56) 7.14 (11.48, 13.61, 15.27) 7.17 (11.21, 13.94, 15.12) 7.18 (11.91, 13.39, 14.72) 7.17 (10.75, 14.63, 14.96) 7.19 (13.99, 16.27, 16.27) 7.07 (14.56, 15.64, 16.14) 7.07 (14.67, 15.44, 16.08) 7.09 (15.15, 19.45, 20.89) 7.25 (14.90, 19.71, 21.76) 7.37 (16.11, 17.69, 21.09) 7.20 (15.63, 18.29, 21.67) 7.21

(µx , µy , µz ) (0.00, 0.00, 0.05) (0.00, -0.06, 0.53) (0.00, 0.00, 0.00) (0.00, 0.87, 0.00) (0.00, -0.60, 0.00) (0.00, 0.00, 0.00) (0.88, 0.00, 0.38) (0.41, 0.00, 0.00) (0.64, 0.50, 0.00) (0.00, 0.68, 0.00) (0.00, 0.00, 0.92) (0.00, 0.89, 0.00) (-0.01, 0.00, 0.45) (0.00, 1.03, 0.67) (1.41, 0.00, 0.00) (1.30, 0.00, 0.00) (0.00, 0.00, 0.74) (1.20, 0.00, -0.90) (0.16, 0.86, 0.00) (0.00, 0.00, 1.38) (-0.18, -0.98, -0.66) (-0.80, 0.01, 0.12) (0.00, 0.00, -0.11) (0.00, 0.00, 0.00) (0.00, -1.31, 0.81) (0.69, -0.95, 1.91) (-0.57, -1.58, 1.27) (0.00, 1.52, 1.68) (0.57, 0.00, 1.24) (0.09, -0.19, 2.13)


|µ | 0.05 0.53 0.00 0.87 0.60 0.00 0.96 0.41 0.81 0.68 0.92 0.89 0.45 1.23 1.41 1.30 0.74 1.50 0.87 1.38 1.19 0.81 0.11 0.00 1.54 2.25 2.11 2.26 1.37 2.15

NICS -38.67 -28.61 12.02 18.58 -14.60 -6.20 -9.82 -8.20 -5.79 -2.55 -7.58 -42.77 -42.59 -43.93 -40.73 -36.22 -35.58 -37.35 -33.71 -14.36 -14.12 -10.25 -13.32 -6.24 -3.63 -2.13 -31.10 -15.83 -16.70 -14.66

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Sn3Bi2

GS

Sn5Bi2

Sn4Bi2

GS

Iso-I Sn6Bi2

GS

Iso-I

Iso-II

GS

Iso-I

Iso-II Sn10Bi2

Iso-I

Iso-II

Sn7Bi2

Iso-III

GS

Iso-I

Sn8Bi2

GS

Iso-I

GS

Iso-I

Iso-II

Iso-III

Sn9Bi2

Iso-II

Iso-II Iso-I Sn11Bi2

GS

Iso-III

GS

Iso-I

Iso-II

Iso-III

Iso-III


Table S5: Calculation results for SnM−N BiN at the aug-cc-pVDZ-PP/PBE0 level of theory. The energy difference ∆E (relative to the above mentioned GS isomer) the moment of inertia Ii and the polarizability per atom α /M are given in units of eV, 10−44 kg·m2 and Å3 , respectively. Additionally dipole moment µi and |µ | in D and the NICS value at the center of the cluster in ppm are given. Isomer ∆E (Ix , Iy , Iz ) α /M Sn11 Bi1 -GA 0.11 (10.87, 18.28, 18.82) 7.42 Sn10 Bi2 -GA 0.23 (11.41, 19.96, 20.87) 7.09 Sn11 Bi2 -GA-I -0.84 (13.94, 21.10, 23.18) 7.42 Sn11 Bi2 -GA-II -0.77 (13.35, 21.78, 22.57) 7.45 Sn11 Bi2 -GA-III -0.71 (13.12, 22.29, 23.36) 7.48

(µx , µy , µz ) (-1.71, 0.35, 0.33) (-0.40, -1.48, 0.05) (0.03, -0.22, 0.54) (0.08, -0.20, -0.26) (-1.27, -0.76, 2.00)


|µ | NICS 1.78 -40.51 1.53 45.87 0.59 -58.30 0.34 -66.94 2.48 -65.64

0 p / mm

2

-1

Sn6Bi2 15 kV 33 K

1

0 p / mm

0 p / mm

2

-1

intensity / arb. units 2

-1

Sn7Bi2 15 kV 33 K

1

0 p / mm

-1

Sn5Bi2 15 kV 33 K

1

0 p / mm

-1

Sn8Bi2 15 kV 33 K

2

1

0 p / mm

-1

Sn9Bi2 15 kV 33 K


2

1

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1

Sn4Bi2 15 kV 33 K


2


Sn3Bi2 15 kV 33 K


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



2

1

0 p / mm

-1

Figure S8: Electric deflection profiles at 33 K and a deflection voltage of 15 kV.

Sn11Bi1-GA

Sn10Bi2-GA Sn11Bi2-GA-I Sn11Bi2-GA-II Sn11Bi2-GA-III



Page 39 of 44

and binding energy Eb = −

1 (E(M) − (M − N) · E(Sn) − N · E(Bi)) M

for the bimetallic clusters is depicted in Figure S10. Additionally, the ten lowest lying occupied a)

0.06

SnM-2Bi2 2SnM

b)

SnM-1Bi1 SnM

2.6

0.04 0.02

Eb / eV

D2 / eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 -0.02 -0.04 6

2.5 2.4

SnM-1Bi1 SnM-2Bi2

2.3 7

8

9 M

10

11

12

2.2

5

6

7

8

9 10 11 12 13 M

2− Figure S10: The a) second differences ∆2 for SnM−1 Bi1 , Sn− M , SnM−2 Bi2 and SnM and b) the binding energy Eb for SnM−1 Bi1 and SnM−2 Bi2 as a function of the cluster size M.

molecular orbitals are compared for Sn2− 9 and Sn7 Bi2 in Figure S11. It is observed that degeneracy of is lifted and the MO’s are deformed for Sn7 Bi2 compared to Sn2− 9 . On the other hand many orbitals of the doped cluster keep the main characteristics of the orbitals.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Sn9

2-

Sn7Bi2

E

Figure S11: Comparison of the ten lowest lying occupied MO’s for Sn2− 9 and Sn7 Bi2 .


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Tin ions 2− In Figure S12 the lowest lying isomers of Sn− M and SnM are depicted for comparison purposes.

Furthermore, the NICS value at the center of the cluster is presented in Table S6. -

-

Sn7

Sn6

Sn5

-

Sn8

-

-

Sn9

a) Sn10

b)

-

Sn11

Sn62-

Sn52-

Sn10

2-

Sn11

-

Sn12

Sn72-

2-

-

-

Sn13

Sn92-

Sn82-

Sn12

2-

Sn13

2-

Figure S12: Lowest lying isomers of tin a) anions and b) dianions at the aug-cc-pVDZ-PP/PBE0 level of theory. Blue arrows indicate the dipole moment in the molecular coordinate system.

Re-calibraion Due to some minor changes of the experimental setup a re-calibration was necessary. In Figure S13 a typical beam deflection profile of the Ba-atom at room temperature is shown. For the calibration the average of 5 deflection measurements were taken into account. With a typical velocity of ∼ 1420 m/s and the known polarizability of Ba 10 the apparatus constant was determined to be (2.83 ± 0.17)107 m−1 in very good agreement with previous results. 11



2− Table S6: Calculation results for Sn− M and SnM at the aug-cc-pVDZ-PP/PBE0 level of theory. The NICS value in ppm corresponds to the tin cluster anion, calculated at the center of the cluster cage.

Isomer Sn− 5 Sn− 6 Sn− 7 Sn− 8 Sn− 9 Sn− 10 Sn− 11 Sn− 12 Sn− 13

NICS -47.12 -11.01 -30.84 -26.69 -40.38 -39.61 -14.84 4.20 -56.85

Isomer Sn2− 5 Sn2− 6 Sn2− 7 Sn2− 8 Sn2− 9 Sn2− 10 Sn2− 11 Sn2− 12 Sn2− 13

NICS -32.00 17.89 -5.32 -5.64 -41.67 -45.52 -11.58 -0.37 -2.75

(238±25)µm Ba 300 K 28 kV


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1

0 -1 p / mm

-2

Figure S13: Typical beam deflection profile of Ba-atom at room temperature and 28 kV deflection voltage.


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Quantum Chemistry Packages For all calculations Quantum ESPRESSO v4.2.1, 1 NWChem v6.0 12 or Gaussian03 13 were used.

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