NaAu and CsAu bimetal clusters

NaxAu and Cs xAu bimetal clusters: Finite size analogs of sodium–goldand cesium–gold compounds

Ueli HeizInstitut de Physique Expe´rimentale, Universite´ de Lausanne, CH-1015 Lausanne, Switzerland

Arthur Vayloyan and Ernst SchumacherInstitute of Inorganic and Physical Chemistry, University of Bern, CH-3000 Bern 9, Switzerland

Chahan Yeretziana)Institut fur Physikalische und Theoretische Chemie, Technische Universita¨t Munchen,D-85748 Garching, Germany

Mauro Stener, Philip Gisdakis, and Notker RoschLehrstuhl fur Theoretische Chemie, Technische Universita¨t Munchen, D-85748 Garching, Germany

~Received 14 May 1996; accepted 25 June 1996!

Mixed metal clusters of sodium and cesium with gold have been generated in a supersonicexpansion from the mixed vapor phase. Their tendency towards binary cluster formation, relativethermodynamic stability, and ionization potentials have been experimentally and computationallyinvestigated. The properties of the NaxAu clusters may be understood within an electronic shellmodel based on delocalized cluster orbitals, whereas the characteristics of CsxAu are indicative ofsubstantial ionic interactions. Relativistic density functional calculations have been performed toelucidate the cluster electronic structure and to rationalize observed properties which may not beaccounted for by the jellium model. The properties of these finite-size clusters are shown to berelated to the known bulk intermetallic compounds sodium–gold and cesium–gold~cesium aurid!,respectively. ©1996 American Institute of Physics.@S0021-9606~96!01837-5#

I. INTRODUCTION

One of the goals of cluster science is to identify unifyingconcepts of matter at the molecular and the bulk limit. Onehopes that the microscopic approach to understand macro-scopic phenomena will help separating local from collectivecontributions to properties of bulk materials.1 The aim of thisstudy is to specifically address these questions for one par-ticular class of clusters—the bimetal clusters—and to relatecluster characteristics to the properties of the correspondingintermetallic compounds.

Over the last 30 years many fascinating structural andunusual electronic properties have been found in intermetal-lic phases.2–5 Among other materials, stoichiometric 1:1alkali–gold compounds have attracted particular attention.6–8

Proceeding through the alkali metal series from LiAu toCsAu, a metal-insulator transition occurs upon going fromKAu to RbAu.9,10 Solid CsAu is known to be a semiconduc-tor with an indirect band gap of 2.6 eV.11 The formation ofthe gap can only be modeled if relativistic effects are in-cluded in a band structure calculation.12 In addition, thissolid is found to have strong ionic character with gold beingthe negative ion. This appreciable charge transfer from ce-sium to gold is attributed to the large difference in electronaffinity of the two elements.13 Also of interest are the struc-tural properties of alkali–gold compounds. RbAu and CsAuadopt the octo-coordinated CsCl structure,7,14 analogous toionic CsBr or CsI crystals, whereas the structures of the me-

tallic NaAu and KAu are more complicated and still not fullyelucidated.9,10,15,16While all of these compounds are stable,the heat of formation decreases from LiAu to CsAu.10 CsAucan only be prepared in high vacuum7 and is extremely sen-sitive to oxygen and moisture.17

Considering the very characteristic properties and trendsreported for alkali–gold compounds, we set out to investi-gate their finite-size analogs, the alkali/gold bimetal clusters.Here, we focus on monogold alkali clusters, MxAu. Twosystems were selected which, at the bulk limit, lie eitherclearly on the metallic~Na/Au! or on the ionic~Cs/Au! sideof the metal–nonmetal transition~MNMT !. The motivationfor this research pertains to fundamental and material scienceoriented aspects. The study of theoretically tractable, small,and isolated bimetal clusters should shed light onto the na-ture of heterometal bonding. In the long run, these kinds ofstudies are expected to lead to a deeper understanding of theelectronic and structural properties of intermetallic com-pounds and liquid alloys such as their ionicity and localorder.18 Furthermore, the single gold atom acts as a welldefined perturbation to the alkali cluster and allows one totest the range of applicability of the electronic shell modelfor metal clusters. Finally, highly stable bimetal clusters arepotentially important building blocks for future cluster as-sembled materials.

The present work was conducted along both an experi-mental and a theoretical line. Experimentally, relative ther-modynamic stabilities together with ionization potentials arepresented for selected cluster sizes. To assist in rationalizingsome of the experimental findings, in particular those outsidethe scope of a jellium model, we carried out quasi-relativistic

a!Permanent address: Nestle´ Research Center, Department of Food Technol-ogy, CH-1000 Lausanne 26, Switzerland.

5574 J. Chem. Phys. 105 (13), 1 October 1996 0021-9606/96/105(13)/5574/12/$10.00 © 1996 American Institute of Physics

density functional calculations continuing our previous quan-tum chemical studies on mixed metal clusters.19 Some struc-tural information was obtained by a symmetry constraint ge-ometry search on a series of selected clusters. The resultingstructural models are in good agreement with experimentalobservations. Moreover, atomization and fragmentation en-ergies as well as first ionization potentials, electron densities,and dipole moments have been calculated in order to achievean overall characterization of the cluster electronic structure.

II. EXPERIMENT

The experimental methods used for this research include~i! cluster generation by supersonic expansion of a mixedmetal vapor from a high-temperature two-chamber oven un-der well characterized thermodynamic conditions,~ii ! photo-ionization and electron impact mass spectroscopy at fixedphoton and electron energies to obtain the relative thermo-dynamical stabilities of the generated clusters, and~iii ! mea-surements of photoionization efficiency~PIE! curves fromwhich vertical ionization potentials are extracted.

A. Experimental setup

The experimental setup has been previously describedand only cursory details are given here.20–22 The mixedmetal clusters have been studied in a molecular beam appa-ratus which consists of a source chamber and an analysischamber. The two chambers are separated by a 1 mmskim-mer and were pumped differentially to pressures of 331026

and 531027 Torr, respectively. For mass spectral analysisthe neutral cluster beam was ionized within the ion extrac-tion region of an Extrel C50 quadrupole mass spectrometer~upper mass limit of 4000 amu!. The ionizing light sourcewas the output of a 1 kW Xe arclamp~unstructured emissionspectrum below 380 nm! which was dispersed through a 0.25m monochromator~PTI; 1200 lines/mm, grating blazed at300 nm!. The spectral resolution was set either to 16.6 nmfull width at half maximum~FWHM! to measure mass spec-tra, or 6.6 nm for obtaining the photoionization efficiencycurves. For subsequent normalization, the photon flux wasmeasured with a calibrated EMI 9783 B photomultiplier. Forelectron impact mass spectroscopy the electron energy wasset to 27 eV. After mass separation the ion current was am-plified with a dynode/channeltron combination and the signalwas then transferred for further processing to a PDP 11/73computer.

B. Cluster generation

In previous experiments on bimetal clusters both metalswere added inside a single resistively heated reservoir~uppertemperature limit 1250 K!, precluding an independent con-trol of the vapor pressures of the two metals.23–25In addition,the ratio of the vapor pressures varied during the experiment.These limitations have now been overcome by introducing anew two-chamber oven which consists of two separatelyheatable cartridges.20 A first, large cartridge~;50 cm3! usedfor the evaporation of the alkali metals can be resistivelyheated up to 1250 K. It is connected via a 25-mm-long,

thin-walled tube~1 mm thickness! with a second, smallergold containing cartridge~;15 cm3! which can be radia-tively heated to a maximum of 1800 K. The mixed metalvapor expands through a 30° conical/0.5-mm-diam nozzleinto the vacuum where cluster growth occurs under condi-tions of high supersaturation via homogeneous nucleation.With proper choices of materials and insulations, a differ-ence in temperature of 1000 K can be maintained during themeasurements.

For the Na/Au coexpansion the large cartridge was filledwith 20 g of sodium and heated to 1100 K~pNa'450 Torr!.The high-temperature cartridge was loaded with 6 g of goldand heated to 1800 K~pAu'0.05 Torr!. Once the final tem-peratures of both cartridges were reached, stable experimen-tal conditions could be maintained for about 80 min.

The CsxAu clusters were generated in a different way.The difficulties normally encountered when handling purecesium metal were circumvented by synthesizing metalliccesiumin situ from calcium and cesium chloride by the fol-lowing reaction:

12 Ca~c!1CsCl~c! ——→900 K 1

2 CaCl2~c!1Cs~g!

DG°900>9@kJ mol21#.

The equilibrium constant thus predicts about 220 TorrCs vapor pressure at 900 K. The cartridge was filled with 95g of CsCl and 17 g of Ca~Cs/Ca mol fraction of 1.3! and thesalt was carefully mixed with the metal. This was done in-side a dry box to prevent the vacuum packed calcium metalfrom incurring an oxide layer. The cartridge was then trans-ferred into the oven and heated to approximately 900 K~220Torr!. As for the Na/Au expansions, the small cartridge wasfilled with 6 g of gold and heated to 1800 K. Once the finaltemperatures of both cartridges were reached, about 50 minof stable beam conditions were available for experimenta-tion. Besides mixed CsxAuy clusters, chlorine containingspecies were also generated in the expansion. These will notbe discussed here.

C. From mass spectral abundances to clusterstabilities

To connect mass spectral ion abundances with thermo-dynamic stabilities of the neutral clusters, several experimen-tal questions have to be addressed.26–28 First, one has tomake sure that the neutral size distribution reliably reflectsdifferences in thermodynamic stability. Extensive studieshave previously been performed to assess the impact of thesource temperature and nozzle geometry on cluster-size dis-tributions and cluster temperatures.20,21 In the experimentsreported here, the source conditions were chosen such thatthe neutral size distributions reflect, as close as possible,relative thermodynamic stabilities.Second, for mass spectraldetection, clusters have to be ionized, rendering the mea-sured ion current a function of the ionization cross section ofthe corresponding cluster. A procedure was developed20,23

which, provided the PIE curves are known, allows for the

5575Heiz et al.: NaxAu and CsxAu bimetal clusters

J. Chem. Phys., Vol. 105, No. 13, 1 October 1996

correction of the mass spectra for relative photoionizationcross sections and at the same time reduces contaminationfrom fragmentation.

D. From photoionization efficiency (PIE) curves toionization potentials (IP)

Despite extensive theoretical and experimental evi-dence,29–32the connection between the PIE curve of a clusterand its vertical or adiabatic ionization potential~IP! is neitherunique nor straightforward. The complications arise from thefact that ionization induced fragmentation, temperature, iso-mer distribution, and the electronic and vibrational spectra ofthe neutral as well as the ion are usually not known. There-fore, different assignment procedures have been proposedwhich are believed to yield internally consistent relative ver-tical IPs.32–35 Here, we apply the assignment proceduretermedpseudo-Watanabewhich in the past has proven to berather robust and reliable.32

III. RESULTS

Figure 1 shows a photoionization mass spectrum from amixed sodium/gold expansion. It is dominated by the pres-ence of Na8Au2. Heteroclusters with up to five gold atomsare observed. The mono- and digold heteroclusters show astrong multimodal distribution. Such a clear size dependenceof cluster intensities is not observed for heteroclusters withthree or more gold atoms. On the other hand, the mass spec-trum of a cesium/gold expansion at similar vapor pressures~Fig. 2! reveals a strong Cs2Au mass peak and only hetero-clusters with one cesium atom are detected. Another distinc-

tion in these expansions is the production of pure cesiumclusters. The observed chloride clusters~CsxCl, CsxAuCl!which appear as additional peaks will not be discussed in thiswork.

As shown in the experimental section, measured massspectral intensities have to be corrected for relative photoion-ization cross sections before conclusions regarding relativestabilities of the neutral species can be drawn.20,23 The cor-rected intensity distributions of NaxAu and CsxAu are shownas stick spectra in Figs. 3 and 4, respectively. These arebelieved to reliably reflect relative thermodynamic stabilitiesof the neutrals. The multimodal distribution of neutralNaxAu stabilities~Fig. 3! shows a first relative maximum atNa3Au and a second absolute one at Na9Au which are both

FIG. 1. Representative photoionization mass spectra of mixed NaxAuy clus-ters. The clusters are generated in a two-chamber oven. The mixing ratio ofthe two metal vapors is controlled via the temperatures of the chambers, onecontaining alkali and the other gold metal. The temperature of the largechamber containing sodium is 1100 K. The small gold chamber is kept at1800 K, corresponding to a vapor pressure of 0.05 Torr. The clusters areionized with a 1 kW Xe arclamp ~unstructured emission spectrum below380 nm!, dispersed through a 0.25 m monochromator~PTI; 1200 lines/mm,grating blazed at 300 nm!. The NaxAuy clusters are ionized at 300 nm~16.5FWHM!.

FIG. 2. Representative photoionization mass spectra of mixed CsxAuy clus-ters. All procedures are as described in the caption to Fig. 1, except that thetemperature of the Cs chamber is 900 K and that the CsxAuy clusters areionized at 350 nm~16.5 FWHM!.

FIG. 3. Corrected intensity distributions of mixed NaxAu clusters. Thesespectra reflect as close as possible the neutral cluster distributions prior toionization ~see Ref. 23!.

5576 Heiz et al.: NaxAu and CsxAu bimetal clusters


followed by flat areas of low intensity. Essentially no NaxAuclusters are formed beyond Na9Au. In contrast, the multimo-dal CsxAu distribution ~Fig. 4! is dominated by CsAu andCs2Au which are the two smallest clusters with CsxAu clus-ters extending up to about Cs13Au. Strong drops in intensityare found after Cs3Au and Cs9Au—analogous toNaxAu—yet with maxima shifted down by one alkali atom,at Cs2Au and Cs8Au. The appearance of CsAu in Fig. 4deserves particular attention. This species is not present inthe photoionization mass spectrum~Fig. 2!. The reason forthis is its low ionization cross section at 350 nm. Its relativestability is estimated from a cluster distribution ionized byimpact with a 27 eV electron beam.20

Photoionization efficiency curves are measured for themost stable clusters. They are shown for NaxAu and CsxAu~x57–9! in Fig. 5. Using a procedure described in Ref. 32,the ionization potentials are determined from the low-energyonsets of the PIE curves. These are tabulated in Table I andshown graphically in Fig. 6. For comparison, published ion-ization potentials of Nax are also included in Table I and Fig.6.32

The most important experimental results can be summa-rized as follows:

~i! Neutral monogold heteroclusters of sodium and ce-sium show strong stability maxima at Na9Au andCs2Au, respectively. In cesium/gold expansions,Cs8Au is the most stable cluster in the higher massrange, but its dominance is much less pronounced. Atvariance with this experimental finding, Cs9Au is cal-culated to be the most stable cluster in the high massrange~see Sec. B!.

~ii ! The ionization potentials of the sodium–gold hetero-clusters NaxAu ~x57–9! are similar to those of iso-electronic pure sodium clusters, with the known odd–even effect and a drop of the ionization potentialwhen going from the octamer~x57! to the nonamer.In contrast, for CsxAu ~x57–9! this odd–even effect

is reversed, showing a larger ionization potential forCs8Au than for Cs7Au. In this mass range the ioniza-tion potentials of the cesium–gold heteroclusters areup to 1 eV smaller than the ones of the correspondingsodium–gold heteroclusters due to the lower bindingenergy of the cesium atom valence electron.

~iii ! With cluster intensities of one order of magnitudelarger and heteroclusters with up to five gold atoms,the gold and sodium have a substantially higher ten-dency towards heterometal bond formation and aggre-gation than their cesium/gold counterparts. This be-havior mimics the trend in the corresponding bulkheat of formation values.10

IV. DISCUSSION

Our primary motivation for this work is to elucidateelectronic and structural properties of mixed metal clustersand to correlate trends and features at the nanoscopic limitwith bulk properties. The~alkali!xAu clusters are here a par-

FIG. 4. Corrected intensity distributions of mixed CsxAu clusters. Thesespectra reflect as close as possible the neutral cluster distributions prior toionization ~see Ref. 23!.

FIG. 5. Intensity-normalized photoionization efficiency curves for NaxAuand CsxAu, x57,8,9. Details concerning measurement and assignment ofionization potentials are given in the text. The spectra are obtained at amonochromator resolution of 6.6 nm. The vertical ionization potentials,given in Fig. 6 and Table I, are extracted from the near-threshold regionswithin 0.5 eV of the ionization onset using pseudo-Watanabe plots~see Ref.32!.

TABLE I. Ionization potentials~IPs! of Nax21Au and Csx21Au clusters~ineV!. For comparison, we also include the IPs of pure sodium clusters Nax

from Ref. 32 which have been measured and analyzed by the same methodas used in this work.

x Nax Nax21Au Csx21Au

3 3.90 ••• 3.244 4.24 ••• 3.405 3.99 ••• •••6 4.23 ••• •••7 4.03 4.01 •••8 4.22 4.13 3.099 3.56 3.75 3.1610 3.84 3.97 2.91



ticularly attractive system. One is able, on the one hand, torelate our findings to a large body of experimental and theo-retical work on pure and mixed monovalent clusters.20,36–38

On the other hand, the properties and trends of alkali/goldintermetallic compounds can hopefully provide clues for aninterpretation of the NaxAu and CsxAu cluster data.8

In a first part~Sec. A! the experimental results are dis-cussed within the framework of a spherical shell model. In asecond part~Sec. B! extensive quantum chemical calcula-tions with inclusion of relativistic effects provide a solid ba-sis for the interpretation of the experimental results. Finally,in Sec. C, we compare the properties of the mixed-metalclusters to those of the corresponding alkali–gold intermetal-lic compounds.

A. Electronic shell model

A widely used approach in the interpretation of monova-lent metal cluster data is the jellium model.36,39–41Experi-mentally, the electronic shell structure can be demonstratedin several ways. An often discussed probe is the measure-ment of mass spectral intensity distributions where maximaare expected at shell closings. A more direct probe is thedetermination of ionization potentials. Both these approacheshave been used here.

1. Mass spectral intensity distributions

The corrected mass spectrum of NaxAu ~Fig. 3! shows apronounced maximum followed by a ledge at Na9Au ~10valence electrons!. Ten-electron maxima have already beenobserved in the past and interpreted via a modified levelorder relative to pure alkali clusters.24,40,42 Assuming thesingle gold atom is sitting at the center of the cluster, itshigher ionization potential causes a depression of the poten-tial well at the center. This leads to a selective stabilizationof ns states and eventually to a reversal of the 1d/2s levels~level order: 1s,1p,2s!. The mass spectral distribution of theCsxAu clusters shows a ledge at Cs9Au as well ~less pro-nounced than for NaxAu!. However, the relative intensitymaximum occurs for Cs8Au.

2. Ionization potentials

One straightforward observable of the shell structure isthe ionization potential and its trend as a function of clustersize.41,43,44 An odd–even alternation is predicted, clusterswith an odd number of electrons having a smaller IP thanthose with an even number. Up until now all IP measure-ments on pure or mixed monovalent clusters conform to thisprediction, including the values for NaxAu reported here~Fig. 6!. Turning our attention to the Cs/Au system, we seethat this trend is reversed in the range CsxAu, x57–9. The IPof Cs8Au is larger than those of Cs7Au and Cs9Au.

A shell model in which alls valence electrons contributeto the sea of delocalized electrons seems appropriate to de-scribe NaxAu mixed clusters. On the other hand, the reversedodd–even alteration in the ionization potentials of the CsxAuclusters cannot be understood within a simple electronicshell model. An alternative electronic shell description was

applied in the past to explain results for compound clusterssuch as CsxOy ,

42 NaxO2,45 and NaxCl.

46 Stabilities and ion-ization potentials are nicely interpreted, assuming that eachoxygen~chloride! consumes two~one! electrons from the seaof delocalized electrons of the alkali clusters. Referring tothe large difference in electron affinity between Cs and Au,13

we may similarly assume that the gold atom takes up onevalence electron from the cesium cluster to form a filleds-orbital ~an ‘‘inert’’ pair! !, @Xe#4 f 145d106s2. The CsxAucluster is then more appropriately described as Csx

1Au2 orCsx21~CsAu! and stabilities are derived from the shell struc-ture of Csx

1 or Csx21. The very intense peaks for CsAu andCs2Au are indeed suggestive of the existence of a stableCsAu or CsAuCs block inside CsxAu clusters, i.e., a Cs-solvated CsAu heterodimer or CsAuCs trimer~analogous toknown dialkali monohalides!.47 Similar arguments mightalso be invoked for NaxAu clusters, since the difference inelectron affinity is again substantial.13 The ledges in the massspectra at Na3Au, Na9Au and Cs9Au would thus correspondto 2 and 8 e closed shell alkali clusters.

Based on the experimental database presented here, it isnot possible to choose definitively between a pure jelliumlikemodel or one containing partial ionic interactions. However,the following theoretical description indicates that the inertpair model is well suited only for CsxAu clusters, while forthe NaxAu series alls valence electrons contribute to thejellium electron ‘‘reservoir.’’ With this difference in mind,one may characterize the cluster bonding of NaxAu asmainly polar covalent and that of CsxAu as more ionic.

FIG. 6. Ionization potentials of Nax21Au and Csx21Au plotted against thetotal number of atomsx ~equal to the number of valence electrons!. Forcomparison we also include the ionization potentials of Nax from Ref. 32,measured and analyzed according to the same procedure.



B. Quantum chemical investigations1. Model aspects and computational details

It is well known that the electronic structure of goldcompounds exhibits significant relativistic effects.48 There-fore, the present alkali gold clusters require a quantumchemical method which allows the inclusion of such relativ-istic effects. We have chosen the scalar relativistic variant49

of the ‘‘first principles’’ linear combination of Gaussian-typeorbitals density functional~LCGTO-DF! method50 which hasbeen shown to provide an efficient, yet accurate approach tothe electronic structure of gold compounds.51,52 We per-formed all-electron self-consistent field~SCF! calculationsusing the local density approximation~LDA ! to theexchange-correlation energy functional as suggested byVosko, Wilk, and Nusair~VWN!.53 After self-consistencyhad been reached, the total energy was evaluated for theresulting electron density employing gradient corrections tothe exchange54 and to the correlation55,56 energy functionalsaccording to the generalized gradient approximation~GGA!.This approximate procedure for taking into account ‘‘nonlo-cal’’ corrections to the exchange-correlation energy is quiteeconomical, yet often of sufficient accuracy.57

The orbital basis set for Au, (21s,17p,11d,7f ) con-tracted to [11s,10p,7d,3f ], was taken as in our previouswork.58 A basis set of the type (12s,8p,1d)→[6s,5p,1d] ~dexponent: 0.122! was used for Na59 and a(23s18p12d)→[13s11p6d] basis set for Cs.60 All orbitalbasis sets were contracted in a generalized fashion usingrelativistic LDA atomic eigenvectors. The accuracy of thebasis sets may be judged by the rather small basis set super-position error~BSSE! for the calculated dimer binding en-ergy of NaAu and CsAu~about 0.01 eV!. In the LCGTO-DFmethod two auxiliary basis sets were used to fit the electrondensity and the exchange-correlation potential. These fittingbasis sets were constructed in a standard fashion49 from theexponents of the various orbital basis sets.

The cluster geometries were optimized at the relativisticgradient corrected level of the theory. Since no analytic gra-dients of the total energy were available for the relativisticvariant of the LCGTO-DF method, the energy minimizationhad to be carried out employing a cyclic strategy involvingeach degree of freedom under an imposed symmetry con-straint. The search was stopped when all interatomic dis-tances were altered by less than 0.005 Å. Once the equilib-rium geometry had been determined, the cluster bindingenergy was analyzed by calculating the cluster fragmentationenergy, i.e., the energy required to formally abstract the goldatom from the otherwise unchanged alkali moiety, as well asatomization energies of the whole cluster and of the alkalimoiety. Ionization potentials were obtained at theDSCFlevel as differences of the corresponding total energies.

In the present investigations we considered the Na7Au,and Cs7Au clusters in both D5h and C6v symmetry, Na8Auand Cs8Au in D4d symmetry, and Na9Au and Cs9Au in D3hsymmetry~see Fig. 7!. The symmetry constraints were cho-sen based on the results of a previous, more elaborate theo-retical comparison19 between Na6Mg and Na6Pb clusters,which indicated that the heavy hetero-atom~differently from

light magnesium! preferentially occupies the central positionof the cluster. Therefore, to reduce the computational effort,we restricted our calculations to geometries which feature ahigh coordination of alkali atoms around gold, with one ex-ception to be discussed below in more detail. Comparing theresults for the clusters M7Au, M5Na, Cs, in D5h and C6vsymmetry~Tables II and III! we note that the binding energyis noticeably higher for the case where gold is higher coor-dinated. The latter symmetry has been included to allow amore direct analysis of the charge distribution in the clustersas the other symmetries prevent the formation of a nonzerodipole moment~see below!. However, the geometric struc-ture of all the alkali gold clusters investigated is not expectedto be rigid, but rather fluxonial, characterized by potentialenergy surfaces with several shallow minima of comparabledepth. The methodology employed here would have ren-dered a global search of such a surface rather expensive, ifnot impossible. On the other hand, the electronic structure isnot expected to significantly change for moderate geometryalterations, as suggested by the more detailed comparisoncarried out for the mixed-metal cluster Na6Pb.

19 Under thesecircumstances, a constraint symmetry optimization seems toprovide an acceptable compromise between accuracy andcomputational expense.

FIG. 7. Optimized geometries of NaxAu and CsxAu clusters from densityfunctional calculations employing a gradient-corrected exchange-correlationfunctional ~see text!. Bond lengths are in Å.



2. Optimized geometries

As can be seen from Fig. 7, the Na–Au bond lengths arerather constant in the series NaxAu, x57–9, while theCs–Au bond lengths are spread over quite a wide range. TheNaxAu bond lengths vary from 2.81 to 3.19 Å~a range of0.38 Å!, whereas for CsxAu, they vary from 3.40 to 5.10 Å~a range of 1.70 Å!. This finding indicates that in the NaxAuclusters the Na–Au bonds are essentially equivalent, while inCsxAu large differences are present among the variousCs–Au bonds. This observation provides additional supportfor the hypothesis suggested by the experimental high abun-dance of CsAu and Cs2Au in the molecular beam that spe-cific CsAu subunits are present in the larger CsxAu clusters.A direct comparison of the Na9Au and Cs9Au clusters is alsoinformative. While the former shows the usual close similar-ity between the two different Na–Au bonds~2.95, 3.05 Å!,the latter exhibits two types of coordination spheres. The firstshell, with a closer Cs–Au distance of 3.83 Å, is formed bythe six ‘‘quasi-axial’’ cesium atoms. The three ‘‘equatorial’’Cs atoms capping the three rectangular faces of the trigonalprism of the first Cs shell are rather far from the central goldatom ~5.10 Å!; these Cs atoms are forming a second shell~Fig. 7!. With only one coordination sphere in the NaxAuclusters, but more than one in the CsxAu clusters, one is ableto explain the distinct ledge following Na9Au in the experi-mental abundance spectrum and the rather dispersed abun-dances following Cs9Au. The calculated Na–Na and Cs–Csbond lengths are somewhat shorter or almost equivalent tothe sum of the covalent radii of the corresponding atoms.61

This suggests that the bonding interaction among the alkalimetal atoms might provide an important contribution to theoverall cluster stability, as will be discussed in detail in thenext subsection.

3. Calculated stabilities

As can be seen from Table II, the atomization energiesof the series NaxAu, x57–9, increases by about 1 eV foreach additional sodium atom in the cluster. This result agreeswell with the clearly increasing stability as deduced from the

experimentally obtained relative abundances~Fig. 3!. Theatomization energy of the mixed-metal clusters may be sepa-rated into two contributions: the fragmentation energy, i.e.,the energy required to separate the gold atom from the alkalifragment, and the atomization energy of the remaining alkalimetal fragment itself. In these formal separation processesthe geometry of the alkali fragments is kept optimized for themixed-metal cluster. For all sodium clusters investigated,these two contributions are nearly equal, 3.7–4.6 eV for thefragmentation energy and 3.0–4.5 eV for the atomization ofthe alkali fragments. For all Na moieties an average contri-bution of about 0.5 eV per sodium atom to the alkali frag-ment stability has been calculated~Table II!. At this point itis worth nothing that the stability increase of Na8Au com-pared to Na7Au, both in D5h and C6v symmetry, is essen-tially due to increased Na–Na interactions, while the stabilitygain of Na9Au compared to Na8Au arises mainly from theNa–Au interaction. This finding may be interpreted as fol-lows: when a sodium atom is added to Na7Au to formNa8Au, the coordination sphere around the gold atom isfilled and optimal Na–Na interactions result. The subsequentbuildup step to Na9Au is less favored by Na–Na interactions,since the attractive interaction within the Na moiety is essen-tially compensated for by the concomitantly increasing stericrepulsion. Thus the overall binding energy increase in Na9Auis due to markedly stronger Na–Au interactions.

A similar analysis for cesium clusters~Table III! leads toa different interpretation of the cluster stability. First, theatomization energy of the mixed-metal clusters increasesalong the series by only 0.6 eV per additional cesium atom.The average atomic contribution to the stability of the Csmoieties is only about 0.25 eV~Table III!. As a consequence,the cluster fragmentation energy and the atomization contri-bution of the alkali moiety no longer contribute equally tothe cluster stability. The cesium–gold fragmentation energyamounts to about two thirds of the cluster stability, whileonly one third is ascribed to the Cs–Cs interaction. Thus, inthe NaxAu series each Na atom is almost equally stronglybonded to Au and to the other Na atoms, while in CsxAueach Cs is mainly bonded to the gold atom, the Cs–Cs inter-

TABLE II. Calculated atomization energiesDEat and fragmentation ener-gies DEfr for various processes are shown together with calculated andexperimental ionization potentials~IP! and the highest occupied molecularorbital ~HOMO!-lowest unoccupied molecular orbital~LUMO! gapDe forNaxAu clusters~x57–9! under various symmetry constraints. All energiesare given in eV.

Cluster Na7Au Na8Au Na9Au

Symmetry D5h C6v D4d D3h

DEat~NaxAu→xNa1Au! 7.21 6.73 8.22 9.15DEfr~NaxAu→Nax1Au! 3.96 3.73 3.84 4.62DEat~Nax→xNa! 3.25 3.00 4.38 4.53DEat~1/xNax→Na! 0.46 0.43 0.55 0.50IP ~calc.! 4.02 4.28 3.70 3.87IP ~exp.!a 4.13 3.75 3.97De~HOMO-LUMO! 0.45 0.73 0.86~0.15b! 0.84

aThis work.bGap of majority spin manifold.

TABLE III. Calculated atomization energiesDEat and fragmentation ener-gies DEfr for various processes are shown together with calculated andexperimental ionization potentials~IP! and the HOMO-LUMO gapDe forCsxAu clusters~x57–9! under various symmetry constraints. All energiesare given in eV.

Cluster Cs-Au Cs8Au Cs9Au

Symmetry D5h C6v D4d D3h

DEat~CsxAu→xCs1Au! 5.27 4.94 5.89 6.49DEfr~CsxAu→Csx1Au! 3.50 3.39 3.78 4.16DEat~Csx→xCs! 1.77 1.56 2.11 2.33DEat~1/xCsx→Cs! 0.25 0.22 0.26 0.26IP ~calc.! 3.17 3.24 3.22 3.09IP ~exp.!a 3.09 3.16 2.91De~HOMO-LUMO! 0.04 0.52 0.81~0.15b! 0.65

aThis work.bGap of majority spin manifold.



actions being much less important. It seems worthwhile toelaborate this last statement by exploring the influence ofsmaller alkali–gold clusters as substructures,~M5Na,Cs!,possibly also as intermediates on the way to a total clusterfragmentation. To this end, the fragmentation energies of thealkali–gold clusters into subunits MAu and M2Au and in theremaining free alkali atoms have been calculated, togetherwith the atomization energies of the subunits for both Na7Auand Cs7Au in C6v and D5h symmetries~Table IV!. Obvi-ously, the atomization energies of the subunits MAu andM2Au are very similar for sodium and cesium~they differ atmost by 0.25 eV!, while the fragmentation energies of thestarting clusters differ much more~by more than 2.0 eV! andare lower for the cesium clusters. This finding implies thatthe contribution to the total cluster atomization energy de-rived from the subunit is larger for cesium clusters and maybe taken as a quantitative indication for the existence ofthese subunits.

The experiments seem to indicate that Cs8Au is the moststable cluster in the CsxAu series, a result which is at vari-ance with the present calculations. It is not easy to explainthis apparent discrepancy between theory and experiment.However, considering that the difference in mass spectralintensity between Cs8Au and Cs9Au is rather small, it isquite conceivable that the measured relative abundances donot reflect the actual thermodynamic stabilities with the re-quired accuracy. The fragmentation of the clusters intosmaller subunits could be the principal cause for the devia-tion from equilibrium. As has already been pointed outabove, sodium atoms are much more strongly bonded to eachother in NaxAu clusters than the cesium atoms in CsxAu.This suggests that in the NaxAu series rather strong Na–Nabonds must be broken in a hypothetical transition state of thefragmentation process. On the other hand, since Cs–Csbonds are significantly weaker in CsxAu, one expects a loweractivation energy for the fragmentation which in turn wouldmake it substantially more difficult to reach experimentalconditions that correspond to thermodynamic stability.

4. Calculated ionization potentials

The theoretical ionization potentials of NaxAu clustersare in good agreement with the measurements~Table II!,deviating at most by 0.1 eV. The calculated and measuredionization potentials exhibit the same odd–even effect. ForCsxAu the reversed odd–even effect observed in the experi-ments is nicely paralleled by the theoretical results~maxi-mum difference between theory and experiment: 0.2 eV!,

although the oscillation amplitude is much reduced com-pared to NaxAu. The trends of the ionization potentials mayprofitably be discussed with the help of an orbital correlationdiagram based on the Kohn–Sham levels. In fact, these one-electron energies may be interpreted as orbital electro nega-tivities via the Slater–Janak theorem62,63which also providesa relationship to ionization potentials by invoking Slater’s‘‘transition state’’ concept.62 In the present case we expectthe ground state Kohn–Sham spectrum to give a reliabledescription of the relevant valence shell ionization potentialsbecause the orbitals under study are highly delocalized andtherefore a transition state procedure implies a more or lessuniform ‘‘relaxation’’ shift to lower orbital energies, keepingthe level ordering essentially unchanged.

As an example, the orbital correlation diagrams ofNa9Au and Cs9Au are constructed with respect to their frag-ments in Fig. 8.~The subsequent conclusions have been veri-fied also for the other clusters of the present investigation.!The levels can be classified according to the jellium model as~Au 5d10! 1s21p62sx27 for NaxAu and as~Au 5d106s2!1s21px23 for CsxAu. Of course the assignment of the Au 6sderived orbital, which is in one case~Na! counted as a jel-

TABLE IV. Fragmentation energies of M7Au ~M5Na, Cs; both for D5h and C6v! for a separation of the clustersinto the subunits and the corresponding number of alkali atoms M as well as atomization energies of thefragments MAu and M2Au. All energies are given in eV.

D5h

M

C6v

M

Na Cs Na Cs

M7Au→M2Au15 M 4.07 2.06 M7Au→MAu16 M 4.33 2.29M2Au→Au12 M 3.14 3.21 MAu→Au1M 2.40 2.65M7Au→Au17 M 7.21 5.27 M7Au→Au17 M 6.73 4.94

FIG. 8. Orbital correlation diagram based on Kohn–Sham energies for theassembly of the Na9Au and Cs9Au ~D3h! clusters from their fragments Au,Na9 and Cs9 ~D3h!. Where meaningful, the levels are labeled according tothe jellium model; the manifold of Au 5d orbitals is represented by shad-owed gray boxes. Filled and open levels indicate doubly occupied andempty orbitals, respectively; for open shells the unpaired electron is explic-itly given as a vertical bar.



lium 1s level and in the other case not~Cs!, is a simplifica-tion that relies on the dominant character of this molecularorbital. Already here we see a principal difference in theNa–Au bonding of the clusters NaxAu and CsxAu. In thefirst systems, the bonds are of polar covalent-type~with ajellium of x11 electrons!, while in the second they may bedescribed as ionic,~Au2!2~Csx

1!, where a jellium ofx21electrons is assigned to the Csx moiety.

The most important finding of the level analysis is thatfor NaxAu the jellium shell structure is evident~the levels 1pand 2s are separated by about 0.8 eV in Na9Au!, rationaliz-ing the maxima for the ionization potentials of the closed-shell clusters Na7Au and Na9Au. On the other hand, inCsxAu the levels 1s and 1p are almost degenerate, in linewith the weaker Cs–Cs interaction. The lower oscillationamplitude of the ionization potentials in the cluster seriesCsxAu is in line with this observation. On the other hand, theunexpected trend in the seriesx57–9, namely a larger mea-sured and calculated ionization potential for the odd-electronsystem withx58 than for the even-electron systemsx57,9,clearly shows that a simple rationalization on the basis ofjellium-type shells does not apply in the case of CsxAu. It isinteresting to note also that the one-electron energies of thehighest occupied molecular orbital~HOMO! display thesame trend as the ionization potentials. However, this lastfinding may be fortuitous because of the rather small differ-ences in the one-electron energies~;0.05 eV! and since itmay to some extent depend on the assumed symmetry con-straints.

As a final observation from Fig. 8, it is worth noting thedifferent energy shifts of the Au 5d orbitals: these levels aredestabilized with respect to the free Au atom, but the desta-bilization in Cs9Au is 1.1 eV stronger than in Na9Au. Thisobservation suggests that the gold atom carries a more nega-tive charge in Cs9Au than in Na9Au and this is corroboratedby the very similar shift~1.2 eV! displayed by the Au 4fcore level. The same behavior has been observed for both theNaxAu and Csx Au series, with differences in the Au 5d corelevel energies ranging from 0.9 to 1.2 eV thus parallelingthose of the Au 4f core level.

5. Comparison of Na 7Au and Cs 7Au in C 6v symmetry

In order to gain a better understanding of the main dif-ferences in the electronic structure of the two cluster series

NaxAu and CsxAu, two representative clusters will be com-pared in more detail. Na7Au and Cs7Au in C6v symmetryhave been selected because they are the only model clusterswhich exhibit a nonzero dipole moment~pointing along theirsixfold symmetry axis!. Therefore additional information onthe electron charge distribution in the clusters may begleaned from this observable.

Both the total electron density as well as the differentialdensity, i.e., the difference of the cluster electron density andthe superimposed fragment electron densities~atomic goldand the alkali metal moiety!, are displayed in Fig. 9. Thefollowing differences in the total electron density~upperpanels! are observed. While in Na7Au the density is uni-formly distributed among the bonds, in Cs7Au the density isnoticeably greater along the Cs–Au axial bond than alongthe Cs–Au equatorial bonds. This is in good accordance withprevious conclusions derived from the optimized geometricalstructures, which lead us to classify the Na–Au bonds as

TABLE V. ShiftsDe of Kohn–Sham core level eigenvaluesa for Na7Au ~C6v! and Cs7Au ~C6v! clusters as wellas for the corresponding Na7 ~C6v! moieties. For the alkali atoms, axial and equatorial positions are discrimi-nated. All energies are in eV.

Core level Au 4f

Na 2p Cs 4d Cs 4p

Ax. Eq. Ax. Eq. Ax. Eq.

Na7Au 10.93 10.63 10.49Na7 10.90 10.35Cs7Au 11.96 10.45 10.43 10.45 10.43Cs7 10.57 10.32 10.57 10.32

aShifts calculated with respect to Kohn–Sham eigenvalues of free atoms:e~Au 4f !5281.01 eV,e~Na 2p!5228.71 eV,e~Cs 4d!5274.17 eV,e~Cs 4p!52160.46 eV.

FIG. 9. Total~upper panels! and differential~lower panels! electron densityplots for the Na7Au and Cs7Au clusters, calculated with a C6v symmetryconstraint. The plots display a plane which contains the sixfold axis and twoof the six equivalent alkali metal atoms as well as the gold atom. The valuesof the contour lines are 102n/2, n53~1!7 a.u.; solid and dashed lines repre-sent positive and negative values, respectively.



more or less uniform in the cluster but which pointed to theexistence of Cs–Au subunits in the larger clusters. The latterhypothesis is also suggested by the experimental data. Thedifferential density plot for@r~Na7Au!2r~Au!2r~Na7!# @Fig.9~c!# shows that a rather complex charge redistribution oc-curs in Na7Au, whereby the electron density increases on thegold atom and is depleted on the Na7 fragment moiety. Thischarge rearrangement is accompanied by significant polariza-tion effects both on the gold and on the equatorial Na atoms.This leads to a local induced dipolar contribution whose vec-torial sum points from the axial Na to Au, i.e., the gold atomrepresents the positive end of the dipole. It is worth notingthat these induced dipoles are oriented opposite to the dipolecaused by the Na–Au charge separation along the main sym-metry axis which points from Au to the axial Na atom. Thedifferential density plot of @r~Cs7Au!2r~Au!2r~Cs7!# ismuch simpler: there is a definite and uniform charge transferfrom the Cs7 fragment as a whole to the gold atom, and noinduced dipoles seem to be present at all. This differentialdensity analysis corroborates the previous classification thatwhile in Na7Au the Na–Au bonds may be termed ‘‘polarcovalent’’, in Cs7Au the Cs–Au binding is of ionic characteraccompanied by an actual charge transfer between the twotypes of hetero atoms.

To quantify the charge separation we have calculated thedependence of the dipole moment of these two clusters fordifferent positions of the gold atom along the symmetry axis,keeping the geometry of the alkali metal moiety fixed in theequilibrium structure~Fig. 10!. If a linear variation of thedipole moment is observed in such an analysis, charges maybe assigned based on the dynamic dipole moment, i.e., on thedisplacement derivative of the dipole moment, by assuming asimple model of rigid point charges. In the case of Na7Au arather linear variation of the dipole moment is found indeed.The corresponding charge separation is 0.50 a.u. with goldbeing negatively charged. This is in good agreement with allprevious considerations concerning the cluster charge distri-bution. However, it should be mentioned that at the equilib-rium geometry the small dipole moment~0.24 a.u.! pointstoward the gold atom, i.e., the gold atom represents the posi-tive end of the dipole. This apparently strange behavior maybe understood by considering the local dipole moments car-ried by the equatorial Na atoms which are clearly visible inthe differential density plot~Fig. 9!. In Cs7Au the variationof the dipole moment is not linear at all, but almost constantin the vicinity of the equilibrium structure. This may be ex-plained by assuming that the highly polarizable jelliumlikevalence electrons of the equatorial Cs6 moiety are apparentlyable to screen the geometrically induced change of the clus-ter dipole moment which is mainly due to the Au2Cs1 sub-unit. However, for Cs7Au the orientation of the dipole mo-ment at the equilibrium geometry is in agreement with anegative charge on the gold atom.

In summary, the behavior of the dipole moment is quitesurprising: in Na7Au the dipole moment varies linearly withthe displacement of Au, but nonlinearly in Cs7Au. This sug-gests that the cluster polarization is higher in the latter case.However, at the equilibrium geometry of Na7Au the dipole

moment has the opposite sign as the charge separation indi-cated by the dynamic dipole moment. On the other hand, inCs7Au the sign of the dipole moment properly reflects thecharge transfer implied by the change of the dipole moment.In order to understand this finding, it may be useful to intro-duce the following distinction concerning the polarizationeffects. In Na7Au the polarization is deduced from the in-duced dipoles~visible in the differential density plot! whichlead to the opposite sign of the total dipole moment at theequilibrium geometry: clearly a large polarization of thecluster electron distribution as a consequence of theforma-tion of the bondbetween the alkali fragment and the goldatom. The linearity of the dipole moment curve suggests thatthe polarization remains rigid with respect to ageometricdistortion. The opposite situation may be pictured for Cs7Au:the ionicity of the Cs–Au bonds implies that during the bondformation the molecular orbitals are not so muchpolarized,but rather differentlypopulatedwith respect to the frag-ments, as a consequence of the actual charge transfer. In thiscase, the electron charge distribution efficiently screens pos-sible effects of a geometry distortion as can be deduced fromthe nonlinear behavior of the dipole moment: this impliesthat the shapes of the molecular orbitals change significantlywith the geometry.

FIG. 10. Calculated dipole moment of Na7Au ~C6v! ~upper panel a! and ofCs7Au ~C6v! ~lower panel b! as a function of the distance of the gold atomfrom the base plane of the pyramid.



Finally, as a further assessment of the charge transferinside these two clusters, we performed a core level analysis~Table V!. In Na7Au the Au 4f core level is destabilized by0.9 eV with respect to the value in a free Au atom. Thecorresponding Au 4f core level shift in Cs7Au is 1.9 eV.These shifts are consistent with a negative charge on the Auatom in the cluster, which is larger in Cs7Au than in Na7Au,in complete agreement with all previous considerations. TheNa 2p core levels show a destabilization by 0.9 and 0.4 eVfor axial and equatorial atoms, respectively, when goingfrom the free atom to the Na7 fragment. The~formal! inser-tion of a gold atom in Na7Au leads to a stabilization of the2p core levels of the axial Na atom by 0.3 eV, but to afurther destabilization by 0.1 eV of the 2p levels of the equa-torial Na atoms. These shifts may be ascribed to the electro-static field inside the cluster: the core levels of the axial Naatom are stabilized because the Na7 moiety is globally posi-tive, while the core levels of the equatorial Na atoms feel thevicinity of the negatively charged gold atom and the twoopposite effects partially cancel each other. For the Cs 4dand Cs 4p core levels, very small shifts are calculated, withthe exception of a destabilization of 0.5 eV for both Cs 4dand Cs 4p in going from the free atom to Cs7Au. This isapparently in contrast with the concept of a globally positiveCs7 fragment, but it should be noted that while the positivecharge is rather diffuse on the Cs7 moiety ~as can be verifiedin paneld of Fig. 9!, the negative gold atom is much morecompact and may be the actual cause of the calculated ce-sium core level destabilization.

C. Relations to NaAu and CsAu bulk compounds

At the end of the discussion we wish to come back toone of our initial motivations for this study—to connect con-cepts and properties at the nanoscopic molecular limit to themacroscopic bulk limit. The alkali/gold systems are an idealtesting ground for such explorations.8,10

1. Heat of formation

The tendency of gold for forming compounds is reportedto increase from cesium to lithium.7,9 This trend is confirmedby calculations.10 At the cluster limit we observe that sodiumand gold readily aggregate, forming mixed NaxAuy clustersover a large mass and compositional range. In contrast, massspectral intensities of CsxAu ~under similar vapor pressureconditions! are one order of magnitude lower and no mixedclusters containing more then one gold atom are detected.

2. Metal –nonmetal transition

Proceeding through the series from LiAu to CsAu, sto-ichiometric 1:1 alkali–gold compounds exhibit a transitionfrom metallic to nonmetallic behavior. Bulk NaAu is metal-lic, whereas CsAu is an ionic semiconductor. At the clusterlimit, experiments and calculations on NaxAu clusters indeedpoint to delocalizeds valence electrons already for clustersas small as Na9Au. This jelliumlike behavior is further sup-ported by prominent stability maxima at Na8Au2 andNa16Au2 and by the drop of the ionization potentials after the

second (1s,1p,2s) and third shell (1s,1p,1d) closings. Onthe other hand, the experimental data on CsxAu disagree witha purely electronic shell model. The computational investi-gation shows an enhanced ionic interaction already for ces-iumaurid clusters consisting of less than 10 atoms.

V. CONCLUSION

A comparative gas-phase study of two sets of mixedmetal alkali/gold clusters is presented, supplemented by rela-tivistic density functional calculations on selected modelclusters. Experimentally, NaxAu and CsxAu clusters havebeen generated via supersonic expansions and their relativestabilities as a function of size and ionization potentials havebeen reported. Data on NaxAu are interpreted within an elec-tronic shell model. In contrast, the trend in the ionizationpotentials for CsxAu contraindicate considerations based ona shell model alone.

The results of the electronic structure calculations sug-gest that in NaxAu clusters the various Na–Au bonds arerather uniform and that the Na–Na interaction is ratherstrong, while in CsxAu clusters the Cs–Au bonds may dis-play large differences, as is expected if CsAu or Cs2Au sub-units are present. In NaxAu clusters the Na–Au bonding isaffected by delocalized electrons which exhibit a somewhatpolarized charge distribution with Au being slightly nega-tive. On the other hand, the calculated properties of theCsxAu clusters are well described by an ionic bondingmodel. In general, there is good overall agreement betweenthe theoretical and the experimental observations.

Throughout the discussion, the correspondence betweenthe macroscopic intermetallic compounds and their nano-scopic counterparts has been stressed. In particular, it is sug-gested that properties of 1:1 sodium–gold alloy and ces-iumaurid, like their heat-of-formation, electronic delocaliza-tion, and geometric structure, are reflected at the smallestpieces of matter.33

ACKNOWLEDGMENTS

The experiments, performed at the University of Bern,were supported by the Swiss National Science Foundation~Grant No. 2.7 2050 178!. C.Y. thanks Professor Edward W.Schlag and the Technische Universita¨t Munchen for theirhospitality and the Alexander von Humboldt Foundation fora fellowship. M.S., P.G., and N.R. thank Dr. K. M. Neymanfor fruitful discussions; M.S. and N.R. are grateful for sup-port from the European Community under the Human Capi-tal and Mobility Programme~Grant No. CHRX-CT94-0532!.The work of N.R. is supported by the DeutscheForschungsgemeinschaft and by the Fonds der ChemischenIndustrie.

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NaAu and CsAu bimetal clusters

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