Multiple valence superatomsJ. U. Reveles*, S. N. Khanna*, P. J. Roach†, and A. W. Castleman, Jr.†‡

*Department of Physics, Virginia Commonwealth University, Richmond, VA 23284; and †Departments of Chemistry and Physics,Pennsylvania State University, University Park, PA 16802

Contributed by A. W. Castleman, Jr., October 6, 2006 (sent for review July 25, 2006)

We recently demonstrated that, in gas phase clusters containingaluminum and iodine atoms, an Al13 cluster behaves like a halogenatom, whereas an Al14 cluster exhibits properties analogous to analkaline earth atom. These observations, together with our find-ings that Al13

� is inert like a rare gas atom, have reinforced the ideathat chosen clusters can exhibit chemical behaviors reminiscent ofatoms in the periodic table, offering the exciting prospect of a newdimension of the periodic table formed by cluster elements, calledsuperatoms. As the behavior of clusters can be controlled by sizeand composition, the superatoms offer the potential to createunique compounds with tailored properties. In this article, weprovide evidence of an additional class of superatoms, namely Al7

�,that exhibit multiple valences, like some of the elements in theperiodic table, and hence have the potential to form stable com-pounds when combined with other atoms. These findings supportthe contention that there should be no limitation in findingclusters, which mimic virtually all members of the periodic table.

3d periodic table � cluster � jellium

The formation of materials with properties different fromthose of the constituent atoms is a known phenomenon in

nature. For example, the formation of NaCl molecules/solid withcharacteristics different from its constituent elements, Na andCl, is a classic example. One of the objectives of the research onsuperatoms (1–3) is to explore if one can carry out, what naturedoes, in a more facile and controlled manner. Developing anunderstanding of the factors governing the chemical behavior ofclusters (4–10) and demonstrating that this knowledge can beused to design stable building blocks for new materials is criticalfor translating this concept into practice. For metal clusters, asimple electronic shell model called jellium (11) is routinely usedto describe the global features of the electronic structure. In thismodel, the nuclei together with the innermost electrons form apositive-charged background, whereupon the valence electronscoming from individual atoms are then subjected to this poten-tial. For pure metal clusters, within a spherical jellium back-ground, this approach results in a shell structure where theelectrons are arranged in electronic shells 1s2, 1p6, 1d10, 2s2, 1f14,2p6 . . . compared with 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10 . . . inindividual atoms. Similar shell structure is also obtained forsquare well and harmonic forms of background potential (12),indicating that the shells derived within a jellium picture repre-sent generic features of electronic states in a confined freeelectron gas. Clusters containing 2, 8, 18, 20, 34, 40 . . . electronscorrespond to filled electronic shells and exhibit enhancedstability as seen via abundances in mass spectra of simple metalclusters, higher ionization potential, lower electron affinity, andchemical inertness seen in reactivity experiments. In this respect,an Al13 cluster with 39 valence electrons and an electronicstructure of 1s2, 1p6, 1d10, 2s2, 1f14, 2p5 lacks a single electron asdo halogen atoms, which, upon addition of a single electron,acquire a filled shell status (13). Indeed, previous studies (14, 15)have shown that Al13 has an electron affinity comparable tohalogen atoms, indicating a chemical behavior reminiscent ofhalogen atoms. In a similar vein, we had recently shown that incluster compounds with iodine, an Al14 cluster exhibits behavioranalogous to alkaline earth atoms (3). We had shown thatAl14I3

� is a stable species and that its stability can be reconciled

by considering Al14 in a � 2 valence state (3). The electronic shellstructure, outlined above, does become modified (16) for com-pound clusters as the combination of atoms with differentelectronegativities can rearrange their geometry and influencethe electronic shells. In particular, the shell closings at 18 and 20are sensitive to the nature of the compound cluster.

Although the above developments bring out a close analogybetween atoms and superatoms, one of the most importantfeatures characterizing atoms is that numerous elements in theperiodic table exhibit multiple valence states. For example,carbon exhibits both divalent and tetravalent characteristics and,strongly binds with O or Si atoms forming CO and SiC, both ofwhich are highly stable. Are there superatoms that share thiscommonality to atoms?

In this article we present the results of a synergistic effort thatcombines first-principles’ theoretical calculations and the reac-tive stability of selected clusters to demonstrate an additionalmember of the superatom family, namely Al7�. What is trulyremarkable is that unlike previous members, this superatomexhibits multiple valence states, enabling it to form stablecompound clusters when combined with diverse atoms. Inparticular, we first demonstrate (8) the exceptional stability ofAl7C� through the production of AlnC� clusters in reactions ofaluminum clusters with benzene, and subsequent reactions of theclusters with oxygen to identify the stable species. The massspectra show the Al7C� peak to be even more pronounced thanAl13

�, another member of the superatom family, which we havepreviously identified, and studied extensively (1–3). Theoreticalconsiderations indicate that a superatom concept enables one tounderstand the electronic origin of the exceptional stability oftenobserved for these species. The same considerations also predictstability of other species such as Al7O�, Al7S�, Al7I2

�, and Al7�.Unlike Al7C�, however, the stability of Al7O�, Al7S�, andAl7I2

� cannot be ascertained by O2 etching experiments.The Al7O� and Al7S� clusters are not stable toward the forma-tion of AlO2

� or Al2O2; Al7I2� is unstable toward the formation

of Al2O2. Consequently, their stability has to be verified by areactant less harsh than O2. Experimental mass spectra, how-ever, do show the stability of Al7� in oxygen-etching experi-ments. The present investigations provide further extensivesupport to the general nature of the superatom concept and showAl7� to be a member of the multivalent superatom family.

Results and DiscussionIn brief, the clusters are produced by vaporizing a rotating andtranslating aluminum rod in a helium atmosphere. The produc-tion of mixed clusters is then accomplished by mixing theablation species with a small percentage of the carrier gascontaining the desired precursor. For example, AlnC� clusters

Author contributions: J.U.R., S.N.K., P.J.R., and A.W.C. designed research, performedresearch, contributed new reagents/analytic tools, analyzed data, and wrote the paper.

The authors declare no conflict of interest.

Abbreviations: HOMO, highest occupied molecular orbital; LUMO, lowest unoccupiedmolecular orbital; BE, binding energy; NRLMOL, Naval Research Laboratory MolecularOrbital Library.

‡To whom correspondence should be addressed. E-mail: awc@psu.edu.

© 2006 by The National Academy of Sciences of the USA

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are produced by adding benzene. To identify the stable species,the generated clusters are subsequently exposed to increasingamounts of etching gas introduced into the flow reactor in whichthe clusters are transported. In this way, the reactive anions areoxidized and often etched into smaller more stable fragments.

The reacted species are mass-analyzed, thus spectra contain thestable species generated in the original mass distribution and thestable products generated in the oxidation and etching reactions.In this way, the peaks in the mass spectra of the reacted speciesidentify the stable species.

Fig. 1 shows the mass spectra of AlnC� clusters obtained byreacting the aluminum plasma with benzene and subsequentlyexposing the generated AlnC� clusters to �200 standard cubiccentimeters per minute of oxygen. Fig. 1 shows that Al7C� is theonly cluster containing one C atom (at small sizes) that survivesin the mass spectra. The peak at Al7C� is conspicuously large andeven more prominent than Al13

�, known to be resistant tooxygen because of its closed shell structure. It was suggestedearlier (17) that the stability of Al7C� could be reconciled withina jellium model framework where the cluster could be lookedupon as a compound jellium formed out of an Al6, with a closedshell of 18 electrons and AlC� with a closed shell of 8 electrons.Such a picture does have difficulties. The electron affinity of AlC(1.1 eV) is less than that of Al6 (2.5 eV). Our calculations showthat, whereas it takes only 3.76 eV to remove an Al atom fromAl7C�, it will take 9.09 eV to break it into Al6 and AlC�. TheC atom in Al7C� is located inside the Al7 cage bonded to all ofthe Al sites, whereas one would expect it to bind to a single Alatom if it were a combination of Al6 and AlC�.

We begin by demonstrating that the true reason for thestability of Al7C� lies in the multiplet nature of Al7�. Fig. 2shows the geometry deduced for Al7C�. Note that the clusterfeatures an endohedral C atom as obtained in earlier studies. Toexamine the stability, we calculated the gain in energy, �E,

�E � E�Aln�1C�) � E�Al� � E�AlnC�� [1]

as a function of size as successive Al atoms are added to thepreceding size Aln�1C�. Here E is the total energy of the cluster.

Fig. 1. Benzene is introduced in the source aluminum plasma to produceAln� (F) and AlnC� (�). The clusters are subsequently reacted with molecularoxygen at thermal energy.

Fig. 2. Structure and energetics of aluminum compound clusters. (a) Al7C�-optimized geometry. (b) Energy gained by adding an Al atom to Aln-1C� speciesand HOMO–LUMO gap for the AlnC� clusters. (c) Electron charge density of the HOMO in Al7C� clusters. (d) Al7O�-optimized geometry. (e) Energy gained byadding an Al atom to Aln-1O� species and HOMO–LUMO gap for the AlnO� clusters. ( f) Electron charge density of the HOMO in Al7O�.

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The results are shown in Fig. 2b. A peak in �E is a signature ofstability as it implies a larger gain in energy in forming the stablespecies from the preceding size and lower energy in breaking thehigher size to form the stable species. Note that there is a peakat Al7C� indicating its preferred formation from the growth ofAl6C� and from the fragmentation of Al8C�. Fig. 2b also showsthe gap between the highest occupied molecular orbital(HOMO) and the lowest unoccupied molecular orbital(LUMO). In metallic clusters, the gap is generally indicative ofstability and chemical inertness. Note that Al7C� has the highestHOMO–LUMO gap.

We now discuss the stability of Al7C� and other aluminum-based clusters toward etching by O2 more quantitatively. Thepossible fragmentation pathways involve the formation of AlO2,AlO2

�, or Al2O2. Note that because the clusters are firstthermalized, then exposed to molecular O2, the OOO bond isprotected by a barrier and remains intact in the formation ofAlO2, AlO2

�, or Al2O2. Our calculations show that the bindingenergy (BE) of AlO2 and AlO2

� with OOO bond intact is 2.83and 5.72, eV respectively, whereas the energy required forbreaking an Al2O2 into two Al atoms and an O2 molecule is 6.75eV. These calculations show that those aluminum-based clusters,where it takes (i) �2.83 eV to remove a single Al, (ii) �5.72 eVto remove an Al�, or (iii) �6.75 eV to remove two Al atoms, willbe energetically unstable toward etching by O2. In this way, thestability of clusters can be tested, as less stable clusters areoxidized and often etched into smaller more stable fragments. Inthe case of Al7C�, the removal of an Al atom requires 3.76 eV,and the removal of an Al� requires 6.40 eV, whereas the removal

of two Al atoms requires 6.78 eV of energy. The correspondingstudies based on the Naval Research Laboratory MolecularOrbital Library (NRLMOL) show that the energy required toremove two Al atoms is 7.04 eV, whereas the BE of Al2O2 towardbreaking into two Al atoms and an O2 is 6.92 eV. Al7C� istherefore stable toward these fragmentation pathways and henceis not etched by O2. The same considerations also explain theobservation of Al7� in etching of the pure Aln� cations byoxygen. In this case, whereas it takes 4.32 eV to remove an Alatom, it takes 7.22 eV to remove two Al atoms. Why is Al7C� sostable? Can Al7� combine with other atoms to create stablespecies?

To answer the above questions, we outline the mechanism bywhich the Al7� cluster combines with other atoms to form stablecompounds. An Al atom has a valence electronic configurationof 3s2 3p1, and it has been proposed that Aln clusters undergo atransition (18) from monovalent to trivalent starting around n �6. The trivalent character in Al7 is further established (19) by themass spectra of the reacted Aln� cations that exhibit a sharp peakat Al7�, indicative of a shell closing at 20 electrons within ajellium picture of the confined free electron gas. If instead, it wasmonovalent in character, it would display prominence as aneight-electron system, which it does not (13). An Al7�, on theother hand, has 22 valence electrons. Within the jellium picture,the cluster has an electronic configuration of 1s2, 1p6, 1d10, 2s2,1f2, and Fig. 3 shows the one-electron levels in the free cluster.The molecular orbitals have been labeled by using the jelliumclassification (the levels roughly correspond to the overall shapeof the molecular orbitals). A carbon atom has a valence structure

Fig. 3. One-electron levels in Al7�, C, Al7C�, O, and Al7O�. The continuous thin lines represent single occupied levels, the continuous thicker lines representdouble occupied levels, the dotted thin lines correspond to single unfilled states, the dotted thicker lines correspond to double unfilled states, and the arrowsindicate the majority (up) and minority (down) spin states.

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of 2s2, 2p2 with four vacancies in the p-shell, and Fig. 3 shows theone-electron levels in carbon. To discuss the formation of Al7C�,let us start with the one-electron levels in Al7C� also shown inFig. 3. The 2s filled state of carbon is far below the manifold ofAl7� and becomes the 1s state of Al7C�. Consequently, the 1sand 2s states of pure Al7� become the 2s and 3s states of thecombined system and are pushed up in energies (the resulting 3sis high in energy and is not shown). The partially filled p-statesof carbon are around the same energy as 1p states of Al7� andform the bonding and antibonding combinations. The bondingcombination leads to the 1p state of Al7C�, whereas the anti-bonding combination leads to the 2p state that characterizes thegroup of highest occupied molecular states in Al7C�. Because acarbon atom has four unfilled p-states, the occupation of thep-states can be looked on as the transition of four electrons fromthe 1f and the 2s states of Al7� to these unfilled states. The 1funfilled states are pushed up in energy, and Fig. 3 shows therevised level structure in Al7C�. Note that the p-states of C formbonding orbitals with Al7� states; hence it is not a charge transferbut a population of these bonding states. A better description isthe transition of Al7� toward a � 4 valence state, which is similarto the transition of Al14 toward a � 2 state reported previously(3). Obviously such a transition cannot be identified throughMulliken or other charge analysis, as recently undertaken bysome authors (20). Fig. 2c shows the electron charge density inthe HOMO orbital. As the bonding states are deep in energy, theoccupation of bonding states stabilizes the cluster whereas themovement of unoccupied states opens a large HOMO–LUMOgap of 1.69 eV consistent with the stability and inertness ofAl7C�. A similar model would also account for the previouslyknown (21, 22) enhanced stability of neutral Al7N because Al7has 21 electrons, and the N states can be filled by occupation ofthree bonding orbitals.

The key issue is whether such simple electronic counting rulesand shell filling can be used to describe the stability of othermembers of the second row of the periodic table. Because theconfined free electron gas exhibits shell closing at 18 and 20electrons, the above arguments would suggest that Al7M� clus-ters should exhibit enhanced stability for cases where the M atomwould require two or four electrons to fill the deep p-bondingorbitals. This criterion would indicate that Al7O� should also bequite stable, and Fig. 3 shows the levels in this cluster and an Oatom (2s state of oxygen is deep in energy and is not shown). Thebonding then proceeds as for Al7C�, with the only differencebeing that only 1f electrons of Al7� are transferred to bondingstates between Al7� and O. To examine quantitatively thestability, we investigated the AlnO� clusters containing five toeight Al atoms and computed �E and the HOMO–LUMO gap(shown in Fig. 2 d and e). Note that �E peaks at Al7O�,indicating enhanced stability. Fig. 2f also shows the HOMOorbital. Although Al7O� is stable, it is not resistant to etching byO2 because it takes 6.10 eV to remove two Al atoms.

It is now interesting to inquire as to whether the aboveconsiderations could be extended to other elements. In partic-ular, could one use the above model to understand the bondingof Al7� to other elements in the second, third, and fourth row ofthe periodic table. To this end, we have calculated the BE of allof the atoms in the second, third, and fourth rows with Al7� usingthe equation

BE � E�Al7�� � E�M� � E�Al7M�� . [2]

Here E(Al7�), E(M), and E(Al7M�) are the total energies of theAl7�, M, and Al7M� species, respectively. For cases where M isa halogen atom, the BE was calculated by breaking into Al7 andM� fragments. In these calculations, the atoms were initiallylocated at different positions around the Al7 motif. The geom-etry was optimized by moving atoms in the direction of forces

until the forces dropped below a threshold value of 3 10�4 a.u.Several spin multiplicities were tried to locate the ground state.Three different types of geometries were obtained. For B, C, andN we obtain an endohedral structure (Fig. 2a). For Li, Be, O, F,Na, Mg, Al, P, S, Cl, Cu, Zn, Ga, Ge, As, Se, and Br we obtainan external geometry (Fig. 2d), and for Si we obtained a cappedgeometry where the Al7 opens up to accommodate the addi-tional atom.

In Fig. 4a, we show the variation of BE for all of the anionic

Fig. 4. Energetics of the Al7M clusters. (a) BE of Al7M� clusters, M is an atomof the second, third, and fourth row of the periodic table. (b) HOMO–LUMOgap for the Al7M� clusters. (c) BE and HOMO–LUMO gap of the Al7Im� clusters.

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clusters. In each case, we have marked the total number ofvalence electrons. Note that Al7C� and Al7O� are not onlystable with respect to addition of Al atoms, as discussed earlier,they also have the highest BE across the entire second row of theperiodic table. What is quite amazing is that the same trendcontinues for the anions of the third-row and fourth-row ele-ments. S in the third row and Se in the fourth row exhibit largergain in BE than previous sizes, again indicative of their stability.In addition to the BE, we examined the variation of theHOMO–LUMO gap (Fig. 4b). Significantly, the HOMO–LUMO gap follows the stability trend, indicating a chemicalinertness. For Si and Ge that correspond to a shell filling at 18,the BE only exhibits a shoulder whereas the HOMO–LUMO gapexhibit minor peaks. This behavior could be caused by the highlydirectional nature of the bonds from these atoms. To furtherconfirm this extensive nature of the multivalence concept andreiterate the theoretical picture, AlnS� clusters were generatedby reacting Aln clusters with SO2. The mass spectra of theresulting clusters contained Al7S� clusters, including othersulfur-containing clusters as well. When the clusters were ex-posed to O2, however, all of the clusters, including Al7S�, wereetched away. The etching of Al7S� is understandable, noting thatthe energy required to remove two Al atoms is only 5.78 eVwhereas energy gain in forming Al2O2 is 6.75 eV. Further, it willtake 5.73 eV to remove an Al� atom, making the formation forAlO2

� a resonant reaction. The corresponding studies based onthe NRLMOL, however, indicate that it will take 5.68 eV toremove an Al� atom, whereas the gain in energy in formingAlO2

� is 6.07 eV, opening this channel for fragmentation. Ineither case, Al7S� is unstable toward oxidation. We furthercalculated the electron affinity of the Al7M� clusters for Mcovering all of the third-row and fourth-row atoms. Al7S� andAl7Se� had the highest electron affinity, attesting to their closedelectronic shell character.

A critical test of the multiple valence would be to combineAl7� with atoms that have only one vacancy in the p-level (3) anda high electron affinity. The formation of the bonding stateswould then remove one electron at a time whereupon the effectof the 2f and 2s depopulation could be mapped out with thenumber of atoms. To carry out this important test, we consideredanionic Al7Im

� clusters. An I atom has an electron affinity of3.06 eV that is considerably higher than the measured electronaffinity (15) of 2.43 for Al7. One would therefore expect eachadditional I atom to combine with one electron from the Al7core. In Fig. 4c we show the variation of the BE and HOMO–LUMO gap as successive I atoms are added to the cluster. Notethat Al7I2

� leading to a core of 20 electrons is particularlyprominent compared with other sizes, again verifying the shellclosures discussed above. More importantly, the correspondingHOMO–LUMO gap shows the same trend. The chemical fea-tures together with the BE again point to the valence status. Toexamine whether the stability of Al7I2

� is borne out by experi-ments, the aluminum clusters anions were reacted with iodinegas. Fig. 5 shows the mass spectra of the bare and reacted species.Note that the mass spectra indeed exhibits a peak at Al7I2

�,confirming the theoretical prediction. We note that the varia-tions in BE and HOMO–LUMO gap in Fig. 4c indicate Al7I4

�

to be more stable than neighboring sizes, consistent with a shellclosure at 18 electrons; however, it is not seen in Fig. 5. Thereason is that it is energetically unstable toward the reaction

Al7I4� � I23 Al6I4

� � AlI2 [3]

by 0.31 eV. Although Al7I� and Al7I3� are less stable than

Al7I4�, as discussed in a previous paper (23), their observation

is linked to the enhanced stability of the corresponding neutralspecies. Al7I2

� is, however, unstable toward etching by O2 as ittakes 6.76 eV to remove two Al atoms, making the formation of

Al2O2 a resonant reaction. Corresponding studies based on theNRLMOL indicate the formation of Al2O2 to be exothermic by0.03 eV.

To summarize, we have demonstrated that bonding patterns ofAl7� can be understood by regarding it as a superatom thatexhibits multiple valence. The valence of 2 and 4 would make itanalogous to C or Si. The stability of Al7C� on the one hand andthat predicted for Al7O� and Al7S� on the other hand could thenbe correlated with the stability of SiC and CO, respectively. Inthe past we have shown that Al13 and Al14 could be regarded assuperhalogen and alkaline earth superatoms. Importantly, un-like Al13

� and Al14, Al7� exhibits multiple valence, thus addingan additional dimension to the chemistry of superatoms.

Materials/MethodsExperimental Methods. Al7C� species were created by ablating analuminum rod in a flow of 8,000 standard cubic centimeters perminute of high-purity helium. Benzene vapor was added restric-tively to the source to maximize the population of AlnC� species.The clusters and helium carrier gas merged into a laminar flowregime where they became thermalized. The clusters were thenreacted with molecular oxygen, and products were extracted,mass-analyzed by a quadrupole mass filter, and detected by achannel electron multiplier. The Al7I2

� species were created byablating an aluminum rod in a flow of 8,000 standard cubiccentimeters per minute of high-purity helium. Molecular iodinewas added externally to the source by flowing a small amount ofhelium through a sublimation cell containing molecular iodine.

Theoretical Methods. The theoretical studies were carried out byusing first-principles electronic structure calculations performedwithin a density functional formalism (24) that incorporatesexchange and correlation using the generalized gradient approx-imation functional proposed by Perdew, Burke, and Ernzerhof(25). In particular, Gaussian basis sets were used to construct theatomic wave function, whereas the cluster wave function wasformed from a linear combination of atomic orbitals. All cal-culations were performed with deMon2k software (26). Here, anauxiliary basis set was used for the variational fitting of theCoulomb potential (27, 28). The numerical integration of theexchange-correlation energy and potential were performed onan adaptive grid (29). The minimum structures were fullyoptimized in delocalized internal coordinates without con-

Fig. 5. Mass spectra of Aln� clusters (A) reacted with I2� (B).

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straints using the rational function optimization method and theBroyden, Fletcher, Goldfarb, and Shanno update (30). Thedouble zeta valence polarized and the GEN-A2 auxiliary basissets were used (31). To eliminate any uncertainty from the basisset or the numerical procedure, in selected cases we carried outsupplementary calculations by using the NRLMOL developedby Pederson and coworkers (32–34) using the same densityfunctional. For details, see refs. 3 and 32–34.

This work was supported by U.S. Air Force Office of ScientificResearch Grant F49620-01-1-0328 (to A.W.C. and P.J.R.) for theexperimental work on Al7C� and Al7In

�, U.S. Air Force Office ofScientific Research Grant FA9550-05-1-0186 (to J.U.R. and S.N.K.)for the theoretical work on these systems, and U.S. Department ofEnergy Grant DE-FG02-02ER46009 for the systematic studies onAl7X� clusters for X covering the second, third, and fourth rows of theperiodic table. S.N.K. thanks Virginia Commonwealth University forproviding a study/research leave.

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