Structures and Stabilities of Clusters of Si12, Si18, and Si20 Containing Endohedral Chargedand Neutral Atomic Species
Delwar Hossain,†,‡ Frank Hagelberg,§,| Charles U. Pittman, Jr.,† and Svein Saebo*,†
Department of Chemistry, Mississippi State UniVersity, Mississippi State, Mississippi 39762, Department ofChemistry, Jahangirnagar UniVersity, SaVar, Dhaka 1342, Bangladesh, and Computational Center forMolecular Structure and Interactions, Department of Physics, Atmospheric Sciences, and Geosciences, JacksonState UniVersity, Jackson, Mississippi 39217
ReceiVed: May 10, 2007; In Final Form: July 9, 2007
Electronic structure calculations based on density functional theory and Møller Plesset perturbation theorywere performed on three isomers of Si12 and on the endohedral clusters Si12 containing neutral or chargedatomic species. The existence of endohedral clusters depends on the Si12 cage shape and the nature of theembedding species. Endohedral clusters of Li0,1,-1, Na0,1,-1, and He in Si12 cages were found. In contrast, K+,Ne, F-, or Cl- do not form endohedral clusters with Si12 due to their large size. All endohedral clusters thatare minima on the potential energy surfaces are stable and have large HOMO-LUMO gaps (>1 eV). Thestability order for the lithium and sodium clusters is: anionic clusters> neutral clusters> cationic clusters.The endohedral complex of two Li atoms with the Si18 cage is lower in energy than the sum of the empty Si18
cage and two Li atoms. In contrast, doping two Na atoms into the Si18 cage forms an exohedral Na2Si18
cluster. An endohedral cluster of Li2 with Si20 was also investigated and characterized. The stability of theendohedral complexes of two Li atoms in Si18 and Si20 suggest that silicon nanotubes, which are unstable,might be stabilized by an internal string of Li atoms.
I. Introduction
Nanoclusters are interesting building blocks for large self-assembled or consolidated materials. The properties of nano-clusters can be manipulated by changing their size, shape, andcomposition. Since silicon is the most widely used material inthe semiconductor and microelectronic industries, extensiverecent theoretical and experimental studies have been carriedout on both pure Si and metal-doped Si clusters to understandtheir structures and properties.1-5 The well-known stablefullerene-shaped carbon cages exhibit unusual stabilities dueto sp2 hybridization of their carbon atoms and their extendedsurface conjugation. Even though Si is isovalent with C, Si sp2
hybridization is less favorable than that for C. Silicon doublebonds are rare, and fullerene-like Si clusters are unstable.6
Recent experimental4 and theoretical research1-3,5-16 suggeststhat introducing guest atoms into the Si cages can stabilize theseclusters. Extensive theoretical studies of metal-encapsulatedsilicon clusters led to the discovery of novel shapes includingfullerene-like, cubic, Frank-Kasper polyhedral, icosahedral, andother cluster geometries.2,3,7-12,15,16Hiura et al.4 reacted silanewith different transition metals and obtained a Si12W clusterwith a hexagonal prism structure and the W atom at the cagecenter. Theoretical studies predicted a similar structure for theendohedral clusters of Cr, Cu, and V with Si12.15-17 Furthersilicon cluster species with transition metal (TM) atom impuritieswere detected by Ohara et al.18 by using a double-rod lasertechnique to vaporize both components, TM (TM) Ti, Hf,Mo, and W) and Si, and letting the atomic species react with
each other. The stabilities of endohedral metal clusters withsilicon cages depend on the size and the shape of the siliconcage as well as the size and electronic structures of the metalatoms. Although small Si clusters tend to have close-packedstructures, clusters with 14-25 atoms have prolate structureswith Si9 and Si10 building blocks.13-19 Kumar and Kawazoeobserved that the composites M@Si16 (M ) Hf, Zr) and M@Si14
(M ) Fe, Ru, Os) favor fullerene-like and cubic cages,respectively.3
Beck et al.20-22 generated metal-silicon clusters with Cu,Cr, Mo, and W by laser vaporization. Clusters of Cr, W, andMo with Si15 and Si16 cages were observed in significantlygreater abundance than any other metal-doped silicon clustersin this series. The mass spectra of the CuSin (6 < n < 12)clusters demonstrated that the endohedral complex of Cu withSi10 is exceptionally stable. Scherer and co-workers experimen-tally produced several metal silicon cage clusters for the metalsCu, Ag, and Au.23-25 Combined experimental and theoreticalstudies of SinNa- (n < 7) found that the Na atom acts as anelectron donor to the Sin framework.26 Na adsorption occurredon the Sin cluster’s surface and left the original Sin frameworknearly unchanged in NaSin. The electronic properties of silicon-based semiconductor surfaces change dramatically by alkalimetal adsorption.
Endohedral silicon clusters with alkali metals, halides, ornoble gases have drawn little attention despite the extensivestudies of corresponding clusters encapsulating transition metals.The present study focused on clusters of alkali metals, noblegases, and halides with Si12 cages; however, larger siliconframeworks were also considered. The following questionsregarding this class of clusters are essential: (1) Can alkalimetals or their ions, halides, or noble gas atoms be successfullyencapsulated into a Si12 cage? (2) Will the endohedral element
† Mississippi State University.‡ Jahangirnagar University.§ Jackson State University.| Present address: Department of Physics, Astronomy and Geology, East
Tennessee State University, Johnson City, TN 37614.
always be located at the center of the Si12 cluster? (3) Howdoes the size of the encapsulated species affect the size of Si12
cluster? (4) How do the clusters’ electronic properties changeafter the atoms or ions are encapsulated? (5) Are alkali metal-doped silicon nanotubes stable?
To address these questions we performed a systematictheoretical study of possible endohedral clusters of Si12 cageswith charged and neutral alkali metals, noble gases, and halides.Throughout this paper we will use the notation X@Si12 forendoheral clusters and XSi12 to describe exohedral clusters. Wealso investigated the structure and stabilities of Li2@Si18,Li2@Si20, and Na2Si20 clusters which are relevant to the possiblestabilization of Si nanotubes.
II. Computational Details
All structures were optimized at the (spin-unrestricted)B3LYP27,28/6-311+G(d) level. Three different start geometriesof the Si12 cage, withD6h (hexagonal),Ih (icosahedral), andD2d
symmetry, respectively, were used. All optimized structuresconstrained to these initial high symmetries had several imagi-nary frequencies. All of these structures were subsequentlydistorted and further relaxed until a structure with only realvibrational frequencies was found. For the systems studiedherein an explicitly correlated method like MP2 would havebeen preferred, in particular since dispersion interactions areneglected in the B3LYP method. Complete geometry optimiza-tion at the MP2 level would be possible, but we decided thisapproach to be too expensive. As a compromise we carried outsingle-point MP2/6-311G(d) calculations at the B3LYP/6-311+G(d) optimized geometries for all 37 clusters and atomicspecies. The programs Gaussian-0329 and PQS30 were used forthe calculations.
Theoretical studies of weak interactions are often plaguedby basis set superposition errors (BSSE). These can be correctedfor by counterpoise calculations.31 To evaluate the magnitudeof the BSSE, we carried out counterpoise calculations forselected clusters. The BSSE are significant but they do not affectany of the predicted trends. Since counterpoise calculations arequite expensive we did not carry out counterpoise calculationsfor the remaining clusters.
To evaluate the stabilities of the clusters, the embeddingenergies (EE) and binding energies (BE) were calculated usingthe following equations:
whereE(Xm@Sin), E(Sin), E(X), andE(Si) denote the calculatedtotal energies for the Xm@Sin clusters, the empty silicon cage,the embedding atom, and the total energy of a silicon atom,respectively. Similar formulas were used for the exohedralcomplexes. Normally, both the BE and the EE are negativenumbers, and the larger negative number denotes greaterstability. Electronic properties were analyzed using the NBO-4program.32
III. Results and Discussion
The calculated embedding energies (EE), binding energies(BE), HOMO-LUMO gaps of empty Si12 cages and clustersof Si12 with neutral and charged atomic species calculated atthe B3LYP/6-311+G(d) level are shown in Table 1, and theresults of the single-point MP2/6-311G(d) calculations at theB3LYP/6-311+G(d) geometries are shown in Table 2. Table 1
also shows the charges on the embedded species obtained fromnatural population analysis (NPA). The optimized geometriesof the empty Si12 cages as well as all distinct clusters found inthis study are shown in Figures 1-4. With a couple ofexceptions, none of the optimized structures had any symmetry;however, some structures, in particular molecular species startingfrom Ih symmetry, deviated only slightly from the originalsymmetry. For identification purposes, the point group of theinitial structure in parentheses was retained. In the discussionbelow, relative energies calculated at the MP2-level are giventhroughout with the B3LYP results in parentheses. The Si12
clusters’ binding energies calculated at the MP2 level areroughly-0.3 eV/atom lower than those calculated with B3LYP,and the difference is slightly larger for the larger clusters. Forthe endohedral complexes, the embedding energies calculatedat the MP2 level are, as expected, more negative than thecorresponding ones calculated at the B3LYP level.
Si12 Cages. The geometry of the empty Si12 cage wasoptimized using three different initial structures ofD6h, D2d,and Ih symmetry, respectively. These three initial geometriesyielded three distinct cage-like Si12 structures shown in partsa-c of Figure 1, respectively. A cage-like structure withC2h
symmetry was obtained from the initialD6h Si12 structure. Uponoptimization, the initialD2d structure underwent a significantstructural change resulting in a nonsymmetrical cage, while theIh (icosahedral) Si12 form distorted only slightly from its initialstructure. The same structures were also obtained by Lee et al.33
The binding energies of these three optimized Si12 clusters are-3.31(-3.05), -3.34(-3.12), and -3.27(-2.95) eV/atom,respectively. The Si12 cluster obtained from the initialD2d isomer(Figure 1b), is more stable than theD6h and Ih forms by 7.2-(19.0) and 17.4(46.9) kcal/mol, repectively.
Complexes of Si12 and Atomic and Ionic Species.The mainobjective of the present study was to investigate possibleendohedral complexes of the Si12 cage with charged and neutralatomic species. In some cases the initial cage-like structure brokedown, resulting in exohedral complexes. Whenever the opti-mization resulted in a structure without any imaginary frequen-cies, this structure was included in Figures 1-3 and in Tables1 and 2. In other cases where the cage structure clearly wasbreaking down, (expensive) geometry optimizations were notpursued to the end, and these partial optimized structures arenot included here.
Several complexes with embedded alkali metals were inves-tigated. Both neutral, positively, and negatively charged com-plexes of alkali metals were studied. Using Li as an example,these complexes are referred to throughout as Li0@Si12,Li+@Si12, and Li-@Si12, respectively. A total of 19 distinctendohedral complexes with Si12 cages were found. These werethe Li@Si12 (D6h, D2d, Ih), Li+@Si12 (D6h, D2d, Ih), Li-@Si12
(D6h, D2d, Ih), Na@Si12 (D6h, D2d, Ih), Na+@Si12 (D6h, D2d, Ih),Na-@Si12 (D2d, Ih), and He@Si12 (D6h, Ih). Insertion of Li, Li+,Li-, Na, Na+, or He into the initial Si12 D6h cage yieldedstructures of similar shape (Figure 2). The shapes of thesecomplexes are best described as complexes for which theembedding species is sandwiched between two chairlike Si6-rings similar to the chair form of cyclohexane. The Si-Li bonddistances in Li+@Si12 vary over a range of 2.520-2.827 Å,and the Si-Si distances are 2.417-2.377 Å. The He-Si andSi-Si bond distances span the ranges of 2.440-2.944 Å and2.361-2.362 Å, respectively. Insertion of Na-, K+, Ne, F-, orCl- inside Si12(D6h) is energetically unfavorable, and theoptimized structures are the exohedral complexes shown in partsf, g, and i-k of Figure 2, respectively.
EE ) E(Xm@Sin) - E(Sin) - mE(X)
BE ) -[E(Xm@Sin) - nE(Si) - mE(X)]/(n + m)
Structures of Si12, Si18, and Si20 Clusters J. Phys. Chem. C, Vol. 111, No. 37, 200713865
Insertion of either Li+, Li0, Li-, Na+, Na0, or Na- into theD2d Si12 cage yields the endohedral complexes shown in partsa-f of Figure 3, respectively. Their shapes are quite similar tothat of the empty Si12 cage shown in Figure 1b. In addition tothese six endohedral complexes, a complex HeSi12 shown inFigure 3h was also found. The optimized K+ complex in thisseries has an interesting structure shown in Figure 3g. In thisstructure the potassium ion is bonded to the corner silicon atomin two nearly planar Si6-sheets. Starting with an endohedralcomplex ofD2d symmetry, minima corresponding to exohedralcomplexes were found for Ne, F-, and Cl-. These structuresare shown in Figure 3i-k.
After inserting Li, Li+, or Li- into an initial Si12 icosahedron(Ih), the optimized X@Si12 (X ) Li, Li +, Li-) geometries distortonly slightly from the initialIh symmetry, and these optimizedendohedral structures are shown in parts a-c of Figure 4,respectively. Insertion of Na, Na+, or Na- into the Si12 Ih isomercage also gives similar endohedral clusters (Figure 4d,e).Insertion of Na+ into the Si12 Ih cage produces a cluster withCs symmetry.
The embedding energies show that the clusters containingendohedral Li-, prepared from all three initial Si12 (D6h, D2d,Ih) geometries, are energetically more favorable than thosecontaining Li0 (Table 1). Furthermore, all three endohedral Li0
clusters are slightly more stable than their corresponding Li+
analogues. At the B3LYP level, theD2d form of Li+@Si12 hasa higher energy than the sum of Li+ and Si12 while theembedding energy becomes negative at the MP2 level. All theLi0 and Li- complexes have negative embedding energies orlower energies than those of their corresponding separatedspecies. The binding energies for all three forms of Li+@Si12
and Li0@Si12 (D6h andIh) are smaller (less negative) than thoseof the respective empty cages, while the binding energies forall three Li- clusters are larger than those of the correspondingempty Si12 cages.
All endohedral Na+@Si12 and Na0@Si12 clusters, except theNa0@Si12 (Ih) cluster, are energetically unfavorable with positiveembedding energies. Furthermore, all three Na+@Si12 clustershave smaller binding energies than the corresponding emptycages (see Tables 1 and 2). All the Na- clusters appear to beenergetically favorable with large negative embedding energies.The binding energies for these complexes are similar to thoseof the corresponding empty cages.
He encapsulation into all three forms of the Si12 cagegenerates endohedral He@Si12 clusters with positive embeddingenergies. The He@Si12 cluster obtained fromD6h isomer hasC2 symmetry while insertion of He into theD2d and Ih Si12
isomers yielded endohedral complexes without symmetry. Bothat the B3LYP and MP2 levels all He complexes were energeti-cally unfavorable compared to the separated species.
TABLE 1: Total Energies (in Hartrees), Molecular Point Groups, Lowest Vibrational Frequencies (ω, cm-1), EmbeddingEnergies (EE, eV), Binding Energies (BE, eV/atom), HOMO-LUMO Gaps (eV), and Natural Electronic Charge on theEmbedding Species
a Point groups in parentheses indicate the symmetry of the initial geometry.b Endohedral complexes are denoted X@Sin and exohedral complexesXSin.
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The calculated charges on the encapsulated species are shownin Table 1. Since Si is more electronegative than alkali metals,the atomic charges on the alkali atoms are expected to be morepositive than the charge on the silicon atoms. The calculationsconfirmed this expectation. Remarkably, the calculated chargeon an alkali metal is largely independent of the charge of thecomplex. Instead, it mainly depends on the shape of the Si12
cage. For example, the calculated charge on Li in Li+@Si12
(D6h) is 0.8. Adding one electron only decreases the positivecharge on Li by 0.2 (in Li0@Si12(D6h)), and adding an additionalelectron (Li-@Si12(D6h)) did not change the charge on Li.Furthermore, the calculated charge on the sodium atom insodium clusters is actually larger in Na0@Si12 (D6h) than inNa+@Si12 (D6h) by a small amount. The charge on the alkalimetal is consistently smaller in theD2d clusters than inD6h andIh clusters for both lithium and sodium endohedral complexes.These calculated charges indicate that the Si12 cage acts like anelectron sink as any variation of charge of the complex is carriedalmost entirely by the silicon cage. Essentially, no chargetransfer occurs between an endohedral He atom and the Si12
cage. The calculated charges on the halides are smaller (lessnegative) than-1, and the charge of the ion and in this casethe silicon is negatively charged.
The energy difference between the HOMO and LUMO isgenerally considered an important parameter of the electronicstability of a small cluster.34 A larger energy gap indicatesgreater cluster stability. Even though density functional theoryis not the best method for calculating HOMO-LUMO gaps,the HOMO-LUMO gaps are included in Table 1. Twoimportant points emerge. First, all the calculated HOMO-LUMO gaps are quite large indicating that these clusters arestable. Second, the HOMO-LUMO gaps do not changesignificantly upon formation of endohedral complexes.
Li 2@Si18, Li 2@Si20, and Na2Si18 Clusters. The geometriesof Si18, Si20, Li2@Si18, Li2@Si20, and Na2Si18 clusters are shownin Figure 5, and total energies, embedding energies (EE), andbinding energies (BE) are given in Tables 1 and 2. The Si18
cluster may be considered a combination of two Si12 units withone Si6 hexagon in common. Two lithium atoms were placedinside the Si18 cluster, and the system was then optimized togive the fully relaxed geometry of the Li2@Si18 cluster shownin Figure 5c. This optimized Li2@Si18 structure hasC2h
symmetry and, as such, it resembles the Li@Si12 unit as shownin Figure 1a. In Li@Si18, the Li atoms are shifted toward theend Si6 units of the Si18 cage. The Li-Li distance in Li2@Si18
is 2.787 Å. The bond length in free Li2 is 2.075 Å. Thiselongated Li-Li distance in the optimized Li2@Si18 structureis due, in part, to bonding of each of the Li atoms with two Si6
layers. In Li2@Si18, 12 silicon atoms surround each Li atom.The electronic charge on each lithium atom in Li2@Si18 clusteris +0.6. The shape of each Si6 unit resembles the cyclohexaneboat configuration. The Si-Si distances in the end Si6 unitsrange between 2.460 and 2.614 Å, and those in the middle Si6
unit are each 2.463 Å. The Si-Li lengths vary from 2.502 to2.902 Å.
The Li2@Si18 cluster has relatively large negative embeddingand binding energies, namely-5.24 (-1.85) eV and-3.85(-2.96) eV/atom, respectively, where the MP2/6-311G(d,p)result is followed by the B3LYP/6-311G(d,p) result in paren-theses. The binding energy of Li2@Si18 is slightly smaller thanthe binding energy of the parent Si18 cage (by 0.08 at the MP2/
TABLE 2: MP2/6-311G(d,p) Energies (in Hartrees) at theB3LYP Optimized Level, Embedding Energies (EE, eV), andBinding Energies (BE, eV/atom)
a Point groups in parentheses indicate the symmetry of the initialgeometry. The point group of the optimized cluster can be found inTable 1.b Endohedral complexes are denoted X@Sin and exohedralcomplexes XSin.
Figure 1. Optimized structures of Si12 clusters. (a) Structure obtainedfrom initial D6h form. (b) Structure obtained from initialD2d form. (c)Structure obtained from initialIh form.
Structures of Si12, Si18, and Si20 Clusters J. Phys. Chem. C, Vol. 111, No. 37, 200713867
6-311G(d,p) level). The HOMO-LUMO energy difference is1.44 eVsslightly larger than for the empty Si18 cage (1.36 eV).Hagelberg et al.35 studied the M2@Si18 (M ) Mo, W) clusters.W and Mo inclusion was predicted to change the originalD6h
symmetry to D3h symmetry in the optimized structure. Incontrast to the bonding predicted here for Li2@Si18, the Mo orW atoms were not predicted to bond to the middle Si6 ring.
An exohedral Na-containing cluster, Na2Si18, is formed whentwo Na atoms are placed inside the Si18 (D6h) cage and thenoptimized. The optimized structure of Na2Si18 is fundamentallydifferent from the Li2@Si18 cluster even though both clustershaveC2h symmetry. The Na atoms have become end-cappingatoms in the optimized structure (see Figure 5e). Each Na atomcaps a chairlike Si6 unit at the opposite ends of the cluster. Naatoms are larger than lithium, making their encapsulation insidethe Si18 tube energetically unfavorable. Second, the Na-Nainteractions are probably repulsive, like those exerted by Li-Li and K-K within a carbon nanotube.36
Yang et al.36 predicted that the Li atom prefers to occupysites along the tube axis inside carbon nanotubes. Inserting Katoms into carbon nanotubes was unfavorable due to their large
radii. The repulsive force between two sodium atoms withinSi18 may be strong enough to overcome any favorable embed-ding energy. Hence, the repulsive sodium-sodium interactionprobably contributes to the observation of the end-capped Na2-Si18 structure rather than an endohedral Na2@Si18 cluster. Inthe end-capped Na2Si18 cluster, each Na has a charge of+0.9,suggesting that 2Na+(Si18)2- is the best way to represent thestructure. The Si-Na distances are 2.544 and 2.511 Å. The Si-Si distances in the central Si6 unit are 2.544 and 2.438 Å. Thedistance between the terminal and central Si6 units are 2.940and 2.990 Å, and the Si-Si distances in the end Si6 units are2.544 and 2.511 Å. Both the embedding and binding energiesof the Na2Si18 cluster are still negative, and the binding energyfor this cluster is slightly smaller than that of the empty cage.The Na2Si18 cluster has a quite large HOMO-LUMO gap(1.20 eV).
We also investigated the Si20 cage and the Li2@Si20 clustergenerated by inserting two Li atoms into the Si20 cage. On thebasis of the result for the Na2Si18 cluster for which the Na-Narepulsion prevented formation of an endohedral complex, theNa2Si20 cluster was not included in our investigation. The Si20
Figure 2. Optimized structures of clusters of Si12 with charged and neutral atomic species. The initial geometries of all clusters were endohedralstructures ofD6h symmetry.
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cage is generated from the Si18 cage by capping each of theterminal Si6 units with a Si atom. Two Li atoms were placedinside the Si20 framework, and after optimization the two lithiumatoms remained inside the cage. The optimized structures ofthe empty Si20 cage and the Li2@Si20 cluster are shown in partsb and d of Figure 5, respectively. The Li-Li distance inLi2@Si20 is 2.391 Å. This is markedly shorter than the Li-Lidistance (2.787 Å) in the uncapped Li2@Si18 cluster. The Siatoms forming the caps repel the Li atoms inward. Thus, the Liatoms come closer to each other in the capped structure. Theseeffects were also observed by Andriotis et al.5 in V2@Si18 andV2@Si20 clusters. The Li-Si distances vary from 3.204 to 2.708Å in Li 2@Si20. The Si-Si distance between the middle Si6 andthe edge Si6 units in Li2@Si20 range from 2.383 to 2.607 Å.The Si-Si distances in the central Si6 unit are 2.555 Å, and theSi-Si distances in the end Si6 units and those between theseSi6 units and the capping atoms vary from 2.487 to 2.706 Å.The Si-Si distances in the central Si6 unit are 2.555 Å; theSi-Si distances in the end Si6 units and those between theseSi6 units and the capping atoms vary from 2.487 to 2.706 Å.
The calculated charges on the lithium atoms are+0.6 in theLi2@Si20 cluster. As for all the other Si18 and Si20 clusters, thebinding energies for both the empty Si20 and the Li2@Si20
clusters are around-3.4 eV at the MP2/6-311(d) level. TheLi2@Si20 cluster has a large (negative) binding energy, and boththe empty Si20 cage and the Li2@Si20 cluster HOMO-LUMOgaps are larger than 1 eV. Examination of the structures inFigure 2a and Figure 5c shows that the Li atoms fit into theextended cage, suggesting that a string of Li atoms might beencapsulated by extended Si nanotubes.
The implication of these findings is intriguing. It is nowwidely accepted that cage and/or nanotube configurations of Siare, in general, unstable.37 However, recent investigations showthat a transition metal suitably positioned inside a siliconnanotube can stabilize these structures.37 Our calculationsdemonstrate, for the first time, that properly positioned Li atomsinside a silicon nanotube can stabilize slightly distorted tubestructures. Recently, Si nanowires were prepared by a laserablation method.39,40However, their surfaces were coated withoxygen. The silicon atoms in Li2@Si18 are highly coordinated
Figure 3. Optimized structures of clusters of Si12 with charged and neutral atomic species. The initial geometries of all clusters were endohedralstructures ofD2d symmetry.
Structures of Si12, Si18, and Si20 Clusters J. Phys. Chem. C, Vol. 111, No. 37, 200713869
with the encapsulated lithium atoms. Hence, endohedral Liatoms within the nanotubes may make silicon nanotubes less
reactive toward oxygen. The stabilities of Li encapsulatednanotubes might be promising for advanced applications.
Figure 4. Optimized structures of clusters of Si12 with charged and neutral atomic species. The initial geometries of all clusters were endohedralstructures ofIh symmetry.
Figure 5. Optimized structures of (a) Si18, (b) Si20, (c) Li2@Si18, (d) Li2@Si20, and (e) Na2Si18.
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IV. Conclusions
The structures and electronic properties of X@Si12 (X )Li0,1,-1, Na0,1,-1, and He), Li2@Si18, Li2@Si20, and Na2Si18
clusters have been predicted at the B3LYP/6-311+G(d) and theMP2/6-311G(d) levels of theory. The results are summarizedas follows:
Encapsulation of atoms and ions by the Si12 cage dependson the size of the encapsulated atoms or ions. Encapsulation ofLi0,1,-1, Na0,1,-1, and He by Si cages leads to endohedral clusters.The larger K+, Ne, F-, and Cl- destroy the cage and favorformation of the corresponding exohedral clusters.
All observed clusters are stable and have large HOMO-LUMO gaps (>1 eV). The anionic alkali metal endohedralclusters are more stable than the neutral and cationic alkali metalendohedral clusters. The stability order is anionic clusters>neutral clusters> cationic clusters.
Silicon nanotubes may be stabilized by encapsulated Li in away that is analogous to stabilization by endohedral Mn, V,and Ni atomic chains inside Si nanotubes.35 In particular, thepresent investigations suggest that the Si12Li cluster unit mightbe used as a building block to form nanotubes of the typeSi6nLin-1. Further studies on these novel systems are currentlyin progress.
Acknowledgment. This work was supported by the AirForce Office of Scientific Research Grant F49620-02-1-026-0,by the National Science Foundation Grants EPS 0132618, HRD-9805465, and DMR-0304036, by the National Institute of Healththrough Grant S06-GM008047, by the Department of Defensethrough the U.S. Army/Engineer Research and DevelopmentCenter (Vicksburg, MS) Contract W912HZ-06-C-0057. Mostof the calculations were carried out on computers at theMississippi Center for Supercomputer Research.
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