13864
J. Phys. Chem. C 2007, 111, 13864-13871
Structures and Stabilities of Clusters of Si12, Si18, and Si20 Containing Endohedral Charged and 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 of Chemistry, Jahangirnagar UniVersity, SaVar, Dhaka 1342, Bangladesh, and Computational Center for Molecular Structure and Interactions, Department of Physics, Atmospheric Sciences, and Geosciences, Jackson State 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 theory were performed on three isomers of Si12 and on the endohedral clusters Si12 containing neutral or charged atomic species. The existence of endohedral clusters depends on the Si12 cage shape and the nature of the embedding 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 that are minima on the potential energy surfaces are stable and have large HOMO-LUMO gaps (>1 eV). The stability 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 the endohedral 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 selfassembled or consolidated materials. The properties of nanoclusters can be manipulated by changing their size, shape, and composition. Since silicon is the most widely used material in the semiconductor and microelectronic industries, extensive recent theoretical and experimental studies have been carried out on both pure Si and metal-doped Si clusters to understand their structures and properties.1-5 The well-known stable fullerene-shaped carbon cages exhibit unusual stabilities due to sp2 hybridization of their carbon atoms and their extended surface conjugation. Even though Si is isovalent with C, Si sp2 hybridization is less favorable than that for C. Silicon double bonds are rare, and fullerene-like Si clusters are unstable.6 Recent experimental4 and theoretical research1-3,5-16 suggests that introducing guest atoms into the Si cages can stabilize these clusters. Extensive theoretical studies of metal-encapsulated silicon clusters led to the discovery of novel shapes including fullerene-like, cubic, Frank-Kasper polyhedral, icosahedral, and other cluster geometries.2,3,7-12,15,16 Hiura et al.4 reacted silane with different transition metals and obtained a Si12W cluster with a hexagonal prism structure and the W atom at the cage center. Theoretical studies predicted a similar structure for the endohedral clusters of Cr, Cu, and V with Si12.15-17 Further silicon cluster species with transition metal (TM) atom impurities were detected by Ohara et al.18 by using a double-rod laser technique to vaporize both components, TM (TM ) Ti, Hf, Mo, and W) and Si, and letting the atomic species react with †
Mississippi State University. Jahangirnagar University. § Jackson State University. | Present address: Department of Physics, Astronomy and Geology, East Tennessee State University, Johnson City, TN 37614. ‡
each other. The stabilities of endohedral metal clusters with silicon cages depend on the size and the shape of the silicon cage as well as the size and electronic structures of the metal atoms. Although small Si clusters tend to have close-packed structures, clusters with 14-25 atoms have prolate structures with Si9 and Si10 building blocks.13-19 Kumar and Kawazoe observed 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, and Mo with Si15 and Si16 cages were observed in significantly greater abundance than any other metal-doped silicon clusters in this series. The mass spectra of the CuSin (6 < n < 12) clusters demonstrated that the endohedral complex of Cu with Si10 is exceptionally stable. Scherer and co-workers experimentally produced several metal silicon cage clusters for the metals Cu, Ag, and Au.23-25 Combined experimental and theoretical studies of SinNa- (n < 7) found that the Na atom acts as an electron donor to the Sin framework.26 Na adsorption occurred on the Sin cluster’s surface and left the original Sin framework nearly unchanged in NaSin. The electronic properties of siliconbased semiconductor surfaces change dramatically by alkali metal adsorption. Endohedral silicon clusters with alkali metals, halides, or noble gases have drawn little attention despite the extensive studies of corresponding clusters encapsulating transition metals. The present study focused on clusters of alkali metals, noble gases, and halides with Si12 cages; however, larger silicon frameworks were also considered. The following questions regarding this class of clusters are essential: (1) Can alkali metals or their ions, halides, or noble gas atoms be successfully encapsulated into a Si12 cage? (2) Will the endohedral element
10.1021/jp0735839 CCC: $37.00 © 2007 American Chemical Society Published on Web 08/29/2007
Structures of Si12, Si18, and Si20 Clusters always be located at the center of the Si12 cluster? (3) How does the size of the encapsulated species affect the size of Si12 cluster? (4) How do the clusters’ electronic properties change after the atoms or ions are encapsulated? (5) Are alkali metaldoped silicon nanotubes stable? To address these questions we performed a systematic theoretical study of possible endohedral clusters of Si12 cages with charged and neutral alkali metals, noble gases, and halides. Throughout this paper we will use the notation X@Si12 for endoheral clusters and XSi12 to describe exohedral clusters. We also investigated the structure and stabilities of Li2@Si18, Li2@Si20, and Na2Si20 clusters which are relevant to the possible stabilization of Si nanotubes. II. Computational Details All structures were optimized at the (spin-unrestricted) B3LYP27,28/6-311+G(d) level. Three different start geometries of the Si12 cage, with D6h (hexagonal), Ih (icosahedral), and D2d symmetry, respectively, were used. All optimized structures constrained to these initial high symmetries had several imaginary frequencies. All of these structures were subsequently distorted and further relaxed until a structure with only real vibrational frequencies was found. For the systems studied herein an explicitly correlated method like MP2 would have been preferred, in particular since dispersion interactions are neglected in the B3LYP method. Complete geometry optimization at the MP2 level would be possible, but we decided this approach to be too expensive. As a compromise we carried out single-point MP2/6-311G(d) calculations at the B3LYP/6311+G(d) optimized geometries for all 37 clusters and atomic species. The programs Gaussian-0329 and PQS30 were used for the calculations. Theoretical studies of weak interactions are often plagued by basis set superposition errors (BSSE). These can be corrected for by counterpoise calculations.31 To evaluate the magnitude of the BSSE, we carried out counterpoise calculations for selected clusters. The BSSE are significant but they do not affect any of the predicted trends. Since counterpoise calculations are quite expensive we did not carry out counterpoise calculations for the remaining clusters. To evaluate the stabilities of the clusters, the embedding energies (EE) and binding energies (BE) were calculated using the following equations:
EE ) E(Xm@Sin) - E(Sin) - mE(X) BE ) -[E(Xm@Sin) - nE(Si) - mE(X)]/(n + m) where E(Xm@Sin), E(Sin), E(X), and E(Si) denote the calculated total 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 exohedral complexes. Normally, both the BE and the EE are negative numbers, and the larger negative number denotes greater stability. Electronic properties were analyzed using the NBO-4 program.32 III. Results and Discussion The calculated embedding energies (EE), binding energies (BE), HOMO-LUMO gaps of empty Si12 cages and clusters of Si12 with neutral and charged atomic species calculated at the B3LYP/6-311+G(d) level are shown in Table 1, and the results of the single-point MP2/6-311G(d) calculations at the B3LYP/6-311+G(d) geometries are shown in Table 2. Table 1
J. Phys. Chem. C, Vol. 111, No. 37, 2007 13865 also shows the charges on the embedded species obtained from natural population analysis (NPA). The optimized geometries of the empty Si12 cages as well as all distinct clusters found in this study are shown in Figures 1-4. With a couple of exceptions, none of the optimized structures had any symmetry; however, some structures, in particular molecular species starting from Ih symmetry, deviated only slightly from the original symmetry. For identification purposes, the point group of the initial structure in parentheses was retained. In the discussion below, relative energies calculated at the MP2-level are given throughout with the B3LYP results in parentheses. The Si12 clusters’ binding energies calculated at the MP2 level are roughly -0.3 eV/atom lower than those calculated with B3LYP, and the difference is slightly larger for the larger clusters. For the endohedral complexes, the embedding energies calculated at the MP2 level are, as expected, more negative than the corresponding ones calculated at the B3LYP level. Si12 Cages. The geometry of the empty Si12 cage was optimized using three different initial structures of D6h, D2d, and Ih symmetry, respectively. These three initial geometries yielded three distinct cage-like Si12 structures shown in parts a-c of Figure 1, respectively. A cage-like structure with C2h symmetry was obtained from the initial D6h Si12 structure. Upon optimization, the initial D2d structure underwent a significant structural change resulting in a nonsymmetrical cage, while the Ih (icosahedral) Si12 form distorted only slightly from its initial structure. 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 initial D2d isomer (Figure 1b), is more stable than the D6h 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 main objective of the present study was to investigate possible endohedral complexes of the Si12 cage with charged and neutral atomic species. In some cases the initial cage-like structure broke down, resulting in exohedral complexes. Whenever the optimization resulted in a structure without any imaginary frequencies, this structure was included in Figures 1-3 and in Tables 1 and 2. In other cases where the cage structure clearly was breaking down, (expensive) geometry optimizations were not pursued to the end, and these partial optimized structures are not included here. Several complexes with embedded alkali metals were investigated. Both neutral, positively, and negatively charged complexes 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 distinct endohedral complexes with Si12 cages were found. These were the 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 yielded structures of similar shape (Figure 2). The shapes of these complexes are best described as complexes for which the embedding species is sandwiched between two chairlike Si6rings similar to the chair form of cyclohexane. The Si-Li bond distances 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 and Si-Si bond distances span the ranges of 2.440-2.944 Å and 2.361-2.362 Å, respectively. Insertion of Na-, K+, Ne, F-, or Cl- inside Si12(D6h) is energetically unfavorable, and the optimized structures are the exohedral complexes shown in parts f, g, and i-k of Figure 2, respectively.
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TABLE 1: Total Energies (in Hartrees), Molecular Point Groups, Lowest Vibrational Frequencies (ω, cm-1), Embedding Energies (EE, eV), Binding Energies (BE, eV/atom), HOMO-LUMO Gaps (eV), and Natural Electronic Charge on the Embedding Species clustera,b
energy
sym.
ω
Si12 (D6h) Si12 (D2d) Si12 (Ih) Li+@Si12 (D6h) Li0@Si12 (D6h) Li-@Si12 (D6h) Na+@Si12 (D6h) Na0@Si12 (D6h) Na-Si12 (D6h) Li+@Si12 (D2d) Li0@Si12 (D2d) Li-@Si12 (D2d) Na+@Si12 (D2d) Na0@Si12 (D2d) Na-@Si12 (D2d) Li+@Si12 (Ih) Li0@Si12 (Ih) Li-@Si12 (Ih) Na+@Si12 (Ih) Na0@Si12 (Ih) Na-@Si12 (Ih) He@Si12 (D6h) He@Si12 (D2d) He@Si12 (Ih) NeSi12 (D6h) NeSi12 (D2d) K+Si12 (D6h) K+@Si12 (D2d) F-Si12 (D6h) F-Si12(D2d) Cl-Si12 (D6h) Cl-Si12 (D2d) Si18 (D6h) Si20 (D6h) Li2@Si18 (D6h) Li2@Si20 (D6h) Na2Si18 (D6h)
-3474.077226 -3474.107561 -3474.032818 -3481.407221 -3481.645523 -3481.770001 -3636.077274 -3636.441967 -3636.561922 -3481.375558 -3481.632728 -3481.767744 -3636.042128 -3636.275094 -3636.530649 -3481.340633 -3481.594503 -3481.726059 -3636.084089 -3636.424859 -3636.376284 -3476.913009 -3476.878471 -3476.854141 -3603.037796 -3481.767744 -4073.846885 -4073.765270 -3574.129056 -3574.132013 -3934.491378 -3934.458643 -5211.202970 -5790.136762 -5226.253536 -5805.294741 -5535.803481
C2h C1 C1 C1 C1 Cs C1 C1 C1 C1 C1 Cs C1 C1 C1 C1 C1 CI Cs C1 C1 C2 C1 C1 Cs Cs C2 C1 C1 C1 C1 C1 C1 C1 C2h Cs C2h
97.27 73.28 38.04 36.77 62.71 105.80 12.08 82.49 108.41 43.10 86.05 99.09 15.38 23.49 72.76 86.94 122.54 136.15 54.83 39.89 57.45 17.08 47.93 103.93 12.31 99.09 16.09 3.86 53.08 55.59 49.38 40.01 84.82 34.50 53.47 43.37 46.10
EE (eV)
-1.23 -2.09 -4.92 2.38 -2.12 -4.80 0.46 -0.92 -4.04 4.16 3.24 -3.12 -0.62 -1.91 -4.94 0.99 -2.86 -0.96 2.10 3.87 2.50 0.00 0.34 -0.23 2.81 -4.44 -3.69 -3.00 -1.28 -1.85 -4.77 -0.73
BE (eV/atom)
HOMO-LUMO (eV)
-3.05 -3.12 -2.95 -2.91 -2.98 -3.20 -2.64 -2.98 -3.19 -2.85 -2.95 -3.19 -2.56 -2.63 -3.12 -2.77 -2.87 -3.10 -2.65 -2.95 -2.80 -2.66 -2.58 -2.53 -2.82 -2.86 -2.83 -2.67 -3.16 -3.17 -3.05 -2.98 -3.19 -3.07 -2.96 -3.00 -2.90
1.94 1.72 1.91 2.15 2.43 2.64 2.20 2.61 2.49 1.79 1.79 1.73 1.64 1.55 1.81 2.60 2.62 2.01 2.19 1.72 2.33 0.38 1.93 1.66 1.47 1.96 2.14 2.45 1.93 1.92 2.43 1.88 1.36 1.72 1.44 1.86 1.20
charge on X
0.79 0.58 0.61 0.79 0.90 0.87 0.41 0.50 0.70 0.50 0.53 0.74 0.25 0.27 0.35 0.57 0.88 0.36 0.02 0.00 0.01 0.00 0.00 0.97 0.80 -0.71 -0.69 -0.41 -0.41
0.58 0.59 0.86
a Point groups in parentheses indicate the symmetry of the initial geometry. b Endohedral complexes are denoted X@Sin and exohedral complexes XSin.
Insertion of either Li+, Li0, Li-, Na+, Na0, or Na- into the D2d Si12 cage yields the endohedral complexes shown in parts a-f of Figure 3, respectively. Their shapes are quite similar to that of the empty Si12 cage shown in Figure 1b. In addition to these six endohedral complexes, a complex HeSi12 shown in Figure 3h was also found. The optimized K+ complex in this series has an interesting structure shown in Figure 3g. In this structure the potassium ion is bonded to the corner silicon atom in two nearly planar Si6-sheets. Starting with an endohedral complex of D2d symmetry, minima corresponding to exohedral complexes were found for Ne, F-, and Cl-. These structures are 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 distort only slightly from the initial Ih symmetry, and these optimized endohedral structures are shown in parts a-c of Figure 4, respectively. Insertion of Na, Na+, or Na- into the Si12 Ih isomer cage also gives similar endohedral clusters (Figure 4d,e). Insertion of Na+ into the Si12 Ih cage produces a cluster with Cs symmetry. The embedding energies show that the clusters containing endohedral Li-, prepared from all three initial Si12 (D6h, D2d, Ih) geometries, are energetically more favorable than those containing Li0 (Table 1). Furthermore, all three endohedral Li0 clusters are slightly more stable than their corresponding Li+
analogues. At the B3LYP level, the D2d form of Li+@Si12 has a higher energy than the sum of Li+ and Si12 while the embedding energy becomes negative at the MP2 level. All the Li0 and Li- complexes have negative embedding energies or lower energies than those of their corresponding separated species. The binding energies for all three forms of Li+@Si12 and Li0@Si12 (D6h and Ih) are smaller (less negative) than those of the respective empty cages, while the binding energies for all three Li- clusters are larger than those of the corresponding empty Si12 cages. All endohedral Na+@Si12 and Na0@Si12 clusters, except the Na0@Si12 (Ih) cluster, are energetically unfavorable with positive embedding energies. Furthermore, all three Na+@Si12 clusters have smaller binding energies than the corresponding empty cages (see Tables 1 and 2). All the Na- clusters appear to be energetically favorable with large negative embedding energies. The binding energies for these complexes are similar to those of the corresponding empty cages. He encapsulation into all three forms of the Si12 cage generates endohedral He@Si12 clusters with positive embedding energies. The He@Si12 cluster obtained from D6h isomer has C2 symmetry while insertion of He into the D2d and Ih Si12 isomers yielded endohedral complexes without symmetry. Both at the B3LYP and MP2 levels all He complexes were energetically unfavorable compared to the separated species.
Structures of Si12, Si18, and Si20 Clusters
J. Phys. Chem. C, Vol. 111, No. 37, 2007 13867
TABLE 2: MP2/6-311G(d,p) Energies (in Hartrees) at the B3LYP Optimized Level, Embedding Energies (EE, eV), and Binding Energies (BE, eV/atom) clustera,b
energy
Si12 (D6h) Si12 (D2d) Si12 (Ih) Li+@Si12 (D6h) Li0@Si12 (D6h) Li-@Si12 (D6h) Na+@Si12 (D6h) Na0@Si12 (D6h) Na-Si12 (D6h) Li+@Si12 (D2d) Li0@Si12 (D2d) Li-@Si12 (D2d) Na+@Si12 (D2d) Na0@Si12 (D2d) Na-@Si12 (D2d) Li+@Si12 (Ih) Li0@Si12 (Ih) Li-@Si12 (Ih) Na+@Si12 (Ih) Na0@Si12 (Ih) Na-@Si12 (Ih) He@Si12 (D6h) He@Si12 (D2d) He@Si12 (Ih) NeSi12 (D6h) NeSi12 (D2d) K+Si12 (D6h) K+@Si12 (D2d) F-Si12 (D6h) F-Si12 (D2d) Cl-Si12 (D6h) Cl-Si12 (D2d) Si18 (D6h) Si20 (D6h) Li2@Si18 (D6h) Li2@Si20 (D6h) Na2Si18 (D6h)
-3468.166358 -3468.177831 -3468.150052 -3475.466750 -3475.674703 -3475.823579 -3629.780964 -3629.950344 -3630.305147 -3475.436834 -3475.688701 -3475.785583 -3629.848672 -3629.950344 -3630.228672 -3475.466750 -3475.688708 -3475.818498 -3629.780965 -3630.063325 -3630.149212 -3470.933900 -3470.904159 -3470.933869 -3596.892001 -3596.934525 -4067.342754 -4067.167578 -3567.991852 -3567.983957 -3927.963278 -3927.952661 -5202.328249 -5780.376658 -5217.385019 -5795.518530 -5526.304878
EE (eV)
-1.76 -2.08 -5.97 1.35 1.69 -7.85 -0.63 -2.15 -4.63 0.18 2.00 -5.46 -2.20 -2.90 -6.28 0.91 -1.83 -4.05 2.51 3.32 2.07 0.16 0.68 -0.43 4.65 -11.5 -11.0 -2.63 -2.03 -5.24 -7.56 -7.75
BE (eV/atom) -3.31 -3.34 -3.27 -3.19 -3.22 -3.52 -2.95 -2.93 -3.66 -3.13 -3.45 -3.44 -3.09 -2.93 -3.49 -3.19 -3.25 -3.50 -2.95 -3.16 -3.33 -2.86 -2.80 -2.86 -3.04 -3.13 -3.08 -2.72 -3.94 -3.92 -3.26 -3.24 -3.43 -3.45 -3.35 -3.48 -3.47
a Point groups in parentheses indicate the symmetry of the initial geometry. The point group of the optimized cluster can be found in Table 1. b Endohedral complexes are denoted X@Sin and exohedral complexes XSin.
The calculated charges on the encapsulated species are shown in Table 1. Since Si is more electronegative than alkali metals, the atomic charges on the alkali atoms are expected to be more positive than the charge on the silicon atoms. The calculations confirmed this expectation. Remarkably, the calculated charge on an alkali metal is largely independent of the charge of the complex. 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 positive charge on Li by 0.2 (in Li0@Si12(D6h)), and adding an additional electron (Li-@Si12(D6h)) did not change the charge on Li. Furthermore, the calculated charge on the sodium atom in sodium clusters is actually larger in Na0@Si12 (D6h) than in Na+@Si12 (D6h) by a small amount. The charge on the alkali metal is consistently smaller in the D2d clusters than in D6h and Ih clusters for both lithium and sodium endohedral complexes. These calculated charges indicate that the Si12 cage acts like an electron sink as any variation of charge of the complex is carried almost entirely by the silicon cage. Essentially, no charge transfer occurs between an endohedral He atom and the Si12 cage. The calculated charges on the halides are smaller (less negative) than -1, and the charge of the ion and in this case the silicon is negatively charged.
Figure 1. Optimized structures of Si12 clusters. (a) Structure obtained from initial D6h form. (b) Structure obtained from initial D2d form. (c) Structure obtained from initial Ih form.
The energy difference between the HOMO and LUMO is generally considered an important parameter of the electronic stability of a small cluster.34 A larger energy gap indicates greater cluster stability. Even though density functional theory is not the best method for calculating HOMO-LUMO gaps, the HOMO-LUMO gaps are included in Table 1. Two important points emerge. First, all the calculated HOMOLUMO gaps are quite large indicating that these clusters are stable. Second, the HOMO-LUMO gaps do not change significantly upon formation of endohedral complexes. Li2@Si18, Li2@Si20, and Na2Si18 Clusters. The geometries of Si18, Si20, Li2@Si18, Li2@Si20, and Na2Si18 clusters are shown in Figure 5, and total energies, embedding energies (EE), and binding energies (BE) are given in Tables 1 and 2. The Si18 cluster may be considered a combination of two Si12 units with one Si6 hexagon in common. Two lithium atoms were placed inside the Si18 cluster, and the system was then optimized to give the fully relaxed geometry of the Li2@Si18 cluster shown in Figure 5c. This optimized Li2@Si18 structure has C2h symmetry and, as such, it resembles the Li@Si12 unit as shown in Figure 1a. In Li@Si18, the Li atoms are shifted toward the end 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. This elongated Li-Li distance in the optimized Li2@Si18 structure is 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 cluster is +0.6. The shape of each Si6 unit resembles the cyclohexane boat configuration. The Si-Si distances in the end Si6 units range 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 to 2.902 Å. The Li2@Si18 cluster has relatively large negative embedding and 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 parentheses. The binding energy of Li2@Si18 is slightly smaller than the binding energy of the parent Si18 cage (by 0.08 at the MP2/
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Figure 2. Optimized structures of clusters of Si12 with charged and neutral atomic species. The initial geometries of all clusters were endohedral structures of D6h symmetry.
6-311G(d,p) level). The HOMO-LUMO energy difference is 1.44 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 original D6h symmetry to D3h symmetry in the optimized structure. In contrast to the bonding predicted here for Li2@Si18, the Mo or W atoms were not predicted to bond to the middle Si6 ring. An exohedral Na-containing cluster, Na2Si18, is formed when two Na atoms are placed inside the Si18 (D6h) cage and then optimized. The optimized structure of Na2Si18 is fundamentally different from the Li2@Si18 cluster even though both clusters have C2h symmetry. The Na atoms have become end-capping atoms in the optimized structure (see Figure 5e). Each Na atom caps a chairlike Si6 unit at the opposite ends of the cluster. Na atoms are larger than lithium, making their encapsulation inside the Si18 tube energetically unfavorable. Second, the Na-Na interactions are probably repulsive, like those exerted by LiLi and K-K within a carbon nanotube.36 Yang et al.36 predicted that the Li atom prefers to occupy sites along the tube axis inside carbon nanotubes. Inserting K atoms into carbon nanotubes was unfavorable due to their large
radii. The repulsive force between two sodium atoms within Si18 may be strong enough to overcome any favorable embedding energy. Hence, the repulsive sodium-sodium interaction probably contributes to the observation of the end-capped Na2Si18 structure rather than an endohedral Na2@Si18 cluster. In the end-capped Na2Si18 cluster, each Na has a charge of +0.9, suggesting that 2Na+(Si18)2- is the best way to represent the structure. The Si-Na distances are 2.544 and 2.511 Å. The SiSi distances in the central Si6 unit are 2.544 and 2.438 Å. The distance between the terminal and central Si6 units are 2.940 and 2.990 Å, and the Si-Si distances in the end Si6 units are 2.544 and 2.511 Å. Both the embedding and binding energies of the Na2Si18 cluster are still negative, and the binding energy for 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 cluster generated by inserting two Li atoms into the Si20 cage. On the basis of the result for the Na2Si18 cluster for which the Na-Na repulsion prevented formation of an endohedral complex, the Na2Si20 cluster was not included in our investigation. The Si20
Structures of Si12, Si18, and Si20 Clusters
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Figure 3. Optimized structures of clusters of Si12 with charged and neutral atomic species. The initial geometries of all clusters were endohedral structures of D2d symmetry.
cage is generated from the Si18 cage by capping each of the terminal Si6 units with a Si atom. Two Li atoms were placed inside the Si20 framework, and after optimization the two lithium atoms remained inside the cage. The optimized structures of the empty Si20 cage and the Li2@Si20 cluster are shown in parts b and d of Figure 5, respectively. The Li-Li distance in Li2@Si20 is 2.391 Å. This is markedly shorter than the Li-Li distance (2.787 Å) in the uncapped Li2@Si18 cluster. The Si atoms forming the caps repel the Li atoms inward. Thus, the Li atoms come closer to each other in the capped structure. These effects were also observed by Andriotis et al.5 in V2@Si18 and V2@Si20 clusters. The Li-Si distances vary from 3.204 to 2.708 Å in Li2@Si20. The Si-Si distance between the middle Si6 and the 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 the Si-Si distances in the end Si6 units and those between these Si6 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; the Si-Si distances in the end Si6 units and those between these Si6 units and the capping atoms vary from 2.487 to 2.706 Å.
The calculated charges on the lithium atoms are +0.6 in the Li2@Si20 cluster. As for all the other Si18 and Si20 clusters, the binding energies for both the empty Si20 and the Li2@Si20 clusters are around -3.4 eV at the MP2/6-311(d) level. The Li2@Si20 cluster has a large (negative) binding energy, and both the empty Si20 cage and the Li2@Si20 cluster HOMO-LUMO gaps are larger than 1 eV. Examination of the structures in Figure 2a and Figure 5c shows that the Li atoms fit into the extended cage, suggesting that a string of Li atoms might be encapsulated by extended Si nanotubes. The implication of these findings is intriguing. It is now widely accepted that cage and/or nanotube configurations of Si are, in general, unstable.37 However, recent investigations show that a transition metal suitably positioned inside a silicon nanotube can stabilize these structures.37 Our calculations demonstrate, for the first time, that properly positioned Li atoms inside a silicon nanotube can stabilize slightly distorted tube structures. Recently, Si nanowires were prepared by a laser ablation method.39,40 However, their surfaces were coated with oxygen. The silicon atoms in Li2@Si18 are highly coordinated
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Figure 4. Optimized structures of clusters of Si12 with charged and neutral atomic species. The initial geometries of all clusters were endohedral structures of Ih symmetry.
Figure 5. Optimized structures of (a) Si18, (b) Si20, (c) Li2@Si18, (d) Li2@Si20, and (e) Na2Si18.
with the encapsulated lithium atoms. Hence, endohedral Li atoms within the nanotubes may make silicon nanotubes less
reactive toward oxygen. The stabilities of Li encapsulated nanotubes might be promising for advanced applications.
Structures of Si12, Si18, and Si20 Clusters 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 the MP2/6-311G(d) levels of theory. The results are summarized as follows: Encapsulation of atoms and ions by the Si12 cage depends on the size of the encapsulated atoms or ions. Encapsulation of Li0,1,-1, Na0,1,-1, and He by Si cages leads to endohedral clusters. The larger K+, Ne, F-, and Cl- destroy the cage and favor formation of the corresponding exohedral clusters. All observed clusters are stable and have large HOMOLUMO gaps (>1 eV). The anionic alkali metal endohedral clusters are more stable than the neutral and cationic alkali metal endohedral clusters. The stability order is anionic clusters > neutral clusters > cationic clusters. Silicon nanotubes may be stabilized by encapsulated Li in a way that is analogous to stabilization by endohedral Mn, V, and Ni atomic chains inside Si nanotubes.35 In particular, the present investigations suggest that the Si12Li cluster unit might be used as a building block to form nanotubes of the type Si6nLin-1. Further studies on these novel systems are currently in progress. Acknowledgment. This work was supported by the Air Force Office of Scientific Research Grant F49620-02-1-026-0, by the National Science Foundation Grants EPS 0132618, HRD9805465, and DMR-0304036, by the National Institute of Health through Grant S06-GM008047, by the Department of Defense through the U.S. Army/Engineer Research and Development Center (Vicksburg, MS) Contract W912HZ-06-C-0057. Most of the calculations were carried out on computers at the Mississippi Center for Supercomputer Research. References and Notes (1) Sun, Q.; Wang, Q.; Jena, P.; Rao, B. K.; Kawazoe, Y. Phys. ReV. Lett. 2003, 90, 135503. (2) Kumar, V.; Kawazoe, Y. Phys. ReV. B 2002, 65, 73404. (3) Kumar, V.; Kawazoe, Y. Phys. ReV. Lett. 2001, 87, 45503. (4) Hiura, H.; Miyazaki, T.; Kanayama, T. Phys. ReV. Lett. 2001, 86, 1733. (5) Andriotis, A. N.; Mpourmpakis, G.; Froudakis, G.; Menon, M. New J. Phys. 2002. 4, 78. (6) Menon, M.; Subbaswamy, K. R. Chem. Phys. Lett. 1994, 219, 219. (7) Kumar, V.; Majumder, C.; Kawazoe, Y. Chem. Phys. Lett. 2002, 363, 319. (8) Kumar, V.; Kawazoe, Y. Appl. Phys. Lett. 2002, 80. (9) Kumar, V.; Kawazoe, Y. ReV. Modern Quantum Chem. 2002, 2, 1421. (10) Kumar, V.; Kawazoe, Y. Phys. ReV. Lett. 2003, 90, 5550. (11) Kumar, V. Comput. Mater. Sci. 2004, 30, 260. (12) Kumar, V.; Singh, A. K.; Kawazoe, Y. Nano Lett. 2004, 4, 677.
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