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Geometric, Electronic, and Optical Properties of Monomer and Assembly of Endohedral Aluminum Superatomic Clusters Takeshi Iwasa†,‡ and Atsushi Nakajima*,†,‡ †

Nakajima Designer Nanocluster Assembly Project, JST-ERATO, 3-2-1 Sakado, Takatsu-ku, Kawasaki 213-0012, Japan Department of Chemistry, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

‡

S Supporting Information *

ABSTRACT: Density functional computations are used to evaluate the geometric, electronic, and optical properties of endohedral aluminum clusters X@Al12 (X = B, Al, Si, P) and their assemblies. All X@Al12+/0/− clusters are perfect or slightly distorted icosahedral structures, with the exception of Al13+, which is highly distorted. The projected density of states (PDOS) onto the spherical harmonics of monomers clearly reveals superatom behavior and electron shell closings of F orbitals in a 40-electron species. The electronic absorption spectrum of SiAl12 is analyzed in terms of the superatom orbitals. The optimized structures of X@Al12−Y@Al12 (X−Y = Si−Si, B−P, Al−P) dimers are constructed by facing the sides of the monomers in a staggered fashion. The PDOS of the dimers mostly exhibit five hybridizations: S, P, SD, PF, and SDG. The exceptions are HOMO, which possesses a DFG hybridized character and lies between the PF and SDG regions, and LUMO, which possesses a DG hybridized character. By analyzing the simulated absorption spectra of the B@Al12−P@Al12 and Al13−P@Al12 heterodimers, charge transfers from B/Al@Al12 to P@Al12 are found in the visible region, weakly accompanying the opposite charge transfer. The heterodimers have substantial charge carriers, estimated as the difference in electron counts from the closed-shell Si@Al12, with slight charge depletions (∼0.2). The charge distributions in B@Al12 and P@Al12 are essentially unaltered by the insertion of Si@Al12 into the heterodimer, resulting in that the heterotrimer possesses a larger dipole moment than the heterodimer.

1. INTRODUCTION Multielement atomic clusters have attracted much interest from both fundamental and engineering perspectives owing to their tunable physicochemical properties. By changing either their cluster size or composition, researchers can alter cluster geometry, electronic structures, optical properties, magnetism, and reactivity.1−3 The discovery of tunable multielement atomic clusters has broadened the scope of cluster science. In nanomaterial engineering, tunable magic clusters are recognized as potential building blocks for novel optoelectronic devices that can be precisely tuned at the nanometer scale.4−6 In recent years, atomic clusters with magic numbered behaviors have been increasingly investigated in a superatom context.6−9 In general, superatoms are typified by complete geometric and electronic shell closings. The shell structures of the latter are similar to those of atomic orbitals, such as 1s, 1p, 1d, 2s, and so on.10,11 In particular, Al13 is known as a superhalogen because its chemical properties such as electron affinity and reactivity mimic those of a true halogen and Al13− satisfies the 40-electron shell closing.7,12−14 Endohedral binary clusters are particularly intriguing because their properties can be tailored by varying the dopant atom while retaining a fixed geometry. A few examples of experimentally obtained endohedral binary clusters are tungsten-doped gold clusters,15,16 metal-doped silicon or group 14 clusters,17−25 and doped aluminum or group 15 clusters.26−28 Among the latter two, Ti-doped silicon clusters Ti@Si1619,29−31 and Si-doped aluminum clusters Si@Al1227,32−35 are known to possess a © 2013 American Chemical Society

closed electronic shell similar to that of the noble gas atoms as well as highly symmetric geometries. Electronic structures similar to a halogen or an alkali metal are realized by substituting the cluster dopant by its neighboring elements in the periodic table, thereby introducing a deficit or excess of electrons.19,26,27 In a semiconductor physics context, these electron deficits and excesses can be interpreted as hole and electron carriers, respectively. Assembling functional clusters is fundamental to bridging the gap between cluster science and material science. In our previous study, we used density functional computations to demonstrate that heteroassemblies of these doped silicon clusters possibly possess strong dipole moment, cluster-based p−n or p−i−n junctions, and photoinduced charge transfer.36 In this study, we investigate endohedral aluminum clusters and their mono- and heteroassembly using density functional computations, focusing on their binary superatom nature. In addition, we explore their potential applicability as novel aluminum-based nanomaterials. The heteroassemblies of doped aluminum clusters will be characterized by enhanced dipole moment and photoinduced charge transfer in appropriate combinations of assembled X@Al12 (where X = B, Al, Si, and P). Received: June 19, 2013 Revised: September 18, 2013 Published: October 3, 2013 21551

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2. COMPUTATIONAL DETAILS All density functional computations were performed at the Resolution of Identity Perdew−Burke−Ernzerhof (RI-PBE) level37,38 using the def-SV(P) basis sets39 implemented in TURBOMOLE 6.4.40,41 This computational method gives the adiabatic electron affinity/vertical detachment energy of Si@ Al12 and B@Al12 as 1.90/2.20 eV and 3.34/3.51 eV, which are in well agreement with the experimental results of 1.69/2.16 eV and not-available/3.8 eV. Also the computed ionization energy of P@Al12 is 5.19 eV and the corresponding experimental result is 5.37 eV.27 The several possible geometries of Si@Al12 and [Si@Al12]2 were locally optimized, and their lowest energy isomers were used for further random geometry samplings by 50-step basin-hopping runs performed using Atomic Simulation Environment (ASE).42 The electronic absorption spectra were simulated in the framework of time-dependent density functional theory,43−46 in which the line spectra are convoluted by a Lorentz function of width 0.01 eV. The absorption spectra of dimers were characterized by charge transfer between the composite monomers, as described in our previous study.36 Note that range-separated functionals are ideally suitable for heterodimer analysis because these structures undergo charge transfer excitations to some extent. However, in our previous study on the MSi16 heterodimer, the absorption spectra did not appreciably differ for the dimer with and without the long-range corrections compared to that of a trimer because of its smaller size. In addition, the valence states of X@Al12 heterodimers are less localized to the monomers than in the MSi16 heterodimer, and the PBE functional can be applied without imposing longrange corrections. To analyze the electronic structures in a superatom context, the Kohn−Sham orbitals ψi were projected onto a real-basis of spherical harmonics Zlm, generated using SymPy.47 The projection process is well documented and is detailed in Walter et al.9 In the present study, the polar grids (r, θ, φ) were first generated and ψi(r,θ,φ) and Zlm(θ,φ) were calculated. To obtain the projection ⟨ψi|Zlm⟩, the product was integrated over θ and φ for each fixed r, and |⟨ψi|Zlm⟩|2 was then integrated over r. The projection for the dimers adopts two polar grids, each centered on the dopant atom of the monomers in the half space to prevent grid overlap. When generating the projected density of states, a suitable polar grid radius was found to be 20 au with a radial grid spacing of 0.5 au and an angular interval of 10°. Each peak was convoluted by a Gauss function of width 0.001 au.

Figure 1. Optimized structures of X@Al12 (X = B, Al, Si, and P) in the cationic (first row), neutral (second), and anionic (third) states. The symmetry and HOMO−LUMO gaps (eV) are also shown.

symmetries eventually yields an icosahedral structure with C5v symmetry, in which the Si atom locates at the symmetrical vertex. The energy of this configuration is 0.57 eV higher than that of the endohedral icosahedron. Furthermore, none of the isomers generated by a basin-hopping run with 30 steps of stochastic distortions possessed lower energy than the endohedral icosahedron. For X = B, Al, and P, a similar behavior is observed in their geometry optimizations. All 40-electron closed shell species, such as B@Al12−, Al13−, and P@Al12+, were perfect icosahedra. The icosahedra of open shell species were slightly distorted by the Jahn−Teller distortions,35 with the exception of Al13+, which converged to a highly distorted structure (see Figure 1). The bond lengths are tabulated in Table 1. The Al−Al distances in closed shell species doped with the third-period elements were comparable; i.e., the Al−Al distances in Al13−, Si@Al12, and P@Al12+ were 2.81, 2.79, and 2.79 Å, respectively. In B@ Al12−, the Al−Al distance was 2.69 Å, about 0.1 Å shorter than in the other species, because of the smaller atomic size of boron. This result is consistent with reports that B@Al12− is more stable than Al13−.32 Given the atomic radius of aluminum, r(Al) = 1.43 Å,1 the diameters of these closed shell species are estimated as 2d(X−Al) + r(Al) = 0.80, 0.82, 0.82, and 0.82 au for B@Al12−, Al13−, Si@Al12, and P@Al12+, respectively. These almost identical cluster sizes are especially advantageous for thin-film heterojunctions with a simple interfacial geometry because they can adopt the same Bravais lattice (for instance, FCC) as well as a similar lattice constant. Table 2 presents the obtained HOMO−LUMO gaps, adiabatic electron affinity (AEA), vertical detachment energy (VDE), ionization energy (IE), and electronegativity, together with available experimental values,26,27 for the neutral species. AEA is calculated as the energy difference between the optimized neutral and anion states, whereas VDE is the energy difference between the neutral and anionic states of the optimized anion structure. IE is the energy difference between the optimized neutral and cation states. Electronegativity is calculated as one-half of the sum of IE and AEA, as proposed by Mulliken.48 The present computational results reasonably agree with the reported experimental results. These electronic properties such as AEA, VDE, and IE as well as the bond lengths (see Table 1) strongly agree with recent computational studies,34,35 in which similar comparisons with previous studies are presented. Although the ENs of B and Al are markedly

3. RESULTS AND DISCUSSION The geometry and electronic properties of the monomers are discussed first, placing special emphasis on their superatomic nature. On the basis of this information, the electronic and optical properties of the optimized X@Al12−Y@Al12 dimers are studied, where (X, Y) = (Si, Si), (B, P), and (Al, P). The results are interpreted in terms of superatom properties and potential applications. 3.1. X@Al12 Monomers. The optimized structures of X@ Al12 (X = B, Al, Si, and P) in their cationic, neutral, and anionic states are summarized in Figure 1. As shown in the figure, the lowest energy isomer of neutral Si@Al12 is an endohedral perfect icosahedron (Ih). Other structures such as the decahedron (D5h) and octahedron (Oh) are geometrically optimized to the icosahedron (Ih). Exohedral doping of Si atoms into either possible position of the above three 21552

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Table 1. Bond Lengths (in Å) of X−Al and Al−Al for X@Al12

a

X

cation

neutral

anion

B Al Si P

2.40−2.64/2.60−2.80 2.62−3.00a 2.66−2.68/2.74−2.95 2.65/2.79

2.38−2.57/2.63−2.72 2.66−2.71/2.76−2.97 2.65/2.79 2.62−2.88/2.74−2.87

2.56/2.69 2.67/2.81 2.63−2.86/2.75−2.87 2.59−2.85/2.71−2.96

For Al13+, no classification is applied between central−surface atoms and surface−surface atoms due to its low-symmetric structure.

All angular momentum are well separated, except for the DG and PH hybridizations, in which (D and G) and (P and H) share the irreducible representations of H g and T 1u , respectively. As observed from the PDOS, the orbital energies of 1S, 2S, and 2P largely depend on the dopant species. This dependence can be ascribed to the large contribution of the dopant orbitals (see Figure S1). On the other hand, the orbital energies of the D, F, and G symmetries are almost constant because these orbitals mainly arise from the surrounding Al atoms; thus, the frontier orbital levels do not appreciably differ among these species. This behavior may also be understood in terms of the well-known jellium model, assuming that a modified jellium potential perturbed by a hollow or bump (depending on the dopant species) appears at the position of the dopant atom. These findings provide insights into the superatomic nature of X@Al12 monomers, enabling further investigation of the electronic and optical properties of dimers. 3.2. X@Al12−Y@Al12 Dimer. Initial and optimized structures for the dimers are shown in Figures 3a−e. In

Table 2. HOMO−LUMO Gap (HLG), Adiabatic Electron Affinity (AEA), Vertical Detachment Energy (VDE), Ionization Energy (IE), and Electronegativity (EN) in eV (Available Experimental Results Given in Parentheses) SiAl12 BAl12 Al13 PAl12 a

HLG

AEA

VDE

IE

EN

2.05 0.43 0.41 0.55

1.90 (1.69)a 3.34 3.47 1.78

2.20 (2.16)a 3.51 (3.8)a 3.71 (3.62)b 2.15

6.87 6.79 6.44 5.19 (5.37)a

4.38 5.07 4.96 3.49

Reference 27. bReference 12.

different, those of B@Al12 and Al13 are very similar, probably because the frontier orbitals responsible for electron affinity and ionization energy are exclusively contributed by the 12 surrounding aluminum atoms (see Figure S1). Figures 2a−d show the projected density of states (PDOS) for neutral X@Al12, X = B, Al, Si, and P (ordered from top to

Figure 3. (a−e) Initial structures of the Si@Al12 dimer. Following geometric optimization, all dimers relax into configuration (a). (f−g) Lowest-energy optimized structures of B@Al12−P@Al12 heterodimers. Relative total energies and HOMO−LUMO gaps in (eV) are provided.

Figure 2. Projected density of states in X@Al12, where X = (a) B, (b) Al, (c) Si, and (d) P. The black arrows indicate the HOMO peaks.

bottom). Overall, the order of the superatomic orbitals agrees with the result of the jellium model, i.e., 1S, 1P, 1D, 2S, 1F, and 2P, followed by 2D, 1G, 3S, 3P, and 3F orbitals.11 Here, the 40electron shell closing is achieved by occupying up to the 2P orbital. These superatom orbitals consist of the hybridized and separated s and p orbitals of the surface Al and X, respectively (see Figure S1). In the Ih symmetry, S, P, D, F, G, and H are represented by the irreducible representations of Ag, T1u, Hg, (T2u + Gu), (Hg + Gg), and (T1u + T2u + Hu), respectively.49,50

short, three types of contacts (point, side, and face) are considered with eclipsed and staggered configurations. All structural forms of the Si@Al12 dimer eventually relax to the structure shown in Figure 3a after several local optimization cycles followed by a relaxation along the vibrational mode with the largest imaginary frequency identified from harmonic frequency analysis. Furthermore, a 50-step basin-hopping run, 21553

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starting from the most stable structure of the Si@Al12 dimer, yielded no lower-energy isomers. This stable structure has also been reported for the C@Al12 cluster dimer.51 In the lowestenergy structure, intercluster bonding was realized by facing both sides of the monomers, such that the four Al atoms were tetrahedrally arranged. The geometric parameters are summarized in Table 3. The Ih symmetry of Si@Al12 is almost preserved

heterodimer occurs from the halogen-like Sc@Si16 to the alkalimetal-like [email protected] This difference is partly attributable to the altered nature of the valence orbitals in the composite monomers. As depicted in Figures S1 and S2 of the Supporting Information, the frontier orbitals of X@Al12 monomers are contributed mainly by the surrounding caged Al12, whereas those of M@Si16 are contributed by the dopant M. Hence, the molecular orbitals of X@Al12 dimers behave similarly to those of a diatomic molecule, and their EN provides a measure of charge transfer. On the other hand, the orbitals of M@Si16 dimers tend to localize within the cluster because of the large weight of the dopant 3d orbitals. To explore the potential of the heterodimers as cluster-based p−n junctions, the amounts of hole and electron were estimated from the natural charges. In this interpretation, the B@Al12−0.17−[email protected] dimer may be expressed as [Si@ Al12]0.83−[Si@Al12]−0.83, where [Si@Al12] denotes the closed electronic structure of Si@Al12. This representation reveals weak charge depletion, indicating that sufficient hole and electron carriers are retained in the B@Al12 and P@Al12 clusters, respectively. The charge transfers in Al13−P@Al12 and B@Al12−P@Al12 are almost identical (marginally higher in the latter). The dipole moment of the Al13−P@Al12 dimer is 1.69 times larger than that of B@Al12−P@Al12, probably because the natural charge of Al13−P@Al12 is 1.53 times higher than that of B@Al12−P@Al12, and the cluster size of Al13 slightly exceeds that of B@Al12 (although the interdopant distance of Al−P is 0.1 Å shorter than that of B−P). Figures 4a−c present the PDOS in the dimers of Si@Al12, B@Al12−P@Al12, and Al13−P@Al12. As shown in Figure 4a, the PDOS are broadly separable into five regions in order of increasing energy: S, P, SD, PF, and SDG hybridized bands. The exceptions are HOMO, which exhibits a DFG hybridized character and exists between the PF and SDG regions, and LUMO, which displays a DG hybridized character. Similar to

Table 3. Bond Lengths (in Å) of X@Al12−Y@Al12 Dimers X, Y

X−Al

Si, Si B, P Al, P

2.62−2.78 2.51−2.71 2.67−2.82

Y−Al

Al−Al

2.57−2.66 2.61−2.70

2.70−3.21 2.61−3.11 2.65−3.41

with only minor distortions. Compared to the Ih symmetry of the monomer, the cluster is slightly elongated along the dimerization axis, resulting in shorter and longer Si−Al distances laterally and longitudinally, respectively. In other words, Si−Al bond distances are increased for the Al atoms located at the interface and ends of the dimer. The intercluster Al−Al distances are around 2.85 Å. The longest Al−Al distance (3.21 Å) is found at the interface, where electron is transferred from the intrabonding to intercluster bonding orbitals. The lowest-energy structure of the B@Al12−P@Al12 heterodimer is that of the Si−Si dimer (see Figure 3f); however, another lowenergy isomer of this species was identified, as shown in Figure 3g. The relative total energies and HOMO−LUMO gaps of the two isomers are shown in the figure. Because the total energies differ by only 0.27 eV, the two isomers can coexist. However, the present study focuses on the lowest-energy isomer. Table 4 summarizes the electronic properties of the dimers. The HOMO−LUMO gaps differ marginally among the dimers Table 4. HOMO−LUMO Gap (HLG) and Dimerization Energy (DE) in eV, Dipole Moment μ in debye, and Natural Charges for the Lowest-Energy Isomers of the X@Al12−Y@ Al12 Dimersa X, Y

HLG

DE

μ

X@Al12

Y@Al12

Si, Si B, P Al, P

0.63 0.60 0.63

2.13 3.19 3.70

0.05 2.38 4.03

0.00 −0.17 −0.26

0.00 0.17 0.26

a DE is derived from the total energy differences between a dimer and their corresponding monomers in their neutral states. Carriers are estimated as the difference from the 40-electron closed electronic shell structure.

because of the similar electronic structures of the monomers, as mentioned above. From the total energy difference, the dimerization energy of [Si@Al12]2 was determined as 2.13 eV (206 kJ/mol), comparable with that of Ti@Si16 dimers52 and approximately equal to the Si−Si bond strength.1 This result suggests that the dimer, like Si-based devices, is thermally stable. The dimerization energy of the heterodimers exceeds that of [Si@Al12]2 by more than 1 eV because the open shell electronic structures of the constituent monomers exert a destabilizing influence. Natural charges summarized for each monomer reveal that small charge transfer occurs between the monomers. The polarization direction is consistent with the electronegativity of the monomers (see Table 2), as observed in typical heteronuclear diatomic molecules such as NaCl. In contrast, unlike the NaCl motif, charge transfer in the M@Si16

Figure 4. Projected density of states in (a) Si@Al12 dimer, (b) B@ Al12−P@Al12, and (c) Al13−P@Al12 heterodimers. For (b) and (c), the partial density of states, calculated for the half-spaces containing B@ Al12 or Al13 and P@Al12, are shown above and below the structures, respectively. 21554

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our previous findings for the M@Si16 dimer, the Si@Al12 dimer shows atom-like bonding and antibonding orbitals, particularly distinct for the inner S, P, and D orbitals, which have fewer nodes than the valence regions. The spatial distributions (data not shown) reveal antibonding and bonding characteristics in HOMO and LUMO, respectively. It is worth mentioning that unusual hybridizations such as PF or DG exist that are scarcely noticeable in atoms because F and G orbitals are generally well localized states. Hence, superatoms are expected to display novel types of bonding with previously unsuspected physical and chemical properties. The PDOS of the heterodimers are similar to those of the Si@Al12 dimer, although no overlaps appear between the constituent monomers in lower-energy states. Because the PDOS differs marginally between the heterodimers, the heterodimers should exhibit similar physical and chemical properties. The HOMOs are rather biased toward B@Al12/Al13, whereas the LUMOs are biased toward P@Al12, both of which possess less localized frontier orbitals compared with those of M@Si16 heterodimers.36 This finding is again attributable to the composition of the frontier orbitals, which largely arise from the surface Al atoms in X@Al12, whereas in M@Si16, they arise chiefly from M. For the B@Al12−P@Al12 dimer, FG hybridization in the HOMO arises largely from B@Al12, whereas the SDG hybridized nature of the LUMO is mainly contributed by P@Al12. This orbital localization, also found in the M@Si16 dimer, invokes the possibility of a photoinduced charge transfer. The absorption spectra of Si@Al12 and the homo- and heterodimers are shown in Figures 5a−d. The absorption peaks

between the composite monomers. The charge transfer rate is estimated from the Mulliken populations, as reported in our previous study.36 As evident in Figures 5c and 5d, efficient charge transfer from B@Al12/Al13 to P@Al12 occurs in the visible region and accompanies weak opposite directional charge transfer, particularly in the Al13−P@Al12 dimer. This result implies that B@Al12/Al13 and P@Al12 could be integrated into a heterojunction that serves as an active charge separation layer. 3.3. Heterotrimer and Tetramer. Finally, the effects of inserting “an insulating cluster” Si@Al12 between B@Al12 and P@Al12 were studied. The Si@Al12 insulator can potentially alter the charge depletion, as in the case for p−i−n junctions. The effect was evaluated on a linear heterotrimer and tetramer. Figures 6a,b show the locally optimized structures resulting

Figure 6. Locally optimized structures of linear (a) heterotrimer B@ Al12−Si@Al12−P@Al12 and (b) B@Al12−Si@Al12−Si@Al12−P@Al12. Natural and carrier charges are shown above and below the structures, respectively, where h and e denote hole and electron, respectively.

from an initial linear arrangement with the same intercluster interface as the lowest-energy dimers. In this figure, the natural charges and carriers are provided above and below the structures, respectively. The insertion of Si@Al12 into the trimer slightly increases the concentration of hole carriers in B@Al12 at the expense of the electron carriers in P@Al12. The insertion of two Si@Al12 monomers into the dimer only slightly decreases the hole carrier concentration in B@Al12 while increasing the electron density in P@Al12. This suggests that electrons are donated from Si@Al12 adjacent to P@Al12. Thus, in a doped aluminum cluster assembly, Si@Al12 displays no insulating properties, unlike its behavior in doped silicon clusters and semiconductors. This might also be attributable to the large contribution of surface Al atoms to the frontier orbitals as well as the metallic nature of Al. The dipole moment is enhanced to 3.89 and 5.29 D in the trimer and tetramer, respectively; this difference is due to the larger distance between B@Al12 and P@Al12. Thus, the insertion of Si@Al12 conclusively enhances dipole moment in both the linear heterocluster and in the heterojunction.

Figure 5. Absorption spectra of (a) Si@Al12, (b) Si@Al12 dimer, (c) B@Al12−P@Al12, and (d) Al13−P@Al12. For (c) and (d), the charge transfer rates from B@Al12/Al13 to P@Al12 and their opposing rates are shown in red and blue, respectively.

are assigned to transitions between the PF and SDG hybridized orbitals. In particular, in the Si@Al12 monomer (Figure 5a), the two lower-energy peaks in the 2.5−3.1 eV range are assigned to electronic transitions from P and F to DG orbitals, whereas the peak at 4 eV is a composite of P to S and D to G transitions. In the Si@Al12 dimer and heterodimers in (Figures 5b−d), the transitions are characterized as PF and DFG (HOMO) to SDG bands. In the heterodimers, we focus on charge transfers

4. CONCLUDING REMARKS We conducted detailed investigation of the geometric, electronic, and optical properties of X@Al12 clusters, where X = B, Al, Si, and P, and their heterodimers. We focused on their superatomic nature and potential applicability in cluster-based devices. The density of states projected onto the spherical harmonics clearly reveals electronic shell closures in 40-electron 21555

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clusters. The dimers exhibited unusual hybridizations not encountered in conventional molecular physics, such as SD, PF, and SDG orbitals. Natural charge analysis of the heterodimers clarifies the existence of slightly depleted charge carriers in each monomer, which are not necessarily suppressed by insertion of the insulator Si@Al12 although the dipole moment is substantially enhanced by the insertion. The charge depletions are consistent with the estimated electronegativity of the clusters, as reported in heteronuclear dimers. Furthermore, the photoinduced charge transfer from B@Al12/Al13 to P@Al12 was observed in the simulated absorption spectra. These results indicate that doped aluminum clusters may be used to construct cluster-based strong dipole layers or photoactive materials. Because the frontier orbitals of X@Al12 arise exclusively from the surface Al atoms, the molecular orbitals of the dimers are more delocalized than those of doped silicon clusters having localized frontier orbitals because of the large weight of the dopant 3d orbitals. This moderate orbital delocalization may yield bandgap tunability when the structures are assembled into one- or two-dimensional nanostructures. To further understand the novel physics and chemistry of superatom assemblies, extended analysis of their behaviors, such as their intercluster bonding, is required.

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ASSOCIATED CONTENT

S Supporting Information *

Partial density of states for X@Al12 (X = B, Al, Si, and P) and M@Si16 (M = Sc, Ti, and V). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Fax +81-45-566-1697 (A.N.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is partly supported by MEXT-Supported Program for the Strategic Research Foundation at Private Universities, 2009−2013.

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REFERENCES

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