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J. Phys. Chem. C 2008, 112, 16324–16330
Structural and Electronic Characteristics of Diamondoid Analogues of Group 14 Elements Antti J. Karttunen,* Mikko Linnolahti, and Tapani A. Pakkanen UniVersity of Joensuu, Department of Chemistry, P.O. Box 111, FI-80101 Joensuu, Finland ReceiVed: May 28, 2008; ReVised Manuscript ReceiVed: August 4, 2008
We have investigated the structures, stabilities, and electronic properties of diamondoids and analogous compounds composed of heavier group 14 elements, silicon, germanium, and tin. Systematic quantum chemical studies on octahedral and icosahedral structures up to C1820H420, Si1100H300, Ge600H200, and Sn600H200 were performed to elucidate periodic trends among the group 14 nanostructures. The octahedral diamondoid analogues, which are superimposable with cubic bulk lattice, were found to be favored over the icosahedral structures for each element. However, due to the increasing metallic character of the heavier group 14 elements, the energy difference between the octahedral and icosahedral structures decreases when moving down from carbon to tin. The electronic characteristics of the icosahedral diamondoid analogues suggest them to possess electronic properties different from materials with a cubic bulk lattice. The obtained structural characteristics and periodic trends are expected to be helpful in the characterization of experimentally known group 14 nanocrystals. Introduction Diamondoids, which are finite hydrogen-terminated carbon clusters cut from the cubic diamond lattice, are representative examples of the rich structural chemistry of hydrocarbons.1 Due to their well-defined structures, functionalized diamondoids possess several promising applications.1 Silicon, germanium, and the R-allotrope of tin also adopt bulk structures similar to the cubic diamond lattice. However, less is known about the possible diamondoid analogues formed by the heavier group 14 elements. The sila-adamantane framework analogous to the smallest diamondoid framework, adamantane,2 has been obtained through a rational synthesis,3,4 illustrating the possibilities of the diamondoid analogue chemistry of heavier group 14 elements. The polysilanyl anion chemistry utilized in the synthesis of sila-adamantane offers a promising route to even more complex polysilane cages.5 In the case of germanium, a Ge10Si-framework structurally related to elemental germanium has been synthesized.6 Other examples of silicon and germanium species structurally related to the cubic elemental state are the layered polysilyne7 and layered polygermyne,8 monolayer sheets of which correspond to fully hydrogenated (111) sheets cut from the cubic bulk. Unlike analogous carbon compounds, polyatomic silicon, germanium, and tin species often possess appealing optical properties such as visible photoluminescence due to the delocalization of the σ electrons.9,10 Therefore, most theoretical studies on diamondoid-related group 14 structures have focused on their optical properties,11 placing less emphasis on their structural characteristics. We have recently investigated the structural principles of octahedral and icosahedral carbon diamondoids,12 two distinctly different structural families of carbon nanostructures. Here, we generalize the structural principles derived for carbon by studying octahedral and icosahedral diamondoid analogues composed of heavier congeners of group 14, silicon, germanium, and tin. The octahedral diamondoid analogues are derived from * To whom correspondence should be addressed. E-mail: antti.karttunen@ joensuu.fi.
the cubic bulk structures of silicon, germanium, and R-tin, while the icosahedral group 14 diamondoid analogues are structurally related to the previously studied icosahedral polysilanes, polygermanes, and polystannanes.13 The structures, stabilities, and electronic properties of the diamondoid analogues are investigated with quantum chemical methods. Computational Details We investigated the structures, stabilities, and electronic properties of silicon, germanium, and tin diamondoid analogues using hybrid density functional B3LYP method.14 The studied structures were fully optimized within their respective point group symmetries by using TURBOMOLE versions 5.9 and 5.9.1.15,16 Karlsruhe split-valence basis set with polarization functions (def2-SVP) was applied for all atoms.17 A 28-electron relativistic effective core potential (ECP) was used to describe the core electrons of tin.18 Structures up to M100H60 (M ) Si, Ge, Sn) were verified as true minima by vibrational frequency calculations.19 Harmonic frequency scaling factor of 0.9614 was adopted for B3LYP frequencies.20 For reference purposes, periodic calculations were performed on several extended bulk structures. The reference structures were (1) (M)n bulk with cubic diamond structure, (2) a perhydrogenated (111) (MH)n sheet cut from the cubic diamond structure, and (3) an infinite, linear (MH2)n chain in trans-conformation. In the case of silicon and germanium, the (MH)n sheet structures correspond to monolayer sheets of the experimentally known layered polysilyne7 and polygermyne,8 respectively. The periodic reference structures were fully optimized with Gaussian03.21 Electronic properties of the cubic bulk silicon, germanium, and tin were studied by using the CRYSTAL06 software package.22 Natural population analyses23 (NPA) were performed at the B3LYP level of theory. Results and Discussion Octahedral Diamondoid Analogues. The fundamental building block in the chemistry of octahedral carbon diamondoids is the Td-symmetric octahedral adamantane, C10H16.1,2 Diamon-
10.1021/jp804695s CCC: $40.75 2008 American Chemical Society Published on Web 09/25/2008
Group 14 Diamondoid Analogues
J. Phys. Chem. C, Vol. 112, No. 42, 2008 16325
Figure 1. The studied Td-symmetric octahedral group 14 diamondoid analogues.
doids larger than adamantane can be considered fused adamantanes, with the number of structural isomers becoming very large for higher diamondoids.24 However, by choosing a well-defined structural series, the stability trends of the bulk-like diamondoid analogues can be studied systematically. Here, we focus on Tdsymmetric octahedral diamondoid analogues which can also be considered as finite hydrogenated clusters cut from cubic bulk lattices of silicon, germanium, and R-tin (Figure 1). The mth member of the studied octahedral structural family can be derived from formula MAHB, where A ) m(4m2 - 1)/3 and B ) 4m2. The first member of the series is the MH4 molecule, well-known for C, Si, Ge, and Sn. The next structure in size is the adamantane framework, M10H16. In the case of carbon, the octahedral C35H36 cage has also been experimentally isolated.25 The octahedral and icosahedral group 14 diamondoid analogues possess variable M/H ratios, due to which the determination of their relative energies is not straightforward. For the octahedral structures, there are three types of M atoms in the system: (1) core atoms analogous to cubic bulk silicon, germanium, and R-tin, (2) surface atoms (MH) analogous to perhydrogenated (111) (MH)n sheet cut from the cubic bulk, and (3) one MH2 unit at each vertex of the octahedron, giving a total of six MH2 units for each cage independent of their size. The bulk lattice and the perhydrogenated monolayer sheet of each element can be considered to represent strain-free systems for stoichiometries of (M)n and (MH)n, respectively. For silicon and germanium, the (MH)n sheet is structurally analogous to a
monolayer sheet of the experimentally known layered polysilyne, (SiH)n7 and layered polygermyne, (GeH)n.8 An infinite linear (MH2)n chain in trans-conformation was used as a strainfree reference for the MH2 stoichiometry. Using the described partition scheme, the relative energy per M atom (∆E) of an octahedral (MxHy) diamondoid analogue is determined as follows:
∆E ) [E(MxHy) - 6E(MH2) - (y - 12)E(MH) (x - y + 6)E(M)]x-1 (1) where E(MH2) is the energy of the infinite linear (MH2)n chain in trans-conformation per MH2 unit, E(MH) is the energy of an infinite (MH)n sheet per MH unit, and E(M) is the energy of the cubic bulk lattice per atom E(MH). Hence, the relative energy obtained for a diamondoid analogue from eq 1 can be considered as strain energy originating from structural deviation from corresponding bulk materials. From the computational point of view, eq 1 has the advantage of being homodesmotic,26 i.e., the number of bonds of each type and the states of hybridization are conserved. The relative energies of the octahedral diamondoid analogues are listed in Table 1. Because the diamondoid analogues can be considered finite clusters cut from the cubic bulk materials, their structural and electronic properties converge toward cubic bulk silicon, germanium, and R-tin as a function of their size. In the case of silicon, the largest studied Si680H256 structure is
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TABLE 1: Relative Energies, HOMO-LUMO Gaps and Diameters of the Octahedral Group 14 Diamondoid Analogues Calculated at the B3LYP Level of Theorya ∆Ea
gap (eV)
diameter (nm)
b
C10H16 C35H36 C84H64 C165H100 C286H144 C455H196 C680H256 C969H324
3.8 2.4 1.5 1.0 0.7 0.4 0.3 0.2
Carbon 9.7 8.2 7.6 7.2 7.0 6.8 6.7 6.6
0.5 0.9 1.2 1.6 1.9 2.3 2.6 3.0
Si10H16 Si35H36 Si84H64 Si165H100 Si286H144 Si455H196 Si680H256
1.7 1.3 1.0 0.8 0.6 0.5 0.4
Silicon 6.5 5.0 4.2 3.6 3.2 2.9 2.7
0.7 1.3 1.8 2.4 2.9 3.5 4.0
Ge10H16 Ge35H36 Ge84H64 Ge165H100 Ge286H144 Ge455H196
2.6 2.5 2.1 1.7 1.5 1.3
Germanium 6.5 4.9 3.9 3.4 2.9 2.6
0.8 1.3 1.9 2.5 3.1 3.6
Sn10H16 Sn35H36 Sn84H64 Sn165H100 Sn286H144 Sn455H196
3.4 3.4 3.0 2.5 2.2 1.9
Tin 4.7 3.3 2.4 1.7 1.3 1.0
0.9 1.5 2.2 2.9 3.5 4.2
a Relative energies in kJ/mol per group 14 atom are calculated from eq 1. b Data for carbon diamondoids taken from ref 12b.
only 0.4 kJ/mol per Si atom higher in energy when compared to strain-free bulk materials. The largest octahedral diamondoid analogues of silicon, germanium, and tin, Si680H256, Ge455H196, and Sn455H196, possess diameters of 4.0, 3.6, and 4.2 nm, respectively. Several methods used to synthesize silicon and germanium nanocrystals have been shown to yield structures
that adopt the cubic bulk lattice,27 although the prepared nanocrystals are not necessarily octahedral in shape. Considering the structural and electronic properties of the octahedral diamondoid analogues, similar systems composed of several group 14 elements, such as SiC or SiGe, would offer additional tuneability in comparison to homoatomic structures. Icosahedral Diamondoid Analogues. The icosahedral diamondoid analogues of silicon, germanium, and tin are structurally related to the previously studied icosahedral polysilanes, polygermanes, and polystannanes with (MH)n stoichiometries (M ) Si, Ge, Sn).13 The smallest icosahedral (MH)n cage, M20H20, is structurally analogous to the experimentally known dodecahedrane, C20H20.28 The dodecahedral 20-membered cage has also been previously shown to be the least strained of all (MH)n cages, where n e 24.29 The larger icosahedral (MH)n cages have been shown to favor a structural series where n ) 20, 80, 180, 320, 500, · · · , 20m2.12,13 The most important structural feature of the icosahedral (MH)n cages is their partial hydrogenation inside the cage, which allows the M atoms to adopt angles favorable for sp3 hydridization.12 The first member of the icosahedral series where the “in-out isomerism” applies is M80H80 with 60 exohydrogens outside the cage and 20 endohydrogens inside the cage (Figure 2). The smallest icosahedral diamondoid analogue, M100H60, can be derived by replacing the 20 endohydrogens of M80H80 with M atoms, generating a dodecahedral M20 core into the interior of the cage (Figure 2). In all cases with M ) Si, Ge, and Sn, the M20 core fits almost perfectly inside the M80H60 outer shell, with the layers being covalently bound by M-M bonds with nearly optimal sp3-hybridization. The next fully perhydrogenated icosahedral (MH)n in size is M180H180 with 60 hydrogens inside the cage.12,13 In analogy to the fit between M80H80 and M20H20 cages, the 60 endohydrogens in M180H180 match with the 60 exohydrogens in M20@M80H60. Removal of the matching hydrogens from both cages and placing the M20@M80 core inside the M180H120 cage results in M20@M80@M180H120, a three-layered icosahedral diamondoid analogue. The described structural principles of layered icosahedral diamondoid analogues can be generalized, producing a series of structures based on the 20m2 series of icosahedral (MH)n cages: the mth member with its exohydrogens removed fits inside the (m + 1)th member with its endohydrogens removed. We studied the icosahedral diamondoid ana-
Figure 2. The structural motif of icosahedral group 14 diamondoid analogues (M ) Si, Ge, Sn). Left: The smallest in-out isomeric icosahedral M80H80 cage with dodecahedral core of 20 hydrogen atoms inside the cage (yellow color). Middle: Cross section of the icosahedral M100H60 diamondoid analogue, where the 20 hydrogen atoms inside the cage have been replaced with group 14 atoms (yellow color). Right: Full view of the icosahedral M100H60 diamondoid analogue.
Group 14 Diamondoid Analogues
J. Phys. Chem. C, Vol. 112, No. 42, 2008 16327 TABLE 2: Relative Energies, HOMO-LUMO Gaps and Diameters of the Icosahedral Group 14 Diamondoid Analogues Calculated at the B3LYP Level of Theorya ∆Ea
gap (eV)
diameter (nm)
b
C20H20 C100H60 C280H120 C600H200 C1100H300 C1820H420
14.7 8.3 6.3 5.2 4.6 4.2
Carbon 8.5 7.4 7.0 6.7 6.5 6.3
0.7 1.1 1.6 2.0 2.5 3.0
Si20H20 Si100H60 Si280H120 Si600H200 Si1100H300
7.6 4.2 3.3 2.8 2.5
Silicon 4.8 3.5 2.7 2.4 2.2
1.0 1.6 2.4 3.1 3.8
Ge20H20 Ge100H60 Ge280H120 Ge600H200
5.7 3.9 3.4 3.1
Germanium 4.9 2.9 2.4 2.1
1.0 1.7 2.5 3.2
Sn20H20 Sn100H60 Sn280H120 Sn600H200
5.8 4.1 3.5 3.1
Tin 3.6 2.2 1.7 1.2
1.1 2.0 2.8 3.7
a Relative energies in kJ/mol per group 14 atom are calculated from eq 2. b Data for carbon diamondoids taken from ref 12b, except for C1820H420 (C20@C80@C180@C320@C500@C720H420), which was calculated for this study at the B3LYP level of theory (see ref 12b for details). The full structural optimization of C1820H420 (point group Ih) was composed of 2240 atoms and 27 580 basis functions.
per M atom (∆E) of an icosahedral (MxHy) diamondoid analogue can be determined as follows:
∆E ) [E(MxHy) - yE(MH) - (x - y)E(M)]x-1
Figure 3. Top: The icosahedral M1100H300 diamondoid analogue (M20@M80@M180@M320@M500H300). Bottom: A cross section of the M1100H300 cage, illustrating the layered nature of the icosahedral diamondoid analogues. The layers are marked by colors: Yellow ) M20; green ) M80; blue ) M180; red ) M320; gray ) M500.
logues of silicon, germanium, and tin up to M20@M80@ M180@M320@M500H300, i.e., M1100H300 (Figure 3). In the case of silicon, the icosahedral diamondoid analogues are structurally related to the previously reported icosahedral silicon quantum dots30,31 polyicosahedral Si nanowires32 and icosahedral Sinanoclusters.33 The relative energies of the icosahedral diamondoid analogues were determined using the approach described above for the octahedral diamondoid analogues. The icosahedral structures consist of two types of sp3-hybridized M atoms: (1) core atoms bound to four other M atoms and (2) surface atoms bound to three M atoms and to one hydrogen. The bonding of the core M atoms is analogous to cubic bulk silicon, germanium, and R-tin, whereas the bonding of the surface M atoms is analogous to bonding in perhydrogenated (111) (MH)n sheet cut from the cubic bulk lattice. Hence, similar to eq 1, the relative energy
(2)
where E(MH) is the energy of an infinite (MH)n sheet per MH unit, and E(M) is the energy of the cubic bulk lattice per atom. Similar to the eq 1, the approach described by eq 2 is homodesmotic.26 The relative energies of the icosahedral diamondoid analogues are listed in Table 2. Similar to the previously studied icosahedral carbon diamondoids,12b the relative energies of the icosahedral structures decrease as a function of their size. Because the icosahedral diamondoids are not superimposable with the cubic bulk lattice of Si, Ge, or R-Sn, their structures can be considered to approach icosahedral quasicrystals.34 The diameters of the largest studied icosahedral diamondoid analogues, Si1100H300, Ge600H200, and Sn600H200, are 3.8, 3.2, and 3.7 nm, respectively. Unlike the bulk-like octahedral diamondoid analogues, the icosahedral diamondoid analogues become slightly compressed as their size increases. In the following discussion, we describe the bonding trends observed within the icosahedral silicon structures in detail, with the germanium and tin structures showing similar size-dependent trends. In Si100H60, the interlayer distance between the Si20 and Si80 layers is 2.36 Å, being very close to 2.38 Å, the Si-Si bond length in the cubic bulk silicon calculated at the B3LYP level of theory. The intralayer bond distances are very close to the bulk bond length. In the next largest cage, Si280H120, the interlayer Si20-Si80 and Si80-Si180 distances are 2.33 and 2.37 Å, respectively. The intralayer Si-Si bond distance in the innermost Si20 layer, 2.35 Å, is slightly
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Figure 4. Relative energies of the octahedral (gray circles) and icosahedral (black squares) diamondoid-like group 14 structures at the B3LYP level of theory.
smaller than the bulk value. In the four-layered Si600H200, the interlayer Si20-Si80, Si80-Si180, and Si180-Si320 distances are 2.31, 2.34, and 2.37 Å. The Si20 layer has intralayer distances of 2.33 Å. In the largest studied Si1100H300 cage, the interlayer distances from the innermost to the outermost layer are 2.30, 2.33, 2.35, and 2.37 Å, with the intralayer distance within the Si20 layer having been shortened to 2.31 Å. If the compression becomes substantial for larger icosahedral structures, the icosahedral diamondoids may possess an optimal size diameter instead of converging toward icosahedral quasicrystal structures. Several different approaches can be utilized to produce silicon and germanium nanocrystals or quantum dots of various size and shape,27 but well-defined icosahedral group 14 nanocrystals have not been structurally characterized yet. The icosahedral carbon nanodiamonds produced with the chemical vapor deposition35 or acetylene flame method36 could also be structurally related to the icosahedral diamondoid analogues considered here. Further examples of group 14 compounds possessing building blocks related to the icosahedral structural motif are the guestfree silicon and germanium clathrates, which contain hollow M20 dodecahedra corresponding to the M20 core of the icosahedral diamondoids.37 Comparisons between the Diamondoid Analogues. To illustrate the periodic trends among group 14 elements, the relative energies of different diamondoid-like structures for elements C-Sn are shown in Figure 4. Generally, the octahedral diamondoid-like structures are favored over the icosahedral ones. However, the energy difference between the two structural series decreases when moving downward in the periodic table. The decrease in the relative stability of the octahedral diamondoid analogues in comparison to the icosahedral structures might be due to the increasing metallic character of the heavier group 14 elements, the cubic R-allotrope of tin already having a competing metallic β-allotrope at normal pressure and temperature. The
relative destabilization of the cubic bulk lattice is also supported by the fact that the M10H16 adamantane framework without bulklike atoms becomes increasingly stable in comparison to larger octahedral structures when moving from carbon down to tin. It should be noted that the relative energies of structures composed of different elements are not directly comparable with each other, as the stabilities are given relative to distinct bulk reference structures in each case. In the case of nonhydrogenated silicon quantum dots, the icosahedral structures have been suggested to be favored over structures related to cubic bulk due to better surface energy minimization in the icosahedral structural motif.30 However, explicit surface termination with hydrogens is expected to play a significant role, with the octahedral diamondoid analogues of silicon studied here being favored over the icosahedral ones. We investigated the electronic structures of the silicon, germanium, and tin diamondoid analogues in more detail by calculating the densities of states (DOS) for the studied structures. The DOS plots of the diamondoid analogues and corresponding cubic bulk materials are shown in Figure 5. Generally, the main characteristics of the DOS plots obtained for octahedral and icosahedral diamondoid analogues are quite similar for all three elements. However, as can best be seen in the case of silicon, the shape of the p-type HOMO-LUMO region is different in the icosahedral structures in comparison to octahedral diamondoid analogues and the cubic bulk material. This suggests that the electronic characteristics of the icosahedral diamondoid analogues could be different from the cubic bulk material, as suggested previously for icosahedral silicon quantum dots.30 The HOMO-LUMO gaps of the icosahedral diamondoid analogues are slightly smaller than the gaps of the octahedral systems of similar size for all elements except tin, where the trend is reversed. In the case of the octahedral silicon and germanium diamondoid analogues, the calculated HOMO-LUMO
Group 14 Diamondoid Analogues
Figure 5. Density of states (DOS) plots for the diamondoid analogues of silicon, germanium, and tin together with the corresponding cubic bulk DOS plots. For each class of diamondoid analogues, all the structures have been plotted in the same chart, with the largest of the studied systems being labeled for clarity. For bulk materials, both the total DOS and individual s-, p-, and d-contributions are shown. The DOS plots of the molecular systems have been created by broadening the discrete energy levels with superimposed Gaussians with width of 0.01 au. The bulk density of states were expanded with 10 Legendre polynomials as implemented in the CRYSTAL06 software.
J. Phys. Chem. C, Vol. 112, No. 42, 2008 16329 be due to the uniform and highly symmetric M-M bonding network of both octahedral and icosahedral structures. The increase in the metallic character of the systems when moving down from silicon to tin is clearly visible, with cubic bulk Sn already being close to metallic. At the B3LYP level of theory, the band gap energies of the cubic bulk silicon, germanium, and tin are 1.9, 0.9, and 0.1 eV, respectively. Overall, the electronic structure of the octahedral diamondoid analogues can be considered to converge toward the corresponding cubic bulk materials, while the icosahedral diamondoid analogues possess slightly different electronic characteristics. To further elucidate the properties of the diamondoid analogues, we investigated the charge distribution of both octahedral and icosahedral structures by means of natural population analysis (NPA). For all studied group 14 diamondoid analogues, core atoms were found to be practically neutral, while the surface atoms showed slight polarization due to hydrogen termination. Depending on the electronegativity of the M atom (M ) C, Si, Ge, Sn), the surface atoms bound to hydrogen possess a slight negative (M ) C) or positive (M ) Si, Ge, Sn) partial charge, while hydrogen atoms possess a slight partial charge of opposite sign. The surface atoms bound to core atoms possess a small partial charge having the same sign as the hydrogen atoms. The only significant difference between the octahedral and icosahedral structures is due to the MH2 groups present in the octahedral cages. Because the M atoms in the MH2 groups are bound to two hydrogen atoms that polarize the M atom, their partial charge is about twice as large as that of the other surface atoms. We investigated the spectroscopic features of the diamondoid analogues by calculating the infrared spectra of the octahedral M84H64 and the icosahedral M100H60 cages. Because the spectral features of the carbon diamondoids have been investigated in detail previously,12b the following discussion is focused on structures composed of silicon, germanium, and tin. The most significant spectral features in both the octahedral and icosahedral diamondoid analogues are the high-energy M-H stretching vibrations and low-energy M-H rocking vibrations. In the case of the octahedral Si84H64, Ge84H64, and Sn84H64 structures, the M-H stretching vibrations occur at 2080-2110 cm-1, 2000-2010 cm-1, and 1720-1780 cm-1, respectively. For the icosahedral Si100H60, Ge100H60, and Sn100H60 cages, the corresponding features are located at wavenumbers very similar to the octahedral cages, namely, at 2090-2100 cm-1, 1970-1980 cm-1, and 1730-1740 cm-1. The M-H rocking vibrations of the octahedral and icosahedral cages overlap as well, occurring at 590-690, 530-610, and 400-490 cm-1 for the octahedral M84H64 structures and 620-670, 560-610, and 440-480 cm-1 for the icosahedral M100H60 structures. However, in addition to the modes described above, the octahedral cages also show a distinct MH2 scissor mode which is clearly separated from the stretching and rocking modes. The fingerprint feature occurs at 880, 820, and 680 cm-1 for Si84H64, Ge84H64, and Sn84H64, respectively. The MH2 scissor mode found in the spectra of the octahedral structures could enable the discrimination of octahedral and icosahedral structures on the basis of IR spectra. Conclusions
gaps are in good agreement with previous results obtained for silicon and germanium nanocrystals of similar size.11a,b Analysis of the characteristics of the HOMO and LUMO in both octahedral and icosahedral structures showed the frontier orbitals to be delocalized, showing no localization on the core or surface parts. The delocalized nature of the HOMO and LUMO might
We have studied the structural and electronic characteristics of two families of group 14 diamondoid analogues with quantum chemical methods. The octahedral diamondoid analogues are structurally related to the cubic bulk lattice, while the icosahedral diamondoid analogues are not superimposable with the cubic bulk. The relative energies of the octahedral and icosahedral
16330 J. Phys. Chem. C, Vol. 112, No. 42, 2008 structures decrease smoothly as a function of their size. The octahedral structures are energetically favored for all the studied elements, but their favorability in comparison to the icosahedral structural decreases when moving down from carbon to tin. The obtained periodic trends in the relative stabilities of the octahedral and icosahedral structures can be attributed to the increasing metallic character of the heavier group 14 elements. Investigation of the electronic characteristics of the studied diamondoid analogues revealed differences between the icosahedral and octahedral structural families, suggesting the icosahedral diamondoids analogues to possess electronic properties different from materials with cubic bulk lattice. The structural characteristics and periodic trends observed for the diamondoid analogues are expected to help in the experimental characterization of tetrahedrally coordinated group 14 nanomaterials. Furthermore, the preparation of the icosahedral diamondoid analogues would produce well-defined group 14 nanostructures possessing electronic properties that are different from nanomaterials with cubic bulk lattice. Acknowledgment. We thank Dr. Uwe Huniar from COSMOlogic GmbH&Co.KG for providing us with a modified version of TURBOMOLE 5.9. Funding from the Academy of Finland is gratefully acknowledged. Supporting Information Available: Cartesian coordinates of icosahedral fulleranes, icosahedral diamondoids, and octahedral diamondoids composed of carbon.This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Fokin, A. A.; Schreiner, P. R.; Schwertfeger, H. Angew. Chem., Int. Ed. 2007, 46, 2–17. (2) Fort, R. C., Jr; Schleyer, P. v.R Chem. ReV. 1964, 64, 277–300. (3) Fischer, J.; Baumgartner, J.; Marschner, C. Science 2005, 310, 825. (4) Pichierri, F. Chem. Phys. Lett. 2006, 421, 319–323. (5) (a) Marschner, C.; Baumgartner, J.; Wallner, A. Dalton. Trans. 2006, 5667–5674. (b) Marschner, C. Organometallics 2006, 25, 2110–2125. (6) Schnepf, A. Chem. Commun. 2007, 192–194. (7) Dahn, J. R.; Way, B. M.; Fuller, E.; Tse, J. S. Phys. ReV. B 1993, 48, 17872–17877. (8) Vogg, G.; Brandt, M. S.; Stutzmann, M. AdV. Mater. 2000, 12, 1278–1281. (9) Miller, R. D.; Michl, J. Chem. ReV. 1989, 89, 1359–1410. (10) Manners, I. Angew. Chem., Int. Ed. Engl. 1996, 35, 1602–1621. (11) (a) Garoufalis, C. S.; Zdetsis, A. D.; Grimme, S Phys. ReV. Lett. 2001, 87, 276402/1–276402/4. (b) Garoufalis, C. S.; Skaperda, M. S.; Zdetsis, A. D. J. Phys: Conf. Ser. 2005, 10, 97–100. (c) Zdetsis, A. D.; Garoufalis, C. S.; Skaperda, M. S.; Koukaras, E. N. J. Phys: Conf. Ser. 2005, 10, 101–104. (d) Sundholm, D. Nano Lett. 2003, 3, 847–849. (e) Sundholm, D. Phys. Chem. Chem. Phys. 2004, 6, 2044–2047. (f) Lehtonen, O.; Sundholm, D. Phys. ReV. B 2005, 72, 085424/1-085424/8. (g) Lehtonen, O.; Sundholm, D Phys. ReV. B 2006, 74, 045433/1-045433/11. (h) Lehtonen, O.; Sundholm, D.; Va¨nska¨, T. Phys. Chem. Chem. Phys. 2008, 10, 4535–4550. (i) Puzder, A.; Williamson, A. J.; Grossman, J. C.; Galli, G. J. Am. Chem. Soc. 2003, 125, 2786–2791. (j) Wang, X.; Zhang, R. Q.; Niehaus, T. A.; Frauenheim, Th.; Lee, S. T J. Phys. Chem. C 2007, 111, 12588–12593. (12) (a) Linnolahti, M.; Karttunen, A. J.; Pakkanen, T. A. ChemPhysChem 2006, 7, 1661–1663. (b) Linnolahti, M.; Karttunen, A. J.; Pakkanen, T. A. J. Phys. Chem. C 2007, 111, 18118–18126. (13) (a) Karttunen, A. J.; Linnolahti, M.; Pakkanen, T. A. J. Phys. Chem. C 2007, 111, 2545–2547. (b) Karttunen, A. J.; Linnolahti, M.; Pakkanen, T. A. J. Phys. Chem. C 2007, 111, 6318–6320.
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