6318
J. Phys. Chem. C 2007, 111, 6318-6320
Icosahedral Polygermane and Polystannane Nanostructures Antti J. Karttunen, Mikko Linnolahti,* and Tapani A. Pakkanen* UniVersity of Joensuu, Department of Chemistry, P.O. Box 111, FI-80101 Joensuu, Finland ReceiVed: February 22, 2007
Stable Ih-symmetric polygermane and polystannane nanostructures have been predicted on the basis of quantum chemical calculations. Structures, stabilities, and electronic properties of cages up to Ge500H500 and Sn500H500 were determined. The facets of the icosahedral cages resemble the monolayer sheets of experimentally known layered GeH. The stabilities and electronic properties of the cages converge toward the corresponding monolayer sheets. Due to their electronic properties, the polygermane and polystannane nanostructures may turn out to be useful in optical applications.
Introduction Inorganic polymers often exhibit phenomena not occurring in their organic counterparts. For example, polysilanes, the catenates of silicon, possess optical and electronic properties not found in analogous carbon-based polymers.1 The properties have been attributed to the delocalization of the Si-Si σ electrons, an effect also present in the polymeric structures of heavier group 14 elements, polygermanes and polystannanes.2 Several polygermane and polystannane structures have been prepared. Small polyhedral cages such as hexagermaprismane,3 octagermacubane,4 decastanna[5]prismane,5 and octastannacubane6 have been synthesized with bulky organic groups as substituents. Generally, the small polygermane and polystannane polyhedra are less strained than the corresponding polyalkanes and polysilanes.7 Various linear and branched polymer chains have been prepared for both germanium and tin.2,8 Polygermynes, (GeR)n, have been obtained both as random-network polymers9 and arranged into ordered layers.10 The structure and the electronic properties of the layered polygermyne11 are very similar to the layered polysilyne.12 In addition to the three-dimensional polygermyne structures, theoretical calculations have predicted GeH nanotubes to be energetically viable.13 The corresponding (SnR)n polymeric systems have been studied less extensively. Partial endohydrogenation has been recently shown to stabilize large icosahedral (CH)n14 and (SiH)n15 cages. Here, we apply analogous structural motifs for the heavier group 14 elements, Ge and Sn, introducing icosahedral polygermane and polystannane nanostructures. Quantum chemical calculations are then performed to determine the structural and electronic character of the cages. Computational Details We investigated the structures, stabilities, and electronic properties of icosahedral polygermane and polystannane cages using hybrid density functional B3LYP and ab initio MP2 methods. All cage structures were fully optimized within the Ih symmetry by the B3LYP method. Single-point MP2 calculations were performed on the B3LYP-optimized geometries. The stabilities of the icosahedral cages were compared with periodic * To whom correspondence should be addressed. E-mail: Mikko.
[email protected] (M.L.);
[email protected] (T.A.P).
calculations of monolayer sheets of polygermyne (GeH) and polystannyne (SnH), representing strain-free systems. The monolayer sheet of polygermyne is structurally equivalent to a layer of the experimentally known layered polygermyne.10 Periodic structures were fully optimized by CRYSTAL06 software.16 All of the other calculations were performed with TURBOMOLE 5.8 and 5.9.17 In combination with the B3LYP method, the Karlsruhe split-valence basis set with polarization functions (SVP) was applied for all elements.18 A 28-electron effective core potential (ECP) was used to describe the core electrons of Sn.19 The largest all-electron basis set calculation, the geometry optimization of the Ge500H500 cage, involved 18500 basis functions. MP2 calculations were performed using the resolution of the identity (RI) technique as implemented in TURBOMOLE.20 In the MP2 calculations, an all-electron triplevalence-zeta basis set21 and the corresponding RI auxiliary basis set22 were used for H and Ge. Sn atoms were described using the 28-electron ECP19 and a triple-ζ valence basis set18 together with an auxiliary RI basis.23 Structures up to Ge80H80 and Sn180H180 were verified as true minima by vibrational frequency calculations.24 A zero-point energy scaling factor of 0.9806 and a harmonic frequency scaling factor of 0.9614 were adopted for B3LYP frequencies.25 Results and Discussion Group 14 polyhedral (MH)n cages up to n ) 24 have been previously studied theoretically.26 Generally, the strain energies decrease in the order C > Si > Ge > Sn. For each of the studied (MH)n cages, the Ih-symmetric 20-membered dodecahedron was found least strained. The preference of the dodecahedral shape is in accordance with experimental findings; the C20H20 dodecahedrane having been synthesized.27 We have recently demonstrated that the larger Ih-symmetric (CH)n14 and (SiH)n15 cages composed of hexagons and 12 pentagons are stabilized by placing a portion of the hydrogens inside the cage. The partial endohydrogenation of hexagons is applicable from the 80membered cage onward, giving rise to advantageous puckering of the hexagons, while allowing the pentagons to retain an optimal planar arrangement. This “in-out” isomerism has also been shown to stabilize other tetrahedrally coordinated cage structures, group 13-15 binary hydrides28 and icosahedral allotropes of phosphorus.29 Applying the structural motifs of in-out isomerism for the Ih-symmetric polygermane and polystannane cages results in
10.1021/jp071480k CCC: $37.00 © 2007 American Chemical Society Published on Web 04/10/2007
Polygermane and Polystannane Nanostructures
J. Phys. Chem. C, Vol. 111, No. 17, 2007 6319 TABLE 1: Relative Total Energies and Gibbs Free Energies (T ) 298.15 K),a HOMO-LUMO Gaps, and Diameters of Ih-Symmetric Polygermanes Together with the Infinite GeH Sheet ∆EB3LYP ∆GB3LYP ∆EMP2 ∆GMP2b Series 20m2 Ge20H20 Ge80H80 Ge180H180 Ge320H320 Ge500H500 Series 60m2 Ge60H60 Ge240H240 GeH sheet b
gapB3LYP diameter (eV) (nm)
0.0 -2.4 -3.3 -3.9 -4.2
0.0 -0.4
0.0 -5.8 -7.1
0.0 -3.8
4.91 3.61 3.59 3.34 3.18
1.01 1.70 2.45 3.20 3.97
6.0 -0.1 -5.3
8.1
6.7
8.8
4.24 3.54 2.28
1.54 2.75
a The energies in kJ/mol per GeH unit are given relative to Ge20H20. Gibbs corrections for total energy obtained from B3LYP calculations.
TABLE 2: Relative Total Energies and Gibbs Free Energies (T ) 298.15 K), a HOMO-LUMO Gaps, and Diameters of Ih-Symmetric Polystannanes Together with the Infinite SnH Sheet ∆EB3LYP ∆GB3LYP ∆EMP2 ∆GMP2b Series 20m2 Sn20H20 Sn80H80 Sn180H180 Sn320H320 Sn500H500 Series 60m2 Sn60H60 Sn240H240 SnH sheet b
Figure 1. Icosahedral (GeH)n and (SnH)n cages of the series n ) 20m2, with m ) 1-5.
Figure 2. Icosahedral (GeH)n and (SnH)n cages of the series n ) 60m2, with m ) 1-2.
two series of (GeH)n and (SnH)n structures, (1) n ) 20, 80, 180, 320, 500, ..., 20m2 and (2) n ) 60, 240, 540, 960, 1500, ..., 60m2 (Figures 1 and 2). Both series of polygermane and polystannane cages become increasingly stable as a function of m (Tables 1 and 2). Series 2, the first member of which is
gapB3LYP diameter (eV) (nm)
0.0 -2.6 -3.6 -4.1 -4.4
0.0 -1.0 -1.6
0.0 -5.2
0.0 -3.6
3.55 2.79 2.34 2.03 1.82
1.15 1.96 2.82 3.70 4.59
3.3 -1.2 -5.4
5.1
5.0
6.7
3.21 2.47 0.94
1.77 3.18
a The energies in kJ/mol per SnH unit are given relative to Sn20H20. Gibbs corrections for total energy obtained from B3LYP calculations.
the M60H60 cage (a topological analogue of the fully hydrogenated C60 fullerene), is less favorable. This is due to increased structural strain caused by 20 fully exohydrogenated hexagons. In the calculated IR spectrum of Ge80H80, the Ge-H stretching mode is located at 2000 cm-1, and the Ge-H bending modes are around 500-620 cm-1. The corresponding Ge-H stretching and bending modes of the experimentally known layered polygermyne occur at 2010 and 550-600 cm-1, respectively.10 For the Sn80H80 cage, the calculated Sn-H stretching mode is located at 1760 cm-1, and the Sn-H bending modes are in the region of 390-530 cm-1. The ring topologies of the icosahedral n ) 20m2 and 60m2 cages are analogous to the icosahedral (h,0) and (h,k), h ) k fullerenes, respectively.30 As the Ih-symmetric polygermanes and polystannanes become larger in size, the cages adopt a faceted icosahedral shape. In the n ) 20m2 series, the puckered hexagon sheets form 20 facets, which resemble the monolayer sheets of the layered GeH. The n ) 60m2 structures consist of 60 such facets due to the 20 exohydrogenated hexagons, thus dividing the 20 facets of the icosahedron into additional facets. Hence, the strain energies of the cages can be estimated from comparisons with the corresponding monolayers of GeH and SnH. At the B3LYP level of theory, the largest studied cages, Ge500H500 and Sn500H500, have strain energies of only 1.1 kJ/ mol/GeH and 1.0 kJ/mol/SnH. For comparison, previous calculations suggest a strain energy of 1.0 kJ/mol/SiH for the Si500H500 cage.15 It should be noted that the strain energy of the C60 fullerene calculated at the same level of theory is about 40 kJ/mol/C.31
6320 J. Phys. Chem. C, Vol. 111, No. 17, 2007 The electronic properties of the predicted polygermane and polystannane structures were studied by calculating the optical gaps of the cages and the monolayers. The HOMO-LUMO gaps of both the polygermane and polystannane cages approach the direct band gaps of the corresponding infinite GeH and SnH monolayers as a function of the size of the cage (Tables 1 and 2). For the experimentally known layered polygermyne, a direct band gap of 1.7 eV has been detected by both experimental photoluminescence measurements and theoretical LDA-DFT calculations.10,11 The relationships in the electronic properties of the cages and monolayer sheets suggest useful optical properties, such as efficient luminescence, for the cages. The sizes of the calculated HOMO-LUMO gaps for the group 14 (MH)n cages systematically decrease in the order Si > Ge > Sn.15 Therefore, the optical gaps of the cages could be engineered by producing mixed cages such as Sin-xGexHn. Analogous Si-Ge network9 and sheet32 polymers with tunable luminescence have already been produced experimentally by utilizing the complete miscibility of Si and Ge. In a similar way to the analogous (SiH)n cages,15 the smaller polygermane and polystannane cages fit inside the larger ones, resulting in a series of multilayered cages. Within the more favorable n ) 20m2 series, the mth member fits inside the (m+2)th member, the two first multilayered cages thus being M20H20@M180H180 and M80H80@M320H320. The cages consisting of different elements can also be combined, leading to mixed multilayered systems like Si20H20@Ge180H180. Experimental synthesis of the group 14 (MH)n icosahedral cages and their mixed or multilayered combinations would give rise to a new class of nanostructures with tunable optical properties. Several experimental approaches are applicable for production of polygermanes and polystannanes. These are, for example, ultrasound activated synthesis and transition-metal-catalyzed polymerizations.2 Furthermore, (SiH)n cages up to n ) 22 have been produced by laser photolysis.33 While the nanostructures may require novel synthetic approaches, the existing experimental techniques could offer useful guidelines. Conclusions Quantum chemical calculations were performed to predict the structures, stabilities, and electronic properties of Ihsymmetric polygermane and polystannane nanostructures. The icosahedral cages are significantly stabilized by partial endohydrogenation of the six-membered rings, resulting in strain energies of only about 1 kJ/mol/MH unit for the largest studied cages, Ge500H500 and Sn500H500. The icosahedra are sewed up from sheets resembling infinite monolayers of GeH and SnH, toward which the stabilities and electronic properties of the cages converge. Due to the efficient luminescence found in inorganic
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