J. Phys. Chem. C 2007, 111, 2545-2547
2545
Icosahedral Polysilane Nanostructures Antti J. Karttunen, Mikko Linnolahti,* and Tapani A. Pakkanen UniVersity of Joensuu, Department of Chemistry, Post Office Box 111, FI-80101 Joensuu, Finland ReceiVed: NoVember 20, 2006
The existence of a family of stable Ih-symmetric polysilane nanostructures is predicted. The smallest member of the family is the dodecahedral Si20H20 cage, followed by Si80H80, Si180H180, and larger structures. The structures and stabilities of the polysilane nanostructures were determined on the basis of B3LYP and MP2 calculations. The larger cages become increasingly stable, consisting of polysilane monolayers sewed up to icosahedral shape. The structures and electronic properties of the polysilane nanostructures resemble those of the experimentally known layered polysilane, suggesting possible applications in optoelectronics.
Introduction Polysilanes possess optical and electronic properties useful for optoelectronics,1 such as photoluminescence.2 The properties differ significantly from those of the carbon-analogous polyalkanes, which has been rationalized to arise from longer bond distances together with higher delocalization of σ-electrons in Si-Si bonds compared to C-C.3 The properties are further influenced by the dimensionality of the polymer, the experimentally known structures varying from chains4 and layered sheets5 to discrete molecular cages. The experimentally known polyhedral cages such as tetrasilatetrahedranes,6 hexasilaprismanes,7 and octasilacubanes8 are highly strained, obtainable in the presence of bulky substituents attached to the silicon backbone.9,10 The structural preferences of polysilane cages can be rationalized by exploiting their analogy with corresponding polyalkanes, that is, (CH)n cages. A comparison, up to 24-membered cages, has been performed by Earley,11 demonstrating the preference of 20-membered dodecahedral cages. The experimentally known C20H20 dodecahedrane12 was found more strained than its Si20H20 polysilane counterpart. Recently, Kumar and Kawazoe13 demonstrated that full hydrogenation of polyhedral Si12, Si16, and Si20 cages would result in stable molecules. Little is known of larger polysilane cages; however, the icosahedral Si60H60 has been shown to be more strained than the dodecahedral Si20H20.9 In the case of (CH)n polyalkanes, no cages larger than C20H20 are experimentally known; most efforts toward their synthesis have been focused on the fully hydrogenated counterpart of buckminsterfullerene, C60H60,14 also known as a fullerane. Very recently, larger icosahedral fulleranes, C80H80 and C180H180, were demonstrated to be significantly less strained than C60H60, surpassing even the experimentally known C20H20 in stability.15 This is accomplished by partial endohydrogenation of the corresponding fullerenes. Here the preference of large cages is shown to apply for polysilanes as well, giving rise to a family of stable icosahedral polysilane nanostructures. Computational Details We investigated the structures, stabilities, and electronic properties of icosahedral polysilane cages at two levels of theory: density functional theory with B3LYP parametrization * Corresponding author: e-mail
[email protected].
Figure 1. Three smallest Ih-symmetric polysilane cages.
and second-order Møller-Plesset perturbation theory (MP2). The polysilanes were constrained to Ih symmetry, within which they were fully optimized by the B3LYP method. Single-point MP2 calculations were performed on the B3LYP-optimized geometries. The optimized crystal structure of the layered polysilane5 was included as a reference system. Periodic calculations of the layered polysilane were performed by CRYSTAL2003 software.16 Elsewhere TURBOMOLE 5.8 was applied.17 Optimized basis sets, necessary for periodic studies, were adopted due to comparisons made with the crystal structure. Therefore, in conjunction with the B3LYP method, a modified 6-21G* basis set for Si was adopted from previous work of Civalleri et al.18 For H, the standard 6-31G** basis set
10.1021/jp067700w CCC: $37.00 © 2007 American Chemical Society Published on Web 01/25/2007
2546 J. Phys. Chem. C, Vol. 111, No. 6, 2007
Karttunen et al.
TABLE 1: Relative Total Energies and Gibbs Free Energies,a HOMO-LUMO Gaps, and Diameters of Ih-Symmetric Polysilanes and Layered Polysilane ∆EB3LYP
∆GB3LYP
∆EMP2
∆GMP2b
gapB3LYP (eV)
diameter (nm)
0.0 -4.7 -5.9
5.10 4.20 4.15 3.95 3.88
0.96 1.63 2.34 3.06 3.77
8.9
5.05 4.13 4.01
1.47 2.63 3.89
-6.3
4.13 3.92
2.34 3.06
Si20H20 Si80H80 Si180H180 Si320H320 Si500H500
0.0 -4.7 -6.1 -6.9 -7.4
0.0 -2.4 -3.5
Series 20n2 0.0 -7.0 -8.6
Si60H60 Si240H240 Si540H540
5.4 -2.4 -4.8
7.6
Series 60n2 6.8
Si20H20@Si180H180 Si80H80@Si320H320
-5.6 -6.5
-3.0
-8.4
Bilayered -8.9 Layered Polysilane
3.37
The energies, in kilojoules/mole (at T ) 298.15 K) per SiH unit, are given relative to Si20H20 at B3LYP/6-21G* and MP2/TZVP levels of theory. b Gibbs corrections for total energy obtained from B3LYP calculations. a
Figure 3. Icosahedral polysilane cages of the series 60n2, with n ) 2-3. The figures on the right are cross-sections of the molecules, illustrating the interior of the cages.
Figure 2. Icosahedral polysilane cages of the series 20n2, with n ) 3-5. The figures on the right are cross-sections of the molecules, illustrating the interior of the cages.
was applied. MP2 calculations were performed with the resolution of identity (RI) technique as implemented in the software.19 A triple-ζ valence basis set with polarization functions20 (TZVP) and the corresponding RI auxiliary basis set21 were applied for both silicon and hydrogen. The polysilane cages up to Si180H180 were characterized as true minima by B3LYP vibrational frequency calculations. A zero-point energy scaling factor of 0.9806 was adopted for the calculation of Gibbs free energies.22 Results and Discussion Optimized structures of the three smallest Ih-symmetric polysilanes are illustrated in Figure 1, and the relative energies are given in Table 1. The dodecahedral Si20H20 cage previously
proposed by Kumar and Kawazoe13 is favored over the Si60H60 truncated icosahedron. The preference of Si20H20 can be understood in terms of strain energies. The bond angles of 108° in a dodecahedron consisting of 12 pentagons are close to the optimal value of 109.5° for sp3 hybridization, whereas the hexagons of a truncated icosahedron adopt angles of 120°. With the relative number of hexagons in icosahedral cages increasing as a function of the size of the cage, one could assume that the larger cages would become increasingly destabilized over Si20H20. However, in the case of the next larger icosahedral cage, Si80H80, the Si atoms interconnecting each set of three pentagons play an important role. Endohydrogenation of the interconnecting Si atoms combined with exohydrogenation of the Si atoms in pentagons results in a species more stable than Si20H20. The strain is relieved due to puckering of the hexagons, in a similar fashion with the proposed silicon nanotubes,23 while the pentagons retain the nearly optimal planar arrangement. The preference of this particular structure among its structural isomers can be rationalized by considering that moving any hydrogen from inside to outside, or vice versa, results in increased structural strain.
Icosahedral Polysilane Nanostructures
J. Phys. Chem. C, Vol. 111, No. 6, 2007 2547 distances between the cages are 5.8 and 5.7 Å for Si20H20@Si180H180 and Si80H80@Si320H320, respectively. The corresponding interplanar distance in the layered polysilane is 5.4 Å in both B3LYP-optimized and experimental5 crystal structure. The stabilities and HOMO-LUMO gaps of the bilayered cages are similar to their monolayered counterparts (Table 1). Conclusions
Figure 4. Cross-sections of bilayered Ih-symmetric polysilane cages: (a) Si20H20@Si180H180, (b) Si80H80@Si320H320.
The structural principles described for Si80H80 can be applied for larger cages, leading to two series of Ih-symmetric polysilanes SixHx: (1) x ) 20, 80, 180, 320, 500, ..., 20n2 and (2) x ) 60, 240, 540, 960, 1500, ..., 60n2 (Figures 2 and 3). The polysilane cages become increasingly stable as a function of the size of the cage (Table 1). Series 2 is less favorable because of the presence of 20 fully exohydrogenated hexagons, resulting in increased structural strain. On the contrary, only the pentagons in series 1 are fully exohydrogenated. The icosahedral polysilanes have ring topologies equivalent to the icosahedral fullerenes,24 with series 1 producing analogues for (h,0) fullerenes and series 2 for (h,k) fullerenes, where h ) k. The structures of icosahedral polysilanes can be considered as monolayers of the layered polysilane, sewed up to a cage. Hence, as the size of the cage is increased, the stabilities approach that of the experimentally known layered polysilane.5 The strain energies are determined as the energy difference between the cages and the strain-free layered polysilane. For Si500H500, the strain energy is only 1.0 kJ mol-1 (SiH unit)-1. The strain energy of C60 fullerene is 43.0 kJ mol-1 (C atom)-1 at the same level of theory,25 providing further evidence of the high stability of the polysilane nanostructures. The B3LYP-calculated highest occupied molecular orbitallowest unoccupied molecular orbital (HOMO-LUMO) gaps of the cages decrease as a function of the size of the cage, starting from 5.10 eV for Si20H20 and approaching the direct band gap of 3.37 eV calculated for the layered polysilane. The structural and electronic similarities between the polysilane cages and the layered polysilane suggest that also the nanostructured polysilanes could possess important optical properties. A viable synthesis route for the polysilane cages could be laser photolysis, previously applied for the synthesis of SixHx cages up to x ) 22.26 Multilayered icosahedral polysilanes can be derived by placing smaller cages inside the larger ones. Focusing on the thermodynamically more favorable series of the Ih-symmetric polysilanes SixHx, where x ) 20n2, the nth member of the series fits inside the (n + 2)th member. The first feasible combination of the cages is thus Si20H20 inside Si180H180, and the next one is Si80H80 inside Si320H320 (Figure 4). The shortest Si-Si
We have predicted the existence of a family of Ih-symmetric polysilanes. The stabilities of the polysilane nanostructures improve as a function of the size of the cage, approaching the experimentally known layered polysilane in both structure and electronic properties. Smaller structures can be fit inside the larger ones, forming multilayered polysilane cages. The similarities between the cages and the layered polysilane suggest the nanostructured polysilanes may find applications in optoelectronics. References and Notes (1) Nesˇpu˚rek, S.; Wang, G.; Yoshino, K. J. Optoelectron. AdV. Mater. 2005, 7, 223. (2) Canham, L. T. Appl. Phys. Lett. 1990, 57, 1046. (3) Inagaki, S.; Yoshikawa, K.; Hayano, Y. J. Am. Chem. Soc. 1993, 115, 3706. (4) Miller, R. D.; Michl, J. Chem. ReV. 1989, 89, 1359. (5) Dahn, J. R.; Way, B. M.; Fuller, E.; Tse, J. S. Phys. ReV. B 1993, 48, 17872. (6) Wiberg, N.; Finger, C. M. M.; Polborn, K. Angew. Chem., Int. Ed. 1993, 32, 1054. (7) Sekiguchi, A.; Yatabe, T.; Kabuto, C.; Sakurai, H. J. Am. Chem. Soc. 1993, 115, 5853. (8) Furukawa, K.; Fujino, M.; Matsumoto, N. Appl. Phys. Lett. 1992, 60, 2744. (9) Sekiguchi, A.; Nagase, S. In The chemistry of organic silicon compounds, Vol. 2; Rappoport, Z., Apeloig, Y., Eds.; John Wiley & Sons, New York, 1998; pp 119-152. (10) Nagase, S. Acc. Chem. Res. 1995, 28, 469. (11) Earley, C. W. J. Phys. Chem. A 2000, 104, 6622. (12) Paquette, L. A.; Ternansky, T. J.; Balogh, D. W.; Kentgen, G. J. Am. Chem. Soc. 1983, 105, 5446. (13) Kumar, V.; Kawazoe, Y. Phys. ReV. Lett. 2003, 90, 055502. (14) Nossal, J.; Saini, R. K.; Alemany, L. B.; Meier, M.; Billups, W. E. Eur. J. Org. Chem. 2001, 4167. (15) Linnolahti, M.; Karttunen, A. J.; Pakkanen, T. A. ChemPhysChem 2006, 7, 1661. (16) Saunders, V. R.; Dovesi, R.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Harrison, N. M.; Doll, K.; Civalleri, B.; Bush, I. J.; D’Arco, Ph.; Llunell, M. CRYSTAL2003 User’s Manual, University of Torino, Torino, Italy, 2003. (17) Ahlrichs, R.; Ba¨r, M.; Ha¨ser, M.; Horn, H.; Ko¨lmel, C. Chem. Phys. Lett. 1989, 162, 165. (18) Civalleri, B.; Zicovich-Wilson, C. M.; Ugliengo, P.; Saunders, V. R.; Dovesi, R. Chem. Phys. Lett. 1998, 292, 394. (19) Weigend, F.; Ha¨ser, M. Theor. Chem. Acc. 1997, 97, 331. (20) Scha¨fer, A.; Huber, C.; Ahlrichs, R. J. Chem. Phys. 1994, 100, 5829. (21) Weigend, F.; Ha¨ser, M.; Patzelt, H.; Ahlrichs, R. Chem. Phys. Lett. 1998, 294, 143. (22) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502. (23) Seifert, G.; Ko¨hler, Th.; Urbassek, H. M.; Herna´ndez, E.; Frauenheim, Th. Phys. ReV. B 2001, 63, 193409. (24) Tang, A. C.; Huang, F. Q. Chem. Phys. Lett. 1995, 247, 494. (25) Linnolahti, M.; Kinnunen, N. M.; Pakkanen, T. A. Chem. Eur. J. 2006, 12, 218. (26) Rechtsteiner, G. A.; Hampe, O.; Jarrold, M. F. J. Phys. Chem. B 2001, 105, 4188.
