Structure and Stability of Tube and Cage (SiH)60 - The Journal of

Apr 1, 2009 - Among all 1812 all-exo (SiH)60 fullerene isomers, the most stable isomer has a tubelike configuration (D5d) with twelve five-membered ri...
0 downloads 0 Views 880KB Size
Download PDF
6887

2009, 113, 6887–6890 Published on Web 04/01/2009

Structure and Stability of Tube and Cage (SiH)60 Jianfeng Jia,† Yan-Ni Lai,† Hai-Shun Wu,*,† and Haijun Jiao*,‡ School of Chemistry and Materials Science, Shanxi Normal UniVersity, Linfen, 041004, China, and Leibniz-Institut fu¨r Katalyse e.V. an der UniVersita¨t Rostock, Albert-Einstein-Strasse 29a, 18059 Rostock, Germany ReceiVed: February 8, 2009; ReVised Manuscript ReceiVed: March 23, 2009

Among all 1812 all-exo (SiH)60 fullerene isomers, the most stable isomer has a tubelike configuration (D5d) with twelve five-membered rings fused and located at the ends of the tube. The most stable cage isomer can admit ten to twelve endo Si-H bonds (H10@Si60H50 and H12@Si60H48), and they also represent the most stable (SiH)60 isomers. It is found that (SiH)60 isomers have much lower angle and torsion strains than (CH)60 isomers. Soon after the discovery of C60 fullerene, the structure of Si60 has become a subject of extensive theoretical studies. Unlike C60, Si60 cage in Ih symmetry is not an energy minimum structure.1 Instead, Si60 and other Sin clusters are found to favor distorted or stuffed cage structures.2 A way to stabilize Si cages is to saturate the dangling bonds of Si with H atoms, as proved experimentally3 and theoretically.4 Computation by Kumar and Kawazoe5 suggested that (SiH)n (n ) 8-20, 24, 28) clusters have similar cage structures as their (CH)n analogous.6,7 Computation by Wang et al.8 showed that (SiH)60 in Ih symmetry is an energetically favorable state and is stable over hydrogen attack and qualified as a potential hydrogen storage medium.9 Recently, we have found that for both (CH)60 and (CF)60, a tubelike isomer (D5d symmetry) with fused five-membered rings located at the ends of the tube is more stable than the Ih cage isomer at the level of B3LYP density functional theory calculations.10,11 It also is found that both cage and tube isomers with endo C-H bonds are more stable than the all-exo cage and tube isomers. The endo H10@C60H50 cage isomer is more stable than the most stable endo H4@C60H56 tube isomer, and represents the most stable (CH)60 isomer. In contrast, the endo F4@C60F56 tube isomer is more stable than the most stable endo F8@C60F52 cage isomer, and represents the most stable (CF)60 isomer. Inspired by these structure and stability relationships of (CH)60 and (CF)60, we have carried out computations on the structure and stability of (SiH)60 isomers. All structures have been optimized first by using the HF method and the Lanl2dz basis set, and the selected stable structures are characterized at the same level as energy minima by frequency calculations. These selected stable structures are further refined at the B3LYP level with the 6-311G(d,p) basis set and the obtained relative energies and structural parameters are used for discussion. The optimized structures are shown in Figure 1 and the computed relative energies are listed in Table 1. The gauge-independent atomic orbital (GIAO)12 method is * To whom correspondence should be addressed. E-mail: (H.-S.W.) [email protected]; (H.J.) [email protected]. † Shanxi Normal University. ‡ Leibniz-Institut fu¨r Katalyse e.V. an der Universita¨t Rostock.

10.1021/jp901158p CCC: $40.75

used for calculations of 29Si NMR shielding constants and the calculated shielding constants are converted to NMR chemical shifts with the reference compound tetramethylsilane (TMS). All calculations have been performed with the Gaussian 03 program.13 All 1812 all-exo (SiH)60 fullerene isomers generated by fullgen program14 were optimized at the HF/Lanl2dz level of theory. The Ih isomer 1 in Figure 1 ranks only the 431st place in the stability order of all-exo (SiH)60 fullerene isomers. Like (CH)60 and (CF)60, the most stable all-exo (SiH)60 isomer is a tube structure (6) in D5d symmetry with twelve five-membered rings fused and located at the ends of the tube and is lower in energy than 1 by 257.5 kJ/mol at B3LYP/6-311G(d,p) (Table 1). However, this energy difference is much smaller than that for (CF)60 (1866.9 kJ/mol)10 and (CH)60 (970.6 kJ/mol).11 In contrast to 1 with all Si-H bonds in eclipsed conformation, 6 has 50 H-Si-Si-H dihedral angles on the boatlike sixmembered rings in gauche conformation with a torsion of 19.0, 40.4, and 40.7°, respectively, and 40 H-Si-Si-H dihedral angles in eclipsed conformation (20 on the five-membered rings at the ends of the tube and 20 on the six-membered rings of the tube wall). Moreover, the distances of the nonbonded hydrogen atoms of the eclipsed Si-H bonds in 6 (3.45 and 3.41 Å on the five-membered rings, and 3.12 and 3.11 Å on the six-membered rings) are longer than those in 1 (2.95 and 3.00 Å). These gauche conformations of the Si-H bonds and the longer nonbonded hydrogen distances reduce the nonbonded repulsive interaction and contribute to the stability 6 over 1. As found for (CH)60 and (CF)60,11 angle distortion is also a factor affecting the stability of (SiH)60 isomers. Here, we used the angle distortion (AD) of a silicon vertex of (SiH)60 isomers according to eq 1, where R and β are the Si-Si-Si and Si-Si-H angles at the silicon atom, respectively, and their references (110.95 and 107.95°) are taken from the fully optimized isobutasilane (SiH3)3SiH. The calculated AD for the silicon atoms in 1 is 39.9°, while those in 6 ranging from 17.4 to 34.9° (the average value is 28.7°) are smaller. This indicates that tube isomer 6 has lower angle strain than cage isomer 1.  2009 American Chemical Society

6888 J. Phys. Chem. C, Vol. 113, No. 17, 2009

AD )

∑ |110.95◦-R| + ∑ |107.95◦-β|

Letters

(1)

To understand why the energy difference between cage (1) and tube (6) (SiH)60 is smaller than that between cage and tube (CH)60, the changes in torsion strain and angle strain from cage to tube isomers are considered. For estimating torsion strain we used Si2H6 and C2H6 as models. For Si2H6, the energy difference between staggered (D3d) and eclipsed (D3h) conformations is about 5 kJ/mol, while that for C2H6 is about 12 kJ/ mol.15 This indicates that eclipsed C-H bonds have stronger torsion strain than eclipsed Si-H bonds; and therefore cage (SiH)60 (1) has lower torsion strain than cage (CH)60. For estimating angle strain we used isobutasilane (SiH3)3SiH and isobutane (CH3)3CH, both in C3V symmetry as models. For fully

optimized (SiH3)3SiH, the central SiSiH angle is 107.95°; reducing this angle to 102.95° raises the energy of (SiH3)3SiH by about 4.2 kJ/mol. For (CH3)3CH, reducing the central CCH angle from the fully optimized 107.75 to 102.75° raises the energy by about 12.5 kJ/mol. This shows that the tetrahedral Si-H center is more elastic or flexible than the corresponding C-H center, and consequently cage (SiH)60 (1) has lower angle strain than cage (CH)60. The total strain energy difference of (SiH)60 and (CH)60 can also be compared on the basis of the homodesmotic reaction eqs 2 and 3. The negative reaction energies show clearly that (CH)60 and (SiH)60 in both cage and tube configurations are strained, but (CH)60 has much greater strain than (SiH)60 for both cage and tube structures, respectively. For example, the

Figure 1. B3LYP/6-311G(d,p) (SiH)60 cage (1-5) and tube (6-10) structures (inside hydrogen atoms in red).

Letters

J. Phys. Chem. C, Vol. 113, No. 17, 2009 6889

TABLE 1: Relative Energies (Erel, kJ/mol) of (SiH)60, (CH)60 and (CF)60 Isomers

a

(SiH)60

Erela

(CH)60

Erelb

(CF)60

Erelc

(SiH)60/Ih (1) H8@Si60H52/D2 (2) H10@Si60H50/C2 (3) H12@Si60H48/Ci (4) H14@Si60H46/Ci (5) (SiH)60/D5d (6) H2@Si60H58/C2h (7) H4@Si60H56/C2h (8) H6@Si60H54/C2h (9) H8@Si60H52/Ci (10)

0.0 -398.9 -441.2 -442.3 -387.3 -257.5 -331.7 -390.3 -398.0 -389.3

(CH)60/Ih H8@C60H52/D2 H10@C60H50/C2 H12@C60H48/Ci

0.0 -1480.7 -1565.6 -1503.7

(CF)60/Ih F8@C60F52/D2 F10@C60F50/C2 F12@C60F48/Ci

0.0 -2408.3 -2187.0 -1714.2

(CH)60/D5d H2@C60H58/C2h H4@C60H56/C2 H6@C60H54/C2

-970.6 -1153.9 -1255.2 -1232.6

(CF)60/D5d F2@C60F58/C2h F4@C60F56/C2 F6@C60F54/C2

-1866.9 -2273.6 -2502.9 -1844.3

At B3LYP/6-311G(d,p). b At B3LYP/6-31G(d,p) (ref 11). c At B3LYP/6-31G(d) (ref 10).

strain energy of the cage and tube isomers of (CH)60 (40.7 vs 24.7 kJ/mol per CH) is much greater than that of (SiH)60 isomers 1 and 6 (11.6 and 7.3 kJ/mol per SiH). The strain energy between the cage isomers (40.7 vs 11.6 kJ/mol) is larger than that between the tube isomers (24.7 vs 7.3 kJ/mol).

or D5d) + (3 ⁄ 2)C2H6(D3d) ) (CH3)3CH(C3V) kJ ⁄ mol ∆E((CH)60 ⁄ D5d) ) -24.7 kJ/mol

(1 ⁄ 60)(CH)60(Ih

∆E((CH)60 ⁄ Ih) ) -40.7

(2) (1 ⁄ 60)(SiH)60(1 or 6) + (3 ⁄ 2)Si2H6(D3d) ) (SiH3)3SiH(C3V) ∆E(1) ) -11.6 kJ/mol ∆E(6) ) -7.3 kJ/mol (3) Since some endo C-H bonds in (CH)60 cage and tube,11,16 (CH)80 and (CH)180 cages,17 and C-F bonds in (CF)60 cage and tube10,18 can reduce the strain and stabilize the structures considerably, we are interested to know the number and strength of the stabilizing effect of endo Si-H bonds in (SiH)60 cage and tube. Structures 2, 3, 4, and 5 are cage isomers with 8 (H8@Si60H52), 10 (H10@Si60H50), 12 (H12@Si60H48), and 14 (H14@Si60H46) endo Si-H bonds, respectively. As given in Table 1, 3 (H10@Si60H50) and 4 (H12@Si60H48) are close in energy and they also are the most stable cage isomers, while the all-exo cage isomer 1 is higher in energy by about 442 kJ/ mol. For (CH)60, the most stable cage isomer has 10 endo C-H bonds (H10@C60H50), and isomer with 12 endo C-H bonds (H12@C60H48) is higher in energy by about 62 kJ/mol.11 This can be attributed to the larger cage size of (SiH)60 over (CH)60 (diameter 10.8 vs 7.1 Å) on one hand and on the other hand the lower torsion as well as angle strains of (SiH)60 over (CH)60. Structures 7, 8, 9, and 10 are tube isomers with two (H2@Si60H58), four (H4@Si60H56), six (H6@Si60H54), and eight (H8@Si60H52) endo Si-H bonds, respectively. As shown in Table 1, the most stable endo tube isomer is 9 (H6@Si60H54), tightly followed by 8 (H4@Si60H56) and 10 (H8@Si60H52) within 10 kJ/mol, while the all-exo tube isomer (6) is less stable by about 132-141 kJ/mol. This indicates that tube (SiH)60 cage can admit up to eight endo Si-H bonds, while tube (CH)60 tube can only admit four endo C-H bonds. The endo H10@Si60H50 and H12@Si60H48 cage isomers represent the most stable (SiH)60 isomer. For comparison, the endo H10@C60H50/C2 cage isomer is the most stable (CH)60 isomer,11 while the most stable (CF)60 isomer is an endo tube isomer (F4@C60F56/C2).10 Each nonadjacent endo bond can reduce the torsion and angle strains in cage and tube isomers. Because of its larger diameter (10.8 vs 7.1 Å) over (CH)60 cage, (SiH)60 cage can admit 10 to

12 endo Si-H bonds, while (CH)60 cage can admit 10 endo C-H bonds, and (CF)60 cage can only admit 8 endo C-F bonds. In isomer 4 (H12@Si60H48/Ci), the shortest distance between the endo hydrogen atoms is 2.69 Å, while that in the most stable endo H10@C60H50/C2 cage isomer is about 2.01 Å.11 Because of its larger diameter and longer tube length (7.0 and 18.6 Å) over (CH)60 tube (4.6 and 12.2 Å), tube (SiH)60 can admit more endo bonds than (CH)60. In the most stable endo tube isomer 9 with six endo Si-H bonds, the shortest nonbonded distance of the endo hydrogen is 1.92 Å, while in the most stable endo H4@C60H56/C2 tube with four endo C-H bonds, the shortest nonbonded distance of the endo hydrogen is 1.68 Å.11 In addition, the 29Si NMR chemical shifts of isomers 1, 4, 5, and 9 are calculated at B3LYP/6-311G(d,p) by using the GIAO method. The calculated 29Si NMR chemical shifts for Si60H60 isomers range from -50 to -110 ppm, and they are in the range of silanes. For example, isomer 1 has unique shift of -104.8 ppm within its Ih symmetry. Taking 12 Si-H bonds into the cage, isomer 4 has shifts from -83.6 to -101.0 ppm. Isomer 5 has shifts from -52.7 to -111.0 ppm, while endo isomer 9 has shifts from -47.4 to -107.9 ppm. All detailed data are given in Supporting Information. At the B3LYP/6-311G(d,p) level of density functional theory, the most stable all-exo (SiH)60 isomer has a tube configuration (D5d) with 12 five-membered rings fused and located at the ends of the tube among all 1812 possibilities. Introduction of Si-H bonds into the cage and tube structures reduces the angle and torsion strains considerably. The most stable tube (SiH)60 isomer can admit four to eight endo Si-H bonds in close energy, while the most stable (CH)60 tube isomer can admit only four endo C-H bonds. The most stable cage isomer can admit 10 to 12 endo Si-H bonds (H10@Si60H50 and H12@Si60H48), and they also represent the most stable (SiH)60 isomers, and the most stable (CH)60 isomer can admit 10 endo C-H bonds (H10@C60H50). (SiH)60 cage and tube isomers have much lower angle and torsion strains than (CH)60 cage and tube isomers. Acknowledgment. This work was supported by the Natural Science Foundations of China (20673070). Supporting Information Available: Total electronic energies of all 1812 all-exo (SiH)60 isomers at HF/Lanl2dz; total electronic energies for endo cage isomers (2-5) and endo tube isomers (7-10) at HF/Lanl2dz; and coordinates and total electronic energies of 1-10 and reference systems at B3LYP/ 6-311G(d,p). The detailed 29Si NMR chemical shifts data for isomers 1, 4, 5, and 9 are included. This material is available free of charge via the Internet at http://pubs.acs.org.

6890 J. Phys. Chem. C, Vol. 113, No. 17, 2009 References and Notes (1) (a) Chen, Z.; Jiao, H.; Seifert, G.; Horn, A. H. C.; Yu, D.; Clark, T.; Thiel, W.; Schleyer, P. v. R. J. Comput. Chem. 2003, 24, 948. (b) Yu, D. K.; Zhang, R. Q.; Lee, S. T. Phys. ReV. B 2002, 65, 245417. (c) Song, J.; Ulloa, S. E.; Drabold, D. A. Phys. ReV. B 1996, 53, 8042. (d) Li, B. X.; Cao, P. L.; Que, D. L. Phys. ReV. B 2000, 61, 1685. (e) Li, B. X.; Jiang, M.; Cao, P. L. J. Phys.: Condens. Matter 1999, 11, 8517. (f) Menon, M.; Subbaswamy, K. R. Chem. Phys. Lett. 1994, 219, 219. (g) Khan, F. S.; Broughton, J. Q. Phys. ReV. B 1991, 43, 11754. (2) (a) Li, B. X.; Cao, P. L. J. Phys.: Condens. Matter 2001, 13, 10865. (b) Zhou, R. L.; Pan, B. C. Phys. Lett. A 2007, 368, 396. (c) Guo, L.-J.; Zhao, G.-F.; Gu, Y.-Z.; Liu, X.; Zeng, Z. Phys. ReV. B 2008, 77, 195417. (d) Yoo, S.; Shao, N.; Zeng, X. C. J. Chem. Phys. 2008, 128, 104316. (e) Zhao, J.; Ma, L.; Wen, B. J. Phys.: Condens. Matter 2007, 19, 226208. (f) Fthenakis, Z. G.; Havenith, R. W. A.; Menon, M.; Fowler, P. W. Phys. ReV. B 2007, 75, 155435. (g) On˜a, O.; Bazterra, V. E.; Caputo, M. C.; Facelli, J. C.; Fuentealba, P.; Ferraro, M. B. Phys. ReV. A 2006, 73, 053203. (3) (a) Rechtsteiner, G. A.; Hampe, O.; Jarrold, M. F. J. Phys. Chem. B 2001, 105, 4188. (b) Belomion, G.; Therrien, J.; Smith, A.; Rao, S.; Twesten, R.; Chaieb, S.; Nayfeh, M. H.; Wagner, L.; Mitas, L. Appl. Phys. Lett. 2002, 80, 841. (4) (a) Kumar, V.; Kawazoe, Y. Phys. ReV. Lett. 2003, 90, 055502. (b) Galashev, A. E. Semiconductors 2008, 42, 596. (5) Kumar, V.; Kawazoe, Y. Phys. ReV. B 2007, 75, 155425. (6) Earley, C. W. J. Phys. Chem. A 2000, 104, 6622. (7) Wu, H.-S.; Qing, X.-F.; Xu, X.-H.; Jiao, H.; Schleyer, P. v. R. J. Am. Chem. Soc. 2005, 127, 2334. (8) Wang, L.; Li, D.; Yang, D. Mol. Simulat. 2006, 32, 663. (9) (a) Zhang, D.; Ma, C.; Liu, C. J. Phys. Chem. C 2007, 111, 17099. (b) Barman, S.; Sen, P.; Das, G. P. J. Phys. Chem. C 2008, 112, 19963. (10) Jia, J.; Wu, H.-S.; Xu, X.-H.; Zhang, X.-M.; Jiao, H. J. Am. Chem. Soc. 2008, 130, 3985. (11) Jia, J.; Wu, H.-S.; Xu, X.-H.; Zhang, X.-M.; Jiao, H. Org. Lett. 2008, 10, 2573.

Letters (12) Wolinski, K.; Hilton, J. F.; Pulay, P. J. Am. Chem. Soc. 1990, 112, 8251. (13) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C02; Gaussian, Inc.: Wallingford, CT, 2004. (14) Brinkmann, G.; McKay, B. The program fullgen and its documentation are obtainable at http://cs.anu.edu.au/∼bdm/plantri/. (15) (a) Urban, J.; Schreiner, P. R.; Vacek, G.; Schleyer, P. v. R.; Huang, J. Q.; Leszczynski, J. Chem. Phys. Lett. 1997, 264, 441. (b) Schleyer, P. v. R.; Kaupp, M.; Hampel, F.; Bremer, M.; Mislow, K. J. Am. Chem. Soc. 1992, 114, 6791. (16) (a) Saunders, M. Science 1991, 253, 330. (b) Guo, T.; Scuseria, G. E. Chem. Phys. Lett. 1992, 191, 527. (c) Dunlap, B. I.; Brenner, D. W.; Mintmire, J. W.; Mowrey, R. C.; White, C. T. J. Phys. Chem. 1991, 95, 5763. (17) Linnolahti, M.; Karttunen, A. J.; Pakkanen, T. A. ChemPhysChem 2006, 7, 1661. (18) (a) Scuseria, G. E.; Odom, G. K. Chem. Phys. Lett. 1992, 195, 531. (b) Clare, B. W.; Kepert, D. L. J. Mol. Struct. (Theochem) 1996, 367, 1.

JP901158P