Rate Coefficient for the Reaction SiO + Si 2 O 2 at T ) 10-1000 K Andre ´ S. Pimentel,* Francisco das C. A. Lima, and Albe ´ rico B. F. da Silva Departamento de Quı ´mica e Fı ´sica Molecular, Instituto de Quı ´mica de Sa ˜ o Carlos, UniVersidade de Sa ˜ o Paulo, AV. Trabalhador Sa ˜ o Carlense, 400 Caixa Postal 780, Sa ˜ o Carlos, SP 13560-970 Brazil ReceiVed: August 23, 2006; In Final Form: October 9, 2006 The reaction paths for the formation of Si 3 O 3 molecules have been investigated at high level ab initio quantum chemical calculations by using the QCISD method with the 6-311++G(d,p) basis set. The cis-Si 2 O 2 isomer does not participate in the chemical mechanism for the formation of Si 3 O 3 molecules. Although the SiO + cis-Si 2 O 2 reaction is exothermic and spontaneous, it is not expected to explain the growth mechanism of Si 3 O 3 in the interstellar silicate grains of circumstellar envelopes surrounding M-type giants. The reaction of SiO with cyclic Si 2 O 2 molecules is exothermic, is spontaneous, and has a nonplanar transition state. The Gibbs free energy for the transition state formation, (ΔG 0 # ), is around 5.5 kcal mol -1 at 298 K. The bimolecular rate coefficient for this reaction, k T , is about 1 × 10 -12 cm 3 molecule -1 s -1 at 298 K and in the collision limit, 1.5 × 10 -10 cm 3 molecule -1 s -1 , at 500 K. The activation energy, E a , is about 8 kcal mol -1 . The enthalpy of Si 3 O 3 fragmentation is 53.9 kcal mol -1 at 298 K. The SiO + cyclic Si 2 O 2 reaction is expected to be the most prominent reaction path for the Si 3 O 3 formation in interstellar environment and fabrication of silicon nanowires. Introduction Silicon monoxide (SiO) materials are the most abundant constituent on Earth, and SiO itself, one of the most reactive molecular species composed of cosmically abundant mineral forming elements. 1,2 The SiO space density in dust is around 3.0 × 10 22 molecules cm -3 , and the SiO column density in circumstellar shells is around 4.1 × 10 14 molecules cm -2 . 3,4 It has been conjectured that the formation of pure oligomeric silicon monoxides ((SiO) x , x ) 2 to 4) should provide the first surface for the kinetics of condensed phase growth of amorphous interstellar silicate grains in the circumstellar envelopes sur- rounding M-type giants. 5,6 Furthermore, this growth mechanism seems to involve the formation of silicates through the loss of Si atoms during the nucleation and growth of SiO oligomers. 7,8 They also play a crucial role in many areas of modern technology, including nanotechnology, glass, and fiber optics industries. The most important example for the application of silicon monoxide is the enhancement in the growth of silicon nanowires during the synthesis of these materials, suggesting the importance of the small silicon monoxide clusters studied in this article. 7,8 Therefore, the study of the elementary associa- tion reactions underlying the nucleation process of SiO is critical in order to understand the formation process of interstellar silicate grains and growth of silicon nanowires. Unfortunately, it is difficult to experimentally study the formation of SiO oligomers due to the high SiO reactivity and the unlikely isolation of the target chemical reaction. Ab initio quantum chemical calculations may offer an alternative way for the understanding of the chemistry of interstellar silicate grains formation in a wide variety of astronomical regions, and the growth of silicon nanowires in different manufacture conditions. For instance, the temperature in circumstellar shells ranges from 1000 down to 10 K, 3,4 and in the production process of silicon nanowires it is from 300 to 1300 K. The SiO vapor pressure is around 2 × 10 -6 Torr at 400 K and evaporates completely at 1400 K. Thus, there is an appreciable SiO concentration in the gas phase of circumstellar shells and the production process of silicon nanowires. Snyder and Raghavachari (1984) 9 have performed a quantum chemical calculation for the dimerization of silicon monoxide. Using fourth-order Møller-Plesset perturbation theory (MP4), they have found a value of -43.0 kcal mol -1 for the heat of formation of the dimer, which is in excellent agreement with the only experimental value, -44.6 ( 3.0 kcal mol -1 . 10 They have also calculated the potential energy surface for this reaction and found no evidence for an energy barrier. Schnockel et al. (1989) 11 have investigated the Si 2 O 2 dissociation by MP4 and found that it is + 43.7 kcal mol -1 . Friesen et al. (1999) 12 have also calculated the oligomerization energies for the SiO species using density functional theory (DFT). They have obtained -48.0 and -57.6 kcal mol -1 for the SiO dimerization and trimerization reactions, respectively. Lu et al. (2003) 7 also calculated by DFT that the Si 2 O 2 and Si 3 O 3 dissociation energies are 46.7 and 54.8 kcal mol -1 , respectively. However, using the MP2 theory, they found 41.6 and 50.4 kcal mol -1 for the same reactions. Thus, it is very important to apply a higher level of theory to this system in order to achieve a better agreement with this data as indicated by Avromov et al. 8 Anderson et al. (1968), 13 Anderson and Ogden (1969), 14 and Ogden (1977) 15 have shown by infrared analysis that SiO, cyclic Si 2 O 2 and Si 3 O 3 molecules are important intermediates in the SiO oligomerization process. Hastie et al. (1969) 16 assigned additional features to pentameric SiO species as well as confirming those features assigned in the literature. 14 Later, Khanna et al. (1981) 17 have also assigned basically the same features using infrared and Raman spectroscopies. However, they have also suggested that the “open” cis-Si 2 O 2 structure is likely to be generated in the process. In fact, it has a higher reactivity compared with the cyclic structure due to their unpaired electrons. Thus, the cis-Si 2 O 2 species may readily react with SiO monomeric or dimeric species to form higher SiO * To whom correspondence should be addressed. E-mail: pimentel@iqsc.usp.br. 13221 J. Phys. Chem. A 2006, 110, 13221-13226 10.1021/jp065462z CCC: $33.50 © 2006 American Chemical Society Published on Web 11/16/2006 Downloaded by PUC RJ on August 31, 2015 | http://pubs.acs.org Publication Date (Web): November 16, 2006 | doi: 10.1021/jp065462z