Prediction of structures and infrared spectra of the candidate circumstellar molecules SinOm

Accepted Manuscript Title: Prediction of structures and infrared spectra of the candidate circumstellar molecules Sin Om Author: Na Liu Li-Jia Zheng Hui-Yan Zhao Sheng-Li Qin Ying Liu PII: DOI: Reference:

S0009-2614(15)00915-X http://dx.doi.org/doi:10.1016/j.cplett.2015.11.046 CPLETT 33450

To appear in: Received date: Revised date: Accepted date:

4-9-2015 20-11-2015 26-11-2015

Please cite this article as: Na Liu, Li-Jia Zheng, Hui-Yan Zhao, Sheng-Li Qin, Ying Liu, Prediction of structures and infrared spectra of the candidate circumstellar molecules Sin Om , Chemical Physics Letters (2015), http://dx.doi.org/10.1016/j.cplett.2015.11.046 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights:

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1. We calculated the geometric and electronic structures of metastable states of silicon oxide clusters using density functional theory 2. The results show silicon-rich clusters and oxygen-rich clusters have different characteristics. 3. We calculated spectrums of the geometric structures to compare with observed spectra. 4. Possible structures which correspond to observed spectral lines are proposed.

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Si 2 O 3 -1; E

 0.051

Si 2 O 3 -2; E

 0.000

Si 2 O 3 -3; E

 0.087

Si 3 O 4 -1; E

 0.024

Si 3 O 4 -2; E

 0.000

Si 3 O 4 -3; E

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*Graphical Abstract (pictogram) (for review)

Si 3 O 5 -1; E

 0.019

Si 3 O 5 -2; E

 0.000

Si 4 O 5 -2; E

 0.083

us

cr

 0.002

 0.118

Si 4 O 5 -3; E

 0.130

 0.000

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te

Si 4 O 5 -1; E

d

M

an

Si 3 O 5 -3; E

Si 4 O 6 -1; E

 0.129

Si 4 O 6 -2; E

 0.000

Si 4 O 6 -3; E

 0.082

Si 5 O 6 -1; E

 0.000

Si 5 O 6 -2; E

 0.152

Si 5 O 6 -3; E

 0.084

Page 2 of 17 Si 5 O 7 -1; E

 0.000

Si 5 O 7 -2; E

 0.150

Si 5 O 7 -3; E

 0.074

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Prediction of structures and infrared spectra of the candidate circumstellar molecules SinOm Na Liua,b , Li-Jia Zhenga , Hui-Yan Zhaoa , Sheng-Li Qinc , Ying Liua,∗ a Department

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of Physics and Hebei Advanced Thin Film Laboratory, Hebei Normal University, Shijiazhuang 050024, Hebei, China b College of Mathematical and Physical Sciences, Shijiazhuang University of Economics, Shijiazhuang 050031, Hebei c Department of Physics science and technology, Yunnan University, Kunming 650091, Yunnan

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Abstract

A systematic study of the geometric structures of steady states and metastable

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states of silicon oxide clusters has been performed using density functional theory. We find that silicon-rich and oxygen-rich clusters have different characteristics. Oxygen-rich clusters usually have oxygen atoms on the edges of the

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clusters, but separated from others by Si atoms. However, silicon-rich clusters

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tend to have rings nested within each other. The spectra for the structures have been calculated to compare with observed spectra. The predicted structures and spectroscopic properties are expected to be useful for the identification of silicon oxide species in the interstellar medium.

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Keywords: Interstellar molecules, Infrared spectra

1. Introduction

Silicates and oxygen are present throughout circumstellar and interstellar

space [1, 2, 3, 4], silicon and oxygen being the main heavy elements beyond H and He in young stellar systems as well as being abundant in interplanetary dust particles. The dominant species in molecular astronomy, containing both Si and I Fully

documented templates are available in the elsarticle package on CTAN. author Email address: [email protected] (Ying Liu)

∗ Corresponding

Preprint submitted to Journal of LATEX Templates

November 20, 2015

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O, is expected to be the SiO molecule, and indeed SiO is one of the interstellar molecules that have been found [5]. Clustering of SiO molecules could favor the

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formation of (SiO)n motifs with oxygen-poor regions resembling silicon clusters [6, 7, 8] and oxygen-rich regions resembling silicates [9]. Beyond the study of

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interstellar molecules, the study of small silicon oxide clusters would provide useful information pertaining to silicon surface oxidation and defects in bulk

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silicon. Much interest has therefore been generated in investigation of Sin Om clusters both theoretically and experimentally [10, 11, 12, 13, 14].

Theoretical studies of possible stable structures of (SiO2 )n (n=1-8, 18) clus-

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ters were reported by Harkless et al. who used molecular dynamics and an additive pair interaction potential [12]. Neutral and charged (SiO)n (n=3-5) clusters and their photoemission spectra (PES) have been studied by Chelikowsky us-

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ing the pseudopotential method and Langevin dynamics [15]. There was good agreement between the simulated spectra and measured spectra. Cheung et al. evaluated the ground-state structures and electronic properties of Sin Om

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(n, m=1-8) clusters using both semiempirical molecular orbital and density func-

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tional (DFT) calculations [16]. In the course of an investigation of the formation of silicates from SiO molecules, Arthur showed the tendency Sin Om clusters to have oxygen-poor regions and oxygen-rich regions [17]. They also presented a

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first principles study of the optical absorption spectra of Sin On±x clusters and calculated the vibrational modes of the clusters. To date, there has been much research regarding silicon and oxygen molecules,

but all has been focused on the steady states of the clusters. In addition, there are inconsistencies between the results obtained by various groups [16, 17]. It is also important to note, however, that in interstellar space, molecules are not necessarily in the steady state, but may also exist in metastable states. In the process of the formation of interstellar molecules, it is quite possible that a large number of fragments may be produced, and they might survive in metastable states. In order to better understand spectroscopic observations of the interstellar and circumstellar mediums, it is therefore necessary to identify metastable silicon-oxygen structures. Whether these metastable molecules actually exist 2

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in circumstellar and interstellar environments can only be ascertained through signatures such as the optical spectra [18]. In this paper, therefore we have

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searched for Sin Om metastable molecules, and calculated their infrared absorp-

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tion spectra.

2. Computation Details

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The first step in the calculations described here was to identify an exhaustive range of possible shapes and bonding patterns for Sin Om clusters. We established as many initiating structures as possible for each molecule, and a

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broad search over these configurations, based on geometric optimization with no symmetry restrictions, was then performed in order to identify isomers with

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local energy minima. The calculations used the Becke and the Lee-Yang-Parr exchange-correlation functional (BLYP) [19, 20] and a double-numerical basis set with polarized functions (DNP) as implemented in the DMol3 package [21].

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After optimization and on the basis of energies and structures, some lowlying isomers were retained for further study. Further optimization was per-

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formed with the Gaussian 03 software. Geometric reoptimization of these isomers was carried out using density functional theory (DFT) based on the B3LYP [21, 22, 23] method with the 6-311+ G(d, p) basis set [24, 25] which yields more

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accurate results. Vibrational frequency calculations were performed to verify whether or not the structures had all positive frequencies or had an imaginary frequency. In the past, we compared the DFT/B3LYP method and the MP2 [26, 27] method for the calculation of the structure and spectra of interstellar molecules [28]. Since the most accurate energies are generally obtained at the CCSD (T) level, CCSD (T) single energy calculations were also performed to refine the energies. The B3LYP and MP2 results showed no significant differences, when compared to the results at the CCSD (T) level in either the structures or in the energy ordering of the various isomers. The MP2 method, however, is very computation intensive. In our work, we first calculated the structure and frequencies of Si2 O2 in

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four levels which are B3LYP, PBE [29, 30], PW91 [31] and MP2 to compare with the experimental values [32]. The structure parameters and frequencies of

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test calculations are summarized in Table 1. As shown, the difference is very

small expect the result of PBE in bond length, the values of B3LYP are closest

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to the experimental values in bond angle. In this paper the results shown were all obtained using the DFT/B3LYP method. In the light of published scale

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factors [33], the calculated spectral frequencies have been scaled by 0.9688 for comparison to experimental frequencies since it is well known that calculated

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frequencies overestimate the fundamental frequencies.

3. Results and discussion

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We have made an exhaustive search for steady and metastable structures of Sin Om (n, m=1-7) clusters. It should be noted that although few structures in which the numbers of Si and O atoms were significantly different such as Si6 O1 ,

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Si5 O1 , Si1 O7 and Si2 O7 were identified, but they were found to be energetically unfavorable and thus will not be discussed further. In total, we optimized

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the initial structures of more than 280 different configurations, most of which have not been previously reported. Our systematic study has enabled us to draw conclusions regarding the trends in the geometric structures of each type

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of silicon oxide cluster. Although the predicted ground-state structures are different for various values of m and n, most of them contain a ring or several

small rings.

We first focus on structures in which the numbers of Si and O atoms are the

same. Fig.1 illustrates the steady and metastable structures of silicon monoxide clusters (SiO)n . Of these structures, SiO is clearly linear, while for Si2 O2 only the square structure is stable and the result is in agreement with the experiment. With increasing numbers of atoms in the structures, however, there are more metastable structures. In addition a single ring structure and structures consisting of two ring structures linked by a single atom are found for Si3 O3 , Si4 O4 and Si5 O5 . It is noteworthy that in all cases with two rings, the rings

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are joined at a shared silicon atom. For Si4 O4 the ring structures of isomers 1 and 3 are distinctly different, and neither is planar, but their energy are almost

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equal. For Si5 O5 there is also a ring structure with the lowest energy, and there

are geometries connecting pentagons and hexagons. For Si6 O6 the structures

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are considerably more complicated with pentagon and hexagon subunits linked by a silicon atom, as well as clusters composed of two buckled rings, and the

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most stable structure with Cs symmetry.

We also investigated structures with twice as many oxygen atoms as silicon atoms, that is, silicon dioxide clusters. The structures of Sin O2n clusters are

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shown in Fig.2. All of them, except Si3 O6 -1 have rhomboid structures. In general, the larger the cluster size, the more rhombuses the clusters contain. Typically, these rhombuses are arranged in a chain with the rhombuses adjacent

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to each other. For Si3 O6 there is a hexagon with three oxygen atoms, and for Si4 O8 one structure is a quadrilateral connecting to a hexagon (Si4 O8 -2), and another has two quadrilaterals connected by two oxygen atoms to form

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a three-dimensional structure (Si4 O8 -3). A common characteristic of all these

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structures is that they have non-adjacent oxygen atoms attached to silicon atoms along the edges, and that the structures with rhombuses of the link have lower energies.

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Fig.3 shows the structures for clusters with 12 or fewer atoms subject to

the constraint that the number of oxygen atoms is either one or two greater than the number of silicon atoms. Stable structures with three or more excess oxygen atoms could not be identified. In most cases, the structures consist of connected rings. For Si3 O4 , Si3 O5 , Si4 O5 , Si4 O6 , Si5 O6 and Si5 O7 , there is one isomer with a hexagonal ring. That is, they have a growth model with a hexagon connecting to multiple rings which increase in size or number as the number of atoms increases. Another type of structures are still rhombuses connected to another and the number of rhombuses increases with the number of atoms. In these structures, it is not always the rhombuses shaped structures have lower energies, only when no more atoms in addition to the rhombuses. Otherwise the structures with a hexagonal ring connected with other shapes are more stable. 5

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Fig.4 shows the stable state and metastable state structures for several isomers where the total number of atoms is less than 11 and where the number

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of O atoms is either 1 or 2 less than the number of Si atoms. The ring structures seen above are still retained. We found that almost every molecule had

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a structure containing a pentagon. It is obvious that the three structures of Si3 O2 are analogous to Si2 O3 clusters although there are differences in the de-

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tails of the shape and bonding. Usually, when the number of silicon atoms is one more than the number of oxygen atoms, each oxygen atom has two neighboring atoms, although Si3 O2 -1 in Fig.4 is an exception. When the number of silicon

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atoms exceeds the number of oxygen by two, the oxygen atom has three or two neighbors. For Si6 O4 , there is a structure with C2h symmetry. These clusters are energetically less favorable and have unsaturated Si atom bonds, suggesting

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that they may not be present in significant amounts in the gas phase. It is well known that knowledge of the molecular spectrum is important in searching for and identifying interstellar molecules. We have therefore calculated

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the infrared absorption spectra of steady and metastable structures. Consid-

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ering the influence of anharmonic inter-mode interactions on the vibrational transition frequencies and intensities, we calculated anharmonic frequencies for all configurations shown above, but give only a few typical spectra which close

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to the experimentally observed values. It is known that calculated frequencies overestimate the observed frequencies in most cases, and calculated spectrums should be modified by different correction factors depending on the methods of calculation used. In this paper we used the B3LYP/6-311G+ (d, p) approach

for which the optimal correction factor is known to be 0.9688 [33]. Fig.5 shows several calculated results which lie very close to the unidentified infrared emission (UIE) bands [34]. The largest peak has a wave number which lies very close to one of the observed spectral lines values for the interstellar medium. The agreement in frequencies suggests that the results obtained in this work are sufficiently accurate to permit the identification of new species in the interstellar medium.

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4. Conclusions

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Geometric structure calculations have been carried out to search for metastable states in clusters of Si and O, and we have identified several possible metastable structures which have not been reported before. The results show that the clus-

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ters have different characteristics depending on the relative numbers of oxygen and the silicon atoms in the clusters. When oxygen is rich there are usually

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oxygen atoms bonded only to silicon atoms on the edges but when silicon is rich there are rings nested within each other. We have also calculated the infrared spectrums for various structures to help identify isomers which may correspond

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to observed spectral lines.

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5. Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11274089, U1331116, and 11304076), and the Science Foundation

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of Hebei Education department for Distinguished Young Scholar (Grant No.

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YQ2013008). We also acknowledge partially financial support from the 973 Project in China under Grant No. 2011CB606401. and the National Natural Science Foundation of China (Grant No. 11104071)

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References References

[1] A.K. Speck, M.J. Barlow, R.J. Sylvester, A.M. Hofmeister, Astron. Astrophys. Suppl. Ser. 146(2000)437.

[2] K.D. Gordon, A.N. Witt, D.G. Friedman, Astrophys. J. 498(1998)522. [3] S.A. Sandford, Meteorit. Planet. Sci. 31(1996)449. [4] T.M. Steel, W.W. Duley, Astrophys. J. 315(1987)337. [5] M.L. Ziurys, Proc. Natl. Acad. Sci. USA. 103(2006)12274. 7

Page 9 of 17

[6] V.G. Zubko, T.L. Smith, A.N. Witt, Astrophys. J. 511(1999)L57.

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[7] K.M. Ho, A.A. Shvartsburg, B. Pan, Z.Y. Lu, C.Z. Wang, J.G. Wacker, J. GFye, M.F. Jarrold, Nature, 392(1998)582.

Chem. C 112(2008)7097.

us

[9] J.A. Nuth, B. Donn, J. Chem. Phys. 78(1983)1618.

cr

[8] H. Wang, J. Sun, W.C. Lu, Z.S. Li, C.C. Sun, C.Z. Wang, K.M. Ho, J. Phys.

[10] L.C. Snyder, K. Raghavachari, J. Chem. Phys. 80(1984)5076.

an

[11] L.S. Wang, H. Wu, S.R. Desai, J. Fan, S.D. Colson, J. Phys. Chem. 100(1996)8697.

M

[12] J.A.W. Harkless, D.K. Stillinger, F.H. Stillinger, J. Phys. Chem. 100(1996)1098.

109(1998)1245.

d

[13] S.K. Nayak, B.K. Rao, S.N. Khanna, P. Jena, J. Chem. Phys.

78(1997)4450.

te

[14] L.S. Wang, J.B. Nicholas, M. Dupuis, H. Wu, S.D. Colson, Phys. Rev. Lett.

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

[15] J.R. Chelikowsky, Phys. Rev. B 57(1998)3333. [16] T.S. Chu, R.Q. Zhang, H.F. Cheung, J. Phys. Chem. B 105(2001)1705. [17] A.C. Reber, S. Paranthaman, P.A. Clayborne, S.N. Khanna, A.W.Jr. Castleman, ACS NANO, 2(2008)1729.

[18] U.P. Vijh, Astrophys. J. 633(2005)262. [19] A.D. Becke, Phys. Rev. A 38(1988)3098. [20] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37(1988)785. [21] B. Delley, J. Chem. Phys. 92(1990)508. [22] W.R. Wadt, P.J. Hay, J. Chem. Phys. 82(1985)284. 8

Page 10 of 17

[23] A.D. Becke, J. Chem. Phys. 98(1993)5648.

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[24] A.D. McLean, G.S. Chandler, J. Chem. Phys. 72(1980)5639. [25] R. Krishnan, J.S. Binkley, R. Seeger, J.A. Pople, J. Chem. Phys.

cr

72(1980)650.

[26] M. Head-Gordon, J.A. Pople, M.J. Frisch, Chem. Phys. Lett. 153(1988)503.

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[27] M.J. Frisch, M. Head-Gordon, J.A. Pople, Chem. Phys. Lett. 166(1990)281.

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[28] H.Y. Zhao, L. Wang, J. Li, Y. Liu, Comput. Theor. Chem. 19(2012)994. [29] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77(1996)3865.

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[30] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 78(1997)1396. [31] J.P. Perdew, Y. Wang, Phys. Rev. B 45(1992)13244.

d

[32] J.S. Anderson, J.S. Ogden. J. Chem. Phys. 51(1969)4189.

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[33] J.P. Merrick, D. Moran, L. Radom, J. Phys. Chem. A 111(2007)11683. [34] K. Sun, Y. Zhang, Nature 479(2011)80.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

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ip t cr us an

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Table 1: Calculated atomic bond lengths (in ˚ A)and band angles of the lowest-stable Si2 O2 structure. The experiment values (Expt.) are listed.

6

SiOSi

OSiO

B3LYP

1.714

93.12

86.88◦

MP2

1.717

93.65◦

86.35◦

PBE

1.734

92.48◦

87.52◦

PW91

1.713

93.22◦

86.78◦

Expt.

1.71

93◦

87◦

te

◦

6

d

Si-O bond length

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

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ip t Si4O4 1; E 0 00 ∆ = .

Si4O4 2 ; E 0 04 ∆ = .

cr

Si3O3 1; E 0 00 ∆ = .

Si3O3 2 ; E 0 06 ∆ = .

an

us

Si2O2 ; E 0 00 ∆ = .

Si4O4 3 ; E 0 00(3) ∆ = .

M d

Si5O5 2 ; E 0 03 ∆ = .

te

Si5O5 1; E 0 00 ∆ = .

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Si6O6 1; E 0 00 ∆ = .

Si6O6 2 ; E 0 03 ∆ = .

Si5O5 3 ; E 0 0 1 ∆ = .

Si6O6 3 ; E 0 02 ∆ = .

Figure 1: (Color online) Schematic representations of Sin Om (n=m) structures at the

B3LYP/6-311+ G(d, p) level. The red circles represent the O atoms, and the yellow circles represent the Si atoms. Also shown, in the label below each structure, are the energies (a.u.) relative to the global minimum.

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Page 13 of 17

ip t cr

Si2O4 2 ; E 0 00 ∆ = .

an

us

Si2O4 1; E 0 18 ∆ = .

Si3O6 2 ; E 0 00 ∆ = .

d

M

Si3O6 1; E 0 06 ∆ = .

Si4O8 1; E 0 00 ∆ = .

te

Si3O6 3 ; E 0 0 1 ∆ = .

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Si4O8 2 ; E 0 0 1 ∆ = .

Si4O8 3 ; E 0 09 ∆ = .

Figure 2: (Color online) Schematic representations of the Sin O2n clusters at the B3LYP/6311+ G(d, p) level. The red circles represent the O atoms, and the yellow circles represent the Si atoms. Also shown, in the label below each structure, are the energies (a.u.) relative to the global minimum.

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Si2O3>3; ∆E = 0.09

Si 3O4>1; ∆E = 0.02

Si 3O4>2; ∆E = 0.00

Si 3O4>3; ∆E = 0.01

ip t

Si2O3>2; ∆E = 0.00

Si 3O5>2; ∆E = 0.00

Si4O5>1; ∆E = 0.00

Si4O5>2; ∆E = 0.08

Si 3O5>3; ∆E = 0. 12

Si4O5>3; ∆E = 0. 13

te

d

M

an

Si 3O5>1; ∆E = 0.02

us

cr

Si2O3>1; ∆E = 0.05

Si4O6>1; ∆E = 0. 13

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Si4O6>2; ∆E = 0.00

Si4O6>3; ∆E = 0.08

Si 5O6>1; ∆E = 0.00

Si 5O6>2; ∆E = 0. 15

Si 5O6>3; ∆E = 0.08

Si 5O7>1; ∆E = 0.00

Si 5O7>2; ∆E = 0. 15

Si 5O7>3; ∆E = 0.07

Figure 3: (Color online) Schematic representations of the Sin Om clusters with m=n+1,2 at the B3LYP/6-311+ G(d, p) level. The red circles represent the O atoms, the yellow circles represent the Si atoms. Also shown, in the label below each structure, are the energies (a.u.) relative to the global minimum.

Page 15 of 17

Si3O2V3; E ∆

ip t

Si3O2V2; E 0 00 ∆ = .

= 0 .03

= 0 .02

Si4O3V2; E ∆

Si4O3V1; E

4

= 0 .0

Si4O3V3; E ∆

= 0 .03

= 0 .00

Si5O4V1; E ∆

= 0 .00

Si5O3V2; E ∆

= 0 .02

Si5O3V3; E

Si5O4V2; E ∆

= 0 .02

Si5O4V3; E

Si6O4V1; E 0 02 ∆ = .

Si6O4V2; E ∆

= 0 .00

Si6O4V3; E 0 07 ∆ = .

Si6O5V1; E ∆

Si6O5V2; E ∆

= 0 .0

∆ = 0 .05

te

d

Si5O3V1; E ∆

M

an

∆ = 0.00

us

cr

Si3O2V1; E ∆

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

= 0 .00

4

∆ = 0 .04

Si6O5V3; E ∆

= 0 .05

Figure 4: (Color online) Schematic representations of the Sin Om clusters with m=n-1,2 at the B3LYP/6-311+ G(d, p) level. The red circles represent the O atoms, the yellow circles represent the Si atoms. Also shown, in the label below each structure, are the energies (a.u.) relative to the global minimum.

Page 16 of 17

exp:740.74 cal : 737.46

400

t nse In

200 100 0

0

100

200

300

400

In

300 200 100 0

100 200 300 400 500 600 700 800 900 1000

te

0

900

d

t nse

800

M

400 ti yo

700

exp:884 .95 cal : 884.38

500 IRf

600

an

600

500

us

it yo

cr

300 IRf

ip t

500

700

exp :740 .74 cal : 742.08

600 500

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

IRf

400

it yo

300

In

200

t nse

100 0

0

100

200

300 400 500 600 Frequency(cmå1)

700

800

900

Figure 5: The infrared absorption spectra of several configurations at the B3LYP/6-311+ G(d, p) level. The values for the frequencies are in cm−1 .

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