Possible Reaction Paths of Small Silicon Clusters with Oxygen

Jul 21, 2010 - This paper reports the possible reaction paths of small silicon clusters Sin (n = 1−4) with the oxygen molecule based on density func...
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J. Phys. Chem. C 2010, 114, 13196–13203

Possible Reaction Paths of Small Silicon Clusters with Oxygen Explored with Density Functional Theory Shu-Ping Huang and Rui-Qin Zhang* Department of Physics and Materials Science, City UniVersity of Hong Kong, Hong Kong SAR, China ReceiVed: April 15, 2010; ReVised Manuscript ReceiVed: July 1, 2010

This paper reports the possible reaction paths of small silicon clusters Sin (n ) 1-4) with the oxygen molecule based on density functional theoretical calculations. It is shown that their potential energy surfaces are very complex, involving spin conserving and inversion. There are no net barriers on any of the proposed reaction paths for the oxidation of Si, Si2, and Si3 clusters, but their reverse reactions are endothermic with high energy barriers. The Si4 cluster cannot react with the ground-state, spin-triplet oxygen molecule because of the potential barrier of its spin inversion. The most favorable and accessible reaction path for Si/Si2/Si3 + O2 may be the one with a high exothermic value since there are no net barriers on the potential energy surfaces. The reactions of silicon clusters with the oxygen molecule are easier than the oxidations of their corresponding suboxides. Our findings are expected to provide valuable information to help understand the growth mechanism of silicon nanowires. Introduction Semiconductor cluster systems, such as silicon and silicon oxide,1–7 have been the subject of many experimental and theoretical investigations. Experiments have shown that the growth of silicon nanowires will be greatly enhanced if silicon oxide is present in the precursors during the synthesis.8 These silicon nanowire synthesis experiments involved a two-step process. The first step was to evaporate the solid state source (a powdered mixture of silicon and SiO2 or SiO powder) at a high temperature. Then the SiO amorphous vapor phase was carried to the substrate by a carrying gas for nucleation. The yields of silicon nanostructures are dependent on the siliconoxygen ratios. Consequently, the chemical reactivity of silicon and silicon oxide clusters can provide valuable information to help understand the growth mechanism of silicon nanowires. The reactivity of silicon clusters has been found to differ from that of bulk silicon.9 Experimentally, several reactivity studies have been performed with silicon clusters, including reactions with H2O, NO2, O2, and others.10–13 Bergeron et al.13 investigated the stability of silicon cluster ions by O2 etching and suggest that Sin+ (n ) 4, 6, 9, 13, 14, and 23) and Sin- (n ) 18, 21, 24, 25, and 28) clusters have very high stability. There have also been several theoretical studies of the reactions of O2 with silicon clusters. Li et al.14 performed molecular dynamics simulations for oxygen adsorption on Sin (n ) 1-7) clusters using the full-potential linear-muffin-tinorbital method. They show that the O2 molecule cannot be adsorbed directly on silicon clusters with more than four Si atoms. The work of Li and Gong15 on the reactions of the O2 molecule with neutral and positively charged Sin (n ) 3-16) clusters, using first-principles calculations, shows that neutral Sin (n ) 4, 7) and charged Sin+(n ) 4,7) clusters show higher inertness to O2 molecule adsorption. Dayou and Spielfiedel16 generated global potential energy surfaces (PES) for the reaction Si(3P) + O2(3Σg-) f SiO(1Σg-) + O(1D/3P). They focused on dynamic simulations and calculations of the temperature de* To whom correspondence [email protected].

should

be

addressed.

E-mail:

pendence of the rate constants for the reaction, using the multireference configuration interaction (MRCI) method. Adamovic and Gordon17 investigated PES for the two competing reactions Si(3P) + O2(3Σg-) ) SiO2(1Σg+) and Si(3P) + O2(3Σg-) ) SiO(1Σ+g ) + O(3P), using the multiconfiguration self-consistent field (MCSCF) level of theory augmented by the multireference second order perturbation theory (MRMP2). They only considered the perpendicular reaction path of the silicon atom with respect to the O2 molecule in the PES. Despite these research efforts, there are still several issues that remain open and need to be addressed. For example, a complete understanding of the fundamental oxidation process, including reaction steps and different reaction paths, has not yet been obtained. Nor have the reaction paths of oxidation of the silicon suboxides been studied. The study of the fundamental oxidation process of small silicon clusters and its reverse (that is, deoxidation) is expected to provide insights into the complex formation processes of silicon nanowires. Therefore, in this research, we investigated various possible reaction paths for small silicon and silicon oxide clusters by putting the O2 around the cluster at different sites and with different orientations. 2. Computational Details The PES of the reactions Sin + O2 were calculated using the Gaussian 03 package.18 To simulate the spin-inversion process of the initial oxidation of Sin we also used the Vienna ab initio simulation package (VASP) in which the spin is allowed to change during the simulation.19 The geometries of the reactants, intermediates, transition states, and products of these reactions were optimized, without imposing symmetry constraints, at the B3LYP density functional level20 using the 6-31G(d) basis set. These optimized geometries were used to calculate the vibrational harmonic frequencies and zero-point energies. The minima were confirmed with all real frequencies, whereas each transition state structure was characterized with one imaginary frequency. To verify that the transition state structure was the right saddle point connecting the corresponding reactants and products of interest, intrinsic reaction coordinate (IRC)21 calculations were performed. As illustrated in Table 1 the B3LYP method with

10.1021/jp103381e  2010 American Chemical Society Published on Web 07/21/2010

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TABLE 1: Geometry Parameters of Silicon Oxide Systems with Bond Length in Ångstroms and Bond Angles in Degrees

a

ref 22.

6-31G(d) basis sets shows excellent agreement with experiments22 and second order Møller-Plesset perturbation theory (MP2) calculations for the geometries of silicon oxide systems. However, B3LYP-calculated energies can deviate from the most accurate values by several kilocalories per mole. We therefore improved the energy of the calculated structures by performing single-point MP2 calculations at their B3LYP-optimized geometries, extending the basis sets from 6-31G(d) to 6-311G(3df). Zero-point energy (ZPE) corrections estimated at the B3LYP level were added to the final MP2 energies. Such an approach is designated using the standard notation MP2/6-311G(3df)// B3LYP/6-31G(d) +ZPE(B3LYP/6-31G(d)). A previous study23 on the silicon oxide system shows that B3LYP can provide reasonable geometries and that the MP2 energies are at least in qualitative agreement with those based on coupled cluster methods. This justifies our method. We also checked the 〈S2〉 values to evaluate the spin contamination in these calculations and found it to be insignificant. The VASP optimizations are based on the density-functional theory24,25 and plane-wave basis set26,27 with spin-polarized generalized gradient approximations (GGA).28,29 During the optimization, the spin and orientation of the molecule are allowed to change along the reaction pathway. The wave functions are expanded in a plane-wave basis set to a cutoff of 400.0 eV. The interaction of the valence electrons with the core is described by the projector augmented wave (PAW) potential.30,31 The atomic positions were optimized by the conjugate gradient32 (CG) method. A supercell with the cell constant of 16 Å was used to make the interactions between the cluster and its periodic images negligible. Only the Γ(0,0,0) point was used for the summation of the Brillouin zone of the simulation cell. 3. Results and Discussion The ground-state structures of small Sin (n ) 1-4) clusters have been unambiguously determined to be linear or planar.33 For Si and Si2 clusters, their respective ground electronic states are calculated as 3P and 3Σ-g ,34 while their singlet states are 29.59 and 17.28 kcal/mol, respectively, higher in energy at the MP2/ 6-311G(3df)//B3LYP/6-31G(d)+ZPE(B3LYP/6-31G(d)) level of theory. For Si3, the singlet C2V molecule is calculated to be the ground state with the 3A1′ (D3h) state lying 0.04 eV above

Figure 1. Optimized geometries of major intermediates, transition states, and products of the reaction of Si with the O2 molecule. Silicon atoms are in gray, and O atoms are in red. Distances are in Ångstroms, and angles are in degrees.

it, in agreement with other theoretical studies.35,36 Our calculations on Si4 show that the ground state (1Ag) structure is a planar rhombus (D2h). Meanwhile, the ground electronic state of O2 is triplet with its singlet state 30.4 kcal/mol higher in energy (using MP2/6-311G(3df)//B3LYP/6-31G(d)+ZPE(B3LYP/6-31G(d)) data), which agrees with the experimental value37 of 22.5 kcal/ mol. Although the interaction of triplet Si/Si2 with triplet O2 can generate singlet, triplet, and quintuplet molecular states, we will not consider the quintuplet here as they correlate with highenergy product excited states. As discussed below, we find the ground electronic states of products of SiO2, Si2O2, and Si4O2 to be singlet. Since the ground states of reactants and products are multiplet and singlet, respectively, for Si/Si2/Si4 + O2, the multiplet potential energy diagram lies below the singlet in the entrance of the channels, and the singlet diagram lies in the exit channels. Therefore, the reaction of Si/Si2/Si4 with O2 should involve spin-conserving and spin-inversion processes. The global minimum structure of Si3O2 is calculated to be triplet. A. Si + O2. The work of Adamovic and Gordon17 considered one reaction channel (the perpendicular approach of the silicon atom to the O2 molecule). We extend this focus to consider both (1) the collinear and (2) the perpendicular channels of the silicon atom to the O2 molecule. We show that the reaction paths depend on the initial position of the O2 relative to the silicon atom. The optimized geometries of the major intermediates, transition states, and products of the reaction of Si with the O2 molecule are shown in Figure 1, while their relative energies are presented in Figure 2. As shown in Figure 2, the reaction of Si with O2 may proceed via different pathways. The investigations of the singlet and triplet PES are within the Cs symmetry. The first step of all pathways is the bonding of the oxygen to Si, which weakens

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Figure 2. The calculated PESs of Si reaction with O2. The 1A′ PES of (a) the collinear approach and (b) the perpendicular approach. (c) The 3A′ PES of the perpendicular approach. (d) The 3A′′ PES of the perpendicular approach. The 3A′ PES and 3A′′PES of the collinear approach are the same as the perpendicular one. Silicon atoms are in gray, and O atoms are in red. The relative energy is in kcal/mol.

the O-O bond. The resulting SiO2 may involve several isomerssIM1, IM2, IM3, and IM4sas presented in Figure 1. For the singlet potential energy, the lowest state is 1A′. Therefore, only the 1A′ PESs are considered here. The reaction path of the perpendicular approach in the singlet potential energy agrees well with the results of Adamovic and Gordon.17 The energies of IM2 and the transition state TS2 relative to the reactants are close to the enthalpy value of the corresponding intermediate and transition states found by Adamovic and Gordon at MCSCF/cc-pVTZ and MCSCF/6-31G*, respectively. Our calculated formation energy of the whole reaction, at -182.98 kcal/mol, is close to the experimental enthalpy change (∆H298.15 ) -181 ( 2 kcal/mol). Compared with the perpendicular approach, there is one more intermediate along the reaction path of the collinear reaction of the silicon atom to an O2 molecule. This reaction first leads to a linear Si-O-O intermediate IM1, which is exothermic by 59.74 kcal/mol. Then, it passes through TS1 to form IM2 with a barrier of 17.57 kcal/ mol. After IM2, the path is the same for both approaches. The O-O bond at IM2 is almost broken, and its distance is 1.579 Å. TS2 connects IM2 with the linear O-Si-O (product 1), with a barrier of 35.14 kcal/mol. These results also demonstrate the dissociation channel of SiO2. The dissociation of the linear O-Si-O, that is, the reverse reaction of the oxidation of silicon, has a high barrier, at 105.29 kcal/mol. The 1A′ state of the linear O-Si-O arises from the transfer of two electrons from Sistwo πp orbitalssinto the two πp* orbitals of O2. Both the 3A′ and 3A′′ electronic states are considered on the triplet surface, as shown in parts c and d of Figure 2. For the 3 A′ state, both the perpendicular and collinear approaches of the silicon atom to an O2 molecule in triplet potential energy result in IM3, with only one side of the O2 bonded to the silicon, which is exothermic by 25.79 kcal/mol. TS3 connects IM3 with product 2 with an activation energy of 6.19 kcal/mol, and the barrier for the reverse reaction is 66.87 kcal/mol. Our product 2 is different from that proposed by Adamovic and Gordon, who posit a SiO(1Σg+) + O(3P). We find that the structure optimization initiated with an oxygen atom at about 3.0 Å away from the SiO molecule goes directly to our product 2. The oxygen radical has an unpaired unstable electron and is very

reactive. It may exist as an intermediate but not as a reaction product. The energy of our product 2 is -439.1493 au by MP2/ 6-311G(3df)//B3LYP/6-31G(d) or -439.2220 au by CCSD(T)/ 6-311G(3df)//CCSD(T)/6-31G(d). Both values are more favorable than that of SiO + O, which is -439.1194 au by MP2/6311G(3df)//B3LYP/6-31G(d) or -439.1577 au by CCSD(T)/ 6-311G(3df)//CCSD(T)/6-31G(d). The formation energy of the whole reaction is -86.47 kcal/mol. For the 3A′′ state, the intermediate, transition state, and product are slightly lower in energy than those for the 3A′ state. We also investigate the oxidation of the silicon atom using VASP. The optimization of the structures of Si + O2 (the collinear and perpendicular channels of the silicon atom to an O2 molecule) leads to structures close to IM1 and IM2 as shown in Figure 1. In both, when the oxygen molecule approaches the silicon atom, the spin changes from quintuplet to triplet and then to singlet. The findings outlined above show that there is no net barrier in the process of the oxidation of the silicon atom, that the main product is a linear singlet O-Si-O, and that the energetically more accessible and feasible pathway is Figure 2b, consistent with the literature. Further oxidation of the linear O-Si-O is difficult because the reaction SiO2 + O2 f SiO4 is endothermic. This is in agreement with previous findings38 that the silicon oxide cluster is less stable if the number of oxygen atoms is more than twice the number of silicon atoms. Under oxygen poor (silicon rich) conditions, the most accessible product (linear O-Si-O) will react further with the silicon atom, as shown in Figure 3a. The structure optimization in which a silicon atom is assumed to be about 3.5 Å away from the linear O-Si-O molecule, going directly to Si2O2, indicates an exothermic reaction involving 77.81 kcal/mol. The exothermic reaction provides heat for the Si2O2 to dissociate into two SiO molecules, the activation energy of which is only 4.14 kcal/mol. This agrees well with previous findings39 that a mixture of Si and SiO2 will vaporize to form pure gaseous SiO. This reaction plays an important role in the initial stage of the oxide-assisted growth of silicon nanostructures. The reverse reaction (2SiO f Si + SiO2) is endothermic (81.33 kcal/mol).

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Figure 3. The calculated PESs of (a) linear O-Si-O reaction with a silicon atom, (b) SiO molecular reaction with a silicon atom, and (c) triangle SiO2 reaction with a silicon atom. Product 1 and IM2 correspond to the ones in Figure 1. Silicon atoms are in gray, and O atoms are in red. The relative energy is in kcal/mol.

The SiO molecule can react further with the silicon atom to form Si2O, a reaction with no energy barrier and which is exothermic by 48.38 kcal/mol, as shown in Figure 3b. Triangular SiO2 is expected to be more reactive than linear O-Si-O. Figure 3c shows that the reaction of triangular SiO2 with the silicon atom leads directly to ground-state rhombus Si2O2, a reaction with no energy barrier and exothermic by 199.92 kcal/ mol. As the above shows, the most likely reaction paths for the formation of SiO from the Si atom can be described as follows

Si(3P) + O2( 1

O-Si-O(

3

-

1

+

∑g ) f O-Si-O( ∑g )

+

1

+

∑g ) + Si(3P) f 2SiO( ∑g )

B. Si2 + O2. The optimized geometries of major intermediates, transition states, and products of the reaction of Si2 with the O2 molecule are shown in Figure 4, while their relative energies are presented in Figure 5. As shown in Figure 5, the reaction of Si2 with O2 may proceed via different pathways. We first consider the singlet PES. Parts a-d of Figure 5 show that the path of the reaction of Si2 with O2 is determined by different initial structures. Initiating a B3LYP/6-31G* optimization from a coplanar, perpendicular orientation leads to IM1, a reaction with no barrier and which is exothermic by 36.58 kcal/mol. The O-O bond length in IM1 is 1.371 Å, a little longer than in the oxygen molecule itself. The activation energy for the transformation of IM1 into IM2 is 10.85 kcal/mol. In TS1, the O-O bond has been elongated from 1.371 to 1.510 Å, indicating that it has been almost

completely broken. Then, the system should pass through another transition state, TS2, to go to product 1, which is the global minimum structure of Si2O2. TS2 is structurally very similar to IM2 but has a larger O-O distance. The energy barrier for this step is calculated to be 40.72 kcal/mol, and the energy of TS2 is still well below the energy of the separated reactants, so there is more than enough energy available to obtain the final product. The barrier of the reverse reaction is very high at 187.5 kcal/mol. Starting from the noncoplanar, perpendicular orientation, the reactants go directly to IM2. The entire path is a two-step reaction, that is, one step less than the coplanar orientation. As shown in parts a or b of Figure 5, it is 243.98 kcal/mol exothermic. As shown in parts c and d of Figure 5, starting from both the parallel symmetric and asymmetric orientations, the final products are two SiO molecules. The reaction energy for the formation of these molecules from Si2 and O2 is 195.54 kcal/ mol. For the parallel symmetric orientation, the interaction of Si2 and O2 leads to IM3, the O-O bond length of which is 1.466 Å. Then, passing through TS3 (with an energy barrier of 7.15 kcal/mol), IM3 dissociates into two SiO molecules. In the parallel asymmetric orientation, the interaction of Si2 and O2 leads to IM4. The oxygen molecule is dissociatively chemisorbed, with one O atom sitting at the bridge site and the other at the end site at IM4. Through TS4, IM4 dissociates into two SiO molecules, with an energy barrier of 4.12 kcal/mol. The PES analysis shows that there is no net barrier in the formation of SiO from Si2+O2. We now consider the triplet PES. Initiating an optimization from the coplanar, perpendicular orientation leads to IM5, a reaction with no barrier and exothermic by 167.55 kcal/mol, as shown in Figure 5e. The oxygen molecule is dissociatively

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Huang and Zhang interact with an O2 molecule assumed to be about 3.0 Å away from Si2 (see Figure S1 in Supporting Information). In the coplanar, perpendicular approach, one oxygen atom of O2 is coordinated with one silicon atom of Si2, and the spin of the system changes from quintuplet to triplet. The spin of the other three channels changes from quintuplet to triplet and then to singlet when the oxygen molecule approaches Si2. The optimized final structures of the noncoplanar, perpendicular, and parallel asymmetric reactions are close to the structures of IM1 and IM4 from the B3LYP/6-31G(d) calculations. The findings outlined above show that the energetically most accessible and feasible pathway to produce a ground state structure of Si2O2 in which the Si-Si bond is not broken up is the one shown in Figure 5b. They also demonstrate that the energetically most accessible and feasible pathway to produce SiO from Si2 and O2 is the one shown in Figure 5d. There is no net barrier to the process of oxidation of the Si2 cluster, although there are intermediate and transition states on the reaction paths. C. SiO +O2, Si2O +O2, Si2O2 + O2. Though the reaction heat (-50.80 kcal/mol) generated by SiO + 1/2O2 f SiO2 is negative, our calculations show that there is a barrier to the oxidation of SiO. SiO2 is obtained by multistep reactions from SiO and O2, shown as follows

SiO + O2 f linear O-Si-O + O ∆E ) 12.65 kcal/mol, barrier ) 43.96 kcal/mol (1) SiO + O f triangular SiO2 ∆E ) -44.11 kcal/mol, no barrier (2) triangular SiO2 f linear O-Si-O ∆E ) -70.15 kcal/mol, barrier ) 35.14 kcal/mol (3)

Figure 4. Optimized geometries of major intermediates, transition states, and products of the reaction of Si2 with the O2 molecule. Silicon atoms are in gray, and O atoms are in red. Distances are in Ångstroms and angles in degrees.

chemisorbed, with one O atom sitting between two silicon atoms and the other at the end site at IM5. Then, IM5 should pass through a transition state TS5 to go to the rhombus product 3, the energy barrier of which is 13.18 kcal/mol. The energy of formation of the rhombus product 3 from Si2 and O2 is 185.93 kcal/mol. As shown in Figure 5f, starting from the noncoplanar, perpendicular orientation, the reactants go directly to product 3, with no energy barrier involved. The parallel symmetric approach leads to product 4, which is exothermic by 75.49 kcal/ mol. A transition state may connect product 4 with product 3 on the triplet surface, but no such structure was found in our calculations. The parallel asymmetric approach results in IM6, a reaction which is exothermic by 123.43 kcal/mol, as shown in Figure 5h. TS6 connects IM6 with P3. The energy calculation for TS6 failed to converge at the MP2 level of calculations. The activation energy for TS6 is only 0.82 kcal/mol at B3LYP/ 6-31G(d) level, indicating that the PES is very flat in the vicinity of the reactant point. Similarly, we used VASP to optimize the structure of Si2 + O2, considering how the various channels of the silicon atom

The first step is an endothermic reaction, with a barrier of 43.96 kcal/mol. The radical O (a product of the first step) is very reactive and combines with SiO to form triangular SiO2. This reaction has no energy barrier and is exothermic by 44.11 kcal/mol. The heat provides the energy to overcome the energy barrier for the third step in the reaction. Also, the net barrier for the reaction 2SiO + O2 f 2SiO2 is 43.96 kcal/mol. This indicates that silicon is more reactive than silicon oxide, which is consistent with our previous finding4 that the chemical stability of silicon segregated silicon monoxide clusters is lower than that of the silicon cored model. The reverse reaction, SiO2 f SiO + 1/2O2, is preferred as a dissociation channel to SiO2f SiO +O (see ref 38), with a dissociation energy of 50.80 kcal/ mol compared to 114.27 kcal/mol. Our result agrees well with the finding39 that SiO2 alone under neutral conditions vaporizes predominantly to SiO and O2 in the gas phase. Furthermore, there are barriers to the dissociation of SiO2, similar to the other dissociation channels of SiO2 and the dissociation of Si3O3 into SiO + Si2O2.40,41 This was not mentioned in ref 38, in which only the dissociation energies of some fragmentation channels of silicon oxide were given. Our calculations show that the ground state structure of Si2O is triangular and singlet, which is consistent with both experimental42 and theoretical23,43 results. Figure 6 shows the PES of the oxidation of Si2O. From the coplanar, perpendicular orientation, a B3LYP/6-31G(d) optimization leads to the global minimum isomer (IS1), which is exothermic by 219.13 kcal/ mol. The noncoplanar, perpendicular approach results in an IS2, exothermic by 131.78 kcal/mol. Through a transition state, IS2 transforms into a monocyclic isomer IS3 with a barrier of 5.95

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Figure 5. The calculated PESs of Si2 reaction with O2. The singlet potential energy of (a) the coplanar perpendicular approach, (b) the noncoplanar perpendicular approach, (c) the parallel symmetric approach, and (d) the parallel unsymmetric approach; the triplet potential energy of (e) the coplanar perpendicular approach, (f) the noncoplanar perpendicular approach, (g) the parallel symmetric approach, and (h) the parallel unsymmetric approach. Silicon atoms are in gray, and O atoms are in red. The relative energy is in kcal/mol. * The relative energies are at the B3LYP/6-31G(d) level, because the energy calculation for TS6 failed to converge at the MP2 level.

kcal/mol. The optimization starting from the parallel orientation (the axis of O2 parallel to the Si-Si bond of Si2O) goes directly into IS3, which is exothermic by 131.78 kcal/mol. We failed to locate a transition state for the isomerization IS3 f IS1. It is shown that the reaction heat is smaller for the oxidation of Si2O than Si2. Table 2 gives the structures, point groups, electronic state, highest-occupied molecular orbital (HOMO)-lowest-unoccupied molecular orbital (LUMO) gap, and relative energy (relative to ground-state Si2O2 and O2) of the Si2O4 isomers. Here, we present some new high-energy isomers (IS1, IS5, IS6, and IS7) as distinct from previous literature. It can be seen that the global minimum isomer of Si2O4 is a Si2O2 rhombus with two SidO double bonds on each side (IS3), consistent with previous theoretical result.23 We have considered several possible reaction pathways for Si2O2 and O2. Only the one which places the axis of the O2 parallel to the long edge of Si2O2 is

accessible. The pathway for the reaction of Si2O2 with the O2 molecule is shown in Figure 7. It first leads to an IS1 with no barrier and which is exothermic by 17.85 kcal/mol. This then passes through a transition state, with a barrier of 14.11 kcal/ mol, to isomerize into IS2. There may be a transition state connecting IS2 with a global minimum isomer IS3, but we failed to locate it. The reaction heat for the formation of IS3 from Si2O2 and O2 is 146.68 kcal/mol. This value is smaller than for the oxidation of Si2O. These results suggest that the yields of silicon nanostructures are indeed dependent on the oxygen ratios in silicon oxides. D. Si3/Si4 + O2. The global minimum structure of Si3O2 is calculated to be in spin-triplet state, consistent with Avramov et al.23 VASP optimizations, initiated with the axis of oxygen parallel to the long edges of Si3, go directly to a singlet IS1(see Figure S2 of Supporting Information). This has no barrier and an adsorption energy of 3.43 eV. The interactions of Si3 with

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Figure 7. The pathway for the reaction of Si2O2 with the O2 molecule. Silicon atoms are in gray, and O atoms are in red.

TABLE 3: Reaction Energy of Silicon Cluster Oxidation from MP2/6-311G(3df)//B3LYP/6-31G(d) Calculations

Figure 6. The PES of (a) the coplanar perpendicular approach, (b) the noncoplanar perpendicular approach, and (c) the parallel approach for the reaction of Si2O with the O2 molecule. Silicon atoms are in gray, and O atoms are in red.

TABLE 2: Structures, Point Groups, Electronic States, HOMO-LUMO Gaps, and Relative Energiesa of Si2O4 Isomers

a

The energy of the reactants (ground-state Si2O2 and O2) is set at 0 kcal/mol. Relative energies were refined at the level of MP2/ 6-311G(3df)//B3LYP/6-31G*+ZPE (B3LYP/6-31G*).

O2 shorten the long Si-Si edge (2.84 f 2.52 Å) and elongate both the short Si-Si edge (2.19 f 2.24 Å) and the O-O bond (1.23 f 1.45 Å). This optimization result is different from that found by Li et al., although the optimized structure of the Si3 agrees with their results, and the same method was used in both studies.15 In the structure they report, the O-O bond has been completely broken. Next, we consider two reaction paths which were not addressed by Li et al. Our optimizations, starting with the axis of oxygen perpendicular to the long edges of Si3 and parallel to the Si3 molecule plane, lead to a singlet IS2 (Figure S2 of Supporting Information). This has no barrier and an adsorption energy of 7.89 eV. The two O atoms insert into one long Si1-Si3 and one short Si1-Si2 edge, which make the short edge longer and the long one shorter. The O-Si-O bridges are asymmetric, with one Si-O bond length 1.79 Å

and the other 1.66 Å. The approach of the oxygen molecule perpendicular to the Si3 plane directly results in a singlet IS3 (Figure S2 of Supporting Information), with no barrier and an adsorption energy of 7.31 eV. One O atom bonds with Si1, Si2, and Si3; the other bonds with Si1 and Si3. These results are similar to those from B3LYP optimizations. For the PES from the singlet IS3, IS2, or IS1 to the triplet global minimum structure, no corresponding transition was identified despite extensive searching. The triplet global minimum structure is thermodynamically more stable than IS1, IS2, and IS3, by 4.89, 0.43, and 1.01 eV, respectively. For the Si4 cluster, our calculations show that the singlet oxygen molecule can react with it directly to form Si4O2 while the ground-state spin-triplet oxygen molecule cannot be adsorbed on it directly. This is reasonably consistent with previous theoretical results.14,15 This suggests that there is a potential barrier to the spin inversion of O2. The calculated potential barrier height is about 30.4 kcal/mol at the MP2/6-311G(3df)// B3LYP/6-31G(d)+ZPE(B3LYP/6-31G(d)) level, which is higher than that predicted in previous work.14,15 The differences between results in the current work and those in the reference may be due to the different theoretical methods used or the different reactions paths. The inertness of Si4 to O2 adsorption is mainly due to the high potential barrier. To determine whether there is any correlation between the reaction energies and the oxidation of the silicon clusters, Table 3 shows the former values for the oxidation of small silicon clusters and their suboxides. The reaction energy for Si4 is significantly lower than for Si, Si2, and Si3, which is in agreement with the experimental and theoretical finding that Si4 shows inertness to O2. This indicates that the low reaction energy also has some effect on the inertness of Si4. The reaction energy for the oxidation of the silicon cluster is higher than that for the corresponding suboxides, indicating that pure silicon clusters are easier to oxidize.

Reaction Paths of Small Silicon Clusters In experimental work on the oxide-assisted growth of silicon nanowires, commercially available nitrogen and argon gases are used as carrier gases. These usually contain a small amount of oxygen. In thermal evaporation at high temperature, oxygen will oxidize silicon to form silicon oxide. This is the key precursor which significantly enhances the nucleation and one-dimension growth of the silicon nanowires. The reverse process, that is, deoxidation, dominates the nucleation step, resulting in the precipitation of silicon nanoparticles. 4. Summary In this paper, we have reported on a systematic study of the oxidation of small silicon clusters. For the oxidation of Si, Si2, and Si3 clusters, the net exothermicity dominates the whole reaction process; furthermore, there are no net barriers, as the transition states in all possible paths are lower in energies than the reactants. Therefore, the oxidation of such clusters can proceed at low temperatures. The corresponding reverse reactions, the dissociations of silicon oxides, have high barriers, in agreement with the high temperature needed in the oxideassisted growth of silicon nanostructures. The inertness of Si4 cluster to the ground-state, spin-triplet oxygen molecule is mainly due to the high potential barrier. The reactions of silicon clusters with the oxygen molecule are easier than the oxidations of their corresponding suboxides. The difficulty in searching for the transition states of some isomerization reactions for Si2O2, Si2O3, and Si2O4 could be overcome by scanning the reaction path or slice of a potential energy surface to identify saddle points. Acknowledgment. The work described in this paper was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (CityU5/CRF/ 08, CityU 103609). Supporting Information Available: Some structures, energies, and Cartesian coordinates. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Garand, E.; Goebbert, D.; Santambrogio, G.; Janssens, E.; Lievens, P.; Meijer, G.; Neumark, D. M.; Asmis, K. R. Phys. Chem. Chem. Phys. 2008, 10, 1502. (2) Zhang, R. Q.; Chu, T. S.; Lee, S. T. J. Chem. Phys. 2001, 114, 5531. (3) Zhang, R. Q.; Fan, W. J. J. Cluster Sci. 2006, 17, 541. (4) Huang, S. P.; Zhang, R. Q.; Li, H. S.; Jia, Y. J. Phys. Chem. C 2009, 113, 12736. (5) Zhang, R. Q.; Zhao, M. W.; Lee, S. T. Phys. ReV. Lett. 2004, 93, 095503. (6) Zhang, R. Q.; Lu, W. C.; Zhao, Y. L.; Lee, S. T. J. Phys. Chem. B 2004, 108, 1967. (7) Zhang, R. Q.; Lu, W. C.; Lee, S. T. Appl. Phys. Lett. 2002, 80, 4223. (8) Zhang, R. Q.; Lifshitz, Y.; Lee, S. T. AdV. Mater. 2003, 15, 635. (9) Jarrold, M. F. Science 1991, 252, 1085.

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