대한화학회지 (Journal of the Korean Chemical Society)

  • 제67권5호
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  • Pages.333-338
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  • 2023
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  • 1017-2548(pISSN)
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  • 2234-8530(eISSN)
대한화학회 (Korean Chemical Society)
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Monte Carlo Simulations and DFT Studies of the Structural Properties of Silicon Oxide Clusters Reacting with a Water Molecule

  • Jisu Lee (Chungbuk National University Middle School) ;
  • Gyun-Tack Bae (Department of Chemistry Education, Chungbuk National University)
  • 투고 : 2023.08.10
  • 심사 : 2023.08.31
  • 발행 : 2023.10.20
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초록

In this study, the H2O reaction with SiO clusters was investigated using ab initio Monte Carlo simulations and density functional theory calculations. Three chemistry models, PBE1/DGDZVP (Model 1), PBE1/DGDZVP (Si atom), and aug-cc-pVDZ (O and H atoms), (Model 2) and PBE1/aug-cc-pVDZ (Model 3), were used. The average bond lengths, as well as the relative and reaction energies, were calculated using Models 1, 2, and 3. The average bond lengths of Si-O and O-H are 1.67-1.75 Å and 0.96-0.97 Å, respectively, using Models 1, 2, and 3. The most stable structures were formed by the H transfer from an H2O molecule except for Si3O3-H2O-1 cluster. The Si3O3 cluster with H2O exhibited the lowest reaction energy. In addition, the Bader charge distributions of the SinOn and (SiO)n-H2O clusters with n = 1-7 were calculated using Model 1. We determined that the reaction sites between H2O and the SiO clusters possessed the highest fraction of electrons.

키워드

INTRODUCTION

SiO clusters have been used in numerous fields, such as optical communications,1,2 thin film technology,3 electronics,4 and biomedical applications.5 Experimentally, the oxygen etching of cationic and anionic Si clusters has been investigated,6 as well as silicon monoxide using TOF-MS7 and Si film with oxygen using synchrotron radiation Si 1s photoemission spectroscopy.8 Theoretically,9-15 the equilibrium geometries, binding energies, and ionization potentials, as well as the vertical and adiabatic electron affinities of SinOm clusters (n ≤ 6, m ≤ 8), have been examined using density functional theory (DFT) calculations.10 A systematic study on the structure and stability of SiOn (n = 1-4), Si2On (n = 1-5), Si3On (n = 1-7), Si4On (n = 1-9), and Si5On (n = 1-11) clusters was reported using ab initio molecular dynamics, Monte Carlo (MC), and DFT calculations.12

Herein, research was conducted to determine the best chemistry model for small SiO clusters.14 Particularly, three chemistry models were investigated: PBE1/DGDZVP (Model 1), PBE1/DGDZVP (Si atom) and aug-cc-pVDZ (O and H atoms) (Model 2), and PBE1/aug-cc-pVDZ (Model 3). DGDZVP is double ζ + valence polarization basis set equivalent one used DGauss16,17 and aug-cc-pVDZ is augmented versions of Dunning’s correlation-consistent polarized valence-only basis set.18-22 The aug-cc-pVDZ basis set is extremely useful in the investigation of metal oxide clusters.23,24 Model 1 was in good agreement with the experimental data and is computationally inexpensive. Using Model 1, neutral, cationic, and anionic SiO clusters, SinOn (n = 1-7), were investigated using ab initio MC simulations and DFT calculations.15 Particularly, the H2O reaction with optimized SiO clusters was investigated using ab initio MC simulations and DFT calculations.

METHODS

All geometries of the (SiO)n-H2O clusters with n = 1-7 were optimized using the Gaussian 09 program.25 The initial geometries were created by adding an H2O molecule to multiple sites of the optimized SiO clusters. For example, to construct the initial SiO-H2O structures, H2O molecules were attached to the optimized SiO cluster at multiple sites. Therefore, seven initial geometries of the SiO-H2O clusters were created, and ab initio MC simulations were performed. The number of the initial geometries of the Si2O2-H2O, Si3O3-H2O, Si4O4-H2O, Si5O5-H2O, Si6O6-H2O, and Si7O7-H2O clusters were 48, 80, 85, 20, 57, and 65, respectively. Ab initio MC simulations using the Gaussian 09 program were home grown scripts. The temperature was decreased from 2000 to 300 K for up to 300 MC steps. Ab initio MC simulations have been explained in detail in previous investigations.15,26-28

Following ab initio MC simulations, DFT calculations were performed to determine the stable (SiO)n-H2O structures with n = 1-7. In the DFT calculations, three chemistry models (Models 1, 2, and 3) were used. Model 1 was in good agreement with the experimental data for the SiO clusters.14 The Bader charge distributions29 were calculated to determine the reaction site between the SiO clusters and H2O. The Bader charge distributions of the SiO clusters and (SiO)n-H2O clusters with n = 1-7 are listed in Tables 1 and 4, respectively.

Table 1. Bader charge distributions of the neutral SinOn cluster with n = 1-7 using Model 1

JCGMDC_2023_v67n5_333_t0001.png 이미지

RESULTS AND DISCUSSION

Neutral and charged SiO clusters using ab initio MC and DFT (Model 1), and the optimized neutral SiO clusters are shown in Fig. 1.15

JCGMDC_2023_v67n5_333_f0001.png 이미지

Figure 1. Optimized SiO clusters, (SiO)n (n = 1-7), using the PBE/DGDZVP chemistry model. Si and O atoms are denoted by gray and red spheres, respectively.15

Among the SiO-H2O clusters, only two types of structures were simulated, and the optimized SiO-H2O clusters using Model 1 are presented in Fig. 2. All (SiO)n-H2O clusters with n = 1-7 were optimized using Models 1, 2, and 3. SiO-H2O-1 cluster was the most stable structure, in which the H atom of the H2O molecule was transferred to the O atom of the optimized SiO cluster, and the OH bond was attached to the Si(1) atom. The average bond lengths of Si-O and O-H in the (SiO)n-H2O clusters using Models 1, 2, and 3 are listed in Table 2. The average bond lengths of Si-O and O-H are 1.67-1.75 Å and 0.96-0.97 Å, respectively, using Models 1, 2, and 3 in all (SiO)n-H2O clusters with n = 1-7. The SiO-H2O-2 cluster was the second most stable structure, and the results revealed that an H2O molecule was not attached to the optimized SiO cluster. The bond lengths between the Si and O atom of the H2O molecule in the SiO-H2O-2 cluster were 2.44, 2.40, and 2.39 Å, in Models 1, 2, and 3, respectively. Table 3 lists the relative energies of the (SiO)n-clusters in Models 1, 2, and 3, respectively. The relative energy was calculated by determining the energy difference between the most stable structural energy and an isomer energy. The relative energies of the SiO-H2O-2 cluster were 30.6, 32.7, and 10.9 kcal/mol in Model 1, 2, and 3, respectively. The highest value among the relative energies of the SiO-H2O clusters was obtained using Model 2, and the value of the relative energy in Model 3 was extremely low (10.9 kcal/mol).

JCGMDC_2023_v67n5_333_f0002.png 이미지

Figure 2. Optimized structures of the SiO-H2O and Si2O2-H2O clusters using Model 1. Si, O, and H atoms are denoted by gray, red, and white spheres, respectively.

Table 2. Average bond lengths (Å) of the Si-O and O-H bonds in the most stable (SiO)n-H2O clusters in Models 1, 2, and 3

JCGMDC_2023_v67n5_333_t0002.png 이미지

Table 3. Relative energies (kcal/mol) of the (SiO)n-H2O clusters in Models 1, 2, and 3

JCGMDC_2023_v67n5_333_t0003.png 이미지

Two types of the Si2O2-H2O clusters were revealed in the simulation results (Fig. 2). The Si2O2-H2O-1 cluster was formed via an H transfer reaction, which was similar to that for the SiO-H2O-1 cluster. This cluster was the most stable among the Si2O2-H2O clusters. The second most stable structure was one in which the H2O molecule did not attach to the optimized Si2O2 cluster (i.e., Si2O2-H2O-2 cluster). The bond lengths of Si-O between the H2O molecule and the optimized Si2O2 cluster were 2.25, 2.22, and 2.22 Å in Models 1, 2, and 3, respectively. The relative energies of the Si2O2-H2O-2 cluster were 14.6, 12.1, and 10.3 kcal/mol in Model 1, 2, and 3,respectively. The relative energies were similar in Models 1, 2, and 3.

Among the Si3O3-H2O clusters, only two types of structures were reported following the simulations. The most stable structure was the optimized Si3O3 cluster with an unattached H2O (Si3O3-H2O-1 cluster). The second most stable structure, Si3O3-H2O-2, was a broken six-memberedring of the optimized Si3O3 cluster formed by the H transfer reaction. The optimized Si3O3-H2O clusters using Model 1 are shown in Fig. 3. Additionally, the bond lengths between the H2O molecule (O atom (7)) and Si3O3 cluster (Si atom (2)) were 2.32, 2.25, and 2.22 Å in Models 1, 2, and 3, respectively. The relative energies of the Si3O3-H2O-2 cluster were low at 3.75, 2.68, and 3.49 kcal/mol in Models 1, 2, and 3, respectively. Notably, the order of stability of the Si3O3-H2O clusters differed from that for the SiO-H2O and Si2O2-H2O clusters. Among the SiO-H2O and Si2O2-H2O clusters, the second most stable clusters were the optimized SiO and Si2O2 clusters with an unattached H2O molecule.

JCGMDC_2023_v67n5_333_f0003.png 이미지

Figure 3. Optimized structures of the Si3O3-H2O and Si4O4-H2O clusters using Model 1. Si, O, and H atoms are denoted by gray, red, and white spheres, respectively.

Among the Si4O4-H2O clusters, only two types of structures were simulated, and the optimized structures are shown in Fig. 3. The most stable structure was the Si4O4-H2O-1 cluster, which was formed by the H transfer from an H2O molecule. The second most stable Si4O4-H2O cluster (Si4O4-H2O-2) was formed when the optimized Si4O4 cluster was unattached to an H2O molecule, as shown in Fig. 3. The relative energies of the Si4O4-H2O-2 cluster were 4.62, 9.11, and 7.32 kcal/mol in Models 1, 2, and 3, respectively. The relative energy exhibited the highest value in Model 2.

Among the Si5O5-H2O clusters, the structures with relative energies below 30 kcal/mol were in Model 1. Si5O5-H2O-1 and Si5O5-H2O-2 structures were formed by breaking the Si(1)-Si(3) bond of the optimized Si5O5 cluster upon reaction with an H2O molecule. The most stable Si5O5-H2O cluster was Si5O5-H2O-1, in which the H atom of an H2O molecule was attached to the Si(3) atom, and the OH bond was attached to the Si(1) atom. The second most stable Si5O5-H2O cluster was the opposite for the Si5O5-H2O-1 cluster, in which the H atom and OH bond of the H2O molecule were attached to the Si(1) and Si(3) atoms, respectively. The third most stable cluster, Si5O5-H2O-3, did not attach to the optimized Si5O5 cluster or H2O molecule. The relative energies of these clusters were 4.70 and 27.6 kcal/mol in Model 1. The relative energies of the Si5O5-H2O-2 clusters were similar in Models 1, 2 and 3. Moreover, the relative energies of the Si5O5-H2O-3 clusters decreased from Model 1 to 3 (Table 3). The bond lengths of Si-H were 1.47, 1.47, and 1.48 Å, in Models 1, 2, and 3, respectively.

JCGMDC_2023_v67n5_333_f0004.png 이미지

Figure 4. Optimized structures of the Si5O5-H2O clusters using Model 1. Si, O, and H atoms are denoted by gray, red, and white spheres, respectively.

Among the Si6O6-H2O clusters, three optimized structures are reported in Fig. 5. The Si6O6-H2O structures exhibited a relative energy below 30 kcal/mol in Model 1. The most stable Si6O6-H2O cluster (Si6O6-H2O-1) was formed by an H2O molecule attacking the Si(1)-Si(3) bond of the optimized Si6O6 cluster. Particularly, the OH bond and H atom of the H2O molecule are attached to the Si(1) and Si(3) atoms, respectively. In the second most stable Si6O6-H2O cluster (Si6O6-H2O-2), the attacking position of the H2O molecule was the same as that for the Si6O6-H2O-1 cluster. However, the positions of the OH bond and H atom of the H2O molecule were opposite to those of the Si6O6-H2O-1 cluster. The relative energies of the Si6O6-H2O-2 cluster were 3.82, 3.73, and 2.54 kcal/mol in Models 1, 2, and 3, respectively. The relative energies of the Si6O6-H2O-2 cluster were low, and no significant differences were observed between Models 1, 2, and 3 (Table 3). The third most stable Si6O6-H2O cluster (Si6O6-H2O-3), in which an H2O molecule attached to the Si(1) atom to generate the hydrogen bonds, exhibited bond lengths of 1.82, 1.73, and 1.70 Å in Models 1, 2, and 3, respectively. The relative energy of the Si6O6-H2O-3 cluster is decreased from Model 1 to 3. Si-H bonds in the Si6O6-H2O-1 cluster exhibited bond lengths of 1.47, 1.47, and 1.48 Å in Models 1, 2, and 3, respectively

JCGMDC_2023_v67n5_333_f0005.png 이미지

Figure 5. Optimized structures of the Si6O6-H2O clusters using Model 1. Si, O, and H atoms are denoted by gray, red, and white spheres, respectively.

Among the Si7O7-H2O clusters, the structures having less than 45 kcal/mol of relative energy were in Model 1. The most stable and the second most stable structures were formed by an H2O molecule attacking the Si(4)-Si(6) bond of the optimized Si7O7 cluster. Particularly, the OH bond attached to the Si(6) atom and the H atom attached to the Si(4) atom in the Si7O7-H2O-1 cluster. The Si7O7-H2O-2 cluster exhibited the opposite phenomenon. In the Si5O5-H2O and Si6O6-H2O clusters, the Si-Si bond broke after attacking an H2O molecule. However, the Si(4)-S(6) bond did not break after reacting with an H2O molecule, because two Si-Si bonds (Si(3)-Si(4)-Si(6)) were in the optimized Si7O7 cluster. The average Si-Si bond lengths of the Si7O7-H2O-1 cluster were 2.33, 2.33, and 2.34 Å in Models 1, 2, and 3, respectively. The Si-H bond lengths were 1.48, 1.49, and 1.49 Å in Models 1, 2, and 3, respectively. The relative energies of the Si7O7-H2O-2 cluster were 4.78, 4.96, and 4.44 kcal/mol in Model 1, 2, and 3, respectively. The relative energies of the three chemistry models were considerably similar. The relative energies of the Si7O7-H2O-3 cluster were extremely high in the three chemistry models (Table 3). The most stable structures of (SiO)n-H2O with n = 1-7 clusters were formed by the H transfer from an H2O molecule, except for the Si3O3-H2O-1 cluster.

Table 4. Bader charge distributions of the (SiO)n-H2O clusters in Model 1

JCGMDC_2023_v67n5_333_t0004.png 이미지

JCGMDC_2023_v67n5_333_f0006.png 이미지

Figure 6. Optimized structures of the Si7O7-H2O clusters using Model 1. Si, O, and H atoms are denoted by gray, red, and white spheres, respectively.

The Bader charge distributions on the Si and O atoms of the optimized SiO and (SiO)n-H2O clusters with n = 1-7 were listed in Tables 1 and 4, respectively. The attachment positions of an H2O on the SiO clusters exhibited the highest fraction of electrons. The clusters were symmetrical from SiO to Si4O4 clusters, and the Bader charge distributions of each Si atom were similar. Therefore, no selectivity in the reaction of the H2O was observed. However, in the Si5O5-H2O-1, Si6O6-H2O-1, and Si7O7-H2O-1 clusters, the positions where the H2O reacted contain the Si atom with the highest fraction of electrons. For instance, the Si(1)-Si(3), Si(1)-Si(3), and Si(4)-Si(6) bonds react with H2O in the Si5O5, Si6O6, and Si7O7 clusters, respectively. The Bader charges of Si(1), Si(1), and Si(4) were 2.13, 2.13, and 2.60, respectively, which were the highest fraction of electrons, as shown in Table 1.

Fig. 7 shows the reaction energies of the SiO clusters reacting with H2O molecules using Models 1, 2, and 3. All reactions are exothermic. The three chemistry models exhibited similar patterns; thus, the reaction energies decreased from SiO to Si3O3 clusters and increased from Si3O3 to Si7O7 clusters. Moreover, the Si3O3 cluster with H2O exhibited the lowest reaction energy among the three chemistry models because the H2O molecule did not attach to the optimized Si3O3 cluster. In the future work, we will study the reaction of SiO clusters with organic compounds.

JCGMDC_2023_v67n5_333_f0007.png 이미지

Figure 7. Reaction energies (kcal/mol) of the SiO clusters with H2O using Models 1, 2, and 3.

CONCLUSION

We investigated the H2O reaction in SiO clusters using ab initio MC and DFT calculations. Three chemistry models were used in the study. Models 1 and 3 showed the PBE1/DGDZVP and PBE1/aug-cc-pVDZ levels of theory. Model 2 is PBE1/DGDZVP (Si atom) and aug-cc-pVDZ (O and H atoms). Two or three stable structures, with their corresponding relative energies, were reported. The reaction energies were endothermic, with the Si3O3-H2O cluster exhibiting the highest values. The three chemistry models exhibited similar patterns with respect to the relative and reaction energies. Model 1 has excellent reaction energies and structural properties like Model 3. The reaction sites of the Si5O5, Si6O6, and Si7O7 clusters between the H2O and SiO clusters constituted the highest fraction of electrons from the Bader charge distributions.

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT)(NRF-2018R1D1A1-B07042931).

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