Monte Carlo Simulations and DFT Studies of the Structural Properties of Silicon Oxide Clusters Reacting with a Water Molecule

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 Si_nO_m clusters (n ≤ 6, m ≤ 8), have been examined using density functional theory (DFT) calculations.¹⁰ A systematic study on the structure and stability of SiO_n (n = 1-4), Si₂O_n (n = 1-5), Si₃O_n (n = 1-7), Si₄O_n (n = 1-9), and Si₅O_n (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 DGauss^16,17 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, Si_nO_n (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.

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.

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

Figure1.

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).

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.

Figure2.

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.

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.

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.

Figure3.

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 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.

Figure4.

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

Figure5.

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 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.

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.

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.

Figure6.

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

Figure7.

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

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.