Revisiting the Nature of Si-O-Si Bridging

Abstract

Non-empirical calculation based on the Schrödinger equation is an appropriate tool for investigating the relationship among Si-O-Si angle, Si-O bond length, Si-O bond strength, and electronic structure. However, past studies could not reach a consensus about the equilibrium structure of the C_2v pyrosilisic acid molecule. Moreover, the structure of disiloxane, the simplest siloxane molecule, could not be reproduced using non-empirical molecular orbital calculations. In this study, I checked the reproducibility of various model chemistries and basis sets, and found that employing the post-Hartree-Fock method and a larger basis set (at least, aug-cc-pVTZ) is necessary for accurate calculation of the disiloxane molecule. In contrast to past studies on molecular orbitals, the present study reveals no significant occupancy in the Si 3d orbitals. The total energy landscape of the C_2v pyrosilisic acid molecule is calculated by using the coupled cluster method concerning three excited electrons and the aug-cc-pVTZ basis set. The stable bond length for Si-O_br is 1.604 Å, and the stable Si-O-Si angle is 159.449°. There are gentle curves around the stable angles for each bond length comparing with bond length direction. The stable angle for each bond length decreased with increasing Si-O_br bond length. The weakening of the Si-O_br bond with decreasing Si-O-Si bond angle can be explained by the decrease in the bond index and the increase in the orbital energy for Si-O_br σ-bond. Consequently, hybridization of the valence electrons of the bridging oxygen with decreasing Si-O-Si angle weakens the Si-O_br σ-bond. Electrostatic potential favors a straight configuration because of the repulsion between the SiO₄ tetrahedra, while the valence electrons of the bridging oxygen favor a bent configuration. These two competing behaviors can explain the bent configuration of pyrosilisic acid without considering d-p π bonding.

Figures

Figure 1.

 Geometry of (a) disiloxane molecule, H₆Si₂O, C_2v and (b) pyrosilisicacid molecule, H₆Si₂O₇, C2v optimized using CCSD (T)/aug-cc-pVTZ. Upper and lower Figures are projected to two different planes parallel to vertical mirror. No particular physical significance is ascribed to those sphere sizes. The Figures are drawn using Winmostar [56].

Figure 2.

 Plots of the difference in (a) Si-O length, (b) Si-H length, and (c) Si-O-Si angle in disiloxane molecule (H₆Si₂O) compared with experimental data reported by Almenningen et al. [16]. Experimental values for Si-O length, Si-H length, and Si-O-Si angle are 1.634Å, 1.486Å, and 144.1°, respectively. Note that the number of basis (N_basis) in the Figure implies the number of contracted basis, not primitive functions.

Figure 3.

 Plots of the differences in the optimized structural parameters of pyrosilisic acid molecule (H₆Si₂O₇, C_2v) from the CCSD (T) model using various model chemistries with the aug-cc-pVTZ basis set. Closed symbols for Si-O_br, Si-O_nbr, and O-H are in angstrom (left axis), and open symbols for Si-O-Si bridging angle are in degree (right axis)

Figure 4.

 Plots of the differences in (a) absolute atomic charge and (b) overlap-weighted bond index of pyrosilisic acid molecule (H₆Si₂O₇, C_2v) using various DFTs with the aug-cc-pVTZ basis set in the CCSD (T) optimized configuration.

Figure 5.

 (a) Plots of the differences in the optimized structural parameters of pyrosilisic acid molecule (H₆Si₂O₇, C_2v) from the aug-cc-pVTZ basis set using various basis sets with the CCSD (T) model. Note that Pople-1p, 2p, 3p denotes augmentation using 1, 2, and 3 polarization and diffusion functions, respectively. Closed symbols for Si-O_br, Si-O_nbr, and O-H are in angstrom (left axis), and open symbols for Si-O-Si bridging angle are in degree (right axis). (b, c) Plots of the differences in (b) absolute atomic charge and (c) overlap-weighted bond index of pyrosilisic acid molecule (H₆Si₂O₇, C_2v) using various basis sets in the CCSD (T)/aug-cc-pVTZ optimized configuration.

Figure 6.

 Total energy landscape of pyrosilisic acid molecule (C_2v) for varying Si-O_br lengths and Si-O-Si angles at the CCSD (T)/aug-cc-pVTZ level. Open star indicates the point of lowest energy.

Figure 7.

 Contour maps of (a) atomic charge of silicon (q_Si), (b) atomic charge of bridging oxygen (q_O), (c) electrostatic potential calculated by atomic charge (E_esp) in MJ/mol, and (d) bond index of Si-O_br bonding with varying Si-O_br bond lengths and Si-O-Si angles.

Figure 8.

 Energy landscapes of (a) Si-O_br σ-bonding orbital, (b) lone pair orbital of the bridging oxygen on the symmetry axis, (c) lone pair orbital of the bridging oxygen perpendicular to the symmetry axis, and (d) sum of valence orbital energies (two different lone pairs, two symmetric σ-bonding, and doubled considering α/β electrons) with varying Si-O_br bond lengths and Si-O-Si angles in MJ/mol.

Figure 9.

 Plots of energy calculated by summing electrostatic potential of atomic charges and sum of the valence orbital energy of bridging oxygen at varying Si-O-Si angles for (a) Si-O_br bond length of 1.54 Å, (b) Si-O_br bond length of 1.60 Å, and (c) Si-O_br bond length of 1.72 Å.

Table

Table 1.  Optimized parameters for the C2v pyrosilisic acid molecule using CCSD (T)/aug-cc-pVTZ.

Si-Obr· (Å)	1.604
Si-Onbr (Å)	1.647
O-H (Å)	0.957
Si-O-Si (degrees)	159.449
Si-O-H (degrees)	118.482

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