The Nature of Si-O-Si Bonding via Molecular Orbital Calculations

Fumiya NORITAKE; Katsuyuki KAWAMURA

doi:10.2477/jccj.2015-0009

Abstract

The nature of Si-O bonding and Si-O-Si bridging is discussed using molecular orbital calculations. We found the equilibrium geometries for two pyrosilisic acid molecules (C_2V and 60° torsion) using Møller-Plesset perturbation theory and 6-311G (d,p) split valence basis set. The bent configuration of the Si-O-Si angle in equilibrium geometries can be explained by the balance of Coulombic repulsion between SiO₄ tetrahedra and the energy of lone pair orbitals belonging to bridging oxygen atom without concerning the contribution of d-p π-bonding from the results of natural bonding orbital analysis. The energy surfaces of two pyrosilisic acid molecules with varying Si-O length to the bridging oxygen and Si-O-Si angle were calculated and we found the relationship between Si-O length to the bridging and Si-O-Si bridging angle. The Si-O bonding strengthens with increasing Si-O-Si angle because of stabilization in energy of Si-O bonding orbital with decreasing the hybridization index λ in sp^λ orbital of bridging oxygen and increase of Coulombic interaction between Si and bridging oxygen atom.

Figures

Figure 1.

Calculated equilibrium geometries of pyrosilisic acid molecule. (a) C_2V model. (b) Each tetrahedra mutually twisted 60° model.

Figure 2.

The contour map of energy surface of pyrosilisic acid molecule (C_2V) with varying Si-O_br and Si-O-Si angle.

Figure 3.

The contour map of energy surface of pyrosilisic acid molecule (60° torsion) with varying Si-O_br and Si-O-Si angle.

Figure 4.

The plots of (a) sum of energy of the valence orbitals belongs to the bridging oxygen atom, (b) energy of each valence orbitals (two lone pairs (LP1, LP2) and Si-O bonding orbital (Si-O_br)) belongs to the bridging oxygen atom and (c) overlap weighted bond order of Si-O_br bonding with varying Si-O-Si angle in the case of 60° torsion model.

Figure 5.

The plots of (a) electrostatic potential energy (ESP) between Si and bridging oxygen atoms calculated from charge and (b, c) charge of Si and bridging oxygen atoms calculated by NBO analysis with varying Si-O-Si angle in the case of 60° torsion. Si-O_br is the orbital energy of Si-O_br σ bond and plotted for comparison.

Figure 6.

The plots of bonding coefficients Si and O atoms for Si-O_br σ-bonding with varying Si-O-Si angle in the case of 60° torsion.

Figure 7.

The plots of (a) electrostatic potential energy of pyrosilisic acid molecule calculated from charge calculated by NBO analysis and (b) sum of the electrostatic potential energy and the energy of lone pair orbital with varying Si-O-Si angle.

Tables

Table 1. The optimized parameters and difference from experimental value in angstrom and degree of disiloxane molecule, (SiH₃)₂O by MO calculation using various model chemistry. The experimental values are taken from Almenningen et al. [17].

	Exp.	HF	Δ	MP2	Δ	B3LYP	Δ	PBE	Δ
Si-O	1.634	1.621	−0.013	1.642	0.008	1.640	0.006	1.635	0.001
Si-H	1.486	1.476	−0.010	1.476	−0.010	1.485	−0.001	1.488	0.002
Si-O-Si	144.1	180.0	35.9	156.5	12.0	179.2	35.1	169.7	25.6
O-Si-H	109.9	109.9	0.0	110.4	0.5	109.9	0.0	110.1	0.2
H-Si-H	109.1	109.0	−0.1	109.0	−0.1	109.0	−0.1	109.0	−0.1

Table 2. The optimized parameters in angstrom and degree of pyrosilisicacid molecule, H₆Si₂O₇ by MO calculation using MP2 level and 6-311G(d,p) basis set.

	C_2V	60° torsion
Si-O_br	1.601171	1.604154
Si-O_nbr	1.648782	1.648563
O-H	0.954669	0.954561
Si-O-Si	172.006	159.647
Si-O-H	117.705	117.857
Total Energy (Hartree)	−1107.5476706	−1107.5482842

Table 3. The occupancy of natural atomic orbital of Si in various Si-O-Si angle in pyrosilisic acid molecule (60° torsion model).

	130°	155°	180°
3s	0.44388	0.43775	0.43546
3px + 3py + 3pz	0.92376	0.91504	0.91303
3dxy + 3dyz + 3dzx + 3dx²y² + 3d²	0.05959	0.05834	0.05808

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