Ab initio calculations of ${}^{29}$Si solid state NMR chemical shifts of silane and silanol groups in silica

Abstract

We report the results of first principles density functional theory (DFT) calculations on the ${}^1$H and ${}^{29}$Si NMR chemical shifts of silane and hydroxyl groups in silica. The structure of the isolated ≡Si–H and ≡Si–OH or of the geminal =Si(H)₂ and =Si(OH)₂ defects has been fully optimized from mechanically embedded cluster models derived from crystalline α-quartz and the nuclear magnetic shielding properties have been determined according to the GIAO method. The computed ${}^{29}$Si chemical shifts, $\text{δ(}{}^{29}$Si) in ppm, are (in parenthesis the experimental values): ≡Si–OH −99 (−99), ≡Si–H −86 (−85), =Si(OH)₂ −85 (−89), =Si–(H)₂ −55 (−50).

Introduction

Solid state NMR is nowadays routinely used for the structural determination of Si-containing inorganic materials 1, 2. Usually, NMR studies of silicon-related compounds are performed using the magic angle spinning (MAS) technique. Where appropriate, MAS NMR has been combined with high-power proton decoupling and ${}^1$H–${}^{29}$Si cross-polarization techniques. ${}^{29}$Si MAS NMR has become a standard method to structurally characterize silicates, aluminosilicates (including zeolites), glasses, minerals, cements, etc. 1, 2, 3, 4. Recently, the technique has been applied to the study of special sites and defects in porous or partially oxidized silicon [5], and to the identification of defects and hydroxyl groups in silicon dioxide 6, 7, 8, 9, 10, 11, 12, 13.

Different from other traditional methods for structural characterization, like diffraction techniques which provide information on type and symmetry of the unit cell and even the atomic positions in the cell, a simple correlation between the measured chemical shifts and the structural parameters of a given Si center is not possible. In 1984 Engelhardt and Radeglia [14]derived a simple relation between the ${}^{29}$Si chemical shift in tetrahedral Si(OSi)₄ units (Q⁴) of the framework silicate and the Si–O–Si angles. This relationship has been extended recently by Sauer and coworkers to include Qⁿ atoms with n<4 [15]. Empirical correlations have been proposed also for bond distances [16]and successfully employed in many cases, although the results are not always satisfactory. Nowadays, however, it is possible to compute NMR chemical shifts of solids by means of ab initio quantum-chemical calculations 15, 17, 18. The local structure around a given Si atom is described by a finite cluster of atoms with more or less refined embedding schemes and the shielding properties in a magnetic field can be computed at various levels of sophistication. This approach opens interesting perspectives for a well grounded assignment of the observed chemical shifts to a given structural model. This is particularly important for point defects where information from diffraction methods is not available.

The study of point defects in SiO₂ by solid state NMR is limited by the low concentration of these centers in the material. On the other hand, some defects like the hydroxyl groups (also called silanols) or silane groups may be present in sufficient numbers to make their detection possible. Silanols have been studied by combining ${}^{29}$Si MAS NMR, infra-red (IR) spectroscopy and ab initio theory 19, 20and at least three groups of silanols have been identified in porous silica or at the silica surface [21]: (a) the isolated silanol, ≡Si–OH; (b) the geminal silanol, =Si(OH)₂; (c) the vicinal pair, where two silanol groups share an O atom, =Si(OH)–O–(OH)Si=. Infra-red (IR) spectroscopy however is unable to discriminate between isolated and geminal silanols [12]while solid state NMR provides an important source of information [12]. Hydroxyls in silica show a proton chemical shift, $\text{δ(}{}^1$H), of 2.0 ppm while for ${}^{29}$Si chemical shifts, $\text{δ(}{}^{29}$Si), values of ≈−90 to ≈−110 ppm have been measured depending on the type of silanol 7, 8, 12. In the case of silane groups, IR spectroscopy can be efficiently used to distinguish isolated ≡Si–H from geminal =Si(H)₂ species: the corresponding vibrational shifts are in fact around 2250 cm⁻¹ and 2190 cm⁻¹, respectively [22]. Recently, ${}^{29}$Si NMR of these two centers have also been reported for oxidized porous silicon and have been assigned as follows [5]: −50 ppm =Si(H)₂, −85 ppm ≡Si–H, and −111 ppm SiO₂. To the best of our knowledge, there are no theoretical attempts to compute the shielding properties of silane groups from first principle calculations.

In this paper we report a systematic all electron density functional theory (DFT) study of ${}^1$H and ${}^{29}$Si chemical shifts of silane, ≡Si–H, and silanol, ≡Si–OH, groups in SiO₂. Both isolated and geminal forms are considered. The structure of the defects has been obtained from cluster models derived from crystalline α-quartz. We will show that the combined use of ab initio theory and cluster models provides quantitative information on the NMR chemical shifts of these defects.