Gas-phase molecular structure and energetics of anionic silicates

Abstract

The gas-phase stabilities of linear, branched and cyclic silicates made of up to five silicon atoms were studied with density functional theory (DFT). The starting geometries for the DFT calculations at the B3LYP/6-311+G(2d,2p) level of theory were obtained from classical molecular dynamics simulations. We have observed that geometric parameters and charges are mainly affected by the degree of deprotonation. Charges on Si atoms are also influenced by their degree of substitution. The enthalpy of deprotonation of the neutral species was found to decrease with the size of the molecule, while the average deprotonation enthalpy of highly charged compounds increased with molecular size. Furthermore, the formation of rings in highly charged silicates is enthalpically preferred to chain growth. These observations result from two competing effects: the easier distribution of negative charge in silicates with low charge density and the strong intramolecular repulsions present in silicates with high charge density. As a consequence, highly charged silicates in the gas phase tend to be as small and as highly condensed as possible, which is in line with experimental observations from solution NMR.

Introduction

The chemistry of silica under basic pH conditions plays a crucial role in geochemical processes (Iler, 1979, Crerar et al., 1981) and in the synthesis of materials such as zeolites (Davis and Lobo, 1992, Auerbach et al., 2003), ceramics (Brinker and Sherer, 1990, Šefčı´k and McCormick, 1997) and periodic mesoporous silicas (Firouzi et al., 1997). A detailed understanding of silicate speciation in alkaline solutions, as well as of the interactions of anionic silicates with other components of the synthesis mixture (such as water, organic solvents, aluminates and molecular or supra-molecular templates) is essential to develop more controlled procedures for the synthesis of these materials. Computational studies can provide important insights into these phenomena, since they are able to probe the system on an atomic and molecular level, yielding information that is not easy to obtain experimentally. Nevertheless, ab initio computational studies of anionic silicates are scarce, and have, for the most part, been restricted to silicic acid monomers and dimers (Moravetski et al., 1996, Xiao and Lasaga, 1996, Rustad et al., 2000, Tossell and Sahai, 2000, Šefčı´k and Goddard, 2001).

Most of the experimental information we now possess regarding the nature and stability of silicate species in solution has been obtained from ²⁹Si NMR studies (Harris et al., 1981, Engelhardt and Hoebbel, 1983, Harris and Knight, 1983, Kinrade and Swaddle, 1988, Kinrade and Pole, 1992, Kinrade et al., 1998). These studies point to the existence of a restricted range of stable silicate species in alkaline solutions. By employing ²⁹Si-enriched materials, Harris, Knight, Kinrade and co-workers have identified 23 distinct species (Harris et al., 1981, Harris and Knight, 1983, Kinrade and Swaddle, 1988, Knight, 1990, Knight and Kinrade, 2002). Recently, a few more anions have been added to this list (Haouas and Taulelle, 2006). The main conclusion that arises is that silicate species in aqueous alkaline solutions tend to adopt morphologies that are as condensed as possible, such as small ring- and cage-like species. Furthermore, the relative abundance of these species, but not their nature, may depend on the components present in the solution (Kinrade and Pole, 1992, Kinrade et al., 1998, Knight and Kinrade, 2002). However, other researchers have suggested the existence of silicate species containing more open structures, resembling fragments of zeolite materials (Kirschhock et al., 1999, Houssin et al., 2003). The presence or absence of these structures in zeolite synthesis solutions has been the subject of heated debate in recent years (Kirschhock et al., 1999, Knight and Kinrade, 2002, Houssin et al., 2003, Knight et al., 2006).

Despite recent advances in experimental techniques, it is still rather difficult, due to the large variety of species present simultaneously in solution and to the high complexity of the chemistry of silicon oxides, to obtain precise information regarding the structures and relative stabilities of silica clusters, as well as energies and mechanisms of possible reactions involving these clusters. To clarify some issues left unanswered by experimental data, computational studies of silicates have been performed. Early theoretical work has focused on small neutral silica clusters as a means to gather information about solid materials (Hill and Sauer, 1994, Teppen et al., 1994). Hill and Sauer (1994) have performed Hartree–Fock (HF) calculations on several zeolite fragments saturated by hydrogen atoms: dimer, linear trimer, cyclic trimer, cyclic tetramer, cyclic pentamer, cyclic hexamer, cubic octamer, hexagonal dodecamer and sodalite cage. The authors then fitted the results of their ab initio calculations in the gas phase to obtain force field parameters for simulating zeolites. Later, Moravetski et al. (1996) reported theoretical ²⁹Si NMR chemical shifts for most of these fragments, as well as for the prismatic hexamer and the tetrahedral tetramer. A systematic study of a large variety of neutral silica clusters using DFT was performed by Pereira et al., 1999a, Pereira et al., 1999b Gas-phase molecular structures, energies, dipole moments and atomic charges were presented. The flexibility of the Si–O–Si angle and the ability to form intramolecular hydrogen bonds were identified as the two main factors controlling the wide variety of observed structures in vacuo. In some cases, general trends in cluster stability matched those observed experimentally. It should be noted, however, that clusters with four or more Si atoms were treated only at the local DFT level, due to restrictions in available computer power.

There have been fewer theoretical studies devoted to anionic silicates. Anionic forms of monosilicic acid have been optimized using HF (Kubicki et al., 1995, Moravetski et al., 1996, Tossell and Sahai, 2000, Šefčı´k and Goddard, 2001), MP2 (Kubicki et al., 1995, Tossell and Sahai, 2000, Šefčı´k and Goddard, 2001) and DFT methods (Rustad et al., 2000, Tossell and Sahai, 2000, Šefčı´k and Goddard, 2001). Šefčı´k and Goddard III (2001) used several different computational approaches to calculate the acidity of monosilicic acid and obtained good agreement with experimental values. They concluded that in order to obtain accurate energies, diffuse functions had to be included in the calculations. Xiao and Lasaga (1996) have presented the HF/6-31G^∗ optimized geometry of the singly-deprotonated dimer as part of a study on quartz dissolution. Kubicki et al. (1996) calculated the deprotonation energy of a branched tetramer in an attempt to represent the deprotonation of mineral surfaces. The anionic monomer and dimer were studied by Tossell and Sahai (2000), who also looked into the deprotonation energies of the cyclic trimer and the cyclic tetramer. The structure for the single-deprotonated dimer obtained by these authors differed significantly from the one calculated by Xiao and Lasaga (1996) at the same level of theory. More recently, two studies have focused on larger deprotonated silicates (Murashov, 2003, Mora-Fonz et al., 2005). Murashov (2003) has applied DFT methods to the neutral and singly-deprotonated forms of the monomer, dimer, trimer and branched tetramer. Energies, structures and charges of these species were presented. However, this author was mainly concerned with characterizing bonding around silica surface sites. As such, he concentrated on structures with a high degree of symmetry and did not perform an exhaustive study of different minima on the potential energy surface. Mora-Fonz et al. (2005) have presented the energies of several neutral and anionic silicates, both in the gas phase and in a continuum model solvent. Their objective was to compare relative energies and discuss trends in deprotonation and condensation reactions. Unfortunately, the energies presented by Mora-Fonz et al. (2005) have been obtained with a basis set where diffuse functions were absent and, as pointed out by Šefčı´k and Goddard III (2001) for the monomer, this is essential for obtaining accurate energies. One should expect the errors introduced by the absence of diffuse functions in the calculations to be even higher for larger charged silicates. Therefore, due to the inconsistencies that seem to affect theoretical studies of anionic silicates, it would be important to perform a systematic analysis of the molecular structure and energetics of these compounds.

In this paper, we present results of a comprehensive DFT study of neutral and anionic silicates in the gas phase, ranging from the monomer to the pentamer. Detailed structures, charges and energies are given, and a discussion of the relative stability of these species is presented. Our calculations complement those of Pereira et al., 1999a, Pereira et al., 1999b on neutral silicates, since we employ a much higher level of theory (now possible due to improvements in computer power). We employ a large basis set, augmented by diffuse functions, so as to obtain accurate deprotonation and condensation energies, avoiding the pitfalls of previous theoretical studies on anionic silicates. Trends in gas-phase energies can provide useful insights about complex reactions in solution (Pereira et al., 1999a, Gomes et al., 2003, Camps et al., 2006, Ferraz et al., 2007), but cannot be quantitatively compared to experimental solution chemistry, since solvation effects are not accounted for. In an attempt to circumvent this problem, we have repeated the energy calculations in the presence of a continuum model solvent. In a subsequent publication, we will present results of a more detailed theoretical study of anionic silicates in continuum model solvents, as well as in the presence of explicit water molecules. Results of our DFT calculations have already been used in molecular dynamics simulations of the early stages of periodic mesoporous silica synthesis (Jorge et al., 2007). The present paper is organized as follows: Section 2 gives details of the computational procedures; Section 3 addresses the main results of our study and discusses the gas-phase structures and charges obtained, as well as trends in deprotonation and condensation energies; finally, in Section 4 we present some conclusions and outline future work to be undertaken.