The crystal structures of a large number of silica polytypes (α-and β-quartz, α-and βcristobalite, β-tridymite, keatite, coesite and stishovite) have been studied using density functional theory, both in the local density approximation and including generalized-gradient corrections to the exchange-correlation functional. All crystal structures have been optimized by minimizing the total energy with respect to all lattice parameters and to the atomic coordinates within the unit cell (up to 40 structural parameters in the case of coesite). The α → β transitions in quartz and cristobalite have been studied in detail, including different variants proposed for the structure of βcristobalite. The tetragonal (I42d) and simple cubic (P 2 1 3) structures are found to be energetically almost degenerate near the equilibrium volume. On volume expansion both structures converge towards the idealized highly symmetric F d3m structure. A similar continuous transition from a more compact orthorhombic (C222 1) to a highly symmetric hexagonal (P 6 3 /mmc) variant is also proposed for β-tridymite. For coesite two monoclinic variants (with C2/c and P 2 1 /c spacegroup symmetries, respectively) have been examined and found to be energetically degenerate to within 1 meV per SiO 2 unit. It is shown that within the local density approximation (LDA) the equilibrium atomic volume of all polytypes is predicted with an accuracy better than one per cent. The LDA also leads to excellent structural predictions and to accurate values of the bulk modulus. Corrections in the framework of the generalized-gradient approximation (GGA) lead to substantially larger equilibrium volumes, although at fixed volume the LDA and GGA lead to identical crystal structures. The increased volume also leads to less accurate structural parameters. However, we find that gradient corrections are essential for achieving accurate structural energy differences between the tetrahedrally coordinated phases found at larger atomic volumes (all polytypes except stishovite) and the octahedrally coordinated high-pressure polymorphs (stishovite and post-stishovite phases).

The effects of the Si → Al substitution on the structure of the siliceous framework and the structure and vibrational properties of Brønsted acid sites in mordenite have been studied using density-functional theory, both in the local-density approximation and including generalized gradient corrections to the exchange-correlation functional. The substitution induces a substantial local deformation of the polytetrahedral geometry of pure-silica mordenite. Also the counterions have a strong influence on the geometry of the framework. Protonation of bridging (Si)−O−(Al) oxygen atoms is accompanied by a further local distortion of the structure. Changes in the bond lengths remain well localized to the nearest neighborhood of the perturbation center; O−H stretching frequencies of acidic protons were calculated in both harmonic and anharmonic approximations, indicating a rather complex relationship among stability, frequencies, and local environment of the Brønsted acid sites.

Isobutene chemisorption within proton-exchanged zeolites is investigated using periodic density functional theory method. This allows us to consider the effect of the zeolite micropore dimension to reactivity. The isobutene reaction pathways that proceed through primary and tertiary carbocation-like transition states have been investigated. The results agree with predicted reactivity trends. Activation energies of isobutene chemisorption are estimated to be around 100 and 25 kJ/mol for primary and tertiary transition states, respectively. Destabilization of transition state complexes and products are as observed before. Interestingly, because of the steric constraints, the chemisorbed alkoxy species appeared to become as unstable as protonated hydrocarbons. The more significant result is the correlation of the zeolite micropore dimension with activation energies. Fluctuations of the activation energies are observed as a function of the match of the transition state structures with the zeolite cavities. We define a limit to the applicability of the semiempirical Polaniy−Evans−Brønsted relation in zeolite catalysis.