Lattice resistance to hydrolysis of Si-O-Si bonds of silicate minerals:: Ab initio calculations of a single water attack onto the (001) and (111) β-cristobalite surfaces

Hydrolysis of Si-O-Si linkages of beta-cristobalite by a single H2O molecule is studied within the cluster approach at the DIPT (B3LYP) and MP2 levels of theory. The 6-31G(d) and 6-311G(d) basis sets are used. Cluster models, including from 6 up to 14 Si atoms, of the (001) and (111) surface planes are considered. These models are specially designed to take into account the steric constraints imposed by the solid matrix on the Si-O-Si linkages and their nearest surroundings. For comparison, the hydrolysis of the Si-O-Si bridge of the free (HO)(3)Si-O-Si(OH)(3) molecule is also calculated. The computed activation energy of the reaction (Delta E-a) for the (001) and (111) planes of beta-cristobalite is larger by 5 and 16 kcal/mol, respectively, than for (HO)(3)Si-O-Si(OH)(3) (17 kcal/mol). The higher energy barrier for the surface is due to the resistance of the lattice to the relaxation of the activated complex of the reaction. The difference in Delta E-a between the (001) and (111) planes suggests that the larger the number of Si-O-Si bridges for a Si atom (2 for the (001) plane and 3 for the (111) plane), the stronger the resistance of the solid matrix to the hydrolysis of a Si-O-Si bridge. This finding allows for the atomic-level substantiation of the earlier hypotheses that (i) the hydrolysis of the first Si-O-Si linkage of a Si atom should be the rate-limiting step for the release of Si(OH)(4) acid (ii) the dissolution should preferentially take place for the low-linked Si species of the surface. The OH groups produced by the reaction form H-bonds with the nearby Si-OH and Si-O-Si surface species. For both planes, the energy of the reaction (Delta E-r) is within the 1-2 kcal/mol range.