Inspite of its wide use as support in heterogeneous catalysis, accurate atomically detailed models of amorphous silicates have been elusive to-date. Amorphous silica, which is composed of SiO₄ tetrahedral units in the form of siloxane rings of different sizes, shows local structural disorder and surface heterogeneity that play a key role in its reactivity. Although it is difficult to identify and understand the distribution of catalytically active sites and their structures from experimental characterization, density functional theory (DFT) simulations allow us to probe the properties of the individual sites. In this contribution, cluster models of amorphous silica are used to study the thermodynamics of the functionalization reaction on the silica surface. We investigate the variation of functionalization energy with the structural parameters of the unfunctionalized site, which are defined as descriptors. We use the random forests regression model to determine the most important descriptor(s) that correlates with the functionalization energy. Considering the different combinations, a two-descriptor set composed of r^_L(longest Si-O bond at the site) and θ_diff^_P(difference between the smallest and largest angles of the unfunctionalized ring) provides the lowest average root mean square error (RMSE), which is still 30% of the average functionalization energy in magnitude. While increasing the size of the data set should improve the machine learning fitting and reduce the RMSE, modelling large clusters is computationally expensive. Thus, for a quantitative simulation of the reaction we attempt to produce minimal models of the site of functionalization that effectively mimic the results of the large clusters. We truncate (and cap the dangling bonds with F atoms) or relax (and freeze the surroundings) the original large clusters. Repeating the calculations by increasing the radii of truncation (or relaxation) of the clusters from the functionalization site, it is seen that the energy changes with increase in size of the clusters until it converges. These results show that not only the local coordination environment but the bulk of amorphous silica significantly affect the functionalization energy.

Marco Caricato

University of Kansas

Appearances