Predicted Properties of Active Catalyst Sites on Amorphous Silica: Impact of Silica Preoptimization Protocol

Heterogeneous catalysts based on metal-doped amorphous silicates are characterized by quenched disorder and dynamical disorder. The first refers to the disordered siloxane network that is locked-in by strong bonds that do not rearrange on the time scale of the catalytic reactions. The second refers to the hydrogen bond network of the silanol groups that can rearrange quickly during the reactions. Both types of disorder affect and define the activity and selectivity of the catalyst. However, in quantum mechanical (QM) simulations of these materials, there is a third type of disorder that is often overlooked: the procedural disorder. This refers to differences in energy and barriers of the active sites that are solely induced by the computational protocol used to create the supermolecular cluster models often used in these simulations. In this work, we present a detailed investigation of this procedural disorder by comparing two geometry optimization protocols for the grafting of CrO₂on the silica surface, i.e., the active site of the Phillips catalyst used for the industrial production of polyethylene. The first protocol, most often used in these simulations, starts from a silica structure obtained from classical molecular dynamics (MD) simulations, and only the central region surrounding the metal is relaxed (MD-Opt). The second protocol (QM-Opt) relaxes a large portion of the cluster at the QM level before grafting. We compare these protocols using an empirical disordered lattice model that allows us to explore significantly larger cluster model sizes and atomistic models treated at the QM level. The results show that the MD-Opt protocol induces large and erratic variations in the grafting energy even if large regions of the silica are relaxed. In fact, this approach produces (unphysical) procedural disorder that is of the same order of magnitude of (physical) quenched disorder. On the other hand, the QM-Opt protocol minimizes the effects of procedural disorder, and the effect smoothly decreases with the size of the relaxed region. Furthermore, the QM-Opt protocol is more computationally efficient than the MD-Opt protocol when the size of the relaxed zone is sufficiently large to provide an acceptably small amount of procedural disorder.