Multi-Time-Scale Simulation of Complex Reactive Mixtures: How Do Polyoxometalates Form?

Understanding the dynamics of reactive mixtures still challenges both experiments and theory. A relevant example can be found in the chemistry of molecular metal-oxide nanoclusters, also known as polyoxometalates. The high number of species potentially involved, the interconnectivity of the reaction network, and the precise control of the pH and concentrations needed in the synthesis of such species make the theoretical/computational treatment of such processes cumbersome. This work addresses this issue relying on a unique combination of recently developed computational methods that tackle the construction, kinetic simulation, and analysis of complex chemical reaction networks. By using the Bell-Evans-Polanyi approximation for estimating activation energies, and an accurate and robust linear scaling for correcting the computed pK_a values, we report herein multi-time-scale kinetic simulations for the self-assembly processes of polyoxotungstates that comprise 22 orders of magnitude, from tens of femtoseconds to months of reaction time. This very large time span was required to reproduce very fast processes such as the acid/base equilibria (at 10^-12 s), relatively slow reactions such as the formation of key clusters such as the metatungstate (at 10³ s), and the very slow assembly of the decatungstate (at 10⁶ s). Analysis of the kinetic data and of the reaction network topology shed light onto the details of the main reaction mechanisms, which explains the origin of kinetic and thermodynamic control followed by the reaction. Simulations at alkaline pH fully reproduce experimental evidence since clusters do not form under those conditions.