Multi-Time Scale Simulation: How do Polyoxometalates Form?

Determining the self-assembly of polyoxometalates in solution still represents a major challenge, due to the multiple variables (e.g., concentration, pH, ionic strength, temperature, counterions) that govern the formation of the final product. Hitherto, the only theory that has attempted to rationalize these processes relies on the concept of a dynamic library of building blocks that spontaneously self-assemble.[1] Even so, the aqueous speciation at chemical equilibrium has been successfully studied for several decades using a wide range of experimental techniques.[2] More recently, a new computational method, POMSimulator, which has also contributed to understanding the speciation of five families of polyoxometalates.[3-5]

While the distribution of species at chemical equilibrium is well-known for many molecular metal-oxide systems, the speciation beyond equilibrium is poorly understood. Therefore, recent studies attempted to combine multiple state-of-the-art techniques to determine the kinetics involved in the self-assembly of polyoxometalates. Isopolyoxotungstates formation was studied, since these species display challenging reactivity due to the metastability of some species, and the slow formation of the main products. Firstly, POMSimulator was used to generate a chemical reaction network containing acid-base, condensation, additions, and isomerization reactions. The geometries of the chemical species were previously optimized using ADF20119. PLAMS was used to automatize and speed-up the process. The Bells-Evans-Polanyi principle was used to estimate the activation barriers of the addition and condensations reactions. The researchers also rescaled the reaction free energies of the protonation reactions, which is a common practice when relying on energies computed with density functional theory. Once the network was complete, the kinetics of the overall process were simulated with KiNeTx. At acid conditions spontaneous self-assembly was observed, starting from the protonation of the monomer at picoseconds (in good agreement with the Grotthuss mechanism), the formation of the metastable -[H₂W₁₂O₄₀]^6-, and the final product [W₁₀O₃₂]^4-. When the simulations were performed under alkaline conditions, no self-assembly was observed, which is consistent with the experimental data. Which mechanism connected the -[H₂W₁₂O₄₀]^6- and [W₁₀O₃₂]^4- was established with simulations using OntoRXN[7] and PathFinder[8]. It was found that the rate determining step of this process was the disassembly of -[H₂W₁₂O₄₀]^6-, since the reassembly to [W₁₀O₃₂]^4- was very favorable (∆G_r = -43 kcal·mol^-1).

In conclusion, a novel approach for unlocking the multi-time kinetic simulation of polyoxometalates (from picoseconds to months) has been developed. It has been demonstrated that the combination of recent techniques based on Graph Theory and ontologies provide an excellent framework for addressing these challenges.

Download the plams script for solvation energies with COSMO.

[1] Müller, A.; Gouzerh, P. From linking of metal-oxide building blocks in a dynamic library to giant clusters with unique properties and towards adaptive chemistry. Chem. Soc. Rev. 2012, 41, 7431–7463

[2] Gumerova, N. I.; Rompel, A. Polyoxometalates in solution: speciation under spotlight- Chem. Soc. Rev. 2020, 49, 7568-7601

[3] Petrus, E.; Segado, M.; Bo, C. Nucleation Mechanisms and Speciation of Metal Oxide Clusters, Chemical Science 2020, 11, 8448

[4] Petrus, E.; Bo, C. Unlocking Phase Diagrams for Molybdenum and Tungsten Nanoclusters and Prediction of Their Formation Constants, J. Phys. Chem. A 2021, 125, 5212

[5] Petrus, E.; Segado-Centellas, M.; Bo, C. Computational Prediction of Speciation Diagrams and Nucleation Mechanisms: Meolecular Vanadium, Niobium, and Tantalum oxide Nanoclusters in Solution. Inorg. Chem. 2022, 61, 35, 13708-13718

[6] Proppe, J.; Reiher, M. Mechanism Deduction from Noisy Chemical Reaction Networks. J. Chem. Inf. Model. 2019, 15, 357–370

[7] Garay-Ruiz, D.; Bo, C. Chemical Reaction Network Knowledge Graphs: The OntoRXN Ontology. J. Cheminf. 2022, 5,1–12

[8] Türtscher, P. L.; Reiher, M. Pathfinder Navigating and Analyzing Chemical Reaction Networks with an Efficient Graph Based Approach. J. Chem. Inf. Model.2023, 63, 147–160