Towards a universal scaling method for predicting equilibrium constants of polyoxometalates

The computational prediction of equilibrium constants is still an open problem for a wide variety of relevant chemical systems. In particular, acid dissociation constants (pKa) are an essential asset in biological, synthetic and industrial chemistry whose prediction encounters several difficulties, requiring the development of novel strategies. The self-assembly of polyoxometalates (POMs) is another complex problem where acid-base reactions play a central role; the successful prediction of the formation constants of these structures is intimately linked with the limitations of pKa determination. Our methodology POMSimulator enables the prediction of these polyoxometalate formation constants from Density Functional Theory (DFT) calculations, using the experimental Kf values available in the literature to fit the resulting predictions. In this work, we carry out a systematic analysis of a very large number of POM formation constants already predicted through the application of POMSimulator. We then propose a universal scaling scheme for the adjustment of the DFT-based formation constants of POMs, relying on a linear scaling of the form y = mx + b. Here, the slope (m) is a constant parameter - hence, universal towards the nature of the polyoxometalate and the calculation method. The intercept (b), in contrast, is a system-dependent parameter that can be predicted with a multi-linear regression model trained with statistical aggregates of the non-scaled formation constants. Thus, we are able to successfully predict the speciation and phase diagrams of POM systems for which available experimental data are minimal, as well as provide a general scaling scheme that might be extended to other kinds of chemical systems.