Gibbs-Helmholtz graph neural network: capturing the temperature dependency of activity coefficients at infinite dilution

The accurate prediction of physicochemical properties of chemical compounds in mixtures (such as the activity coefficient at infinite dilution gamma ij infinity) is essential for developing novel and more sustainable chemical processes. In this work, we analyze the performance of previously-proposed GNN-based models for the prediction of gamma ij infinity, and compare them with several mechanistic models in a series of 9 isothermal studies. Moreover, we develop the Gibbs-Helmholtz Graph Neural Network (GH-GNN) model for predicting ln gamma ij infinity of molecular systems at different temperatures. Our method combines the simplicity of a Gibbs-Helmholtz-derived expression with a series of graph neural networks that incorporate explicit molecular and intermolecular descriptors for capturing dispersion and hydrogen bonding effects. We have trained this model using experimentally determined ln gamma ij infinity data of 40 219 binary-systems involving 1032 solutes and 866 solvents, overall showing superior performance compared to the popular UNIFAC-Dortmund model. We analyze the performance of GH-GNN for continuous and discrete inter/extrapolation and give indications for the model's applicability domain and expected accuracy. In general, GH-GNN is able to produce predictions with a mean absolute error below 0.3 for extrapolated binary-systems if at least 25 systems with the same combination of solute-solvent chemical classes are contained in the training set and a Tanimoto similarity indicator above 0.35 is also present. This model and its applicability domain recommendations have been made open-source at https://github.com/edgarsmdn/GH-GNN. A hybrid model that combines the Gibbs-Helmholtz equation with Graph Neural Networks for predicting limiting activity coefficients.