Toward Predicting Solubility of Arbitrary Solutes in Arbitrary Solvents: Prediction of Density and Refractive Index...

Density and refractive index (nD) are routinely used in organic process development to support solvent selection, mixture formulation, phase behavior analysis, and rapid assessment of composition during scale-up and manufacturing. Reliable knowledge of these properties enables informed process decisions when chromatographic or spectroscopic methods are impractical or unavailable, particularly at the early development stages. In addition, the two properties are strongly related to the van der Waals (VDW) energy of a molecule. Thus, accurate prediction of these two properties has great value in both organic process development, molecular mechanics force field development, and solvation free energy and solubility prediction of any arbitrary molecules. In this study, we gathered molecular characteristic information on roughly 5000 organic compounds for density records and 4000 organic compounds for nD values. Subsequently, the distinct GAFF (General AMBER Force Field) descriptors and RDKit descriptors of the compounds were generated and then applied to train various prediction models with a variety of machine learning (ML) algorithms for both properties, respectively. As a result, both GAFF and RDKit descriptors yielded various robust models with low average percent errors (APE), low root-mean-square errors (RMSE), and high correlation coefficients R², while RDKit showed slightly better performance for predicting both properties. For each property, we further optimized the best-performing model and conducted both global sensitivity analysis (GSA) and Shapley analysis to identify specific features and feature groups that outstandingly contributed to model robustness. We next investigated the effect of temperature on model construction for each property by developing two additional models using a subset of data with available temperature information: one incorporating temperature as a feature and the other excluding it. Finally, we identified 72 outliers for the density property and performed molecular dynamics (MD) simulations of the pure liquids to predict their densities. We also conducted a thorough literature search for alternative experimental measurements. For most of these outliers, alternative values were found, and the updated experimental densities showed much better agreement with both the MD-predicted values and the AI model predictions. For density, the best-performing AI model has an average percent error (APE) of 3.15% for the test set if including the outliers and 2.67% if not. For nD, the best-performing model achieves an APE of 0.53% for the test set. The successful prediction of the two key molecular properties paves the road toward accurately predicting the solubility of an arbitrary solute in an arbitrary solvent, an endeavor that not only facilitates the pharmaceutical industry to develop better drug candidates but also increases efficiency regarding overall wet lab work. Certainly, robust ML models can be applied in organic process development.