Empirical regressions between system parameters and solute descriptors of polyparameter linear free energy relationships (PPLFERs) for predicting solvent-air partitioning

Abstract

Polyparameter Linear Free Energy Relationships (PPLFERs) are an empirical tool used to predict the equilibrium partitioning of solutes between two phases, referred to as a system. There are experimentally determined solute descriptors for thousands of chemicals, but there are only on the order of 100 systems with calibrated system parameters, the majority of which are solvents and environmental matrixes in equilibrium with air or water. The goal of this work is to create empirical regressions which use the much more numerous solute descriptors to predict the system parameters of systems which have not yet been calibrated due to a lack of partitioning data. The special case of liquid solvents in equilibrium with air is the focus of this work because this is the case in which the relationship between solute and solvent properties is most clear. First a consistent dataset of PPLFER equations was compiled using partition coefficient data from the literature to recalibrate equations for solvent-air partitioning into the Goss form (Goss, K.-U. 2005) for 89 solvents including water. All 89 solvents have also solute descriptors available in a database curated for this work which describe their behaviour as solutes. The pool of descriptors drawn from to create the empirical regressions were the solute descriptors of the solvents normalized to McGowan volume (V), along with interaction parameters between the normalized descriptors. An applicability domain (AD) for the empirical regressions was defined using leverage to measure similarity to the training dataset of solvents, and solvents in the AD typically had lower RMSE for predictions. Some of the empirical regressions for the six system parameters have good predictive power (s, a, b, c) while others are only adequate (v, l). However, when these equations are combined to predict partition coefficients there is a significant cancellation of error and when predicting partition coefficients in an external validation dataset the RMSE is in the range 0.30–0.35. The empirical regressions combined with the PPLFER equations and solvent density can also be used to predict vapor pressures as an additional external validation. Predictions for a dataset of vapor pressures from the literature had an RMSE of 0.26–0.75. Analysing and comparing the results from these two external validation datasets the RMSE for predicting datasets of partition coefficients for arbitrary solutes in arbitrary systems of solvents in equilibrium with air is estimated to be 0.66 on average.