Theoretical models of solubility for organic solvents. A conceptual density functional theory approach

We present a simple semi-empirical model for solubility in organic solvents, based on the conceptual density functional theory (CDFT) and inspired on the well-known empirical linear solvation energy relationships (LSER) proposed by Kamlet and Taft, where a multiparametric correlation between solubility and empirical descriptors including the hydrogen bond acidity (HBA) and basicity (HBB) plus an additional term describing the dipole polarizability of the solvents was presented. Herein, we set up an analogue model that describes HBA, HBB and dipole polarizability with electronic descriptors derived from the conceptual density functional theory. The main relevant results are as follows: (i) as expected, HBA and HBB properties are not absolute but regional properties, thereby suggesting that any solvent can display both properties with different weights (bifunctional solvents); (ii) while HBA can nicely be represented by a regional electrophilicity index, the HBB property can be accounted for by a regional nucleophilicity. The dipole polarizability is consistently represented by the global softness of the solvent molecule; (iii) the regionalization of these properties is achieved by defining electrophilic and nucleophilic basins within a given solvent molecule by using the electrophilic and nucleophilic Fukui Functions integrated within these basins. The resulting model is validated against the experimental solubility of vanillin and hesperidin in different organic solvents. Further perspectives of the present study should be of special interest in theoretical studies concerning ionic liquids and deep eutectic solvents.