Prediction of aqueous solubility by treatment of COSMO-RS data with empirical solubility equations: the roles of global orbital cut-off and COSMO solvent radius

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Aqueous solubility values of (E)-2-(ethyl(4-((4-nitrophenyl)diazenyl)phenol)amino)ethanol [B1], (E)-2,2′-((4-((4-nitrophenyl)diazenyl)phenyl)azanediyl)diethanol [B2], (E)-2,2′-((3-methyl-4-((4-nitrophenyl)diazenyl)phenyl)azanediyl)diethanol [B3] and (E)-2-((4-((2,4-dinitrophenyl)diazenyl)phenyl)(ethyl)amino)ethanol [B4] were predicted by the treatment of relevant COSMO-RS data with Cramer et al. solubility equation (CSE) and general solubility equation (GSE). DMol3 computational code was employed for the study, where all calculations were carried out using VWN-BP level of theory with double numerical basis set containing polarization functions (DNP). Effects of global orbital cut-off and COSMO solvent radius (CSR) on the predicted results were examined. The results revealed that COSMO-RS data performed very well with both the CSE and GSE, but the latter exhibited a greater prediction strength on average. For nearly all the studied molecules, GSE calculated solubility (SGSE) was found to increase with orbital cut-off and reached an optimum value at a cut-off of 5.5 A. SGSE values obtained at this and higher cut-off values studied are comparable to experimental solubility values, especially for B1, B3 and B4, while better results were obtained for B2 at lower cut-off values. CSE calculated solubility (SCSE) showed no constant trend with cut-off variation, but at cut-off values ≥ 7.0 A the SCSE values compare well with the experimental values, especially in the cases of B2 and B3. For all the studied molecules, SGSE decreased with the increase in CSR and the most reliable CSR value for GSE was found to be 1.3 A. On the contrary, SCSE increased with CSR and for B1 and B4, this increase was followed by a drop in predicted values at CSR > 1.3 A. However, the best CSR value for CSE was found to be 0.5 A for almost all the molecules. Our findings have shown that aqueous solubility (in mol/L) of azo dyes can be accurately predicted using CSE or GSE with some COSMO-RS data and that global orbital cut and COSMO solvent radius are essential parameters for accurate prediction.