Prediction of pharmaceutical solubility in mixed-solvents with a local composition-quantum energy parameter model

Theoretical approaches for estimating pharmaceutical solubility in solvents can reduce experimental effort for optimizing design of separation and purification steps. In this work, an approach is developed for solvent selection of pharmaceuticals that is based on geometric energy difference (GED), determined from interaction energies via density functional theory and time dependent density functional theory calculations. Interaction energies were optimized through surface charge density predictions at the aug-cc-pvdz/blyp level of theory, with computational efficiency enhanced via machine learning. Comparison between GED and Hansen solubility parameter (HSP) approaches for solvent selection revealed that the GED approach was more selective than the HSP relative energy difference solubility sphere approach. An activity coefficient model was developed to predict pharmaceutical solubility in mixed-solvents based on local composition theory and optimization of quantum energy parameters (LC-QEP model). For 41 pharmaceutical-mixed-solvent systems, the LC-QEP model predicted API solubility to within an average relative deviation logarithm (ARDln) of 0.669, compared with an ARDln of 1.755 for the RST model based on HSP. The LC-QEP model was compared with other molecular-based models for prediction of API solubility. For naproxen- and paracetamol- mixed-solvent systems, average ARDln values for the LC-QEP model (0.117) were lower than those of the PC-SAFT equation of state model (0.369). For the vanillin-water-ethanol system, average ARDln values were lower for the LC-QEP model (0.137) than the COSMO-RS model (ARDln=0.294). For the aspirin-methylcyclohexane-ethanol system, average ARDln values of the PC-SAFT equation of state based on COSMO (0.102) were lower than those of the LC-QEP model (0.153) which may be attributed to weak interactions being over-estimated by the LC-QEP model. The GED approach can be used to reliably select solvents for pharmaceuticals and the LC-QEP model is able to predict API solubilities in mixed-solvent systems with lower deviations than several predictive models.

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