Computational methodology for solubility prediction: Application to the sparingly soluble solutes

Abstract

The solubility of a crystalline substance in the solution can be estimated from its absolute solid free energy and excess solvation free energy. Here, we present a numerical method, which enables convenient solubility estimation of general molecular crystals at arbitrary thermodynamic conditions where solid and solution can coexist. The methodology is based on standard alchemical free energy methods, such as thermodynamic integration and free energy perturbation, and consists of two parts: (1) systematic extension of the Einstein crystal method to calculate the absolute solid free energies of molecular crystals at arbitrary temperatures and pressures and (2) a flexible cavity method that can yield accurate estimates of the excess solvation free energies. As an illustration, via classical Molecular Dynamic simulations, we show that our approach can predict the solubility of OPLS-AA-based (Optimized Potentials for Liquid Simulations All Atomic) naphthalene in SPC (Simple Point Charge) water in good agreement with experimental data at various temperatures and pressures. Because the procedure is simple and general and only makes use of readily available open-source software, the methodology should provide a powerful tool for universal solubility prediction.

A simulation study of homogeneous ice nucleation in supercooled salty water

“…On the other hand, we perform thermodynamic integration [35] from previous calculations of the chemical potential of the solvent and the solute [30,34] and from the melting point of pure water [54] in order to find the melting temperature as that for which the chemical potential of water in ice and in solution coincide. The calculation of the chemical potential of the components of a solution is a difficult task that has recently received great attention in the context of the computation of crystal solubilities [55][56][57][58][59][60].…”

Challenges in the use of atomistic simulations to predict solubilities of drug-like molecules

“…The solubility of naphthalene was recently estimated using a similar methodology, the Extended Einstein Crystal Method 23 , but with additional approximations. Specifically, since naphthalene molecules interact very weakly with each other in the crystal lattice and with water molecules in solution, the differences between the internal partition function of a naphthalene molecule in the solid and in the solution were assumed to be negligible.…”

“…We are aware of three main approaches to compute the solubility of solids in solution using physical approaches: ECM-based methods 21, 23 , EMM-based methods 22, 51, 55 , and the approach of Michael Schnieders and collaborators which computes sublimation and solvation free energies and uses these in an alternate thermodynamic cycle to obtain solubility estimates 15, 56 .…”

“…Li et al . 23 used the ECM to estimate the solubility of napthalene, but made several approximations such as assuming that the internal partition function component of the solute cancels between environments (perhaps justified given napthalene’s low solubility).…”

“…While these physical methods for predicting solubilities have received some attention in the literature, most are still in their infancy, with only a handful of studies applying them, and it is not yet clear how broadly applicable they will be 17– 20 , and others have only been suggested or demonstrated in proof-of-principle tests 16, 21– 23 . Our view is that the time is ripe for physical methods to predict solubility, especially given the routine nature of solvation free energy calculations at present 24– 29 , which comprise essentially half of the solubility problem (see the Theory section).…”