Computation of entropy values for non-electrolyte solute molecules in solution based on semi-empirical corrections to a polarized continuum model

Abstract

A simple heuristic model was developed for estimating the entropy of a solute molecule in an ideal solution based on quantum mechanical calculations with polarizable continuum models (QM/PCMs). A translational term was incorporated that included free-volume compensation for the Sackur–Tetrode equation and a rotational term was modeled based on the restricted rotation of a dipole in an electrostatic field. The configuration term for the solute at a given concentration was calculated using a simple lattice model that considered the number of configurations of the solute within the lattice. The configurational entropy was ascertained from this number based on Boltzmann's principle. Standard entropy values were determined for 41 combinations of solutes and solvents at a set concentration of 1 mol dm⁻³ using the proposed model, and the computational values were compared with experimental data. QM/PCM calculations were conducted at the ωB97X-D/6-311++G(d,p)/IEF-PCM level using universal force field van der Waals radii scaled by 1.2. The proposed model accurately reproduced the entropy values reported for solutes in non-aqueous solvents within a mean absolute deviation of 9.2 J mol⁻¹ K⁻¹ for 33 solutions. This performance represents a considerable improvement relative to that obtained using the method based on the ideal gas treatment that is widely utilized in commercially available computation packages. In contrast, computations for aqueous molecules overestimated the entropies because hydrophobic effects that decrease the entropy of aqueous solutions were not included in the present model.