Weighted-density functionals for cavity formation and dispersion energies in continuum solvation models

TL;DR

This paper develops a minimally-empirical continuum solvation model using physical principles to accurately predict solvation energies across various solvents with minimal parameter fitting.

Contribution

It introduces a new solvation model that replaces empirical terms with physically derived functions, reducing the need for extensive parametrization.

Findings

Accurately predicts solvation energies with low RMS errors

Uses a single solvent-independent parameter ($n_c$)

Employs a single solvent-dependent parameter ($s_6$)

Abstract

Continuum solvation models enable efficient first principles calculations of chemical reactions in solution, but require extensive parametrization and fitting for each solvent and class of solute systems. Here, we examine the assumptions of continuum solvation models in detail and replace empirical terms with physical models in order to construct a minimally-empirical solvation model. Specifically, we derive solvent radii from the nonlocal dielectric response of the solvent from ab initio calculations, construct a closed-form and parameter-free weighted-density approximation for the free energy of the cavity formation, and employ a pair-potential approximation for the dispersion energy. We show that the resulting model with a single solvent-independent parameter: the electron density threshold ($n_c$), and a single solvent-dependent parameter: the dispersion scale factor ($s_6$), reproduces solvation energies of organic molecules in water, chloroform and carbon tetrachloride with RMS errors of 1.1, 0.6 and 0.5 kcal/mol respectively. We additionally show that fitting the solvent-dependent $s_6$ parameter to the solvation energy of a single non-polar molecule does not substantially increase these errors. Parametrization of this model for other solvents, therefore, requires minimal effort and is possible without extensive databases of experimental solvation free energies.