Accurate Determination of Molecular Sizes of a Solute in Water From its Translational Self-Diffusion Coefficient

Abstract

Determining accurate molecular dimensions in water, from measured translational self-diffusion coefficients (D_t), is extremely important in biochemistry, supramolecular chemistry, organometallic chemistry and beyond, but it still represents a big challenge especially for small and medium-sized molecules. Indeed, current semiempirical adaptations of the Stokes-Einstein equation, which allow accurate determination of molecular size of solutes in organic solvents, proved inadequate for aqueous systems. To overcome such a major limitation, herein, we introduce a novel approach that unlocks the quantitative interpretation of D_t in water. By analyzing ~70 diverse molecules with volumes ranging from 10¹ ų to 10³ ų, and selecting the partial molar radius (r_M) as a reliable proxy for the hydrodynamic radius (r_H), we derived a semiempirical equation that enables accurate determination of hydrodynamic volume (V_H) of solutes in aqueous solutions, effectively accounting for the distinctive hydrogen-bonding properties of water. This approach fills a crucial gap, enhancing precise molecular characterization of polar and non-polar solutes in water.