Approximate additivity in the solvent-mediated potential of mean force for ultrasoft particle systems

Recently, an approximate additivity principle has been successfully applied to molecular chemical potentials in ultrasoft particle systems [Hendrikse et al., Phys. Chem. Chem. Phys. 27, 1554 (2025)]. We articulate this additivity principle as one of two Ansätze and apply these to dimers in the infinite dilution limit. In this limit, we show that the solvent-mediated potential of mean force (PMF) between solutes, extracted from the hypernetted-chain closure of the Ornstein-Zernike equations, can be expressed as a convolution between solute-specific generalized excluded volume functions. In the limit of a structureless solvent of point particles and hard-core solutes, this recovers the exact Asakura-Oosawa depletion potential as the overlap between excluded volume spheres. The theory extends to the opposite limit of ultrasoft particle solvents and solutes, such as those encountered in dissipative particle dynamics (DPD), where the solvent-mediated PMF can be recovered with considerable accuracy. These results confirm that in coarse-grained molecular DPD simulations, the parameterization of solute-solvent interactions is sensitive to intramolecular bond lengths if they are smaller than the range of the solvent-solvent interaction potential, due to the overlap of the soft excluded volume functions.