Density-functional theory for soft interactions by dimensional crossover.

A density-functional theory for spherical particles interacting via an arbitrary soft pair potential is presented. The derivation is solely based on limits, where the behavior is exactly known, namely, a zero-dimensional cavity and the low-density virial expansion. The approach generalizes the fundamental-measure theory for hard bodies and yields the structure and thermodynamics of the homogeneous fluid as an output. We apply the theory to an ultrasoft logarithmic potential that mimics star polymers in a good solvent. The theory, when supplemented by a rescaling procedure, reproduces the peculiar features of the pair correlations in this system that we also find in computer simulations.