The Gordian knot of density-functional theories for classical molecular liquids remains finding an accurate free-energy functional in terms of the densities of the atomic sites of the molecules. Following Kohn and Sham, we show how to solve this problem by considering noninteracting molecules in a set of effective potentials. This shift in perspective leads to an accurate and computationally tractable description in terms of simple three-dimensional functions. We also treat both the linear- and saturation- dielectric responses of polar systems, presenting liquid hydrogen chloride as a case study. © 2008 The American Physical Society.