An ab initio density functional for penetrable spheres

We develop a density functional theory for a system of penetrable spheres that interact with a constant pair potential energy if their separation distance is smaller than their diameter. As sufficient input, just the geometrical properties of the particles and the exactly known statistical behaviour of the system under strong confinement are needed. The theory predicts the bulk fluid properties in good agreement with computer simulations and better than liquid integral theories, as well as the freezing transition to a multiply occupied face-centred-cubic lattice. It becomes exact in the limits of strong confinement and high temperature, and coincides with a successful hard-sphere theory for zero temperature.