Reformulation of nonperturbative density-functional theories of classical nonuniform systems

It is shown that most nonperturbative density-functional theories of classical systems can be reformulated as second-order truncations of exact perturbative expansions, thus eliminating the ad hoc nature of such theories. This reformulation is used as a basis for discussion as to why some theories work better than others when applied to hard spheres, why most theories perform poorly for continuous potentials, and in what direction they might be modified so as to improve their performance.