  In the current article, we rederive the lattice-fluid excess models UNIQUAC,
UNIFAC, and COSMO-RS from a continuum functional. The calculation explains the
missing dependence on the particle geometry and how to include the Coulomb
interaction, problems that are common to all three models. It is then shown
that the Wilson ansatz, used in UNIQUAC and UNIFAC to minimize the grand
potential, is not a physically valid solution of the Euler-Lagrange equation. A
consistent approach is the Larsen-Rasmussen equation, which forms the
foundation of COSMO-RS. We then analyze the various approximation methods and
interpret them in the framework of a molecular density functional.
