Combining integral equation closures with force density functional theory for the study of inhomogeneous fluids

Classical density functional theory (DFT) is a powerful framework to study inhomogeneous fluids. Its standard form is based on the knowledge of a generating free energy functional. If this is known exactly, then the results obtained by using standard DFT or its alternative, recently developed version, force-DFT, are the same. If the free energy functional is known only approximately then these two routes produce different outcomes. However, as we show in this work, force-DFT has the advantage that it is also implementable without knowledge of the free energy functional, by using instead liquid-state integral equation closures. This broadens the range of systems that can be explored, since free energy functionals are generally difficult to approximate. In this paper we investigate the utility of using inhomogeneous integral equation closures within force-DFT thus demonstrating the versatility and accuracy of this approach.