Revisiting density functionals for the primitive model of electric double layers.

Density functional theory (DFT) calculations are typically based on approximate functionals that link the free energy of a multi-body system of interest with the underlying one-body density distributions. Whereas good performance is often proclaimed for new developments, it is difficult to vindicate the theoretical merits relative to alternative versions without extensive comparison with the numerical results from molecular simulations. Besides, approximate functionals may defy statistical-mechanical sum rules and result in thermodynamic inconsistency. Here we compare systematically several versions of density functionals for ionic distributions near a charged surface using the primitive model of electric double layers. We find that the theoretical performance is sensitive not only to the specific forms of the density functional but also to the range of parameter space and the precise properties under consideration. In general, incorporation of the thermodynamic sum rule into the DFT calculations shows significant improvements for both electrochemical properties and ionic distributions.