Using test particle sum rules to construct accurate functionals in classical density functional theory.

Area of Science:

• Statistical Mechanics
• Physical Chemistry
• Computational Physics

Background:

• Fundamental Measure Theory (FMT) is a robust approach within classical density functional theory (DFT) for modeling hard-sphere fluids.
• A prior FMT formulation by Lutsko introduced two free parameters requiring external physical constraints for determination.
• Previous work focused on crystalline phase stability, leaving fluid phase constraints less explored.

Purpose of the Study:

• To introduce and apply two statistical mechanical sum rules to refine FMT for the hard-sphere fluid phase.
• To determine the two free parameters in FMT by ensuring consistency with fluid phase sum rules.
• To enhance the predictive accuracy of FMT for hard-sphere fluid properties.

Main Methods:

• Employed two statistical mechanical sum rules relevant to the fluid phase.
• Minimized deviations between different calculation routes for excess chemical potential and isothermal compressibility.
• Determined FMT free parameters by enforcing consistency with the chosen sum rules.

Main Results:

• The application of fluid phase sum rules improved the accuracy of FMT predictions for hard-sphere fluids.
• Consistency with sum rules provides a method for parameter determination within FMT.
• The developed approach offers a way to assess the performance of general DFT approximations.

Conclusions:

• Incorporating fluid phase sum rules enhances the predictive power of FMT for hard-sphere systems.
• The test particle sum rules are applicable across various interparticle potentials.
• This method provides a valuable tool for validating and improving DFT approximations.