Comparative study of force-based classical density functional theory.

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Computational Physics

Background:

• Density functional theory (DFT) is crucial for modeling fluids.
• A recent force-DFT framework offers a new approach.
• Evaluating its performance against simulations and standard DFT is necessary.

Purpose of the Study:

• To reexamine and assess the recently proposed force-density functional theory (force-DFT).
• To compare force-DFT predictions for inhomogeneous hard sphere fluids against standard DFT and simulations.
• To develop and test a hybrid scheme to improve force-DFT performance.

Main Methods:

• Comparison of inhomogeneous density profiles from force-DFT, standard DFT, and grand canonical Monte Carlo simulations.
• Analysis of dynamical relaxation of hard spheres using event-driven Brownian dynamics data.
• Development and testing of a hybrid scheme combining standard and force-DFT.

Main Results:

• Equilibrium force-DFT alone did not outperform the standard Rosenfeld functional for hard sphere fluids.
• Force-DFT also showed similar limitations in predicting dynamical relaxation.
• A simple hybrid scheme, combining standard and force-DFT, significantly improved accuracy for both equilibrium and dynamics.

Conclusions:

• Standard force-DFT, in its current form, does not offer advantages over established methods for hard sphere fluids.
• A hybrid approach effectively rectifies the deficiencies of force-DFT.
• The developed hybrid method achieves performance comparable to advanced theories like White Bear theory, despite its simpler foundation.