Comparative study of force-based classical density functional theory

TL;DR

This study compares force-based density functional theory with standard methods and simulations for hard sphere fluids, proposing a hybrid approach that improves accuracy in both equilibrium and dynamical scenarios.

Contribution

It introduces a hybrid scheme combining force-DFT and standard DFT to enhance predictions for hard sphere fluids, demonstrating comparable performance to advanced theories.

Findings

Force-DFT alone does not outperform standard Rosenfeld functional.

A hybrid method improves accuracy in equilibrium and dynamical cases.

Performance is comparable to the White Bear functional.

Abstract

We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [Tschopp et al., Phys. Rev. E 106, 014115 (2022)]. We compare inhomogeneous density profiles for hard sphere fluids to results from both standard density functional theory and from computer simulations. Test situations include the equilibrium hard sphere fluid adsorbed against a planar hard wall and the dynamical relaxation of hard spheres in a switched harmonic potential. The comparison to grand canonical Monte Carlo simulation profiles shows that equilibrium force-DFT alone does not improve upon results obtained with the standard Rosenfeld functional. Similar behavior holds for the relaxation dynamics, where we use our event-driven Brownian dynamics data as benchmark. Based on an appropriate linear combination of standard and force-DFT results, we investigate a simple hybrid scheme which rectifies these deficiencies in both the equilibrium and the dynamical case. We explicitly demonstrate that although the hybrid method is based on the original Rosenfeld fundamental measure functional, its performance is comparable to that of the more advanced White Bear theory.