Routes to the Density Profile and Structural Inconsistency.

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Computational Physics

Background:

• Classical density functional theory (DFT) is crucial for studying inhomogeneous fluids under external fields.
• DFT relies on the excess Helmholtz free energy functional and the Euler-Lagrange equation.
• Force-DFT, a variant, uses the Yvon-Born-Green equation, aligning with the virial thermodynamic route.

Purpose of the Study:

• To present an alternative DFT scheme utilizing the Lovett-Mou-Buff-Wertheim (LMBW) equation.
• To demonstrate the consistency of the LMBW DFT with the compressibility route of thermodynamics.
• To explore an optimization scheme for minimizing structural inconsistencies between thermodynamic routes.

Main Methods:

• Implementation of an alternative DFT scheme based on the Lovett-Mou-Buff-Wertheim (LMBW) equation.
• Utilizing a closure relation on the level of two-body correlation functions for both force-DFT and LMBW DFT.
• Numerical simulations for density profiles of 2D hard-core Yukawa systems in planar geometry.

Main Results:

• The LMBW DFT scheme is shown to be consistent with the compressibility route for thermodynamics.
• Both force-DFT and LMBW DFT can be implemented using a closure relation on two-body correlation functions.
• Numerical results demonstrate density profiles for 2D systems with repulsive or attractive Yukawa tails.

Conclusions:

• The proposed LMBW DFT offers an alternative consistent with the compressibility route.
• The shared implementation feature of force-DFT and LMBW DFT enables minimization of structural inconsistencies.
• This approach provides a unified framework for studying inhomogeneous fluids, optimizing density profile calculations.