Explicitly stable fundamental-measure-theory models for classical density functional theory.

Area of Science:

• Statistical Mechanics
• Physical Chemistry
• Computational Physics

Background:

• Fundamental Measure Theory (FMT) provides a framework for classical Density Functional Theory (DFT) for hard spheres.
• Recent work introduced global stability criteria for density functionals based on boundedness.

Purpose of the Study:

• To reexamine the derivation of tensorial FMT in light of global stability.
• To assess the trade-offs between functional stability and accuracy, particularly at low densities.

Main Methods:

• Revisiting the mathematical derivation of tensorial FMT.
• Introducing and evaluating an explicitly stable FMT functional.
• Performing explicit calculations for various systems.

Main Results:

• Explicit stability within the current FMT paradigm necessitates reduced accuracy at low densities.
• A proposed explicitly stable functional demonstrates competitiveness with established White Bear models.
• The new functional shares limitations with existing models when applied to non-close-packed solids.

Conclusions:

• The trade-off of low-density accuracy for explicit stability in FMT is acceptable, given DFT's utility for dense systems.
• The developed explicitly stable functional offers a viable alternative to current models.
• Further refinement is needed to address challenges with non-close-packed solids.