Density functional for hard sphere crystals: A fundamental measure approach

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Chemistry

Background:

• Existing density functional approximations for hard spheres face challenges in accurately describing fluid and crystal phases.
• Accurate theoretical models are crucial for understanding the behavior of simple systems like hard spheres.

Purpose of the Study:

• To develop a new free energy density functional for hard spheres based on fundamental measure theory.
• To reproduce known results for fluid phases and improve the description of crystalline phases.

Main Methods:

• The new functional is formulated using a tensor-weighted density within the framework of fundamental measure theory.
• It is derived from the zero-dimension limit and validated against one-dimensional density distributions.
• The functional is applied to hard sphere crystals, including face-centered cubic (fcc) and body-centered cubic (bcc) lattices.

Main Results:

• The functional accurately reproduces the Percus-Yevick equation of state and direct correlation function for the fluid phase.
• It provides excellent results for hard sphere crystals, resolving issues like unit cell anisotropy in fcc.
• The functional successfully describes the metastable bcc lattice, a significant improvement over previous methods.

Conclusions:

• The developed free energy density functional offers a significant advancement in the theoretical description of hard sphere systems.
• It successfully bridges the gap between fluid and solid-state descriptions, offering accurate predictions for both.
• This new functional provides a robust tool for studying phase transitions and properties of hard sphere matter.