Full canonical information from grand-potential density-functional theory.

Area of Science:

• Statistical Mechanics
• Computational Physics
• Quantum Chemistry

Background:

• Classical density functional theory (DFT) is a powerful tool for studying many-body systems.
• Calculating canonical properties (like free energy and density) from grand ensemble DFT can be challenging.
• Existing methods may lack accuracy or generalizability for finite systems.

Purpose of the Study:

• To present a general and formally exact method for deriving canonical properties from grand ensemble DFT.
• To validate the proposed method using a precisely defined model system.
• To establish the method's utility for finite systems and dynamical DFT.

Main Methods:

• Direct decomposition of classical density functional results in the grand ensemble.
• Application to confined one-dimensional hard-core particles.
• Comparison with exact analytical solutions and Monte Carlo simulations.

Main Results:

• The method successfully obtains the canonical one-body density distribution.
• Canonical free energy is accurately determined via direct decomposition.
• Results show high agreement with exact methods and many-body simulations.

Conclusions:

• The presented method offers a formally exact and general approach for canonical property calculation.
• It provides a reliable tool for analyzing finite systems within DFT.
• The method is applicable to dynamical density functional theory.