Density functional theory for fractional charge: Locality, size consistency, and exchange-correlation

Area of Science:

• Quantum Chemistry
• Computational Physics
• Density Functional Theory

Background:

• The exact universal density functional is fundamental in electronic structure calculations.
• Extending functionals to fractional charges is a long-standing challenge in quantum chemistry.
• Molecular size consistency is a key principle for accurate theoretical models.

Purpose of the Study:

• To extend the exact universal density functional to systems with fractional electronic charge.
• To introduce and explore the concept of i-locality in density functionals.
• To establish a theoretical framework for accurately describing fractional molecules.

Main Methods:

• Application of the exact universal density functional to asymptotically separated densities.
• Development of the concept of i-locality for density functionals and external potentials.
• Constrained search for electronic charge distribution in systems with fractional electrons.
• Analysis of the Kohn-Sham (KS) noninteracting kinetic energy functional for fractional molecules.

Main Results:

• The exact universal density functional, when extended, exhibits i-locality for fractional charges.
• A method for explicitly searching fractional electronic charge at different locales is presented.
• Fractional molecules are shown to be physically sensible and equivalent to asymptotic separability.
• The KS kinetic energy functional for fractional molecules is well-defined and i-local.
• A novel exchange-correlation functional for fractional occupancies is derived and validated.

Conclusions:

• The concept of i-locality provides a rigorous extension of density functionals to fractional charges.
• Fractional molecules are a valid and useful concept in molecular research.
• The developed framework accurately describes systems with fractional electronic charge, improving computational chemistry methods.