What can lattice DFT teach us about real-space DFT?

Area of Science:

• Computational Chemistry
• Condensed Matter Physics
• Quantum Chemistry

Background:

• Density Functional Theory (DFT) is a powerful quantum mechanical method for electronic structure calculations.
• Lattice DFT models offer a simplified approach to complex systems, but their connection to real-space DFT is not always clear.
• Understanding electronic behavior in molecules and materials is crucial for developing new technologies.

Purpose of the Study:

• To establish a formal connection between lattice DFT and real-space DFT.
• To investigate the role of specific interactions (density-density, Hund's rule, pair-hopping) in lattice DFT models.
• To demonstrate the applicability of the developed lattice DFT model to real molecular systems, such as the hydrogen molecule.

Main Methods:

• Utilizing Mermin's DFT formulation in the grand canonical ensemble at finite temperature.
• Developing a two-level lattice DFT model incorporating density-density, Hund's rule, and pair-hopping interactions.
• Applying the model to a hydrogen molecule in a minimal basis and embedding it in standard DFT calculations for larger systems.

Main Results:

• The lattice DFT description with density-density and Hund's rule interactions is equivalent to exact-exchange in real-space DFT.
• The inclusion of pair-hopping interaction leads to non-integer Kohn-Sham (KS) occupations, even at zero temperature.
• The two-level lattice DFT model accurately reproduces full configuration interaction results for the hydrogen molecule, including dissociation limits and spin symmetry preservation.
• Embedding the model into standard DFT calculations yields results in good agreement with exact calculations.

Conclusions:

• A clear link between lattice and real-space DFT has been established.
• The developed lattice DFT model provides an accurate and efficient method for electronic structure calculations.
• The model's ability to handle non-integer KS occupations and preserve spin symmetry offers advantages over traditional methods.