Kinetic-Energy Density-Functional Theory on a Lattice.

Area of Science:

• Condensed Matter Physics
• Quantum Chemistry
• Computational Materials Science

Background:

• Standard density-functional theory (DFT) relies on the electron density as the sole fundamental variable.
• Accurate calculation of kinetic energy is crucial for describing electronic systems.
• Limitations exist in standard DFT approximations for capturing complex electronic correlations.

Purpose of the Study:

• To develop a novel kinetic-energy density-functional theory (keDFT) and kinetic-energy Kohn-Sham (keKS) scheme.
• To establish a one-to-one correspondence between external potentials and internal kinetic-energy density and density.
• To construct accurate orbital-dependent functionals for improved electronic structure calculations.

Main Methods:

• Formulation of a keKS scheme on a lattice, treating kinetic-energy density as a fundamental variable.
• Establishing effective fields (mean-field exchange-correlation potential and hopping) to map interacting systems to keKS.
• Decomposition based on equations of motion for density and kinetic-energy density to derive orbital-dependent functionals.

Main Results:

• Demonstrated that including kinetic-energy density explicitly leads to highly accurate results with simple approximations.
• Established a unique mapping between external potentials and the pair of density and kinetic-energy density.
• Developed orbital-dependent functionals that outperform the standard exact-exchange Kohn-Sham approximation.

Conclusions:

• The proposed keDFT and keKS scheme provide a more accurate and robust framework for electronic structure calculations.
• Explicitly incorporating kinetic-energy density offers significant advantages over traditional DFT methods.
• The developed functionals pave the way for more precise predictions in condensed matter and quantum chemistry.