Models and corrections: Range separation for electronic interaction-Lessons from density functional theory.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Model Hamiltonians are crucial for understanding electron-electron interactions.
• Density functional approximations (DFAs) are widely used but have limitations.
• Range separation techniques offer potential improvements in accuracy.

Purpose of the Study:

• To develop a method for correcting model Hamiltonian energies using short-range electron-electron interaction behavior.
• To explore the foundations of density functionals combined with range separation.
• To enable accurate calculations of ground and excited states without the Hohenberg-Kohn theorem.

Main Methods:

• Correction of model Hamiltonians by incorporating universal short-range electron-electron interaction behavior.
• Application of approximations to the harmonium model system.
• Asymptotic analysis for improvable techniques and error estimation.

Main Results:

• Accurate calculation of ground and excited states for model systems approaching the Coulomb system.
• Demonstration that the method can be used independently of density functionals and range separation.
• Development of error estimates for result validation.

Conclusions:

• The presented technique offers a pathway to accurate electronic structure calculations, particularly for systems where standard DFAs may falter.
• The method provides a foundation for future improvements and error-controlled calculations.
• Results are comparable to accurate density functional approximations, validating the approach.