Kinetic Correlation Functionals from the Entropic Regularization of the Strictly Correlated Electrons Problem

Area of Science:

• Quantum Chemistry
• Computational Physics
• Density Functional Theory

Background:

• The strictly correlated electrons (SCCE) formalism is crucial for accurate electronic structure calculations.
• Understanding quantum kinetic energy and classical entropy is fundamental in many-body physics.
• Density functional theory (DFT) provides a framework for electronic structure but requires accurate functionals.

Purpose of the Study:

• To investigate the entropic regularization of the SCCE formalism.
• To explore the implications of this regularization for density functional theory.
• To establish connections between SCCE, quantum kinetic energy, and classical entropy.

Main Methods:

• Applying entropic regularization to the strictly correlated electrons formalism.
• Developing and utilizing simplified models for preliminary investigations.
• Analyzing lower and upper bounds of the Hohenberg-Kohn functional.

Main Results:

• Established a link between entropic regularization of SCCE and existing theories of quantum kinetic energy and classical entropy.
• Preliminary models suggest the potential for building approximations for kinetic correlation functionals at large coupling strengths.
• Derived bounds for the Hohenberg-Kohn functional using the entropic regularized SCCE problem.

Conclusions:

• Entropic regularization offers a promising avenue for advancing the SCCE formalism.
• The approach has potential implications for improving density functional theory approximations.
• Further research is warranted to fully develop approximations for kinetic correlation functionals.