Kohn-Sham Theory with Paramagnetic Currents: Compatibility and Functional Differentiability.

Area of Science:

• Quantum Chemistry
• Mathematical Physics

Background:

• Density-functional theory (DFT) is a cornerstone of modern computational chemistry and physics.
• Moreau-Yosida regularization provides mathematical rigor for functional differentiability in DFT.
• Paramagnetic current-density-functional theory (PCDFT) extends DFT to include magnetic field effects.

Purpose of the Study:

• To extend Moreau-Yosida regularization to PCDFT.
• To establish a well-defined Kohn-Sham iteration scheme within this extended framework.
• To analyze the necessary function space compatibility for PCDFT.

Main Methods:

• Formulation of Moreau-Yosida regularization for reflexive and strictly convex function spaces.
• Derivation of optimal L^p-characterization for paramagnetic current density (L^1 ∩ L^{3/2}) from N-representability conditions.
• Analysis and recursive construction of compatible function spaces for particle and current densities.

Main Results:

• Successful extension of Moreau-Yosida regularization to PCDFT.
• A Kohn-Sham iteration scheme with a partial convergence result is established.
• The compatibility of function spaces, crucial for convex PCDFT, is identified and analyzed.
• Numerical calculation of regularized, exact functionals on a quantum ring demonstrates performance.

Conclusions:

• The extended Moreau-Yosida regularization offers a robust mathematical foundation for PCDFT.
• The developed Kohn-Sham scheme and function space analysis pave the way for more accurate calculations of magnetic field effects.
• Numerical results validate the practical applicability of the regularization method.