A novel density functional theory for atoms, molecules, and solids

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Standard density functional theory (DFT) faces challenges with the asymmetry of the Kohn-Sham (KS) potential.
• Existing methods may lead to inconsistencies in describing molecular and solid-state systems.

Purpose of the Study:

• To prove a theorem establishing a unique relationship between spherical electron densities and external potentials.
• To resolve inconsistencies in the KS potential within DFT.
• To enable more accurate molecular calculations by exploiting local symmetries.

Main Methods:

• A novel theorem is presented concerning the relationship between spherical electron densities and external potentials.
• The symmetry properties of the induced KS potential are analyzed.
• The implications for determining the ground state and minimizing subspaces of Hamiltonians are explored.

Main Results:

• The set of spherical parts of the density around each nucleus uniquely determines the external potential.
• The induced KS potential is shown to possess spherical symmetry around each nucleus and the symmetry of the external potential.
• The ground state and minimizing subspaces are uniquely determined by these spherical densities.

Conclusions:

• The presented theory remedies inconsistencies in standard DFT regarding KS potential asymmetry.
• This approach opens avenues for developing new density functionals and improving the accuracy of molecular calculations.
• The theory provides a DFT-based explanation for Bader's
• Atoms in Molecules
• theory.