Noninteracting v-Representable Subspaces of Orbitals in the Kohn-Sham Method

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Density Functional Theory (DFT) relies on the electron density to describe electronic structure.
• Noninteracting v-representability is a key concept in DFT, ensuring a density can arise from a Kohn-Sham potential.
• Extending this concept to orbital subspaces is crucial for finite basis set calculations.

Purpose of the Study:

• To generalize the concept of noninteracting v-representability from electron densities to finite-dimensional orbital subspaces.
• To establish a practical method for assessing the representability of densities within specific basis sets.
• To explore the connection between orbital subspaces, electron densities, and Kohn-Sham potentials.

Main Methods:

• Extension of the noninteracting v-representability notion to linear subspaces of orbitals.
• Application of a necessary condition: invariance of the orbital subspace under a one-electron Kohn-Sham Hamiltonian.
• Analysis of the relationship between linearly independent orbital products and ground-state electron densities.

Main Results:

• A transparent necessary condition for the noninteracting v-representability of orbital subspaces was identified.
• This condition allows for the theoretical and practical determination of whether a basis set can represent a given N-electron density.
• The Kohn-Sham effective potential can be deduced from the basis set itself for certain densities.

Conclusions:

• The study provides a framework for understanding and verifying v-representability in the context of finite basis sets.
• This work facilitates the accurate application of Kohn-Sham theory with limited basis sets.
• The findings pave the way for deducing effective potentials directly from basis set properties.