Reconstruction of Exchange-Correlation Potentials from Their Matrix Representations.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• The Kohn-Sham (KS) approach is central to density functional theory (DFT) for electronic structure calculations.
• Constructing accurate exchange-correlation potentials is crucial for predictive power in DFT.
• The inversion problem in DFT aims to find the potential given the electron density.

Purpose of the Study:

• To develop a method for constructing atomic and molecular exchange-correlation potentials.
• To rigorously solve the Kohn-Sham inversion problem within a defined subspace.
• To explore the properties of potentials reconstructed from KS orbitals.

Main Methods:

• Utilizing basis sets of one-electron functions that form linearly independent products (LIPs).
• Constructing local real-space potentials equivalent to arbitrary operators.
• Reconstructing exchange-correlation potentials from their matrix representations in LIP basis sets of occupied KS orbitals.

Main Results:

• Atomic and molecular exchange-correlation potentials were successfully constructed.
• The reconstructed potentials consistently imitated the original potentials, albeit in an exaggerated manner.
• The procedure yielded the same ground-state electron density and energy as the original potentials within the LIP basis set.

Conclusions:

• The method provides a rigorous solution to the Kohn-Sham inversion problem within the subspace spanned by occupied KS orbitals.
• This approach offers a novel way to generate and analyze exchange-correlation potentials.
• The findings have implications for improving the accuracy and understanding of DFT calculations.