Kohn-Sham potentials from electron densities using a matrix representation within finite atomic orbital basis sets

Area of Science:

• Computational chemistry
• Quantum chemistry
• Density Functional Theory

Background:

• The Kohn-Sham (KS) inversion procedure aims to find the effective potential for a target electron density.
• Traditional methods often rely on auxiliary basis sets for potential expansion, which can introduce limitations.

Purpose of the Study:

• To develop and validate a matrix-based KS inversion procedure using finite atomic orbital basis sets.
• To explore the direct matrix representation update of the KS effective potential.
• To apply the method to density functional embedding theory and solvated systems.

Main Methods:

• A static response function-based KS inversion procedure.
• Direct update of the KS effective potential in its matrix representation, avoiding auxiliary basis sets.
• Application to density functional embedding theory and a solvated proton transfer reaction.

Main Results:

• The reconstructed electron density rapidly converges to the target density.
• Demonstrated the possibility of obtaining a local potential in real space from the matrix representation.
• Proof-of-concept study shows promise for density functional embedding theory.

Conclusions:

• The matrix-based KS inversion is an efficient and accurate method for determining KS effective potentials.
• The approach is suitable for advanced applications like density functional embedding theory.
• This method offers a promising avenue for studying complex chemical systems.