Density inversion method for local basis sets without potential auxiliary functions: inverting densities from RDMFT.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Electronic Structure Theory

Background:

• Accurate local potentials are crucial for electronic structure calculations.
• Existing methods face challenges in reproducing exact ground-state densities and asymptotic behaviors.
• Density Functional Theory (DFT) and Reduced Density Matrix Functional Theory (RDMFT) rely on approximations for these potentials.

Purpose of the Study:

• To develop and present a refined density inversion method for obtaining constrained, optimal local potentials.
• To improve the accuracy of single-particle descriptions in quantum mechanical systems.
• To demonstrate the method's capability in deriving accurate correlation potentials.

Main Methods:

• A density inversion technique is employed to derive local potentials.
• The screening density is expanded using orbital basis element products.
• The method is applied to electronic densities from various quantum chemical calculations (DFT, Hartree-Fock, CAS-SCF, RDMFT).

Main Results:

• The method successfully reproduces prescribed asymptotic behaviors and optimizes local potentials.
• Accurate correlation potentials are obtained by inverting accurate electronic densities.
• For RDMFT, density inversion provides a viable single-particle description, validated by comparing calculated ionization potentials to experimental data for atomic and molecular systems.

Conclusions:

• The presented density inversion method offers a robust approach for determining accurate local potentials.
• It enhances the reliability of single-particle descriptions in quantum chemistry.
• The method shows promise for deriving accurate correlation potentials from high-quality electronic densities.