Reduction of Hartree-Fock Wavefunctions to Kohn-Sham Effective Potentials Using Multiresolution Analysis

Area of Science:

• Computational chemistry
• Quantum chemistry
• Electronic structure theory

Background:

• Kohn-Sham (KS) density functional theory (DFT) is a cornerstone of modern electronic structure calculations.
• Accurate computation of the KS effective potential is crucial for reliable molecular properties.
• Traditional methods often face challenges with basis set incompleteness and oscillating potentials.

Purpose of the Study:

• To present a highly accurate numerical implementation for computing Kohn-Sham effective potentials.
• To address issues of basis set incompleteness and oscillating potentials in KS calculations.
• To generate molecular Kohn-Sham potentials of benchmark quality.

Main Methods:

• Utilizing a Hartree-Fock wavefunction and density within the regularized KS (RKS) approach.
• Employing a multiresolution wavelet analysis (MRA) for representing potentials and orbitals.
• Implementing the RKS method in a wavelet basis to avoid basis set incompleteness.

Main Results:

• Achieved highly accurate numerical computation of Kohn-Sham effective potentials.
• Successfully removed oscillating potential issues common in other methods.
• Generated molecular Kohn-Sham potentials of benchmark quality for atoms up to Kr and various molecules.
• Demonstrated the significance of nodal planes in calculations using HCN and benzene as examples.

Conclusions:

• The MRA implementation of the RKS method provides a robust and accurate approach for electronic structure calculations.
• This method offers a reliable way to obtain high-quality molecular Kohn-Sham potentials.
• The findings are significant for advancing computational chemistry and materials science.