Density Matrix Implementation of the Fermi-Löwdin Orbital Self-Interaction Correction Method

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Self-interaction error (SIE) is a fundamental issue in standard density functional theory (DFT) approximations.
• The Perdew-Zunger (PZ) framework offers a way to correct SIE but requires localized orbitals.
• Fermi-Löwdin orbitals provide a localized orbital set for SIE correction.

Purpose of the Study:

• To present a detailed workflow for implementing the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method.
• To enable the removal of self-interaction error in DFT calculations on an orbital-by-orbital basis.
• To facilitate the integration of FLOSIC into existing electronic structure codes.

Main Methods:

• Implementation of FLOSIC using Fermi-Löwdin descriptors (FODs) and occupied canonical orbitals or density matrix.
• Casting self-consistent energy minimization with fixed FODs similar to standard Kohn-Sham.
• Introducing an additional term in the Kohn-Sham Hamiltonian for PZ self-interaction correction.
• Dividing energy minimization into substeps for density matrix and FODs.
• Deriving expressions for the effective Kohn-Sham matrix and FOD gradients.

Main Results:

• A practical workflow for FLOSIC implementation is provided, suitable for various electronic structure codes.
• The method's convergence characteristics are analyzed.
• Applications demonstrate the utility of FLOSIC for calculating NMR shielding constants.
• FLOSIC is applied to real-time time-dependent DFT simulations for excitation energy calculations.

Conclusions:

• The developed FLOSIC implementation effectively removes self-interaction error in DFT.
• The method is versatile and applicable to diverse quantum chemistry problems.
• FLOSIC enhances the accuracy of electronic structure calculations, including NMR and excitation energies.