Complex Fermi-Löwdin orbitals for Perdew-Zunger self-interaction correction*

The Fermi-Löwdin orbital self-interaction correction [1] (FLO-SIC) is a size extensive and unitarily invariant approach for implementing the Perdew-Zunger self-interaction correction [2] (PZ-SIC) to density functional theory (DFT). The ingredients to define the FLO transformation are a set of orthonormal occupied orbitals and a set of parameters known as Fermi-orbital descriptors (FODs).  In the original FLO-SIC implementation, FODs are defined as real vectors. Here we define FODs to be complex vectors. This leads to a complex transformation and complex FLOs. The complex FLOs are expected to be smoother/less noded localized orbitals. Such orbitals are important to obtain accurate and larger SIC corrections, particularly for semi-local functionals [3,4]. In this work, we find the optimal complex FODs for atoms and small molecules and calculate the complex FLO-SIC total energies. Then we investigate the performance of the complex FLO-SIC method for atomization energies of the molecules.

1] J. Chem. Phys., 140, 121103 (2014).

[2] Phys. Rev. B, 23, 5048, (1981).

[3] Phys. Rev. A, 84, 050501 (2011).

[4] J. Chem. Phys., 150, 174102 (2019).