Using complex degrees of freedom in the Kohn-Sham self-interaction correction

The Perdew-Zunger self-interaction correction (SIC) to local and semilocal density functionals systematically underestimates molecular bond lengths, yet improves many other ground-state properties. An alternative definition of a SIC is reached by using the Perdew-Zunger energy with a global, multiplicative Kohn-Sham potential instead of the orbital-specific potentials of traditional SIC. Due to the unitary variance of the SIC energy, the most general construction of the SIC Kohn-Sham potential involves a unitary transformation of the Kohn-Sham orbitals. We systematically investigate the Kohn-Sham version of the SIC, in particular with respect to the bond-length question, and present a detailed analysis of the influence of different unitary transformations. Using a complex-valued energy-minimizing transformation appears to be the most favorable approach, and we explain this result by analyzing orbital densities. We discuss how to calculate the transformations efficiently.