Locally Scaled Self-Interaction Corrected Energy Functionals with Complex Optimal Orbitals

We present a fully variational locally scaled self-interaction corrected (SIC) energy functional using complex optimal orbitals. This represents an important milestone for fully variational SIC energy functionals, which have been shown to improve the prediction of the properties of atomic, molecular and solid state systems in general, in both ground and excited states. However, it depends on the system and property of the system whether it is beneficial to scale the SIC correction by a factor of one-half, which makes the application of SIC inconsistent. In the limit of a single electron the SIC exactly cancels the self interaction error, but overcorrects the error in regions of high density where there is large overlap between occupied orbitals. The newly implemented local scaling function, z(𝐫), which is based on an iso-orbital indicator derived from considering the kinetic energy density in the iso-electron and many electron case, and takes into account that the orbitals are complex, naturally scales the SIC correction from 0≤ z(𝐫) ≤ 1 in regions of high and low (isolated orbital) electron density. The locally scaled and fully variational SIC framework is general and applicable to atomic, molecular and solid-state systems.