Orbital Lobedness and the Perdew-Zunger Self-Interaction Correction

Density Functional Theory (DFT) offers a practical way to approximate the energy of large electron systems using an energy density functional, reducing the complexity from 3N spatial coordinates to just three. However, approximate DFT suffers from self-interaction error (SIE), which arises from an incomplete cancellation between the self-Hartree and self-exchange-correlation energies, leading to unphysical results. The Perdew–Zunger Self-Interaction Correction (PZ-SIC) addresses SIE but often overcorrects when orbitals are highly lobed. This work explores the relationship between SIE and orbital shape using a lobedness measure aiming to develop a scaling scheme for improved SIC.