Exploring local range separation: The role of spin scaling and one-electron self-interaction

Range-separated hybrid functionals with a fitted or tuned global range-separation parameter are frequently used in density functional theory. We here explore the concept of local range separation, i.e., of turning the range-separation parameter into an explicit semilocal density functional. We impose three simple constraints on the local range-separation parameter that are frequently used in density functional construction: uniform density scaling, the homogeneous electron gas limit, and freedom from one-electron self-interaction. We further discuss different ways of how to model the spin dependence in combination with local range separation. We evaluate our local range-separation energy functionals exactly for closed-shell atoms using the previously suggested hypergeneralized gradient approximation for molecules and assess the quality of this approximation. We find a local range-separated hybrid functional that yields accurate binding energies for a set of small molecules.