Predicting fundamental gaps accurately from density functional theory with non-empirical local range separation

We present an exchange–correlation approximation in which the Coulomb interaction is split into long- and short-range components and the range separation is determined by a non-empirical density functional. The functional respects important constraints, such as the homogeneous and slowly varying density limits, leads to the correct long-range potential, and eliminates one-electron self-interaction. Our approach is designed for spectroscopic purposes and closely approximates the piecewise linearity of the energy as a function of the particle number. The functional’s accuracy for predicting the fundamental gap in generalized Kohn–Sham theory is demonstrated for a large number of systems, including organic semiconductors with a notoriously difficult electronic structure.