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Quantum mechanical methods based on the density functional theory (DFT) offera realistic possibility of first-principles design of organic donor-acceptorsystems and engineered band-gap materials. This promise is contingent upon theability of DFT to predict one-particle states accurately. Unfortunately,approximate functionals fail to align the orbital energies with ionizationpotentials. We describe a new paradigm for achieving this alignment. In theproposed model, an average electron-exchange hole separation controls the onsetof the orbital-dependent exchange in approximate range-separated functionals.The correct description of one-particle states is thus achieved withoutexplicit electron removal or attachment. Extensive numerical tests show thatthe proposed method provides physically sound orbital gaps and leads toexcellent predictions of charge-transfer excitations and other propertiescritically depending on the tail of the electron density.

Density-Dependent Onset of the Long-Range Exchange: A Key to Donor-Acceptor Properties