Steps in the Exact Kohn-Sham Potential of Ensemble Density-functional Theory for Excited States and Their Relation to the Derivative Discontinuity

An accurate approximation to the exchange-correlation (xc) part of the Kohn-Sham (KS) potential is essential for any density-functional calculation. Density-functional theory (DFT) is widely used in condensed matter physics, quantum chemistry and many other fields. Therefore, understanding the behaviour of the exact xc potential and developing improved approximations to it are of the utmost importance. The focus of calculations within DFT is usually on the ground state. However, knowledge of how the system responds to an excitation is important. In this talk we present the exact KS potential of an ensemble of the ground state and the first excited state of a 1D diatomic molecule. For this system, upon excitation, a small amount of charge transfers from one atom to the other. In the corresponding exact ensemble xc potential we find two plateaus: one that forms around the nucleus of the acceptor atom, associated with the derivative discontinuity of that atom (Δ), and another that forms around the donor atom and corresponds to a new phenomenon which we term the 'charge-transfer derivative discontinuity'. The relevance of the aforementioned features to an accurate prediction of the excitation spectrum is discussed.