State-specific density functionals for excited states from ensembles

Abstract: We present a first principles strategy for developing state-specific density functional approximations for excited states. We first clarify why approaches based on conventional ground state approximations miss density-driven correlations, by considering excited state physics through the lens of ensemble density functional theory. To solve this issue we gain insights on density driven correlations by exploiting the recently understood low-density limit of electrons in excited states. The theory developments are then combined to produce a proof-of-concept excited state approximation that resolves urgent paradigmatic failures (double excitations, charge transfer excitations, piecewise linearity) of existing state-of-art density-functional approaches, directly from differences of self-consistent field calculations; i.e., $\Delta$SCF. In light of its observed impressive performance, we conclude that the approach represents a major step toward unified and accurate modelling of neutral and charged excitations.