In the usual treatment of electronic structure, all matter has cusps in the electronic density at nuclei. Cusps can produce nonanalytic behavior in time, even in response to perturbations that are time analytic. We analyze these nonanalyticities in a simple case from many perspectives. We describe a method, the s expansion, that can be used in several such cases and illustrate it with a variety of examples. These include both the sudden appearance of electric fields and disappearance of nuclei in both one and three dimensions. When successful, the s expansion yields the dominant short-time behavior, no matter how strong the external electric field, but agrees with linear-response theory in the weak limit. We discuss the relevance of these results to time-dependent density functional theory. © 2013 American Physical Society.

A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.