Density functional resonance theory of unbound electronic systems

Density Functional Resonance Theory (DFRT) is a complex-scaled version of ground-state Density Functional Theory (DFT) that allows one to calculate in-principle exact resonance energies and lifetimes. The energy and lifetime of the lowest-energy resonance of unbound systems is encoded into a complex density\u27\u27 obtained via complex-coordinate scaling. Two electron exactly-solvable models are used to test the theory before proceeding to a three-dimensional implementation which uses approximate functionals. DFRT subsumes ground-state DFT in that it can facilitate calculations for both bound and metastable states, and thus failures of current approximate DFT methods can be studied from a new perspective. Following this line of thinking, derivative discontinuities in the DFT energy functional, orbital energies, and numerical behavior are explored. Finally, a time-dependent version of DFRT is developed to treat high-lying resonances. An analog of the Runge-Gross theorem is established, and the first order complex density response is shown to contain poles at both bound and metastable excitations motivating an eigenvalue problem for calculating excitations