  Aspects of Density Functional Resonance Theory (DFRT) [Phys. Rev. Lett.
\textbf{107}, 163002 (2011)], a recently developed complex-scaled version of
ground-state Density Functional Theory (DFT), are studied in detail. The
asymptotic behavior of the complex density function is related to the complex
resonance energy and system's threshold energy, and the function's local
oscillatory behavior is connected with preferential directions of electron
decay. Practical considerations for implementation of the theory are addressed
including sensitivity to the complex-scaling parameter, $\theta$. In Kohn-Sham
DFRT, it is shown that almost all $\theta$-dependence in the calculated
energies and lifetimes can be extinguished via use of a proper basis set or
fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are
related to a physical affinity and width, and the threshold energy of the
Kohn-Sham system is shown to be equal to the threshold energy of the
interacting system shifted by a well-defined functional. Finally, various
complex-scaling conditions are derived which relate the functionals of
ground-state DFT to those of DFRT via proper scaling factors and a
non-Hermitian coupling constant system.
