  We show that under well-defined conditions the Hohenberg-Kohn theorem (HKT)
can be extended to the lowest-energy resonance of unbound systems. Using the
Gel'fand Levitan theorem, the extended version of the HKT can also be applied
to systems that support a finite number of bound states. The extended version
of the HKT provides an adequate framework to carry out DFT calculations of
negative electron affinities.
