  In the recent work of S. Sharma \emph{et al.}, (arxiv.org: arxiv:0912.1118),
a single-electron spectrum associated with the natural orbitals was defined as
the derivative of the total energy with respect to the occupation numbers at
half filling for the orbital of interest. This idea reproduces the bands of
various periodic systems using the appropriate functional quite accurately. In
the present work we apply this approximation to the calculation of the
ionization potentials and electron affinities of molecular systems using
various functionals within the reduced density-matrix functional theory. We
demonstrate that this approximation is very successful in general and in
particular for certain functionals it performs better than the direct
determination of the ionization potentials and electron affinities through the
calculation of positive and negative ions respectively. The reason for this is
identified to be the inaccuracy that arises from different handling of the
open- and closed-shell systems.
