In the recent work of S. Sharma et al. (e-print 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.