A simple method was recently proposed [D. J. Tozer and F. De Proft, J. Chem. Phys., 2007, 127, 034108] for performing explicit density functional theory (DFT) calculations on temporary anions. The excess electron in the anion is bound by a potential wall, the position of which is determined by a single parameter lambda, chosen to reproduce an approximate, theoretical negative electron affinity in the corresponding neutral. In the present study, the system-dependence of lambda and the sensitivity of the negative affinities to this parameter are investigated for 34 organic molecules. The results demonstrate that the system-dependent lambda values can be replaced by a global, average value, with minimal effect on the affinities. It follows that the orbitals, electron density, and other properties of a temporary anion can be determined from a single DFT calculation on that anion, using a large, diffuse basis set. As an illustration, singly occupied molecular orbitals and spin densities are determined for the anions of guanine and adenine nucleobases. Despite the use of a diffuse basis set, the method yields quantities that are localised in the molecular framework, associated with vertical electron affinities of -1.2 eV and -0.8 eV, respectively.