According to this paper, and contrary to popular belief, diffuse functions are far from being necessary for the calculation of the electron affinities of the polycyclic aromatic hydrocarbon(PAH)s, due to delocalisation of the additional charge that overweighs the Coulomb repulsion between the additional electron and the existing electrons. The paper also says that electron affinities of individual atoms do need diffuse functions for their calculation, for the fact that atoms with known positive (i.e. bound) electron affinities could be misinterpeted as having negative (i.e. unbound) electron affinities when diffuse functions are not used. All was fine- or seemed to be.
After reading the paper, I suddenly realised that some highly conjugated neutral molecules are still known to have negative electron affinities- benzene and naphthalene to name a few. Delocalisation of the additional charge would not mandate diffuse functions, while the unbound nature of the radical anions formedanion would(see e.g. this paper, which explicitly states that the 'traditional method' for modeling unbound anions is to minimise the basis sets used). So one now has a dilemma- which is generally more important, delocalisation or unboundness, for deciding whether to use diffuse functions or not?