Typically, when a neutral organic molecule receives an electron, it may either decompose because a bond breaks while the electron is being transferred or it may form a radical anion (RA),^1,2 an open-shell species that bears an unpaired spin density and a net negative charge.

These reactive species are important intermediates of many organic and biological processes and a detailed knowledge of their energetics and properties becomes crucial to the study of these reactions.^1–3

In those cases in which the lower anionic surface lies at higher energies than the neutral precursor (i.e. molecules with negative electron affinities), the anionic state is short lived, since it may suffer spontaneous electron detachment to the neutral ground state.

These species, also referred to as temporary anions, unbound anions, resonances or shapes, can be studied by means of electron transmission spectroscopy (ETS) methods.⁴

The first vertical electron affinity (VEA), some higher affinities (i.e. those that lead to excited anion states), as well as an estimate of the anion lifetime are accessible by these means.^4,5

Besides the short-lived nature of the anions formed from species with negative electron affinities (10⁻¹¹–10⁻¹⁵ s),⁴ EAs are always difficult properties to calculate.^5,6

Recently, hundreds of compounds with positive EAs have been reviewed, and the expected accuracy for their theoretically predicted values has been also discussed.⁷

At this point it has to be remarked that there are no straightforward ways of either estimating the lifetime or obtaining the higher electron affinities by means of standard methods.⁸

Despite these attempts, many authors have carried out detailed studies, mainly focused on the reactivity of the anionic species,^3,9 by applying conventional ab initio and DFT procedures as if they were species with positive EAs.^2,6b,10 It is surprising that while some authors claim that the results obtained with standard methods are unreliable for these anions,^8,11a,c–d some others have obtained useful data for chemically interesting systems,^3,9,12,13b sometimes without any specific mention of the unbound or temporary condition of these states.^6b,10

Naturally, autodetachment (and therefore the unbound nature of the anions) is not observed either in water or in a polar solvent as in this medium they lie at lower energy than the neutrals.^3,9,14

However, as is known, most theoretical studies concerning reactivity have to combine data from the gas phase and solution.^{3,9,10a–b,14b–d}

In view of the importance of RAs in organic and biological chemistry it is worthwhile to clearly determine the quality of the EAs calculated by conventional DFT procedures.

This objective is based on the following main facts: (i) most of the anions of our interest (vide supra) are of molecular size similar to or quite larger than the species in this work; (ii) reactivity in ET processes implies the calculation of many points on the potential energy surface of the neutrals and of the possible anions as well as a further simulation of an adequate model solvent.^1,3,14

Besides, it has been found that, even for the easier case of positive EAs, this property is difficult to reproduce for compounds containing halogen atoms;⁷ (iii) compounds with different functional groups and heterocycles (including N, O, S heteroatoms) when experimental information is available; (iv) nucleobases, since not only have their absolute EAs remained dubious for three decades but also their relative order has been discussed nowadays;¹⁷ (v) a few radicals in order to widen our trial set to include closed shell anions and (vi) species with no permanent total dipole moment, with a small and a very large dipole moment, as will be discussed later on.

The EAs obtained for this second group (N type) are not intended to reproduce the experimental values listed in Table 1, since most informed VEA comes from ETS studies and they generally correspond to valence anions.⁴

For example, while substituted ethylenes have an unique ETS band or ‘shape’ which has been assigned to the electron capture in the π* orbital,³⁰ the calculated anion of cis-dimethylethylene, as an illustration, is a different state, in which the extra electron is surrounding the methyl groups in a diffuse orbital without any π* contribution.²⁹

For example, after decades of research due to the biological interest, it was not until 1996 that it was unambiguously shown that some nucleobases may have dipole-bound anions, when prepared under the adequate conditions.^11a,31 We do not have enough evidence to state that the non-valence anions found for 31–45 actually exist and they do have the calculated VEA.

In any case, their potential energy surfaces seem to appear at lower energy than the lowest valence states, the method being unable to characterize the latter.³²

On the other hand, Schaefer et al. have successfully computed the electron affinities of a variety of compounds, most of them having positive EAs, by extensively using the B3LYP, and other hybrid functionals (B3P86, BHandHLYP) with the Huzinaga–Dunning full double and triple-zeta-quality basis, with diffuse functions exponents obtained by themselves according to the prescription of Lee and Schaefer.³⁷