Species with negative electron affinity and standard DFT methods

Concerned about the feasibility of traditional bound-electron models to properly describe ground state anion surfaces, we calculated the negative electron affinity of a representative set of compounds, finding a good correlation between the experimental data and theoretical values obtained with the popular B3LYP functional and Pople′s relatively inexpensive standard basis sets (6-311+G(2df,p)//6-31+G*) in the cases of valence anions.

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

Primarily intended to reproduce ETS data, some specialized theoretical methods have been developed in order to address both the vertical electron affinities (first and higher) and the lifetimes of the lower and some of the first excited temporary anions.8

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,cd 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

We are interested in the study of radical anions owning to their relevance in organic reactions involving electron transfer (ET) steps,3,14 such as the SRN1 radical chain mechanism,2 among others.

Besides, RAs of nucleobases play a central role in the understanding of DNA damage and repair and some nucleobase derivatives also have been proposed as anti-tumoral pro-drugs.9,11,12,15

In order to interpret the reactivity of these species, it is essential to characterize and determine the stability of their ground anion states.

This meaning, to accurately or at least reasonably well know its first vertical and adiabatic electron affinities.

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.3,9,10ab,14bd

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.

In this aim, a set of organic compounds with known negative electron affinities were calculated with the B3LYP functional,16 as representative standard DFT method.

The basis sets were choose keeping in mind reliability at the minimum computational cost.

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

The trial set selected is an attempt to cover chemically different compounds measured by different techniques and different experimental groups.

At difference with the case of positive EAs, an accuracy of a few meV is not expected for compounds with negative EAs.

This limits the trial set as it was not possible to gather hundreds of experimental data highly accurate and without larger discrepancies.

We focused on compounds for which: (i) ET in solution leads to the formation of RAs since in those cases an intimate knowledge of the anionic potential energy surface is required; (ii) halogenated species, due to the importance of their dissociation into radicals.2,3,14

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 VEAs were computed as the difference between the electronic energy of the anion and the neutral at the frozen geometry of the latter (eqn. (1)).3,6b,7,9 The adiabatic electron affinities (AEA, eqn. (2)) were obtained as the corresponding difference in the total energies with full geometry optimization of both species, including the zero point energy (ZPE) corrections.

VEA = E(optimized neutral) − E(anion on the optimized geometry of the neutral)AEA = E(optimized neutral) − E(optimized anion) + ZPE(neutral) − ZPE(anion)Table 1 summarizes the experimental11a,13,18–25,28,30 and calculated VEA and AEA (when available) of the lowest anion state, to which the present discussion refers exclusively, with standard 6-311+G(2df,p)//6-31+G* basis.26,27

For the first group of compounds the lower anion state is of valence type (V); the extra electron being held in a valence MO.

As shown in Fig. 1a for the radical anion of cytosine, taken as representative, the extra electron locates in a valence a″(π*) orbital.29

For these species, the equilibrium geometry of the neutral and the anion may differ (see Fig. 1a).

The geometric rearrangements observed rationalize the fact that even though the pyrimidine nucleobasis have negative VEA, they have positive or slightly negative AEA, in agreement with both theoretical and experimental results recently reported.9,12b,13,28 The geometry differences observed between fluorobenzene (16) and its RA, mainly relate to changes in bond alternancies of the ring, which is attributed to the node between the ortho and meta carbons of the a2(π*) MO in which the extra electron goes.

This causes an elongated C–C length between these positions, as previously discussed.3,29

The most evident difference, not only in geometry but also between VEAs and AEAs, appears in the t-butyl and cyclopentyl radicals whose sp2 center evolves to sp3 in the anion.

This fact is accompanied by remarkable changes in the steric repulsion and in distortion of the cycle, respectively.29

For the second series of compounds, the lowest vertical anion state found does not correspond to a valence state and has been labeled as non-valence type (N).

In these anions the extra electron lies in a very diffuse orbital around the molecule, oriented against the dipole.

Pyrrole, with a charge and spin distribution typical of a dipole-bounded anion, is shown as representative in Fig. 1c.

The compounds that fall into this category have the most negative EAs and bear either an important total dipole or strong local dipoles (owning to the presence of CH3 or NH2 substituents).

In general, the anion type depends on a combination between VEA and dipole moments.

For example, while species with the first VEA less negative than −1.1 eV have been found of valence type, guanine (VEA > −1.1 eV), having a huge dipole, yields a RA which is non-valence (Fig. 1b), despite it bearing a small amount of π density.

The electronic distribution found for this RA resembles that recently reported by Schaefer et al., with the same functional and different basis sets.12c Ethylene (VEA = −1.78 eV), with μ = 0, is V type and trimethylethylene (VEA = −2.24 eV), despite its total dipole of 0.31 D is N.

In the latter species, the extra electron locates in front of the three CH3 groups which bear local dipoles; no π spin density is observed on the double bound of this compound.

It was observed that, at difference with the first group of compounds, for the N anions, the differences in geometry with respect to their neutral parents are smaller.

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

As can be seen, the method failed in finding the lowest valence state, which is the anion of interest, since the dipole-bound anions do not exist in solution.11a Unfortunately, dipole-bound anions are better characterized by different techniques11a and the experimental evidence related to them is sparser than in the case of valence anions.

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 3145 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

In Fig. 2, the B3LYP/6-311+G(2df,p) values are compared with the experimental VEA and AEA.

The experimental VEA for the compounds 3146 are included for comparison purposes when available, but they are not fitted since they do not correspond to valence states.

The correlation between the calculated and experimental VEAs for all the valence states found has a slope very close to the unity and a small abscissa [Fig. 2, y = (1.00 ± 0.04)x + (0.10 ± 0.04)], the correlation index, when using the triple zeta basis set, being 0.978.

The very compact 6-31+G* basis yields a slightly poorer fit [y = (0.97 ± 0.05)x + (0.16 ± 0.05), with a correlation index of 0.973].33

The standard errors expected from these studies, even including the AEA and their harmonic errors34 are very good from the practical point of view adopted and they are not greater than those compiled by Rienstra-Kiracofe et al. for positive electron affinities (in agreement within ∼0.2 eV).7

Finally, it is worthwhile to devote a few lines to the basis set effects.

Dunning and co-workers' correlation-consistent basis sets AUG-cc-pVDZ and AUG-cc-pVTZ35 have been used for testing part of the trial set of compounds.

These basis sets with more diffuse components (and more expensive computationally), fall more frequently into the non-valence states, even for some species found of valence type with standard Pople bases.

For these reasons, the correlation involves fewer points than those of Table 1.

However, the results obtained seemed of poorer quality [see plots in the electronic supplementary information (ESI)].33

Similarly, Li, Cai and Sevilla,36 with the B3LYP functional and the 6-311++G(2d,p) basis, [with an extra diffuse set on hydrogens and without higher angular momentum polarization on heavy atoms with respect to the 6-311+G(2df,p) in this work], have fallen in non-valence states for adenine, cytosine, thymine and uracil (4, 12, 27 and 30); these compounds being of valence type with either the 6-31+G* (as both in our results and in their work) or the 6-311+G(2df,p) set (Table 1).

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

Besides, the negative EAs thus obtained for benzene,7 naphthalene (18),6b and the nucleobases 4, 12, 27 and 3012 are very close both to our results and the experimental values.

Although the use of Koopmans' theorem for electron affinities has been criticized for EAs, in particular with DFT approaches,38 and our goal is to obtain quantitatively reliable EAs using eqns. (1) and (2), the energies of the lowest valence unoccupied orbitals (LVUMO), obtained with the smaller basis used, were compared to the experimental VEAs.

Species with non-valence anions were also included; their correlation being similar to that of the valence anions 130.

Besides the considerable dispersion, which is not surprising and has also been observed for compounds with positive EAs, the LVUMO energies could still be useful as a fast hand-rule estimation of experimental VEAs (see ESI).39,40

It is concluded that the standard DFT methods are well suited for the systematic study of the potential energy surfaces of RAs and reactivity when the species have negative electron affinities and the valence state is calculated.

The method may or may not be able to find the lowest valence state when it lies more than 1 eV above of the neutral, depending on the total dipole moment or local dipolar groups.

The care required to ensure that the right anion state and the appropriate basis set were selected are, among others, common problems in the chemistry of anions.

The pros and cons of the DFT methods appear to be similar for valence anions having either positive or negative electron affinities.

According to the fitting obtained for our trial set, the calculated values are suitable predictions to the actual absolute values of the EAs with triple zeta quality basis set and even with the smaller 6-31+G* one.

For the latter, a slight systematic correction of +0.16 eV and a scale factor of 0.97 are suggested.

Computational details

All calculations were done with the Gaussian 98 package,41 with standard Pople's basis sets and the augmented cc-pVDZ and cc-pVTZ bases.35

All the neutral species were characterized by the usual normal analysis as well as their optimized anions whenever their experimental adiabatic EAs were available.

No scale factors were included in the vibrational energies.

Molecular graphics in Fig. 1 and those in the supplementary material were generated with the Molekel 4.3 program42.