Novel Hückel stabilised azole ring-based lithium salts studied by ab initio Gaussian-3 theory

Gaussian-3 theory calculations have been performed for a new family of lithium salts with heterocyclic anions–Li+[N5C2n] (0 ≤ n ≤ 5).

Eight different anions and the most stable 1∶1 lithium ion pairs have been studied for each anion.

The lithium ion affinity of the anions decreases with the gradual CN-substitution and is thus lowest for the [N5C10] anion.

The stability vs. oxidation, inferred from the HOMO values, is large for all anions.

In addition, the volume and aromaticity of the anions have been evaluated.


In recent years the hypothetical existence of various poly-nitrogen species has attracted scientific attention, mainly from theoretical chemists.

Of special interest has been the existence of new all-nitrogen anions like the N5 pentagon.1–4

This anion remained elusive until very recently,5 yet long time predicted by computational chemists to be relatively stable due to a large aromatic character.

Such compound is the end member of a series on which our research groups have recently focused, as forming new types of lithium salts [e.g. Li(TADC) and Li(PATC)], where the anion is of the “Hückel” type, i.e. the charge is stabilised on a 5-membered azole ring formed by progressive substitution of nitrogens by the more electron-withdrawing (C–CN) group.6–8

Some such derivatives of the [N5] anion, ([N5C2n], (2 ≤ n ≤ 5), have been made before, but for most only in minute amounts by laser ablation techniques.9

The original synthesis of an [N5C4] anion was made as early as .192310

This and the other [N5C2n] anions are proposed to be chemically stable and their lithium salts to be very dissociated i.e. having very low lattice energies.

Application interest for anions with very high dissociation capabilities exists e.g. as counter-ions for metal catalysts in organic synthesis and in modern non-aqueous (liquid and solid) electrolytes for lithium batteries.11,12

For the latter application a facile dissociation of the lithium salts into lithium ions and anions is of prime interest to obtain large numbers of charge carriers.

Arguably Gibbs energy values for the anions and the corresponding 1∶1 lithium ion pairs allow a simple theoretical measure of the dissociation of the lithium salts.

Kim et al. have found a linear relationship between dissociation energies computed in this way and experimental lattice energies in the present energy range.13

By using very accurate quantum mechanical methods, developed beyond the level of reproducing experimental data, thermodynamic data such as Gibbs energy differences (ΔG) can be predicted where experiments are yet to be made.

With this in mind we here use the highly accurate composite Gaussian-3 (G3) theory of Curtiss et al14. and apply to the [N5C2n] (0 ≤ n ≤ 5) azole ring anions and their 1∶1 lithium ion pairs.

Computational details

Initial calculations, to obtain reasonable starting values for the pure anion geometries as well as to screen possible 1∶1 lithium ion pair candidates, were made using ab initio Hartree–Fock (HF) methods employing the standard 6-31G* basis set (HF/6-31G*).

Second derivative calculations (with respect to nuclei coordinates) were performed to validate the obtained stable structures as minima energy structures.

In accordance with Tang et al9. only singlet state calculations were performed.

Several guesses for 1∶1 lithium ion pair minima were made for each anion and the relatively most stable ion pairs were transferred for further analysis.

In this way, only a few ion pairs remained for each anion.

The computationally highly demanding G3 theory calculations were then performed for these ion pairs and the anions.

The volumes of the anions were determined on the MP2(full)/6-31G(d) level using a Monte Carlo based algorithm and a 0.001 e bohr−3 electron density cut-off.

Geometry optimizations were performed for the H3C–CH3, H2C–CH2, H2N–NH2, HN–NH, H3C–NH2, and H2C–NH molecules to obtain reference values for the C–C, N–N, and C–N single and double bond lengths.

These calculations used the final geometry optimization level in the composite G3 theory: MP2(full)/6-31G(d).

Also the atomic charges, using the Mulliken scheme, and HOMO and LUMO values to obtain η, were obtained at this level of theory.

All calculations were made using the program packages Spartan’0215 and Gaussian9816.

Results and discussion

The energies and geometries of the anions

In Table 1 the obtained G3 Gibbs energies (G) of the [N5C2n] (0 ≤ n ≤ 5) azole ring based anions are listed, together with the G3 enthalpy values (H) and all the Eel values (E) obtained from the sub-calculations performed during a composite G3 calculation in Gaussian98.

For some anions, computational restrictions hindered a complete G3 calculation and therefore the relative error of the sub-calculations with respect to the final G3 results are shown in Fig. 1.

Scaling factors based on these results can be used to extrapolate G3 Gibbs energies (G) for similar larger systems or for similar systems where a full G3 calculation for some reason fails.

From Fig. 1 the preferred sub-steps for a scaling procedure are 1: HF/6-31G(d), 3: MP2(full)/6-31G(d), and 4: QCISD(T)/6-31G(d)//MP2(full)/6-31G(d), while step 6 is clearly inappropriate with its large spread.

Sub-step 7 has a low scattering, but this is the last step in a full G3 calculation.

Sub-step 2 has no associated energy value.

Scaling factors will be used where needed in section C below.

In Fig. 2a–h the resulting geometries of the anions at the MP2(full)/6-31G(d) level are schematically shown.

The [N5C4a] and the [N5C6a] anions are also known as the tri-azole di-carbonitrile (TADC) anion and pyrazole tri-carbonitrile (PATC) anion, respectively.6–8

For the larger anions one possible resonance structure is shown.

The present value for the [N5] N–N bond length (1.3421 Å) corresponds nicely to the values obtained by Gagliardi et al. (1.338 Å), Tang et al. (1.330 Å), and particularly well with Glukhovtsev et al. (1.342 Å).2,9,17

While many studies exist for the [N5] anion this is not the case for the other members of this family.

The recent combined experimental and computational DFT (B3LYP/6-31G*) study9 and our own ab initio (HF/6-31G* and HF/Sadlej p-VTZ) studies6,7 seem to be all the relevant literature.

Tang et al9. computationally covered the range of the present anions, but reported only the most stable isomer for each value of n (i.e. [N5C4a] and [N5C6a] were not included).

Our present ring bond distances are in general close to those of Tang et al., the worse comparison for [N5] (Δ = 0.012 Å), while almost equal for the [N5C10] anion (Δ = 0.001 Å).

Our values for the [N5] anion are, however, closer to the very accurate CASPT2 calculations found in .ref. 2

The data of Tang et al. also suggest a sudden shortening of the C–C ring bond length for [N5C10], compared to [N5C8], an effect that we do not observe.

The change, if true, could reflect a possible stabilising effect of all bonds being now equal in the ring of [N5C10].

[N5C10] is an analogue to the cyclopentadiene anion that has a very large aromatic character.

This issue will be discussed further below.

For the C–N bonds our values are on average ca. 0.007 Å longer, while the C–C bonds are a similar amount shorter for [N5C6b] and [N5C8].

It is difficult to interpret the different bond lengths individually for the structural isomers of [N5C4] and [N5C6].

However, it was found9 that each additional N–N bond, for structural isomers, increased the energy by 0.8 eV (∼77 kJmol−1) with a slight size dependency.

The energy values in Table 1 show increases of ∼55 and ∼70 kJmol−1, from [N5C4a] to [N5C4b] and from [N5C6a] to [N5C6b], respectively.

In Fig. 3 the obtained volumes for the [N5C2n] anions together with corresponding values for the ClO4, PF6, TFSI, and BOB anions18 are shown.

Most [N5C2n] anions are larger than the ClO4 and PF6 anions, smaller than TFSI, and on average comparable to BOB.

The volume of the “b” isomer of the [N5C6] anion is significantly smaller than that of the “a” isomer.

For electrolyte purposes a larger anion should lower the anionic part of the total ion conductivity, thus directly increase the cation (lithium ion) transport number, but might also reduce the overall ion conductivity due to increased viscosity.

While not treated here, the interactions with the solvent/matrix molecules are crucial to determine the dominant factor.

The stability of the anions

The safety and thus stability issues are of paramount importance for any practical usage of the present lithium salts, especially for battery applications.

Hence, four different criteria are applied to theoretically assess the stabilities of the anions.

Associated data are collected in Figs. 4 and 5.

First, the special stability of ring compounds, their aromaticity, is considered.

Aromaticity can be analysed in many different ways,19 being especially important for five-membered heterocycles.20

A simple geometric measure, the double bond character index (I) as outlined by Nyulászi et al.,20 can be obtained by using the formula: Here B1i and B2i are the lengths of the isolated single and double bonds of type i, and R the length of the actual bond i in the ring, respectively.

Relevant reference values for single and double bonds were obtained as outlined in the computational details.

From index I an overall decrease in aromaticity from [N5] (highly aromatic) to [N5C10] is obtained (Fig. 4).

However, both [N5C8] and [N5C10] are more aromatic than [N5C6b].

Noteworthy is that the energetically less stable [N5C4a] and [N5C6a] anions have larger I indices than their “b” isomers.

From this we infer that the C–C bonds outside the ring systems of the “a” isomers are responsible for the relative energy instabilities.

The index for the [N5C10] anion is larger than for the cyclopentadiene anion (0.475),20 though having the same ring atoms.

In20 it was found that the presence of nitrogen atoms in the ring increased the aromatic character of five-membered heterocycles, which the present data supports.

The [N5] anion index is very close to the theoretical maximum value of 2/3 and all [N5C2n] anions are well above the theoretical minimum value of 0.40 (corresponding to two totally localised double-bonds).

Second, the charge remaining in the ring system, not withdrawn by the CN-groups, can be used as a measure of anion stability.

The charge of the ring increases from [N5] (−1.0 e) to finally becoming positive for [N5C10] (+0.09 e).

The charge of the ring is approximately reversely proportional to the index I, especially for the smaller anions.

Thus, the more charge withdrawn from the ring system by the CN-groups, the lower the aromaticity, a logical consequence.

However, the [N5C4b] anion behaves differently having about the same ring charge as the larger anions [N5C6a] and [N5C6b].

This is unexpected, as the charge withdrawn normally is believed to increase with the number of CN-groups.

Also, an imaginary line connecting the [N5C6a/b], [N5C8] and [N5C10] anion values has the same slope as a corresponding line connecting the three smallest anions; an anomaly as the charge withdrawing effect of each incremental CN-group is expected to be reduced.

The third parameter is the chemical hardness (η), obtained from the difference between the highest occupied molecular orbital (HOMO) and the lowest un-occupied molecular orbital (LUMO) energies of the anions, using Koopmans' theorem.

The chemical hardness reflects how stable a specific system is towards chemical attack, and in general follows the index I for the [N5C2n] anions.

However, for the isomers of [N5C4] and [N5C6], the index I and the hardness η give contradictory results with respect to their relative stability.

The choice of electron correlation level and especially the basis set size (which is far from convergence) in the calculations may be the source of these differences and thus no definite conclusions based on these small differences in η should be drawn.

Finally, as the fourth measure of stability, the HOMO energies are used (Fig. 5).

These values allow an estimation of the stability versus oxidation for a system, in practice reflecting the electrochemical window within which the anions can be used safely in a battery.

The present HOMO values are in the range −6.10–−5.10 eV.

Although these energy values not should be interpreted as absolute, all [N5C2n] anions can be considered being rather stable towards oxidation.

The TADC anion is stable up to 4 V vs. Li+/Li0.21

As seen in Fig. 5 the absolute HOMO values are quite irrational with respect to the calculation level, but the relative oxidation stability of the [N5C2n] anions is the same: [N5C10] > [N5C6a] > [N5] > [N5C8] > [N5C4a] > [N5C2] > [N5C4b] > [N5C6b] Thus, for the [N5C4] and [N5C6] anions the lower HOMO energies are obtained for the “a” isomers, in contrast to the energy data in Table 1.

For both anions with D5d symmetry, [N5C10] and [N5], the HOMO and LUMO have E1″ and E2″ symmetries, respectively.

For [N5] this is in agreement with earlier work.2,4,17

Symmetries of the other HOMO's are: [N5C6a]: A2, [N5C8]: A2, [N5C4a]: B1, [N5C2]: B1, [N5C4b]: A2, [N5C6b]: B1 We fail to find any trend of symmetry vs. energy for the orbital.

The energies and geometries of the 1∶1 lithium ion pairs

To estimate the change in energy upon the dissociation of the salts into cations and anions calculations on various Li+–[N5C2n] ion pairs were made.

In Fig. 6 the obtained energies, ΔEel (HF/6-31G*), are plotted for the 1∶1 ion pairs schematically depicted in Fig. 2a–h.

In addition, the apex position central above the ring plane was tested for all anions, but found to be significantly less stable (for [N5] this is in agreement with17).

The ion pairs depicted in Figs. 2a–h not present in Fig. 6 were either found by the second derivative calculations to be transition states: Li+–[N5]:A, Li+–[N5C4a]:A, Li+–[N5C8]:A (all with imaginary B2 symmetry modes) or converged to another ion pair structure during the geometry optimisation.

From Fig. 6 it is clear that lithium ion bi-dentate coordination to two ring nitrogen atoms (B) is strongly preferred whenever possible.

Thus, the major jump in maxima ΔEel:−529 to −487 kJmol−1, an absolute decrease by 8%, occurs between [N5C6a] to [N5C6b] when this coordination is impossible.

For the mono-dentate coordination to CN-groups, E and E2, there is an almost linear decrease in ΔEel with n, but for all anions these minima are more than 40 kJmol−1 above the other minima energy ion pair.

Therefore only the A, B, C, and D ion pairs, in total 15 structures, were subject to G3 theory calculations.

In Fig. 7 the largest obtained ΔG for the 1∶1 ion pair dissociation for each choice of anion are presented.

By correlating all G3 sub-step level difference results whenever a full G3 calculation was successful, we find the best extrapolations to full G3 ΔG results to be obtained using sub-steps 4 and 1.

Considering the scatter of the results in section A (Fig. 1) and in order for this method to be applicable to as many and large anions as possible, the recommended sub-step level is 1, though the sub-step level 4 results could be more slightly more precise.

The scaling factors obtained were: 0.9255 (±0.009) and 0.8916 (±0.007), respectively.

Here we apply the scaling procedure to the ion pairs involving the [N5C8] and [N5C10] anions.

The B and C structures are the most stable 1∶1 Li+–[N5C2n] ion pairs.

In Fig. 7 these 1∶1 ion pairs are also compared to computed G3 values for the Li+–PF6, Li+–ClO4, Li+–TFSI, and Li+–BOB ion pairs: −546, −564, ∼−586 and −486 kJmol−1, respectively.18

Clearly all the salts presented in this study are as, or more, dissociated than the classical reference salts and on average on par with the LiBOB salt; the salts based on the larger anions being the more dissociated.

Thus the entire family of Li[N5C2n] salts keeps the promise to be excellent candidates wherever high ionic dissociation is needed.


By applying G3 theory computations we have shown that the Li[N5C2n] salts have great promise to be highly dissociated.

Furthermore, the anions are aromatic and preliminarily due to be stable towards oxidation, thus having a wide electrochemical window.

The present study shows that there is great promise to design new weakly coordinating, highly dissociated, anions without resorting to use of the most electronegative elements (F, O, Cl).

There is a paramount need for this kind lithium salts to obtain high ion conductivities in aprotic media in general, and especially in polymer electrolytes, where the importance of dissociation is even more stringent.

From the present computational results we suggest that synthesis efforts should primarily focus on anions where the bi-dentate coordination of the lithium ion to two ring nitrogen atoms (B) is inhibited i.e. the Li[N5C6b], Li[N5C8], and Li[N5C10] salts.