One of the ubiquitous examples of the Hückel rule is cyclooctatetraene dianion (COT2-). This annulene has, presumably, 10 π electrons and therefore should be aromatic, satisfying the 4n+2 rule. Therefore, the molecule should be planar, right? Well, an article by Dominikowska and Palusiak call into question these assumptions.1
COT2-
First off, with either B3LYP or MP2 and a variety of basis sets, optimization of COT2- starting from the tub-shape of COT itself led to the planar or nearly planar structure most of the time. The exceptions include B3LYP/6-311++G(d,p) and MP2/aug-cc-pVDZ. More interesting is that a number of the MP2 planar structures have one or more imaginary frequency; for example, MP2/6-311G has four imaginary frequencies.
I reoptimized a number of these structures assuming D8h symmetry, and looked for the number of imaginary frequencies. B3LYP/6-311G(d,p) had no imaginary frequencies, but B3LYP/6-31++G(d,p) and B3LYP/6-311++G(d,p) had 2 and 4 imaginary frequencies, respectively. Many of the MP2 optimizations had imaginary frequencies, with MP2/6-311G(d,p) having 3 imaginary frequencies. The optimized structures of COT2- at ωB97X-D/6-311G(d,p) had no imaginary frequencies but with the 6-311++G(d,p) basis set, it had two imaginary frequencies. Interestingly, Truhlar’s M06-2x functional with both 6-311G(d,p) and 6-311++G(d,p) gives no imaginary.
This is reminiscent of the situation with benzene and other arenes, where certain combinations of method and basis set gave multiple imaginary frequencies.2 The ultimate culprit was identified as intramolecular basis set superposition error. Dominikowska and Palusiak discount this explanation here for two reasons. First, multiple imaginary frequencies are seen with the Dunning correlation consistent basis sets – MP2/aug-cc-pVDZ has 7 imaginary frequencies (though my computation at D8h gives only one imaginary frequency), something not observed for benzene. Secondly, they noticed that in the non-planar COT2- optimized structure there are bond paths connecting the hydrogens to non-nuclear attractors situated way outside the molecule. They suggest that the COT2- might really be a Rydberg state, with the extra electrons located outside the molecule. This implies that the π system has only 8 electrons, giving the tub shape. They note that COT2- has a very short lifetime and suggest that it is not an aromatic compound, a larger annulene congener of benzene, at all.
It would be interesting to see what would happen with COT2- correcting for intramolecular basis set superposition error via the method of Asturiol, Duran and Salvador,3 which I described in this post. This correction led to planar benzene having no imaginary frequencies. This type of computation would help assess just what is going on here – is COT2- afflicted with basis set problems or is it a very unusual, non-aromatic system?
References
(1) Dominikowska, J.; Palusiak, M., "Cyclooctatetraene dianion—an artifact?," J. Comput. Chem., 2011, 32, 1441-1448, DOI: 10.1002/jcc.21730
(2) Moran, D.; Simmonett, A. C.; Leach, F. E.; Allen, W. D.; Schleyer, P. v. R.; Schaefer, H. F., III, "Popular Theoretical Methods Predict Benzene and Arenes To Be Nonplanar," J. Am. Chem. Soc., 2006, 128, 9342-9343, DOI: 10.1021/ja0630285
(3) Asturiol, D.; Duran, M.; Salvador, P., "Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem," J. Chem. Phys., 2008, 128, 144108, DOI: 10.1063/1.2902974
Henry Rzepa responded on 13 Jul 2011 at 1:09 am #
I have a different suggestion. Although unbound di-anionic systems need very diffuse basis sets, a much better way of compactifying anions (and di-anions) is to take them out of the gas phase, and put them into a much more realistic medium. There would be four ways of doing this:
1. Add the counterions. After all, the only place one might find naked anions is a mass spectrometer, and if they are unbound, not even there! All one now has left is a possible resonance in some obscure spectroscopy!
2. Put them into a cavity and surround them with a continuum field.
3. Add explicit solvent
4. Do all the above.
I think it is rather pointless to speculate about the properties of a system unless one creates it in at least an attempt at a realistic environment. I would predict here that if any of 1-4 above is modelled, the result will turn out differently from the gas phase!
As it happens, this is related to the theme of my WATOC talk next Wednesday.
Steven Bachrach responded on 13 Jul 2011 at 7:20 am #
I agree with you Henry that all of these suggestions are things to be explored. But none of them address the unusual problem of the imaginary frequencies in the gas phase. Also, and more importantly, none of these address the fact that COT dianion has an experimentally observed short lifetime in solution. That fact does call into question whether COT dianion is aromatic – why would an aromatic species, which is associated with unusual stability – have a short lifetime?
Henry Rzepa responded on 13 Jul 2011 at 2:08 pm #
If one believes that a Frost-Musulin diagram is at least approximately correct, then four of the 10π electrons in COT (2-) would be ~nonbonding rather than strongly bonding as in benzene. That presumably is where aromatic stability originates from? Coupled with the less than ideal angle at carbon (135°) I suspect one might not have that far to look for a simple minded explanation for a short lifetime.
Henry Rzepa responded on 13 Jul 2011 at 2:17 pm #
Here is yet another take. Other monocyclic 10π systems are a series of neutral molecules known as heterononins and heterocins, for which crystal structures are known. These do not suffer from the vexed question of (computationally unbound) di-anions. Their crystal structures are known in several cases (DOI: 10.1080/00268970512331317796 and 10.1039/b312724a) reveal a delicate balance between buckled non planar motifs and planar delocalised ones (we studied this at the CCSD(T) level).