Ouroboros Breathes Benzene

Kekulé and Ouroboros

Aromaticity and antiaromaticity ebb and flow in the benzene ring because of so-called “breathing” modes as revealed by derivative current-density maps. The discovery could help improve our understanding of the properties of this important and ubiquitous chemical group.

Ever since Friedrich August Kekulé von Stradonitz had his apocryphal daydream of the autophagous snake Ouroboros and reasoned that the only way six carbon and six hydrogen atoms could sit comfortably together was in a ring, chemists have been fascinated by the benzene molecule. Until 1865, chemists had struggled to reconcile much of the empirical data in the burgeoning field of organic chemistry, especially where bonding was concerned and most particularly, double bonds between carbon atoms.

By 1872, Kekulé had refined his model of benzene to suggest that it oscillates between two forms in which the three alternating double bonds around the ring swap places endlessly. This essentially means that the carbon atoms are all equivalent but it was not until the advent of quantum mechanics and Linus Pauling’s 1928 proposal of bond resonance that an understanding of the truly aromatic nature of the benzene ring could move forward.

Understanding Aromaticity

The benzene ring is almost ubiquitous in organic and biological chemistry. It and its chemical cousins are at the heart of millions of compounds. So, understanding the aromaticity of the benzene ring and how it changes is therefore critical to understanding the synthesis of these molecules, their reactions and interactions, and the mechanisms by which they themselves change and how they change other molecules with which they come into contact.

Chemists have more than a century’s worth of studies on benzene in a vast research literature, but there are always new nuances to unearth about this critical ring. Now, researchers in theoretical chemistry at Sheffield University, UK, have looked at the effects of vibration on the ring currents present in aromatic and antiaromatic rings. They hoped to reveal how aromaticity changes as the molecules breathe in and out through vibration and to compare this behavior in the benzene ring with the archetypal antiaromatic compound cyclooctatetraene (COT) and the non-aromatic borazine. Borazine, B₃N₃H₆, is isoelectronic with benzene, but although some chemists refer to it as the inorganic benzene, it is neither aromatic nor antiaromatic so acts, essentially, as a “control”. Previous studies have focused only on benzene itself.

Mapping the Current Density

David Bean and Patrick Fowler have derived current-density maps for the three molecules and found that both the symmetric ‘breathing’ and the distortive Kekulé vibration of benzene lead to a drop in net ring-current aromaticity. The corresponding vibrations in COT increase its antiaromaticity. In essence, the calculations show whether or not a molecule sustains an induced diatropic (paratropic) ring current in a perpendicular external magnetic field, the team explains. If it does, then it retains its aromaticity or antiaromaticity. If it changes, then one can say that the vibrational distortions change those properties. In other words, showing how non-equilibrium conformations can contribute to the average aromaticity or antiaromaticity of a system.

The perhaps startling conclusion from the work of Bean and Fowler is that despite what you might imagine, the aromaticity of benzene is not at a maximum at its equilibrium geometry and nor is COT in its most antiaromatic in the transient geometry, the D_4h transition state that lies midway between two non-aromatic tub-shaped conformations. It seems that although it is almost a century and a half since Kekulé daydreamed of Ouroboros, we have much to learn about aromaticity.

Distortive Tendencies

Theoretical chemist Henry Rzepa of Imperial College London, UK, is also interested in benzene and points out that others (Yamaguchi and Schaeffer) have studied the second derivative of the π-orbital energy for this vibration as an indicator of distortive tendencies of this mode. “What [Fowler and Bean] have done is study the 2nd derivative of the current-density map,” he explains. “In terms of energy the π energy reduces with the Kekulé mode, as apparently does the current density. So, more stable π electrons, but less aromatic.” He adds that the work “is a very useful addition to our knowledge of the behavior of benzene.”

Rzepa suggests that the researchers might repeat the investigation for the quintet state of benzene — an idea mentioned on his blog and in more detail in his 2009 PhysChemChemPhys paper — because the triplet state is complicated by Jahn-Teller distortions.

“We studied first and second derivatives and we have studied both breathing and Kekulé modes,” Fowler adds. “For the Kekulé mode, we might well expect the aromaticity as judged by ring current to be reduced and indeed in our paper we rationalize our finding in terms of a π distortivity model applied to our frontier-orbital approach to ring current. The first derivative map gives a beautiful illustration of the growing-in of localized double bond character as the vibration progresses. I would say it is quite striking that energy/distortivity and magnetic concepts of aromaticity agree in this way. After all, there are researchers who believe that aromaticity is a multidimensional phenomenon, in which case there would be no reason for the two measures to agree at all.”

Fowler adds that he was not sure what to expect before they did the calculations on COT. “We can understand the results using π distortivity models,” he explains. “For the breathing mode, there are no strong a priori grounds for expecting it to go one way or the other, and the indications from other aromaticity indicators are contradictory, so in that sense, the result had to be a surprise.”