In 1825, the British physicist and chemist Michael Faraday isolates a particular compound in the residual liquid present in the bottom of lighting bottles: benzene. Suggested in 1861, the chemical structure of benzene was correctly described in 1933 by Linus Pauling. However, since its discovery, chemists have always wondered about its extremely complex electronic structure. And recently, a team of researchers finally described it in detail.
Nearly 200 years after the molecule was discovered by Michael Faraday, researchers have finally revealed the complex electronic structure of benzene. This not only settles a debate that has been raging since the 1930s, this step has important implications for the future development of opto-electronic materials, many of which are built on benzenes.
The atomic structure of benzene is pretty well understood. It's a ring consisting of six carbon atoms, and six hydrogen atoms, one attached to each of the carbon atoms.
Benzene: a structure of 42 electrons described in 126 dimensions
Where it gets extremely tricky is when we consider the molecule's 42 electrons. "The mathematical function that describes benzene's electrons is 126-dimensional," said the chemist Timothy Schmidt of the ARC Centre of Excellence in Exciton Science and UNSW Sydney in Australia"That means it is a function of 126 coordinates, three for each of the 42 electrons. The electrons are not independent, so we cannot break this down into 42 independent three-dimensional functions. The answer computed by a machine is not easy to interpret by a human, and we had to invent a way to get at the answer."
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| Structural portion of the benzene molecule modeled according to the Voronoi algorithm. (d): Voronoi website showing electronic spins. (d): cross section of the Voronoi site, showing the two electron spins of the CC bond (in blue and red). Credits: Yu Liu et al. 2020 |
So, that means mathematically describing the electronic structure of benzene needs to take 126 dimensions into account. As you can imagine, this is not exactly a simple thing to do. In fact, this complexity is why revealing the structure has remained a problem for so long, leading to debates about how benzene's electrons even behave. There are two schools of thought: that benzene follows valence bond theory, with localised electrons; or molecular orbital theory, with delocalised electrons. The problem is, neither really seems to quite fit.
Electronic dynamics much more complex than expected
"The interpretation of electronic structure in terms of orbitals ignores that the wavefunction is antisymmetric upon interchange of like-spins," the researchers wrote in their paper. "Furthermore, molecular orbitals do not provide an intuitive description of electron correlation."The team's work was based on a technique they recently developed. It's called dynamic Voronoi Metropolis sampling, and it uses an algorithmic approach to visualise the wavefunctions of a multiple-electron system. This separates the electron dimensions into separate tiles in a Voronoi diagram, with each of the tiles corresponding to electron coordinates, allowing the team to map the wavefunction of all 126 dimensions. And they found something strange.
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| (a): Classic Kekule structures of the benzene molecule. (b): Structure proposed by the authors with the spins indicated in red and blue. Credits: Yu Liu et al. 2020 |
"The electrons with what's known as up-spin double-bonded, where those with down-spin single-bonded, and vice versa," Schmidt said in statement. "That isn't how chemists think about benzene."
The effect of this is that the electrons avoid each other when it is advantageous to do so, reducing the energy of the molecule, and making it more stable. "Essentially, this unites chemical thought, by showing how the two prevailing paradigms by which we describe benzene come together," he added.
"But we also show how to inspect what is called electron correlation - how the electrons avoid each other. This is almost always ignored qualitatively, and only invoked for calculations where only the energy is used, not the electronic behaviour."
In other words, this result describes the main effect of electronic correlation in benzene, and emphasizes that electrons are not paired in space when it is energetically advantageous.
| Bibliography: The electronic structure of benzene from a tiling of the correlated 126-dimensional wavefunction Yu Liu, Phil Kilby, Terry J. Frankcombe & Timothy W. Schmidt Nature Communications volume 11, Article number: 1210 (2020) https://doi.org/10.1038/s41467-020-15039-9 |
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Chemistry