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Scientists Just Revealed The Electronic Structure of a Molecule That Exists in 126 Dimensions

Michelle Starr

6 March 2020

Well, those crazy chemistry cats have done it. 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.

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," chemist Timothy Schmidt of the ARC Centre of Excellence in Exciton Science and UNSW Sydney in Australia told ScienceAlert.

"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."

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.

"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."

Voronoi site showing electron spins (left), and cross sections of the site (right). (Liu et al. Nature Communications, 2020)

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.

"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 told ScienceAlert.

"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."

The research has been published in Nature Communications.