Nearly 200 years after the molecule was discovered by Michael Faraday, researchers have finally discovered the complex electronic structure of benzene.
This not only resolves a controversy that has been raging since the 1930s, but has important implications for the future development of optoelectronic materials, many of which are based on benzene.
The atomic structure of benzene is fairly well understood. It is a ring made up of six carbon atoms and six hydrogen atoms, one for each carbon atom.
This becomes extremely difficult when we consider the 42 electrons of a molecule.
“The mathematical function describing the electrons of benzene is 126-dimensional,” said chemist Timothy Schmidt of the ARC Center of Excellence in Exciton Science and UNSW in Australia.
This means that it is a function of 126 coordinates, three for each of the 42 electrons. Electrons are not independent, so we cannot break this down into 42 independent 3D functions.
The machine's answer is not easy to interpret by humans, and we had to invent a way to get the answer. '
Thus, this means that the mathematical description of the electronic structure of benzene must take into account 126 measurements. As you can imagine, this is not an easy thing to do. In fact, because of this complexity, uncovering the structure has remained a problem for such a long time, leading to controversy about how benzene electrons behave.
There are two schools of thought: benzene follows the theory of valence bonds with localized electrons; or molecular orbital theory with delocalized electrons. The problem is, none of them seem to be quite right.
“Interpreting the electronic structure in terms of orbitals ignores that the wave function is antisymmetric when exchanged with the same spins,” the researchers wrote in their paper. “Moreover, molecular orbitals do not provide an intuitive description of electron correlation.”
The team's work was based on a technique they recently developed. It is called dynamic sampling of the Voronoi Metropolis and uses an algorithmic approach to visualize the wave functions of a multi-electron system.
This divides the electronic dimensions into individual tiles in a Voronoi diagram, where each of the tiles corresponds to electronic coordinates, allowing the team to display the wavefunction of all 126 dimensions.
Cross section of a molecule. (Liu et al. Nature Communications, 2020)
And they found something strange.
“Electrons with so-called double bonds with an increase in the speed of rotation, where electrons with single bonds with a decrease in the speed of rotation and vice versa,” said Schmidt. “This is not how chemists think about benzene.”
As a result, electrons avoid each other when beneficial, decreasing the energy of the molecule and making it more stable.
“It basically brings chemical thinking together, showing how the two prevailing paradigms we use to describe benzene come together,” he said.
'But we also show you how to test what's called electron correlation – how electrons avoid each other. This is almost always qualitatively ignored and used only for calculations where only energy is used, not electronic behavior. '
The research was published in Nature Communications.
