True structure of Benzene revealed – electrons exist in 126 dimensions

Benzene is an organic compound, comprising 6 carbon atoms and 6 hydrogen atoms in a hexagonal structure. Benzene is clear, colorless, and aromatic and is formed as a by-product of oil refining. Benzene is also a component of wood, DNA, proteins, and petroleum. It is the fundamental building block for many Polystyrenes, Polycarbonates, Expoxy resins, Nylon fibers, and Phenolic resins.

Since 1930, the scientific community has debated on the fundamental electronic structure of benzene, and in recent times this has taken an increased urgency due to the fact that benzene is used in many optoelectronic materials that are revolutionizing the modern renewable energy and telecommunication technologies

Although Benzene has few electronic components, the electrons exist in a state of 126 dimensions when compared to the four dimensions we commonly know. Owing to this complexity, the precise behavior of benzene’s electrons couldn’t be discovered until now. Without this knowledge, the stability of the molecule in technological applications could never be understood completely.

Scientists from the ARC Center of Excellence in Exciton Science and UNSW Sydney, led by Timothy Schmidt, have succeeded in mapping the wave functions of benzene molecules across all 126 dimensions. The key to unraveling the complexity was the new mathematical algorithm, Dynamic Voronoi Metropolis Sampling (DVMS), developed by co-author Dr. Phil Kilby from CSIRO’s Data61. This allows scientists to partition the dimensional space into multiple tiles of the wavefunction, from which the wavefunction may be re-generated in its entirety upon application of the set of permutations of like-spin electrons

An image of how the 126-dimensional wave function tile is cross-sectioned into our 3-dimensions 42 times, once for each electron. This shows the domain of each electron, in that tile. Credit: UNSW Sydney

Understanding the spin of electrons was of particular interest to the scientists. As the understanding of how they interact with each other forms the basis for a wide range of technologies from optoelectronics to quantum computing. According to Professor Schmidt, “The electrons with what’s known as up-spin double-bonded, where those with down-spin single-bonded, and vice versa. That isn’t how chemists think about benzene. Essentially it reduces the energy of the molecule, making it more stable, by getting electrons, which repel each other, out of each other’s way.”

According to co-author Phil Kilby from Data61, the algorithm developed for “matching with constraints” can also be applied to a wide variety of areas from Staff rostering to Kidney exchange programs.

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