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# Understanding the dance of electrons

## Applying quantum mechanics to chemistry

Predicting electronic structures is difficult because electrons seem to move in a very crazy and not well-understood way to avoid on another. So an ensemble of electrons all dance around like bees trying to avoid one another while staying close to the hive. Understanding this dance of electrons is called the ‘Electron Correlation Problem’.Quantum physicists currently use the Schrödinger wave equation to locate the probable position of an electron around the nucleus of an atom by considering its mass and energy. This is relatively straightforward for a hydrogen atom, as it only has one electron. However, an exact solution of the wave equation until now has never been found for a helium atom because of the mutual disturbances caused by the Coulomb interaction between the two negatively charged electrons and the positively charged nucleus.

It is similar to the ‘Three Body Problem’ in physics: when a planet has a couple of moons in orbit and the exact mass and velocity of each one is known, it is virtually impossible to accurately predict the location of them at other times using the laws of classical mechanics. The complex nature of the motion of the three bodies due to the to their mutually perturbing gravitational interactions means that scientists have never found an exact solution.

Quasiexact models can be solved, such as Hooke’s Atom. This uses harmonic potential to represent the electron-nucleus interaction, which is a consequence of Hooke’s law. It is as if the three particles are connected by helical springs. Such computer models are very useful for predicting how chemicals will react before costly laboratory experiments have even begun. They are used in many research fields such as the development of new materials or drugs.

Dr Pierre-Francois Loos arrived at ANU from Nancy in France to begin his post-doctoral research at the Research School of Chemistry. His supervisor, Professor Peter Gill, gave him the challenge of studying two electrons as points on the surface of a sphere. Gill openly admits that he never expected Loos to solve the Schrödinger equation exactly. However, less than a year later their results appeared in the prestigious journal, Physical Review Letters.

Gill says, “What he has found is that the surface of a normal 3D sphere is not a very good model for real life; that actually the surface of the 4D sphere is the best model for real life. That is because the surface of a 4D sphere is three-dimensional… So if you really want to understand our 3D world, the best model to look at is the 4D ball’s surface.” This is one of the key points of this paper.

The pair have since written a paper about what happens when the sphere reduces to a point, thus crushing both electrons and this was recently published in The Journal of Chemical Physics. For his next paper, Loos says that rather than increase the number of electrons on his sphere, he would like to see if he could do the same for different systems. He says, “For example, if we consider two [concentric] spheres and see what happens if we put one electron on each one.”

Gill says, “We know that the real world is very complicated, but by reducing it down to this essence and understanding that perfectly, we hope we can then build up slowly from that. So that a perfect understanding of a system like this can often be the beginning of an imperfect understanding of more complicated things such as real atoms, real molecules.”

In other words, if you want to understand how a hundred bees dance, you can get a pretty good start by understanding two bees.

(by Guy Micklethwait)

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