Experimentally-inspired theorists describe electron choreography in a hydrogen molecule.

An artistic rendering of the experiment. The photon is the yellow beam, the protons are the red particles, and the expected positions of the electrons are in blue. The “butterfly wing” web around the electrons shows the wave function for electron position: essentially, how likely it would be for an experimenter to find the electron at a given location.Credit: Wim Vanroose et al. and S. Lemmens

Picture two fencers with their swords locked, tip-to-tip. They step neither closer together nor farther apart; either change would leave them vulnerable. But they do not stand still, either. Rather, they engage in a delicate dance, responding immediately to one another.

Electrons in a hydrogen molecule (H2) repel one another (both having a negative charge), but they cannot escape the bond of the molecule. So their motions are correlated, much like those of the fencers.

The choreography of this electron dance has been a mystery for years, but now, thanks to an innovative collaboration between experimentalists and theorists, science has its first direct glimpse at electron correlation.

Inspired by an experiment performed last year, where researchers blew up hydrogen molecules with photons, theorists at Lawrence Berkeley National Laboratory have derived physically-descriptive equations for the initial and final states of the two-proton-two-electron system, as well as an expression for how those states are connected. Their findings, published in the December 16th issue of Science, comprise the first-ever complete quantum mechanical solution of a system with four charged particles.

“If we can do this for other molecules, it means we have a very, very sensitive picture of this intricate dance that electrons do in a bond,” said coauthor William McCurdy. “Trying to image dynamics of electrons in a bond is something that’s been a goal of scientists—chemists and physicists—for decades.”

In last year’s experiment, scientists from the US, Spain and Germany brutally destroyed hydrogen molecules by firing a single x-ray photon at each one. Using sensitive detectors, they recorded where each of the four charged particles went after the photon hit. From that, they were able to determine the exact initial orientation of the molecule with respect to the photon beam.

“What they noted was that the pattern changed radically when the molecule’s orientation or the instantaneous position of the nuclei of the molecule were changed by a small amount,” said Thomas Rescigno, a theorist and coauthor of the new paper.

Without an exact calculation of the quantum mechanical state of the system, the experimenters couldn’t determine why such small changes in the initial state would cause such different ejection patterns. However, the theorists had a sneaking suspicion it had something to do with the dance of electron correlation.

Rescigno said electron correlation is key to the very nature of last year’s experiment: If the electrons were not correlated, the one photon could only have knocked a single electron out of the molecule; the other electron would stay, keeping the molecule intact. It would only have been possible to knock out both electrons with a single photon if the electrons were correlated. With the electrons gone, the two hydrogen nuclei are stripped of the negative charge that held them together. The two positively charged nuclei repel each other in a Coulomb explosion.

“We had to have an essentially exact solution of the quantum mechanics to prove that [electron correlation is] in fact what they were seeing,” said McCurdy. “This is maybe opening the door to a very powerful new experimental technique for looking at electrons in bonds and their correlated motion with each other.”

The theoretical solution of electron correlation showed very clearly that small changes in bond length—the distance between the two nuclei—would produce enormous changes in ejection patterns of the electrons. In fact, the theorists’ found the effects were even more extreme than the experiment had led them to believe.

“The experiment couldn’t quite see how radical the change was,” McCurdy said. “The experimental resolution and the experimental errors that are inherent in any physical experiment really obscured how beautiful and how dramatic the changes [in ejection pattern] were with just these small changes in internuclear distance.”

Originally published December 19, 2005


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