Physicists create first direct images of the square of the wave function of a hydrogen molecule

January 9, 2018 by Lisa Zyga, feature
Image of the square of the wave function of a hydrogen molecule with two electrons. Credit: Waitz et al. Published in Nature Communications

For the first time, physicists have developed a method to visually image the entanglement between electrons. As these correlations play a prominent role in determining a molecule's wave function—which describes the molecule's quantum state—the researchers then used the new method to produce the first images of the square of the two-electron wave function of a hydrogen (H2) molecule.

Although numerous techniques already exist for imaging the individual of atoms and , this is the first that can directly image the correlations between electrons and allow researchers to explore how the properties of electrons depend on one another.

The researchers, M. Waitz et al., from various institutes in Germany, Spain, the US, Russia, and Australia, have published a paper on the new imaging method in a recent issue of Nature Communications.

"There are other methods that allow one to reconstruct correlations from different observations; however, to my knowledge, this is the first time that one gets a direct image of correlations by just looking at a spectrum," coauthor Fernando Martín at the Universidad Autónoma de Madrid told "The recorded spectra are identical to the Fourier transforms of the different pieces of the square of the wave function (or equivalently, to the representation of the different pieces of the wave function in momentum space). No reconstruction or filtering or transformation is needed: the spectrum directly reflects pieces of the wave function in momentum space."

The new method involves combining two imaging methods that are already widely used: photoelectron imaging and the coincident detection of reaction fragments. The researchers simultaneously employed both methods by using the first method on one electron to project that electron onto a detector, and using the second method on the other electron to determine how its properties change in response.

The simultaneous use of both methods reveals how the two electrons are correlated and produces an image of the square of the H2 correlated two-electron wave function. The physicists emphasize one important point: that these are images of the square of the wave function, and not the wave function itself.

"The wave function is not an observable in quantum physics, so it cannot be observed," Martín said. "Only the square of the wave function is an observable (if you have the tools to do it). This is one of the basic principles of quantum physics. Those who claim that they are able to observe the wave function are not using the proper language because this is not possible: what they do is to reconstruct it from some measured spectra by making some approximations. It can never be a direct observation."

The researchers expect that the new approach can be used to image molecules with more than two electrons as well, by detecting the reaction fragments of multiple electrons. The method could also lead to the ability to image correlations between the wave functions of multiple molecules.

"Obviously, the natural step to follow is to try a similar method in more complicated molecules," Martín said. "Most likely, the method will work for small molecules, but it is not clear if it will work in very complex molecules. Not because of limitations in the basic idea, but mainly because of experimental limitations, since coincidence experiments in complex molecules are much more difficult to analyze due to the many nuclear degrees of freedom."

The ability to visualize electron-electron correlations and the corresponding molecular has far-reaching implications for understanding the basic properties of matter. For instance, one of the most commonly used methods for approximating a wave function, called the Hartree-Fock method, does not account for electron-electron correlations and, as a result, often disagrees with observations.

In addition, electron-electron correlations lie at the heart of fascinating quantum effects, such as superconductivity (when electrical resistance drops to zero at very cold temperatures) and giant magnetoresistance (when electrical resistance greatly decreases due to the parallel alignment of the magnetization of nearby magnetic layers). Electron correlations also play a role in the simultaneous emission of two electrons from a molecule that has absorbed a single photon, a phenomenon called "single-photon double ionization."

And finally, the results may also lead to practical applications, such as the ability to realize imaging with field-electron lasers and with laser-based X-ray sources.

Explore further: A space-time sensor for light-matter interactions

More information: M. Waitz et al. "Imaging the square of the correlated two-electron wave function of a hydrogen molecule." Nature Communications. DOI: 10.1038/s41467-017-02437-9

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Whydening Gyre
4 / 5 (2) Jan 09, 2018
The pictures can be really helpful to those of us with "dysleftia"...
3.7 / 5 (3) Jan 09, 2018
But he wrote non-fiction
5 / 5 (1) Jan 09, 2018
The wave function is signed, hence the need to square it in order represent the probable electron densities, euphemistically called "keeping it Real" (note capital). Read your quantum chemistry, folks.

What I find interesting is that the visualization suggests that some LUMO states are populated, i.e., the H2 molecule of interest is well above the ground state, and is not trivially modeled by ab initio methods.
5 / 5 (2) Jan 10, 2018
The wave function is signed, hence the need to square it in order represent the probable electron densities, euphemistically called "keeping it Real" (note capital). Read your quantum chemistry, folks.

I believe you meant to say "The wave function is complex, ...."
5 / 5 (1) Jan 10, 2018
I believe you meant to say "The wave function is complex, ...."

Didn't want to start a discussion about visualizing sqrt(-1) and other snipe hunts.

That said, if you model H2 with f-orbital polarization and look at LUMO+4,5,6, THEN you'll see the orbital shapes they describe far above ground state.
Da Schneib
not rated yet Jan 10, 2018
All we can see is the probability in position (or as the article points out, in momentum). The use of this imaging technique is valuable.
Da Schneib
3 / 5 (2) Jan 10, 2018
@khar, thanks for turning me on to HOMO and LUMO. I expect they had to excite the hydrogen molecules for their imaging technique.
not rated yet Jan 10, 2018
Anyone remember the old picture to describe the atom (3 circular orbitals + nucleus in the center), which was superseded by the fuzzy ball type image used today.

We have gone full circle (pun intended) and now back to the old image - it also looks like the combination view of all S + P-orbitals superimposed.
5 / 5 (1) Jan 13, 2018
hat is all this unclear and illogical here?
First, can one eject a molecule of hydrogen and observe it so separated, as someone gog is examined by a doctor.
Second, if the electron rotates around the core so fast, who can insert anything into that path, while the electron is on the opposite side.
Third, what researchers see from this electron: a particle or a wave or both
Fourth, If a hydrogen molecule can not be separated to be alone, how does this molecule behave in its own society with its "friends"?
Fifth, Do the researchers know what the electron is, how it does and how it behaves, about its spin, which determines all of its properties.
Sixth, do researchers know where this molecule is "submerged" and how this substance works on all the elements of this molecule. If this is not known, what are these fictitious results for?

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