3D Electron Wavefunction Imaging

An illustration of how researchers used state-of-the-art photoelectron spectroscopy (left hand side) with a lab-based soft-X-ray light source that provides ultrashort light pulses, which was combined with powerful mathematical algorithms, to image the wavefunction of electron orbitals (right-hand side).
 Image Credit: Lukas Kroll

Scientific Frontline: Extended "At a Glance" Summary: Three-Dimensional Electron Wavefunction Imaging

The Core Concept: This technique captures and maps the complete three-dimensional wavefunctions, or molecular orbitals, of a nanometer-sized organic molecule. It provides a visual mathematical map of an electron's probability distribution regarding its specific position and momentum.

Key Distinction/Mechanism: Previous three-dimensional wavefunction imaging required time-intensive measurements at large-scale synchrotron facilities. This new methodology overcomes these limitations by combining a table-top, ultrashort soft-X-ray light source with photoelectron spectroscopy to measure emitted electron momentum, while newly redesigned computer algorithms deduce the unmeasured half of the wavefunction.

Major Frameworks/Components:

• Photoelectron Spectroscopy: An observational method used to measure the momentum of emitted electrons, accessing one half of the wavefunction without physically altering its state.
• Advanced Computational Algorithms: Redesigned mathematical models capable of deducing the complete three-dimensional orbital image from significantly less experimental data than previously required.
• Soft-X-Ray Light Source: A laboratory-based laser system providing ultrashort, femtosecond-scale light pulses to illuminate the molecule.

Branch of Science: Quantum Mechanics, Molecular Physics, and Physical Chemistry.

Future Application: The technology paves the way for stroboscopic videography of atomic dynamics. Researchers anticipate recording three-dimensional videos with femtosecond (one quadrillionth of a second) resolution to observe how molecular wavefunctions adapt during chemical, optical, or electronic changes.

Why It Matters: Knowledge of the complete three-dimensional wavefunction is critical because it dictates how a molecule interacts with its surroundings. Transitioning this capability from massive synchrotrons to standard laboratories allows scientists to develop new methods for observing and controlling molecular interactions at the atomic level.

One of the 3D wavefunction photographs, here showing the highest-occupied molecular orbital of PTCDA, a molecule that is often used for the fabrication of red dyes due to the strong interaction with light. In the centre, a 3D representation is shown, while the side panels show slices through the orbital at 1 Å (one ten-billionth of a meter) away from the centre of the molecule.
Photo: Reproduced from Bennecke, W. et al. Nature Communications (2026)
(CC 4.0 license).

One of the most famous and intriguing results of quantum mechanics is the finding that fundamental particles, such as electrons, cannot be pinned down to a single location. Instead, a particle is described by its "wavefunction," which allows researchers to derive probability distributions—a sort of mathematical map that shows the possibilities—of fundamental properties such as its position and momentum. In particular, the electron wavefunctions within a molecule, known as "molecular orbitals," carry information about how the molecule interacts with its surroundings. For example, they show how the molecule may absorb light or how a chemical reaction might take place. As a consequence, knowledge of the complete three-dimensional wavefunction is highly desirable, but imaging the wavefunction has proven to be a major experimental challenge. An interdisciplinary research team at the University of Göttingen has now managed to image the three-dimensional wavefunction of a nanometer-sized organic molecule. They overcame previous limitations by combining state-of-the-art photoelectron spectroscopy with powerful mathematical algorithms. 

"The wavefunction is a fundamental quantity in quantum mechanics, yet it cannot be directly observed or measured," explains Professor Stefan Mathias of the University of Göttingen. Instead, the team relied on an indirect approach: photoelectron spectroscopy, in which the momentum of emitted electrons is measured to provide access to one half of the wavefunction without physically altering its state. Sophisticated computer algorithms then deduced the other half, allowing researchers to image the complete molecular orbital and resolve features that are smaller than the distance between the carbon atoms that make up the molecule. However, applying this principle in 3D previously required time-intensive measurements at large-scale synchrotron facilities, limiting its widespread application and, in particular, its extension toward imaging "dynamical" wavefunctions in a 3D video at the atomic scale.

Dr. Matthijs Jansen of the University of Göttingen and co-leader of the study highlights the originality of the team's approach: "We introduce two powerful new concepts. First, by redesigning the computer algorithm from the ground up, we can now obtain reliable 3D images using much less experimental data. Second, the experiment is based on a powerful, lab-based soft X-ray light source that provides ultrashort light pulses. It is the combination of these two techniques that has this remarkable impact." Dr. Wiebke Bennecke, first author of the study, adds, "This technique might mean that stroboscopic videography becomes a reality, allowing us to observe not just the shape of wavefunctions but also to see how they change with ultrafast—even femtosecond, or one-quadrillionth of a second—resolution. This will mean we can learn how a molecule adapts to optical, electronic, or chemical changes, and find new ways to control these interactions at the level of a few atoms."

Published in journal: Nature Communications

Title: Table-top three-dimensional photoemission orbital tomography with a femtosecond extreme ultraviolet light source

Authors: Wiebke Bennecke, Thi Lan Dinh, Jan Philipp Bange, David Schmitt, Marco Merboldt, Lennart Weinhagen, Bent van Wingerden, Fabio Frassetto, Luca Poletto, Marcel Reutzel, Daniel Steil, D. Russell Luke, Stefan Mathias, and G. S. Matthijs Jansen

Source/Credit: Georg-August-Universität Göttingen

Edited by: Scientific Frontline

Reference Number: qs080426_01

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