Quantum mechanics has long forced scientists to abandon the idea that electrons occupy fixed, sharply defined locations. Instead, each electron is described by a wavefunction, a mathematical object that encodes the probabilities of where the particle may be found and how it may move. Now, researchers at the University of Göttingen have achieved a major advance in making that invisible object visible: they have reconstructed the three-dimensional wavefunction of an electron orbital in a nanometer-sized organic molecule using a laboratory-based light source and advanced computational methods.
The result, reported in Nature Communications, brings scientists closer to recording the motion of molecular electrons in real time. Although the reconstructed images are not photographs of electrons frozen in space, they represent the spatial amplitude and phase of a molecular orbital—the quantum state that determines how an electron is distributed across a molecule. Molecular orbitals govern many of the properties that make chemistry possible, including how molecules absorb light, form bonds, transfer charge and undergo chemical reactions.
The Göttingen team used a technique known as photoemission orbital tomography, an approach that extracts information about a molecular orbital from the electrons released when a molecule is struck by high-energy light. In the experiment, an ultrashort pulse of extreme ultraviolet radiation ejects an electron from the molecule. The outgoing electron behaves like a matter wave, and its momentum distribution carries information about the shape of the orbital from which it originated.
That information is collected in momentum space rather than ordinary photographic space. By measuring the direction and energy of many emitted electrons, researchers can construct a pattern related to the Fourier transform of the initial molecular wavefunction. Mathematical reconstruction then converts this momentum-space information into a real-space image. In effect, the experiment records how the electron leaves the molecule and works backward to infer the quantum structure that produced the measured pattern.
The method is powerful but technically demanding because a wavefunction contains both amplitude and phase. The amplitude indicates where an electron is more or less likely to be found, while the phase describes the sign and interference structure of the quantum state. Conventional measurements often provide only partial information, creating an inverse problem in which many possible wavefunctions might appear compatible with the same experimental data. The researchers addressed this challenge by redesigning the reconstruction algorithm to extract reliable three-dimensional information from a substantially smaller data set.
This reduction in the amount of required data is central to the advance. Three-dimensional photoelectron measurements have traditionally required extensive scans at large synchrotron facilities, where intense and tunable radiation is available. Such experiments can deliver exceptional detail, but their scale and time requirements make them difficult to apply broadly or repeat rapidly. The Göttingen approach instead uses a compact, laboratory-based soft-X-ray and extreme-ultraviolet source capable of producing femtosecond pulses, allowing the measurements to be carried out on a tabletop system.
Femtosecond pulses last only a few quadrillionths of a second. Their brevity is essential because molecular electrons can respond to light and chemical forces on similarly rapid timescales. A sufficiently short pulse can act like a stroboscopic flash, capturing a transient electronic configuration before it changes. By combining these pulses with the new reconstruction strategy, the researchers say their method could eventually move beyond static orbital imaging and produce three-dimensional “videos” of molecular wavefunctions as they evolve.
Such movies would provide a new way to examine the earliest stages of chemical and physical change. When a molecule absorbs light, its electrons can redistribute almost instantly, sometimes before the atomic nuclei have had time to move appreciably. Those electronic rearrangements can determine whether a molecule fluoresces, transfers energy, breaks apart or begins a chemical reaction. Directly following the changing orbital structure could therefore reveal how molecular systems respond to optical, electronic and chemical stimuli at the scale of individual atoms.
The technique may also help scientists design more efficient materials and control chemical reactions with greater precision. Understanding the phase and shape of molecular orbitals is important for fields ranging from organic electronics and photovoltaics to photocatalysis and quantum technologies. However, the researchers emphasize that the reconstructed wavefunction is obtained indirectly through a carefully modeled measurement, rather than observed as a conventional image. Its significance lies in combining experimentally measured electron momenta with quantum-mechanical theory and computational analysis to recover information that cannot be accessed by a simple camera.
The study marks a step toward making quantum dynamics visually understandable while preserving the underlying technical detail. A laboratory system that can reconstruct molecular orbitals in three dimensions with ultrashort pulses could make advanced orbital tomography available to more research groups and enable repeated measurements under changing conditions. If future developments succeed in improving temporal resolution and applying the method to more complex molecules, scientists may be able to watch electrons reorganize during a chemical reaction—turning one of quantum mechanics’ most abstract concepts into an observable, evolving molecular phenomenon.
Subject of Research: Single molecule analysis and three-dimensional imaging of molecular electron wavefunctions.
Article Title: “Table-top three-dimensional photoemission orbital tomography with a femtosecond extreme ultraviolet light source.”
News Publication Date: 19-Jun-2026
Web References: https://doi.org/10.1038/s41467-026-74308-1
References: Bennecke, W. et al., “Table-top three-dimensional photoemission orbital tomography with a femtosecond extreme ultraviolet light source,” Nature Communications (2026). DOI: 10.1038/s41467-026-74308-1.
Image Credits: Lukas Kroll
Keywords
Quantum mechanics, electron wavefunctions, molecular orbitals, photoelectron spectroscopy, orbital tomography, three-dimensional imaging, femtosecond extreme ultraviolet light, soft X-rays, molecular imaging, quantum dynamics, spectroscopy, electron systems, image processing.
