The first real-space observation of an ultrafast change in electron-pair density inside an isolated molecule during a quantum process was recently presented in Nature Physics. Using non-resonant hard X-ray scattering, researchers measured changes in the radial distribution of electron pairs after the molecule absorbed a high-energy photon. These changes were recorded within approximately 15 femtoseconds before the molecule fragmented.
Study: Real-space imaging of the electron-pair density hole in molecular Auger–Meitner decay. Image Credit: anaseristiane/Shutterstock.com
The findings show how electrons rearrange under repulsive Coulomb forces, addressing a significant challenge in molecular imaging. The measurements gained provide real-space information about short-lived electronic states and, when combined with theoretical modeling, help explain how they change.
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Auger-Meitner Decay and Electron Redistribution
Understanding how electrons move within matter is key to optics, materials science, and physical chemistry. When a high-energy X-ray ejects a tightly bound core electron, it creates an inner-shell vacancy that triggers Auger-Meitner decay. An outer electron fills this vacancy, and the released energy ejects another electron, resulting in a positively charged molecule.
The redistribution of electrons is a complex many-body process due to Coulomb interactions among them. While attosecond spectroscopy can effectively track these ultrafast changes by measuring energy signatures over time, it cannot directly visualize the spatial motion of electrons. Capturing this motion before the molecule breaks apart has therefore remained a significant challenge in ultrafast molecular imaging.
Single-Pulse Approach for Ultrafast Imaging
To overcome the limitations of conventional pump-probe measurements, researchers developed a single-pulse approach capable of tracking ultrafast electronic motion with sub-15 femtosecond resolution. The experiment was conducted at the Coherent X-ray Imaging (CXI) end station of the Linac Coherent Light Source, where gas-phase sulfur hexafluoride (SF6) molecules were exposed to intense, non-resonant hard X-ray pulses.
A single X-ray pulse triggered the electronic transition and probed its evolution through a second-order interaction. The X-ray pulses had a mean photon energy of 9.486 keV, an average duration of 31.9 femtoseconds, and peak intensities of 1017–1018 W cm-2. More than one million laser shots were recorded, with 171,757 meeting the analysis criteria.
The intensity fluctuations of the free-electron laser were used to isolate the quadratic-scattering signal produced during Auger-Meitner decay from the background scattering. The scattered X-rays were recorded using a Jungfrau 4M detector, allowing researchers to measure changes in electron-pair density over a momentum-transfer range of 0.27–4.27 Å-1.
Mapping the Evolution of Electronic Vacancies
The isolated second-order scattering data was transformed into a real-space radial electron-pair density using an inverse zeroth-order spherical Bessel transform. This reconstruction mapped the probability of finding two electrons at a given separation, and simulations were performed to reveal the evolution of the electronic vacancy during Auger-Meitner decay.
These simulations indicated that, within the first three femtoseconds after core ionization, distinct minima appeared at electron-pair distances of approximately 0.16 Å, 1.56 Å, and 2.21 Å. These distances correspond to the atomic core, sulfur-fluorine bonds, and neighboring fluorine atoms within the molecule.
After an average delay of 14.6 femtoseconds, these localized features merged into a broad minimum centered near 2.50 Å. The performed simulations indicate that the vacancy had spread from the atomic core into the valence region.
The measurements suggest that an average of 3.1 electrons were ejected during the process, aligning closely with theoretical predictions.
The data also demonstrated a measurable decrease in electron-pair repulsion energy, providing evidence of changing electrostatic interactions within the excited molecule. However, the limited momentum-transfer range meant the full magnitude could not be quantitatively determined.
Implications for Radiation Damage
Direct imaging of changes in radial electron-pair density has great potential for molecular imaging and medical physics applications. In femtosecond crystallography and single-particle imaging, intense X-ray free-electron laser pulses can rapidly alter the electronic structure of samples.
By mapping changes in electron density, this method could be used to help researchers model radiation damage and correct shifts in atomic scattering factors, thereby improving the accuracy of protein and biomolecular structures. The findings also enhance the understanding of electron damage, which is key for radiobiology and radiation therapy.
Conclusion and Future Directions
This study demonstrates that ultrafast non-resonant X-ray scattering can directly image changes in electron-pair density during molecular decay. Beyond this, the method also measures changes in electron-pair repulsion energy, providing a novel approach to studying electronic interactions in molecules.
The close agreement between the experiment and theoretical modeling supports the researchers’ interpretation of the measured changes in electron-pair density.
Future advancements in attosecond hard X-ray sources are expected to transition from the current single-pulse approach to true multi-color pump-probe measurements. Combined with temporal ghost imaging, these systems could produce detailed maps of changes in electron-pair density, offering a clear view of chemical reactions and light-matter interactions across fields.
Journal Reference
Simmermacher, M., Goff, N., Moreno Carrascosa, A., et al. (2026). Real-space imaging of the electron-pair density hole in molecular Auger–Meitner decay. Nature Physics. https://www.nature.com/articles/s41567-026-03363-8.
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