Physicists at Göttingen University imaged three-dimensional wave functions using a tabletop soft X-ray laser. An electron inside a molecule does not occupy one fixed point. Quantum mechanics instead describes it through a “wavefunction,” a mathematical map that gives the probabilities of properties such as position and momentum. Within molecules, these electron wavefunctions are known as “molecular orbitals.” Their shapes contain information about how a molecule may absorb light, interact with its surroundings, or undergo a chemical reaction. Capturing the complete three-dimensional wavefunction would therefore give researchers a powerful view of molecular behavior. Yet producing such an image has remained a major experimental challenge. An interdisciplinary group at the University of Göttingen has now imaged the three-dimensional wavefunction of a nanometer-sized organic molecule. By combining advanced photoelectron spectroscopy with mathematical algorithms, the researchers reconstructed details at scales smaller than the distance between neighboring carbon atoms. The results were published in Nature Communications. An indirect method reconstructs the orbital “The wavefunction is a fundamental quantity in quantum mechanics, yet it cannot be directly observed or measured,” explains Professor Stefan Mathias at the University of Göttingen. The researchers instead used photoelectron spectroscopy, an indirect technique that measures the momentum of electrons emitted from a molecule. Those measurements revealed one half of the wavefunction without physically changing its state. Advanced computer algorithms then calculated the missing half, producing an image of the complete molecular orbital. The reconstruction resolved features smaller than the spacing between the carbon atoms within the molecule. Previously, extending this technique into three dimensions required lengthy measurements at large-scale synchrotron facilities. That limited its wider use and made it particularly difficult to capture “dynamical” wavefunctions as three-dimensional videos at the scale of individual atoms. Less data could enable molecular movies Dr Matthijs Jansen of the University of Göttingen, co-leader of the