We’ve never looked closer at the quantum nature of chemical bonds

What is it about?

We all learned at school that molecules would not exist without the bonds holding the atoms together. But quantum physics has transformed the classroom balls and stick model. The Schrödinger equation, introduced a century ago in 1926, governs the wave nature of electrons that create the bonds as they buzz around the atomic nuclei. However, in 1927 Heisenberg’s uncertainty principle shook our classical conceptions and set fundamental limits on how precisely the electron’s positions and speed can be defined simultaneously. A legitimate question then arises: how close can we get to the quantum reality of electrons involved in chemical bond? Obviously, computers can now provide increasingly accurate theoretical description by solving the Schrödinger equation. But can experiments bring us equally close to this quantum reality? In this paper, we report the first experimental reconstruction of a one-electron Wigner function in a molecular crystal. The Wigner function offers an unusual and yet rich representation of an electronic quantum state of the electrons. It brings together position and momentum representations, on equal footing, in a single phase-space description. It is not a conventional probability map, as one might expect from quantum mechanics. Indeed, the negative regions in phase-space reveal how the electrons in the chemical bond escape classicality. Thereby, the one-electron-Wigner function provides a new pespective onto the quantum mechanisms at work in chemical bonding, complementing the familiar position-space pictures of electron density. This phase-space tomography of electrons in a molecule was performed by jointly refining a physically constrained model against data from two complementary experimental techniques: high-resolution X-ray diffraction and directional Compton scattering. The reconstructed Wigner function agrees remarkably well with correlated electronic-structure calculations. The agreement thus demonstrates that these complementary measurements can be combined to recover subtle features of electron behaviour in molecules.

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Photo by Logan Voss on Unsplash

Photo by Logan Voss on Unsplash

Why is it important?

This method provides the full quantum description of chemical bonds at the one electron level. It thus offers a more robust experimental reference for validating sophisticated ab initio approaches, such as those based on density matrix functional theory. It also gives unprecedented experimental access to the local kinetic energy contribution of electrons responsible for holding the atoms together in a molecule.

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