Chemical bonding is the central concept of chemistry that has been used to explain the properties of molecules and solids as well as chemical processes. In recent years, considerable progress has been made toward a simple and yet fundamental understanding of this concept for isolated systems. Here we propose the quantum pressure to study electron localization in molecules and solids as well as the influence of an external magnetic field. A high pressure indicates chemical bonding and electron localization, while a low pressure indicates intershell region and electron delocalization. We find that electrons become more localized between nuclei when exposed to a magnetic field. We demonstrate that our quantum pressure not only can reveal electronic shell structure of atoms, but also can be used to visualize chemical bonding in molecules and solids, significantly extending the applicability of this tool to wide-ranging problems.

• Received 12 February 2015

DOI:https://doi.org/10.1103/PhysRevB.92.060401