Atomic shell structure determined by the curvature of the electron position uncertainty

Abstract

The electron density logarithm is closely connected to the Shannon information entropy characterising the spread of the electron density. It can be seen as the uncertainty to predict the position of an electron. The position uncertainty curvature, defined as the negative of the Laplacian of the electron density logarithm, describes regions of space where the uncertainty of the electron position is higher, respectively lower, than the average in the surrounding. The atomic shells can be located in regions of high-position uncertainty curvature, thus resolving the atomic shell structure of the atoms Li to Xe. The shell boundaries are given as minima of the uncertainty curvature. This indicator, based alone on the electron density, is suitable to describe the bonding situation in molecules and solids.