Atomic shell structure from Born probabilities: Comparison to other shell descriptors and persistence in molecules.

Real space chemical bonding descriptors, such as the electron localization function or the Laplacian of the electron density, have been widely used in electronic structure theory thanks to their power to provide chemically intuitive spatial images of bonded and non-bonded interactions. This capacity stems from their ability to display the shell structure of atoms and its distortion upon molecular formation. Here, we examine the spatial position of the N electrons of an atom at the maximum of the square of the wavefunction, the so-called Born maximum, as a shell structure descriptor for ground state atoms with Z = 1-36, comparing it to other available indices. The maximization is performed with the help of variational quantum Monte Carlo calculations. We show that many electron effects (mainly Pauli driven) are non-negligible, that Born shells are closer to the nucleus than any other of the examined descriptors, and that these shells are very well preserved in simple molecules.