How topological partitions of the electron distributions reveal delocalization

The topological partitions of the electron distributions are based on the gradient field analysis of local functions which carry the relevant physical or chemical information. They yield a set of contiguous non-overlapping volumes called basins which entirely span the geometrical space. The integral of the charge density distribution over a given basin, say ΩA, is the basin population ΩA which is the expectation value of the population operator ΩA. It is shown that the basin population operators are correlated and I propose to study this correlation with the help of the covariance matrix of the basin populations. A covariance operator is derived accordingly. This method is applied to the basin populations calculated in the AIM and ELF topological approaches in order to provide a tool enabling one to discuss the reliability of simplified representations of electron densities in terms of superposition of promolecular densities or of resonant Lewis structures.