Generalized electron number distribution functions: real space versus orbital space descriptions

The algebraic expressions previously derived to compute the electron number distribution functions (EDF) for exhaustive partitions of the physical space into sharp-boundary atoms are generalized to allow for the use of fuzzy atoms and orbital-based partitions. In some of the latter, the atomic overlap matrix required to obtain the EDF is analytical. This makes them attractive alternatives to other definitions, as the one based on the atomic basins of the quantum theory of atoms in molecules (QTAIM), which are more physically sound but also much more demanding computationally. We will compute the EDF for a series of test molecules using different fuzzy and orbital-based partitions and compare them to QTAIM EDF. The effects of electron correlation and the use of the core approximation on the EDF will also be explored.