Voronoi, Hirshfeld and Stewart atomic charges

The AIM approach partitions the physical space into atomic basins based on a topological analysis of the electron density itself, but several other methods have been proposed for dividing the space into atomic contributions. 

Hirshfeld (or stockholder) charges are based on using atomic densities for partitioning the molecular electron density. The promolecular density is defined as the sum of atomic densities placed at the nuclear geometries in the molecule. The actual molecular electron density at each point in space is then partitioned by weighting factors according to the promolecular contributions. 

Hirshfeld charges may be considered as a soft-boundary version of the Voronoi charges. An ambiguity in the Hirshfeld method is the source of the atomic densities. 

The normal approach is to use spherically averaged ground state densities for neutral atoms but, in some cases, other valence configurations may be considered. Furthermore, the level of theory (method and basis set) for calculating the atomic density is a potential variable. 

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