Voronoi atomic charges

The Voronoi deformation density approach, is based on the partitioning of space into the Voronoi cells of each atom A, that is, the region of space that is closer to that atom than to any other atom (cf. Wigner-Seitz cells in crystals see Chapter 1 of Ref. 202). The VDD charge of an atom A is then calculated as the difference between the (numerical) integral of the electron density p of the real molecule and the superposition of atomic densities SpB of the promolecule in its Voronoi cell (Eq. [42]) ... 

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. 

In this table, P is the density matrix and S is the overlap matrix of the atomic GTOs iji and v). is the nuclear charge of atom A. For the Becke, Flirshfeld, and VDD approaches, the electron density is integrated numerically over a grid of points. The Voronoi cell of atom A is the ensemble of points closer to A than to any other atom. The Becke cell is defined similarly except that a smoothing function is applied at the borders between the cells, is the electron density of the neutral atom A. 

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