# Hirshfeld charge analysis

Hirshfeld charges (Hirshfeld, 1977) are defined relative to the deformation density, this is the difference between the molecular and unrelaxed atomic charge densities.

For quantitative descriptions of charge distributions in molecules or solids it is convenient to divide a system into well-defined atomic fragments. A general and natural choice is to share the charge density at each point between the atoms, in proportion to their free-atom densities at the corresponding distances from the nuclei. This prescription yields well-localized bonded-atom distributions each of which closely resembles the molecular density in its vicinity. Integration of the atomic deformation densities - bonded minus free atoms - defines the net atomic charges and multipole moments which concisely summarize the molecular charge reorganization. This permits calculation of the external electrostatic potential and the interaction energy between molecules or between parts of the same molecule.