Correcting atomic charges to reproduce molecular dipoles

Electron densities are often subdivided into smaller units, which can then be allocated to atomic centers. The resulting atomic charges usually do not reproduce the total electronic dipole moment of the molecule. We describe a simple optimization procedure for finding atomic populations closest to some input atomic charges, e.g., the Mulliken or Bader ones, but reproduce the molecular dipole when the atomic coordinates are summed up weighted by the new charges. The proposed procedure can be coded by a few lines and is practically cost-less.