A new charge analysis is presented that gives an accurate description of the electrostatic potential from the charge distribution in molecules. This is achieved in three steps: first, the total density is written as a sum of atomic densities; next, from these atomic densities a set of atomic multipoles is defined; finally, these atomic multipoles are reconstructed exactly by distributing charges over all atoms. The method is generally applicable to any method able to provide atomic multipole moments, but in this article we take advantage of the way the electrostatic potential is calculated within the Density Functional Theory framework. We investigated a set of 31 molecules as well as all amino acid residues to test the quality of the method, and found accurate results for the molecular multipole moments directly from the DFT calculations. The deviations from experimental values for the dipole/quadrupole moments are also small. Finally, our Multipole Derived Charges reproduce both the atomic and molecular multipole moments exactly. c 2000 John Wiley & Sons, Inc. J Comput Chem 22: 79-88, 2001