The atomic electrostatic potential (AEP) and multipole moments were determined through topological analysis of the electron density. High-rank spherical tensor multipole moments were used to study the multipole expansion convergence. The root mean square values were found to be between 0.1 and 1.6 kJ/mol for the atoms of carbon, nitrogen, oxygen and sulfur on a spherical grid with a 0.001 a.u. convergence radius and lmax = 4. The study shows that fast convergence results from electron density decay, and that the multipole moments produced by finite atoms can be used in the multipole expansion of the electrostatic potential.