Quantum microscopic vs. classical macroscopic calculations on the phenomenon of electrostatic influence

In order to compare microscopic and macroscopic approaches to the phenomenon of electrostatic influence, we have studied the atomic charges of an electric conductor, obtained either from macroscopic classical electrostatics, or microscopic quantum ab initio calculations. A torus was chosen as conducting material, built from valence monoelectronic atoms and influenced by an external point charge. The classical electric charges are obtained by integrating the macroscopic density over "atomic" sectors. This density is determined from a numerical integration of linearized electrostatic equations. The quantum charges are defined from Natural Orbitals in MP2/6-31G* calculations on clusters of different sizes. The overall agreement is good, with reasonable discrepancies due (i) to the continuity of the macroscopic model, which ignores the oscillations on atomic distances; and (ii) to the linearity constraint in the macroscopic equations.