The ionic charging free energy is a very sensitive probe for the treatment of electrostatics in any given simulation setting. In this work, we present methods to compute the ionic charging free energy in systems characterized by atomic charges and higher-order multipoles, mainly dipoles and quadrupoles. The results of these methods for periodic boundary conditions and for spherical clusters are then compared. For the treatment of spherical clusters, we introduce a generalization of Gauss’ law that links the microscopic variables to the measurable macroscopic electrostatics via a work function.
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Herce et al. (2003) studied this question.