Theories of solvation free energies often involve electrostatic potentials at the position of a solute charge. Simulation calculations that apply cutoffs and periodic boundary conditions based on molecular centers result in center-dependent contributions to electrostatic energies due to a systematic sorting of charges in radial shells. This sorting of charges induces a surface-charge density at the cutoff sphere or simulation-box boundary that depends on the choice of molecular centers. We identify a simple solution that gives correct, center-independent results, namely the radial integration of charge densities. Our conclusions are illustrated for a Lennard-Jones solute in water. The present results can affect the parametrization of force fields.