  We present general arguments for the importance, or lack thereof, of the
structure in the charge distribution of counterions for counterion-mediated
interactions between bounding symmetrically charged surfaces. We show that on
the mean field or weak coupling level, the charge quadrupole contributes the
lowest order modification to the contact value theorem and thus to the
intersurface electrostatic interactions. The image effects are non-existent on
the mean-field level even with multipoles. On the strong coupling level the
quadrupoles and higher order multipoles contribute additional terms to the
interaction free energy only in the presence of dielectric inhomogeneities.
Without them, the monopole is the only multipole that contributes to the strong
coupling electrostatics. We explore the consequences of these statements in all
their generality.
