  We study the properties of convex functionals which have been proposed for
the simulation of charged molecular systems within the Poisson-Boltzmann
approximation. We consider the extent to which the functionals reproduce the
true fluctuations of electrolytes and thus the one-loop correction to mean
field theory -- including the Deby-H\"uckel correction to the free energy of
ionic solutions. We also compare the functionals for use in numerical
optimization of a mean field model of a charged polymer and show that different
functionals have very different stiffnesses leading to substantial differences
in accuracy and speed.
