  Treating water as a linearly responding dielectric continuum on molecular
length scales allows very simple estimates of solvation structure and
thermodynamics for charged and polar solutes. While this approach can
successfully account for basic length and energy scales of ion solvation,
computer simulations indicate not only its quantitative inaccuracies but also
its inability to capture some basic and important aspects of microscopic
polarization response. Here we consider one such shortcoming, a failure to
distinguish the solvation thermodynamics of cations from that of
otherwise-identical anions, and we pursue a simple, physically inspired
modification of the dielectric continuum model to address it. The adaptation is
motivated by analyzing the orientational response of an isolated water molecule
whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for
dipole fluctuations that accounts implicitly for the influence of higher-order
multipole moments, while respecting constraints of molecular geometry. We
propose a field theory with the suggested form, whose nonlinear response breaks
the charge symmetry of ion solvation. An approximate variational solution of
this theory, with a single adjustable parameter, yields solvation free energies
that agree closely with simulation results over a considerable range of solute
size and charge.
