FREE-ENERGY OF IONIC HYDRATION

The hydration free energies of ions exhibit an approximately quadratic dependence on the ionic charge, as predicted by the Born model. We an alyze this behavior using second-order perturbation theory. The averag e and the fluctuation of the electrostatic potential at charge sites a ppear as the first coefficients in a Taylor expansion of the free ener gy of charging. Combining the data from different charge states (e.g., charged and uncharged) allows calculation of free-energy profiles as a function of the ionic charge, The first two Taylor coefficients of t he free-energy profiles can be computed accurately from equilibrium si mulations, but they are affected by a strong system-size dependence, W e apply corrections for these finite-size effects by using Ewald latti ce summation and adding the self-interactions consistently. An analogo us procedure is used for the reaction-field electrostatics. Results ar e presented for a model ion with methane-like Lennard-Jones parameters in simple point charge water, We find two very closely quadratic regi mes with different parameters for positive and negative ions. We also studied the hydration free energy of potassium, calcium, fluoride, chl oride, and bromide ions. We find negative ions to be solvated more str ongly (as measured by hydration free energies) compared to positive io ns of equal size, in agreement with experimental data. We ascribe this preference of negative ions to their strong interactions with water h ydrogens, which can penetrate the ionic van der Waals shell without di rect energetic penalty in the models used, In addition, we consistentl y find a positive electrostatic potential at the center of uncharged L ennard-Jones particles in water, which also favors negative ions. Rega rding the effects of a finite system size, we show that even using onl y 16 water molecules it is possible to calculate accurately the hydrat ion free energy of sodium, if self-interactions are considered.