| Abstract
| - The hydration free energies of ions exhibit anapproximately quadratic dependence on the ionic charge, aspredicted by the Born model. We analyze this behavior usingsecond-order perturbation theory. The averageand the fluctuation of the electrostatic potential at charge sitesappear as the first coefficients in a Taylorexpansion of the free energy of charging. Combining the data fromdifferent charge states (e.g., chargedanduncharged) allows calculation of free-energy profiles as a function ofthe ionic charge. The first two Taylorcoefficients of the free-energy profiles can be computed accuratelyfrom equilibrium simulations, but theyare affected by a strong system-size dependence. We applycorrections for these finite-size effects by usingEwald lattice summation and adding the self-interactions consistently.An analogous procedure is used forthe reaction-field electrostatics. Results are presented for amodel ion with methane-like Lennard-Jonesparameters in simple point charge water. We find two very closelyquadratic regimes with different parametersfor positive and negative ions. We also studied the hydration freeenergy of potassium, calcium, fluoride,chloride, and bromide ions. We find negative ions to be solvatedmore strongly (as measured by hydrationfree energies) compared to positive ions of equal size, in agreementwith experimental data. We ascribe thispreference of negative ions to their strong interactions with waterhydrogens, which can penetrate the ionicvan der Waals shell without direct energetic penalty in the modelsused. In addition, we consistently find apositive electrostatic potential at the center of unchargedLennard-Jones particles in water, which also favorsnegative ions. Regarding the effects of a finite system size, weshow that even using only 16 water moleculesit is possible to calculate accurately the hydration free energy ofsodium, if self-interactions are considered.
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