Free energy of hydration of a molecular ionic solute: Tetramethylammonium ion

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Abstract
We have performed Monte Carlo simulations of the tetramethylammonium ion, hydrated by 256 simple point charge (SPC) water molecules, as a function of total charge on the ion. The total charge was varied between −3e to +3e at intervals of 1e, and was distributed equally on the four methyl sites on the ion. Derivatives of the free energy with respect to charge were related to the fluctuations in the ion–water interaction energies using a cumulant expansion. This derivative information for the different charge states was found to give an accurate description of the free energy of hydration. The calculated hydration free energies were also found to be only weakly dependent on system size and the method used for calculating the electrostatic interactions (Ewald summation or generalized reaction field), when finite system size corrections are applied. The quadratic charge dependence was obtained for the free energy of hydration for both positive and negative ions as expected from the Born model. The hydration is, however, asymmetric. Negative ions are more favorably hydrated compared to positive ions. We relate this asymmetry of hydration to water structure; that is, to differences in the water oxygen and water hydrogen density profiles surrounding positive and negative ions. Another manifestation of this asymmetry is seen in the positive electrostatic potential at the center of methyl sites in the uncharged state of the tetramethylammonium solute.