Transferable Ion Force Fields in Water from a Simultaneous Optimization of Ion Solvation and Ion-Ion Interaction

Abstract

The poor performance of many existing nonpolarizable ion force fields is typically blamed on either the lack of explicit polarizability, the absence of charge transfer, or the use of unreduced Coulomb interactions. However, this analysis disregards the large and mostly unexplored parameter range offered by the Lennard-Jones potential. We use a global optimization procedure to develop water-model-transferable force fields for the ions K⁺, Na⁺, Cl^-, and Br^- in the complete parameter space of all Lennard-Jones interactions using standard mixing rules. No extra-thermodynamic assumption is necessary for the simultaneous optimization of the four ion pairs. After an optimization with respect to the experimental solvation free energy and activity, the force fields reproduce the concentration-dependent density, ionic conductivity, and dielectric constant with high accuracy. The force field is fully transferable between simple point charge/extended and transferable intermolecular potential water models. Our results show that a thermodynamically consistent force field for these ions needs only Lennard-Jones and standard Coulomb interactions.

Figure 1

Mean squared difference k defined in eq 11 between the simulated a_cc and experimental activity derivatives a_cc,exp for the optimal parameters of the four salts, as a function of the Lennard-Jones parameters of the Cl^– ion. Circles depict the parameter combinations for which the simulations were performed, and the contour map is calculated by a cubic interpolation.

Figure 2

Salt solvation free energies for ion parameters using different water models. Experimental free energies at 300 K (solid black lines) are calculated from Marcus and Tissandier et al. Symbols show the solvation free energy of reported force fields.^,, The dotted black line corresponds to the solvation free energy of NaCl used in our previous work as well as in the work of Mamatkulov and Schwierz; see section S2 of the Supporting Information.

Figure 3

Activity derivative according to eq 4 of NaCl, KCl, NaBr, KBr as a function of the salt concentration. Different colors depict different water models. The cross symbols denote results from the force fields by Smith and Dang (SPC/E, pink), CHARMM (TIP3P, brown), and reproduced from Mamatkulov and Schwierz (TIP3P, purple). Solid black lines depict the experimental activity derivatives. Errors are between 0.1 and 0.3 (estimated using a block averaging with five blocks; see Figure S4 for individual error bars).

Figure 4

(a) Simulated mass density ρ for the four salts using the optimized force field (●) and literature force fields^, (×) together with the experimental densities^, (solid lines) as a function of the salt concentration. (b) Ionic conductivities κ together with the experimental values (solid lines).^, (c) Dielectric decrement Δε together with the experimental values (solid lines).⁻ (d) Water diffusion constant normalized by its value for pure water together with the experimental values (solid lines). The SPC/E water model is used in all panels. Results from other water models are shown in Figure S8.