Rational design of ion force fields based on thermodynamic solvation properties

Most aqueous biological and technological systems contain solvated ions. Atomistic explicit-water simulations of ionic solutions rely crucially on accurate ionic force fields, which contain most commonly two adjustable parameters: the Lennard-Jones diameter and the interaction strength. Assuming these parameters to be properly optimized, the plethora of parameters one finds in the literature for one and the same ion is surprising. In principle, the two parameters should be uniquely determined by matching two ionic properties obtained for a particular water model and within a given simulation protocol with the corresponding experimental observables. Traditionally, ion parameters were chosen in a somewhat unsystematic way to reproduce the solvation free energy and to give the correct ion size when compared with scattering results. Which experimental observable one chooses to reproduce should in principle depend on the context within which the ionic force field is going to be used. In the present work we suggest to use the solvation free energy in conjunction with the solvation entropy to construct thermodynamically sound force fields for the alkali and halide ions for the simulation of ion-specific effects in aqueous environment. To that end we determine the solvation free energy and entropy of both cations and anions in the entire relevant parameter space. As an independent check on the quality of the resulting force fields we also determine the effective ionic radius from the first peak of the radial ion-water distribution function. Several difficulties during parameter optimization are discussed in detail. (i) Single-ion solvation depends decisively on water-air surface properties, which experimentally becomes relevant when introducing extrathermodynamic assumptions on the hydronium (H(3)O(+)) solvation energy. Fitting ion pairs circumvents this problem but leaves the parameters of one reference ion (here we choose chloride) undetermined. (ii) For the halides the problem is almost underdetermined, i.e., there is a whole set of degenerate parameters that equally well describe, e.g., chloride and bromide ions. (iii) For the heavy cations the problem is overdetermined, i.e., no combination of Lennard-Jones parameters is able to reproduce simultaneously energy and entropy of solvation. We discuss various possibilities to deal with these problems and finally present an optimized force field for the halide anions that reproduces the free energy and the entropy of solvation. For the alkali metal cations there is no unambiguous choice of parameters. Therefore, we give three different parameter sets for every ion with a small, intermediate, or large Lennard-Jones interaction strength, where the Lennard-Jones diameters are optimized to reproduce the solvation free energy. The ionic radius is reproduced with acceptable accuracy by this optimization strategy, meaning that the proposed force fields are reliable beyond the target observables (i.e., free energy and entropy of solvation).