Transition path sampling of water exchange rates and mechanisms around aqueous ions

The rates and mechanisms of water exchange around two aqueous ions, namely, Na(+) and Fe(2+), have been determined using transition path sampling. In particular, the pressure dependence of the water exchange rates was computed to determine activation volumes. A common approach for calculating water exchange rates, the reactive flux method, was also employed and the two methods were compared. The water exchange rate around Na(+) is fast enough to be calculated by direct molecular dynamics simulations, thus providing a reference for comparison. Both approaches predicted exchange rates and activation volumes in agreement with the direct simulation results. Four additional sodium potential models were considered to compare the results of this work with the only activation volume for Na(+) previously determined from molecular simulation [D. Spangberg et al., Chem. Phys. Lett. 276, 114 (1997)] and provide the best possible estimate of the activation volume based on the ability of the models to reproduce known properties of the aqueous sodium ion. The Spangberg and Hermansson [D. Spangberg and K. Hermansson, J. Chem. Phys. 120, 4829 (2004)] and X-Plor/Charmm-22 [M. Patra and M. Karttunen, J. Comput. Chem. 25, 678 (2004)] models performed best and predicted activation volumes of -0.22 and -0.78 cm(3) mol(-1), respectively. For water exchange around Fe(2+), transition path sampling predicts an activation volume of +3.8 cm(3) mol(-1), in excellent agreement with the available experimental data. The potential of mean force calculation in the reactive flux approach, however, failed to sufficiently sample appropriate transition pathways and the opposite pressure dependence of the rate was predicted as a result. Analysis of the reactive trajectories obtained with the transition path sampling approach suggests that the Fe(2+) exchange reaction takes place via an associative interchange mechanism, which goes against the conventional mechanistic interpretation of a positive activation volume. Collectively, considerable insight was obtained not only for the exchange rates and mechanisms for Na(+) and Fe(2+) but also for identifying the most robust modeling strategy for these purposes.