A Classical Point Charge Model Study of System Size Dependence of Oxidation and Reorganization Free Energies in Aqueous Solution

Abstract

The response of water to a change of charge of a solvated ion is, to a good approximation, linear for the type of iron-like ions frequently used as a model system in classical force field studies of electron transfer. Free energies for such systems can be directly calculated from average vertical energy gaps. Exploiting this feature, we have computed the free energy and the reorganization energy of the M2+/M3+ and M1+/M2+ oxidations in a series of model systems all containing a single Mn+ ion and an increasing number of simple point charge water molecules. Long-range interactions are taken into account by Ewald summation methods. Our calculations confirm the observation made by Hummer, Pratt, and Garcia (J. Phys. Chem. 1996, 100, 1206) that the finite size correction to the estimate of solvation energy (and hence oxidation free energy) in such a setup is effectively proportional to the inverse third power (1/L3) of the length L of the periodic cell. The finite size correction to the reorganization energy is found to scale with 1/L. These simulation results are analyzed using a periodic generalization of the Born cavity model for solvation, yielding three different estimates of the cavity radius, namely, from the infinite system size extrapolation of oxidation free energy and reorganization energy, and from the slope of the linear dependence of oxidation free energy on 1/L3. The cavity radius for the reorganization energy is found to be significantly larger compared to the radius for the oxidation (solvation) free energy. The radius controlling the 1/L3 dependence of oxidation free energy is found to be comparable to the radius for reorganization. The implication of these results for density functional theory-based ab initio molecular dynamics calculation of redox potentials is discussed.

Calculating solution redox free energies with ab initio quantum mechanical/molecular mechanical minimum free energy path method

“…Caution may be needed in the simulation of special systems with FNE to reduce possible artifacts caused by DFT method. 30,[79][80][81] Also, if the interpolated reaction path is bumpy, e.g., for reactions with significant geometrical changes between the redox states, the optimization for a smooth path is desired to reach the convergence. Even if the optimization of a reaction path rather than an interpolated path is necessary, the computational cost in terms of time may not significantly increase since the optimization of the intermediate states can be performed parallelly.…”

“…[22][23][24][25][26][27][28][29] However, the high computational cost and finite system size limit the application of the ab initio MD method. 24,30 With well balanced computational cost and accuracy, the combined quantum mechanical and molecular mechanical ͑QM/MM͒ method 31 becomes a very promising approach to simulate the biological ET processes, in which one treats the redox centers quantum mechanically and the rest of the system molecular mechanically. 32 In previous work, we have…”

Computational methods for intramolecular electron transfer in a ferrous–ferric iron complex

“…The most promising approach to date involves the use of umbrella sampling within an ab initio molecular dynamics (AIMD) scheme, as presented by Sprik and co-workers [26,27] and by Vladimirov et al [28]. However, these simulations cannot be done routinely due to computational expense, and proper charge distributions required to obtain the normal and reverse states are often difficult to impose or require arbitrary parametrization.…”

“…Gaussian statistics of energy gap fluctuations (i.e., the free energy difference between normal and reverse charge states) is one of the consequences of the linearity in solvent response [27,29]. Researchers have reported several examples for which the assumption of linear response was deemed inappropriate.…”

“…For instance, when there is strong electrostatic coupling of the solute and solvent molecules [31], when local binding/unbinding events are taking place [32], or when significant variations in ion coordination occur with a change in ion charge (solvent density fluctuations) [27]. In addition, it has been recently shown that the Gaussian nature of energy gap fluctuations is a required but not sufficient condition for linear solvent response [27,33,34]. Finally, it has also been shown that even if the solvent response is not strictly linear, the Marcus approximation can still be used to quantify the reorganization energy [27].…”