Assessing the accuracy of approximate treatments of ion hydration based on primitive quasichemical theory

Abstract

Quasichemical theory ͑QCT͒ provides a framework that can be used to partition the influence of the solvent surrounding an ion into near and distant contributions. Within QCT, the solvation properties of the ion are expressed as a sum of configurational integrals comprising only the ion and a small number of solvent molecules. QCT adopts a particularly simple form if it is assumed that the clusters undergo only small thermal fluctuations around a well-defined energy minimum and are affected exclusively in a mean-field sense by the surrounding bulk solvent. The fluctuations can then be integrated out via a simple vibrational analysis, leading to a closed-form expression for the solvation free energy of the ion. This constitutes the primitive form of quasichemical theory ͑pQCT͒, which is an approximate mathematical formulation aimed at reproducing the results from the full many-body configurational averages of statistical mechanics. While the results from pQCT from previous applications are reasonable, the accuracy of the approach has not been fully characterized and its range of validity remains unclear. Here, a direct test of pQCT for a set of ion models is carried out by comparing with the results of free energy simulations with explicit solvent. The influence of the distant surrounding bulk on the cluster comprising the ion and the nearest solvent molecule is treated both with a continuum dielectric approximation and with free energy perturbation molecular dynamics simulations with explicit solvent. The analysis shows that pQCT can provide an accurate framework in the case of a small cation such as Li + . However, the approximation encounters increasing difficulties when applied to larger cations such as Na + , and particularly for K + . This suggests that results from pQCT should be interpreted with caution when comparing ions of different sizes.

Probing the Thermodynamics of Competitive Ion Binding Using Minimum Energy Structures

“…18,19,21–23 If this is not done, the problem of multiple, anharmonic minima arises, and less satisfactory results are obtained. 39 Anharmonic corrections, 55 internal rotors and other approximations involving redundant internal coordinates 56 may be used in the future to extend the harmonic approximation to larger clusters. However, the general success of the RRHO approximation seen in Fig.…”

Prediction and interpretation of the hydration entropies of monovalent cations and anions

“…Concerning predictive approaches, a large number of methods have been developed or applied to calculate the related Gibbs energy of ion hydration which is easier to quantify than entropy because it connects directly with the equilibrium constant. These include the Born equation [7][8][9], Kirkwood-Buff theory [10,11], perturbation methods [12][13][14][15][16][17][18][19][20][21], quasichemical theory [22][23][24], scaled particle theory [25], and correlation functions [26,27]. Hydration entropy calculations are less commonly reported for ion hydration and may be evaluated from the Born equation [8], the temperature derivative of the Gibbs energy change [21], subtracting off the enthalpy change from the Gibbs energy change [28][29][30], scaled-particle theory [25,31], correlation functions [26,27], or Langevin dipoles [32,33].…”

Ion Binding Sites and Their Representations by Reduced Models

“…Quasi-chemical theory (QCT) offers one example of how to carry out this type of formal separation in the case of a solute immersed in a bulk liquid 19,20,25 . The general concept goes back to the method of “local configurations” formulated by Bethe, Guggenheim, Fowler and Kirkwood 31–35 , which was extended by Pratt and co-workers to study solvation 19,20 .…”

“…The general concept goes back to the method of “local configurations” formulated by Bethe, Guggenheim, Fowler and Kirkwood 31–35 , which was extended by Pratt and co-workers to study solvation 19,20 . In QCT, the system is rigorously partitioned into a small spherical subvolume centered on the solute, and a second region corresponding to the remaining bulk liquid phase 19,20,25 . Most thermodynamic properties can then be expressed as sum over simple terms.…”