Calculation of Solvation Free Energies of Charged Solutes Using Mixed Cluster/Continuum Models

Abstract

We derive a consistent approach for predicting the solvation free energies of charged solutes in the presence of implicit and explicit solvents. We find that some published methodologies make systematic errors in the computed free energies because of the incorrect accounting of the standard state corrections for water molecules or water clusters present in the thermodynamic cycle. This problem can be avoided by using the same standard state for each species involved in the reaction under consideration. We analyze two different thermodynamic cycles for calculating the solvation free energies of ionic solutes: (1) the cluster cycle with an n water cluster as a reagent and (2) the monomer cycle with n distinct water molecules as reagents. The use of the cluster cycle gives solvation free energies that are in excellent agreement with the experimental values obtained from studies of ion-water clusters. The mean absolute errors are 0.8 kcal/mol for H(+) and 2.0 kcal/mol for Cu(2+). Conversely, calculations using the monomer cycle lead to mean absolute errors that are >10 kcal/mol for H(+) and >30 kcal/mol for Cu(2+). The presence of hydrogen-bonded clusters of similar size on the left- and right-hand sides of the reaction cycle results in the cancellation of the systematic errors in the calculated free energies. Using the cluster cycle with 1 solvation shell leads to errors of 5 kcal/mol for H(+) (6 waters) and 27 kcal/mol for Cu(2+) (6 waters), whereas using 2 solvation shells leads to accuracies of 2 kcal/mol for Cu(2+) (18 waters) and 1 kcal/mol for H(+) (10 waters).

Computational Study of Copper(II) Complexation and Hydrolysis in Aqueous Solutions Using Mixed Cluster/Continuum Models

“…Mixed solvation models explicitly include chemically important solute-solvent interactions and account for charge transfer to the solvent that are particularly important for hydrated transition-metalion complexes. [73][74][75][76] The use of mixed cluster/continuum solvation models has been the subject of some criticisms, 77 including the incorrect orientations of water molecules near the dielectric boundary and the accurate evaluation of the entropic effects for the explicit water molecules. The first problem can be alleviated by the addition of a full first or second solvation shell.…”

“…The second problem has been insufficiently appreciated in the literature and we concur with the criticism that the inclusion of explicit water molecules in a continuum calculation could be troublesome in some cases when the model is used improperly. 73 A key assumption of continuum models is that the solute is considered as rigid species with no solventinduced change of its internal partition function. This assumption is appropriate for small rigid molecules, but it is not valid for hydrogen-bonded complexes due to their high mobility in solution and the diffusion of water molecules inside a cluster.…”

“…Nevertheless, it is usually possible to alleviate this problem using hydrogen-bonded complexes of similar size on both sides of the thermodynamic cycle/reaction of interest. 73 The presence of the full second shell has the effect of preventing a strong overpolarization of the first shell due to the redistribution of the total polarization energy among a much larger number of molecules. Additionally, a substantial amount of the polarization energy is included explicitly through the charge transfer effect.…”

Hydration of Copper(II): New Insights from Density Functional Theory and the COSMO Solvation Model

“…An improved methodology for calculation of solvation free energies of charge solutes using mixed cluster/continuum solvent models has been recently described in ref 85. In this study, we employ the thermodynamic cycle shown in Figure 10 to calculate the hydration free energy of Cu(II).…”

Molecular basis of the selective binding of MDMA enantiomers to the alpha4beta2 nicotinic receptor subtype: Synthesis, pharmacological evaluation and mechanistic studies

“…It must be noted, however, that the reliability of this assumption was further supported by MM/PBSA computations performed for the subsystems used in QM/MM calculations. Finally, the solvation free energy of the water molecule was corrected to take into account the contributions due to the changes in standard states in the process of transferring a water molecule from the gas phase (at 1 atm and 298 K) to bulk water [67].…”