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Computation of methodology-independent single-ion solvation properties from molecular simulations. III. Correction terms for the solvation free energies, enthalpies, entropies, heat capacities, volumes, compressibilities, and expansivities of solvated ions

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10.1063/1.3567020

### Abstract

The raw single-ion solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions (finite or periodic system, system or box size) and treatment of electrostatic interactions (Coulombic, lattice-sum, or cutoff-based) used during these simulations. However, as shown by Kastenholz and Hünenberger [J. Chem. Phys.124, 224501 (2006)]10.1529/biophysj.106.083667, correction terms can be derived for the effects of: (A) an incorrect solvent polarization around the ion and an incomplete or/and inexact interaction of the ion with the polarized solvent due to the use of an approximate (not strictly Coulombic) electrostatic scheme; (B) the finite-size or artificial periodicity of the simulated system; (C) an improper summation scheme to evaluate the potential at the ion site, and the possible presence of a polarized air–liquid interface or of a constraint of vanishing average electrostatic potential in the simulated system; and (D) an inaccurate dielectric permittivity of the employed solvent model. Comparison with standard experimental data also requires the inclusion of appropriate cavity-formation and standard-state correction terms. In the present study, this correction scheme is extended by: (i) providing simple approximate analytical expressions (empirically-fitted) for the correction terms that were evaluated numerically in the above scheme (continuum-electrostatics calculations); (ii) providing correction terms for derivative thermodynamic single-ion solvation properties (and corresponding partial molar variables in solution), namely, the enthalpy,entropy, isobaric heat capacity, volume, isothermal compressibility, and isobaric expansivity (including appropriate standard-state correction terms). The ability of the correction scheme to produce methodology-independent single-ion solvation free energies based on atomistic simulations is tested in the case of Na^{+} hydration, and the nature and magnitude of the correction terms for derivative thermodynamic properties is assessed numerically.

© 2011 American Institute of Physics

Received 03 May 2010
Accepted 08 December 2010
Published online 08 April 2011

Acknowledgments: Financial support from the Swiss National Science Foundation [NSF(CH); Project No. 200020-109261/1] is gratefully acknowledged.

Article outline:

I. INTRODUCTION

II. THEORY

A. Assumptions and notations

B. Analytical or numerical free-energy correction terms

1. Type-A correction

2. Type-B correction

3. Type-C correction

4. Type-D correction

5. Cavity-formation contribution and standard-state correction term

6. Summary of the free-energy correction scheme

C. Empirical (fitted) correction terms

1. Type-A_{2} correction for PBC/CT schemes

2. Type-B correction

D. Temperature and pressure derivatives of the correction terms

1. General considerations

2. Derivatives with respect to the solventpermittivity

3. Derivatives with respect to the effective ionic radius

4. Derivatives with respect to the box-edge length or droplet radius

5. Derivatives with respect to interfacial potential properties

6. Derivatives based on the empirical (fitted) correction terms

E. Generalized correction scheme for derivative solvation properties

1. General considerations

2. Standard-state correction terms

3. Solvation and partial molar entropies

4. Solvation and partial molar isobaric heat capacities

5. Solvation and partial molar volumes

6. Solvation and partial molar isothermal volume-compressibilities

7. Solvation and partial molar isobaric volume-expansivities

8. Other approaches

III. RESULTS

A. Calculation of methodology-independent hydration free energies

B. Correction scheme for derivative thermodynamic properties

IV. CONCLUSIONS

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2011-04-08

2014-04-25

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