^{1,a)}and Sandeep Patel

^{1,b)}

### Abstract

Hydration free energies of nonpolarizable monovalent atomic ions in transferable intermolecular potential four point fluctuating charge (TIP4P-FQ) are computed using several commonly employed ion-water force fields including two complete model sets recently developed for use with the simple water model with four sites and Drude polarizability and TIP4P water models. A simulation methodology is presented which incorporates a number of finite-system free energy corrections within the context of constant pressure molecular dynamics simulations employing the Ewald method and periodic boundary conditions. The agreement of the computed free energies and solvation structures with previously reported results for these models in finite droplet systems indicates good transferability of ion force fields from these water models to TIP4Q-FQ even when ion polarizability is neglected. To assess the performance of the ion models in TIP4P-FQ, we compare with consensus values for single-ion hydration free energies arising from recently improved cluster-pair estimates and a reevaluation of commonly cited, experimentally derived single-ion hydration free energies; we couple the observed consistency of these energies with a justification of the cluster-pair approximation in assigning single-ion hydration free energies to advocate the use of these consensus energies as a benchmark set in the parametrization of future ion force fields.

The authors gratefully acknowledge support from the National Institute of Health sponsored COBRE (Center of Biomedical Research) Grant Number P20-RR017716 at the University of Delaware (Department of Chemistry and Biochemistry). One author (S.P.) acknowledges the generous support from the University of Delaware for startup funds.

I. INTRODUCTION

II. THEORY AND METHODS

A. Water force fields

B. Ion models

C. Simulation details

D. Free energy calculations

E. Free energy corrections

III. RESULTS AND DISCUSSION

A. Finite-size corrections

B. Interfacial potential

C. Hydration free energies

D. Single-ion hydration free energies

E. Structure

IV. CONCLUSIONS

### Key Topics

- Free energy
- 137.0
- Solvents
- 51.0
- Polarizability
- 21.0
- Water energy interactions
- 19.0
- Polarization
- 17.0

## Figures

The dependence of the LJ-decoupling free energy path on the separation-shifted scaling parameter for the ion of set A in TIP4P-FQ water. The bottom curve corresponds to (unmodified interaction). The remaining curves from bottom to top correspond to values ranging from in unit increments. The darker curve with solid points represents the free energy path for a nearly optimal value of .

The dependence of the LJ-decoupling free energy path on the separation-shifted scaling parameter for the ion of set A in TIP4P-FQ water. The bottom curve corresponds to (unmodified interaction). The remaining curves from bottom to top correspond to values ranging from in unit increments. The darker curve with solid points represents the free energy path for a nearly optimal value of .

Finite-size corrections to the free energy relative to for the ion of set A as a function of system size, plotted in terms of . The solid horizontal line represents an extrapolated free energy of determined from a best fit to the finite-size corrected values of (solid points and error bars) obtained for various system sizes. The dashed curve, dashed line, and dotted curve represent , , and , respectively, for this ion.

Finite-size corrections to the free energy relative to for the ion of set A as a function of system size, plotted in terms of . The solid horizontal line represents an extrapolated free energy of determined from a best fit to the finite-size corrected values of (solid points and error bars) obtained for various system sizes. The dashed curve, dashed line, and dotted curve represent , , and , respectively, for this ion.

Computed values of for the ion of set A as a function of system size, plotted in terms of . The solid horizontal line represents an extrapolated free energy of determined from a best fit to the finite-size corrected values of (squares) obtained for various system sizes. The upper solid curve is derived from the extrapolated free energy by removing the , , and corrections and is compared with values of obtained by removing the ion self-energy *in situ*. The lower dashed curve is derived from the extrapolated free energy by removing the and corrections and is compared with values of obtained by decoupling the ionic lattice and manually removing the vacuum self-energy via Eq. (7).

Computed values of for the ion of set A as a function of system size, plotted in terms of . The solid horizontal line represents an extrapolated free energy of determined from a best fit to the finite-size corrected values of (squares) obtained for various system sizes. The upper solid curve is derived from the extrapolated free energy by removing the , , and corrections and is compared with values of obtained by removing the ion self-energy *in situ*. The lower dashed curve is derived from the extrapolated free energy by removing the and corrections and is compared with values of obtained by decoupling the ionic lattice and manually removing the vacuum self-energy via Eq. (7).

Dipole and quadrupole moment contributions to the vacuum-liquid interfacial potential for a thick slab of TIP4P-FQ water. The upper dotted curve represents , the potential due to dipole orientational polarization along the direction of the surface normal. The lower dashed curve is the potential due to the molecular quadrupole moment density. The solid curve is the sum of the dipole and quadrupole contributions which is compared to a value of (dotted horizontal line) obtained by direct integration of the charge density .

Dipole and quadrupole moment contributions to the vacuum-liquid interfacial potential for a thick slab of TIP4P-FQ water. The upper dotted curve represents , the potential due to dipole orientational polarization along the direction of the surface normal. The lower dashed curve is the potential due to the molecular quadrupole moment density. The solid curve is the sum of the dipole and quadrupole contributions which is compared to a value of (dotted horizontal line) obtained by direct integration of the charge density .

Neutral salt energies of the polarizable ion set A in TIP4P-FQ water less than the salt energies of Lamoureux and Roux (Ref. 39) computed in polarizable SWM4-DP water. For each cation, the bars represent each of the four anions , , , and , in order.

Neutral salt energies of the polarizable ion set A in TIP4P-FQ water less than the salt energies of Lamoureux and Roux (Ref. 39) computed in polarizable SWM4-DP water. For each cation, the bars represent each of the four anions , , , and , in order.

Neutral salt energies of the nonpolarizable ion set E in TIP4P-FQ water less than the salt energies of Jensen and Jorgensen computed in nonpolarizable TIP4P water. For each cation, the bars represent each of the four anions , , , and , in order.

Neutral salt energies of the nonpolarizable ion set E in TIP4P-FQ water less than the salt energies of Jensen and Jorgensen computed in nonpolarizable TIP4P water. For each cation, the bars represent each of the four anions , , , and , in order.

Neutral salt hydration energies computed using the polarizable ion set A in TIP4P-FQ less than the salt energies derived from the absolute free energies of Kelly *et al.* For each cation, the bars represent each of the four anions , , , and , in order.

Neutral salt hydration energies computed using the polarizable ion set A in TIP4P-FQ less than the salt energies derived from the absolute free energies of Kelly *et al.* For each cation, the bars represent each of the four anions , , , and , in order.

Salt hydration energies computed using the nonpolarizable ion set E less than the salt energies computed from the absolute free energies of Kelly *et al.* For each cation, the bars represent each of the four anions , , , and , in order.

Salt hydration energies computed using the nonpolarizable ion set E less than the salt energies computed from the absolute free energies of Kelly *et al.* For each cation, the bars represent each of the four anions , , , and , in order.

Radial distributions functions for the set A cations computed in TIP4P-FQ water. The corresponding peak positions reported for SWM4-DP water (Table III) are marked for comparison.

Radial distributions functions for the set A cations computed in TIP4P-FQ water. The corresponding peak positions reported for SWM4-DP water (Table III) are marked for comparison.

Radial distributions functions for the set A anions computed in TIP4P-FQ water. The corresponding peak positions reported for SWM4-DP water (Table III) are marked for comparison.

Radial distributions functions for the set A anions computed in TIP4P-FQ water. The corresponding peak positions reported for SWM4-DP water (Table III) are marked for comparison.

## Tables

Ion LJ parameters and computed absolute free energies of hydration for monovalent ions in TIP4P-FQ water including various correction terms as described in Sec. II E. As a consequence of our decoupling method, the vacuum self-energy contribution of is already included in . All energies are in units of . Parentheses indicate the standard error of and do not reflect any uncertainties in the applied corrections.

Ion LJ parameters and computed absolute free energies of hydration for monovalent ions in TIP4P-FQ water including various correction terms as described in Sec. II E. As a consequence of our decoupling method, the vacuum self-energy contribution of is already included in . All energies are in units of . Parentheses indicate the standard error of and do not reflect any uncertainties in the applied corrections.

Experimentally derived absolute hydration energies for monovalent ions corresponding to idealized standard states of in the liquid and gas phases. The values are offset so that the absolute hydration free energy for is the same for each set and is equal to . Values for Tissandier *et al.* containing typographical errors for , , and are substituted with the corrected values as described by Kelly *et al.* The standard state correction applied by Marcus appears to be inconsistent with that employed in more recent studies; the values listed above have been corrected.

Experimentally derived absolute hydration energies for monovalent ions corresponding to idealized standard states of in the liquid and gas phases. The values are offset so that the absolute hydration free energy for is the same for each set and is equal to . Values for Tissandier *et al.* containing typographical errors for , , and are substituted with the corrected values as described by Kelly *et al.* The standard state correction applied by Marcus appears to be inconsistent with that employed in more recent studies; the values listed above have been corrected.

Coordination numbers and positions for the first minimum and maximum of the ion-oxygen radial distribution function of the set A ions in TIP4P-FQ water and in SWM4-DP water. Coordination numbers in the present study are determined by the integration of the RDF to the first minimum.

Coordination numbers and positions for the first minimum and maximum of the ion-oxygen radial distribution function of the set A ions in TIP4P-FQ water and in SWM4-DP water. Coordination numbers in the present study are determined by the integration of the RDF to the first minimum.

Coordination numbers and positions for the first minimum and maximum of the ion-oxygen radial distribution functions of the set E ions in TIP4P-FQ water and in TIP4P water. Coordination numbers in the present study are determined by the integration of the RDF to the first minimum.

Coordination numbers and positions for the first minimum and maximum of the ion-oxygen radial distribution functions of the set E ions in TIP4P-FQ water and in TIP4P water. Coordination numbers in the present study are determined by the integration of the RDF to the first minimum.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content