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Free energy partitioning analysis of the driving forces that determine ion density profiles near the water liquid-vapor interface
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10.1063/1.3689749
/content/aip/journal/jcp/136/10/10.1063/1.3689749
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/10/10.1063/1.3689749

Figures

Image of FIG. 1.
FIG. 1.

Repulsive Fermi-function potential utilized for the growth process to obtain the cavity formation free energy. The potentials are shown for 10 values of λ. The last curve on the right is the repulsive wall of the vdW potential. A final perturbation step is employed to obtain the free energy change to go from the last Fermi potential to the repulsive vdW potential.

Image of FIG. 2.
FIG. 2.

The integrand 〈∂U(r, λ)/∂λ〉λ as a function of the coupling parameter λ computed during the cavity creation process for the I ion. The solid line with circles is the integrand obtained in the forward direction by growing in the repulsive particle, while the dashed line with squares was obtained in the reverse direction.

Image of FIG. 3.
FIG. 3.

(a) Free energy profiles for the I ion. The origin for the x axis (z location of the ion) is the center of the water slab, and the dividing surface is located very close to 12.5 Å. Starting from the bottom near the dividing surface: cavity formation (black), far-field electrostatics (blue), total free energy for I (magenta), total free energy profile for Na+ (orange), attractive vdW or dispersion (red), and local electrostatics (green). Based on the error estimate of 0.1 kcal/mol for each term, the estimated errors for each point in the total PMFs are roughly 0.2 to 0.3 kcal/mol. (b) Free energy profiles for the Na+ ion. Starting from the bottom near the dividing surface: cavity formation (black), local electrostatics (green), attractive vdW or dispersion (red), total free energy for Na+ (magenta), and far-field electrostatics (blue).

Image of FIG. 4.
FIG. 4.

The number of waters in the first hydration shell of the I (full curve) and Na+ (dashed curve) ions, as a function of z (distance from center of slab). The dividing surface occurs very close to 12.5 Å. The hydration numbers were computed for the ions fully coupled to the water solvent.

Tables

Generic image for table
Table I.

Hydration free energy data for the I ion. All energies are in kcal/mol. The electrostatic damping length (following Ref. 30) is η−1 = 5.00 Å. The first column labels the ion location: the first entry is the bulk result (periodic boundaries with no interface), while the following entries give the distance (in Å) from the center of the water slab. The dividing surface is very close to 12.5 Å. The remaining columns label the various contributions to the free energy, which are in order: cavity formation, vdW dispersion interactions, local electrostatics, far-field electrostatics, and the total. Thermodynamic corrections are not included in the data. The estimated error in each contribution is roughly 0.1 kcal/mol or less. The cavity formation free energy for the bulk case was taken from the z = 0 slab calculation. The bulk result adjusted for the thermodynamic corrections and the SPC/E water surface potential contribution is −57.2 kcal/mol. The experimental result taken from the compilation of Ref. 59 is −59.3 kcal/mol.

Generic image for table
Table II.

Hydration free energy data for the Na+ ion. All energies are in kcal/mol. The electrostatic dampling length (following Ref. 30) is η−1 = 4.35 Å. The first column labels the ion location: the first entry is the bulk result (periodic boundaries with no interface), while the following entries give the distance (in Å) from the center of the water slab. The dividing surface is very close to 12.5 Å. The remaining columns label the various contributions to the free energy, which are in order: cavity formation, dispersion interactions, local electrostatics, far-field electrostatics, and the total. Thermodynamic corrections are not included in the data. The estimated error in each contribution is roughly 0.1 kcal/mol or less. The cavity formation free energy for the bulk case was taken from the z = 0 slab calculation. The bulk result adjusted for the thermodynamic corrections and the SPC/E water surface potential contribution is −101.4 kcal/mol. The experimental result taken from the compilation of Ref. 59 is −103.2 kcal/mol.

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/content/aip/journal/jcp/136/10/10.1063/1.3689749
2012-03-08
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Free energy partitioning analysis of the driving forces that determine ion density profiles near the water liquid-vapor interface
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/10/10.1063/1.3689749
10.1063/1.3689749
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