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)], 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.
REFERENCES
1.
H. J. C.
Berendsen
, in: Proceedings of Workshop on Molecular Dynamics and Protein Structure, University of North Carolina, 13–18 May 1984
, edited by J.
Hermans
(Polycrystal Book Service, Western Springs
, Illinois, USA
, 1985
).2.
3.
S. C.
Harvey
, Proteins: Struct., Funct., Genet.
5
, 78
(1989
).4.
W. F.
van Gunsteren
and H. J. C.
Berendsen
, Angew. Chem., Int. Ed.
29
, 992
(1990
).5.
M. E.
Davis
and J. A.
McCammon
, Chem. Rev.
90
, 509
(1990
).6.
P. E.
Smith
and W. F.
van Gunsteren
, “Methods for the evaluation of long range electrostatic forces in computer simulations of molecular systems
,” in Computer Simulation of Biomolecular Systems, Theoretical and Experimental Applications
, edited by W. F.
van Gunsteren
, P. K.
Weiner
, and A. J.
Wilkinson
(ESCOM Science Publishers B.V.
, Leiden, The Netherlands
, 1993
), Vol. 2
, pp. 182
–212
.7.
H. J. C.
Berendsen
, “Electrostatic interactions
,” in Computer Simulation of Biomolecular Systems, Theoretical and Experimental Applications
, edited by W. F.
van Gunsteren
, P. K.
Weiner
, and A. J.
Wilkinson
(ESCOM Science Publishers B.V.
, Leiden, The Netherlands
, 1993
), Vol. 2
, pp. 161
–181
.8.
M. K.
Gilson
, Curr. Opin. Struct. Biol.
5
, 216
(1995
).9.
C. L.
Brooks
III, Curr. Opin. Struct. Biol.
5
, 211
(1995
).10.
R. M.
Levy
and E.
Gallicchio
, Annu. Rev. Phys. Chem.
49
, 531
(1998
).11.
12.
A.
Warshel
and A.
Papazyan
, Curr. Opin. Struct. Biol.
8
, 211
(1998
).13.
T.
Darden
, L.
Perera
, L.
Li
, and L.
Pedersen
, Structure
7
, R55
(1999
).14.
C.
Sagui
and T. A.
Darden
, Annu. Rev. Biophys. Biomol. Struct.
28
, 155
(1999
).15.
16.
T.
Hansson
, C.
Oostenbrink
, and W. F.
van Gunsteren
, Curr. Opin. Struct. Biol.
12
, 190
(2002
).17.
M.
Karplus
and J.A.
McCammon
, Nat. Struct. Biol.
9
, 646
(2002
).18.
P.
Gibbon
and G.
Sutmann
, Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms
, Lecture Notes, NIC Series
Vol. 10
, edited by J.
Grotendorst
, D.
Marx
, and A.
Muramatsu
(John von Neumann Institute for Computing
, Jülich, Germany
, 2002
), pp. 467
–506
.19.
J.
Norberg
and L.
Nilsson
, Q. Rev. Biophys.
36
, 257
(2003
).20.
P.
Koehl
, Curr. Opin. Struct. Biol.
16
, 142
(2006
).21.
A.
Warshel
, P. K.
Sharma
, M.
Kato
, and W. W.
Parson
, Biochim. Biophys. Acta
1764
, 1647
(2006
).22.
S. A.
Adcock
and J. A.
McCammon
, Chem. Rev.
106
, 1589
(2006
).23.
W. F.
van Gunsteren
, D.
Bakowies
, R.
Baron
, I.
Chandrasekhar
, M.
Christen
, X.
Daura
, P.
Gee
, D. P.
Geerke
, A.
Glättli
, P. H.
Hünenberger
, M. A.
Kastenholz
, C.
Oostenbrink
, M.
Schenk
, D.
Trzesniak
, N. F.A.
van der Vegt
, and H. B.
Yu
, Angew. Chem., Int. Ed.
45
, 4064
(2006
).24.
M. M.
Reif
, V.
Kräutler
, M. A.
Kastenholz
, X.
Daura
, and P. H.
Hünenberger
, J. Phys. Chem. B
113
, 3112
(2009
).25.
C. L.
Brooks
III, J. Phys. Chem.
90
, 6680
(1986
).26.
C. L.
Brooks
III, J. Chem. Phys.
86
, 5156
(1987
).27.
J. D.
Madura
and B. M.
Pettitt
, Chem. Phys. Lett.
150
, 105
(1988
).28.
T. P.
Straatsma
and H. J. C.
Berendsen
, J. Chem. Phys.
89
, 5876
(1988
).29.
30.
C.
Chipot
, C.
Millot
, B.
Maigret
, and P. A.
Kollman
, J. Phys. Chem.
98
, 11362
(1994
).31.
F.
Figueirido
, G. S.
Del Buono
, and R. M.
Levy
, J. Chem. Phys.
103
, 6133
(1995
).32.
S. G.
Kalko
, G.
Sese
, and J. A.
Padro
, J. Chem. Phys.
104
, 9578
(1996
).33.
G.
Hummer
, L. R.
Pratt
, and A. E.
Garcia
, J. Phys. Chem.
100
, 1206
(1996
).34.
G.
Hummer
, L. R.
Pratt
, A. E.
Garcia
, B. J.
Berne
, and S. W.
Rick
, J. Phys. Chem. B
101
, 3017
(1997
).35.
G.
Hummer
, L. R.
Pratt
, and A. E.
Garcia
, J. Chem. Phys.
107
, 9275
(1997
).36.
F.
Figueirido
, G. S.
Del Buono
, and R. M.
Levy
, J. Phys. Chem. B
101
, 5622
(1997
).37.
H. S.
Ashbaugh
and R. H.
Wood
, J. Chem. Phys.
106
, 8135
(1997
).38.
T.
Darden
, D.
Pearlman
, and L. G.
Pedersen
, J. Chem. Phys.
109
, 10921
(1998
).39.
H. S.
Ashbaugh
and R. H.
Wood
, J. Phys. Chem. B
102
, 3844
(1998
).40.
S.
Garde
, G.
Hummer
, and M. E.
Paulaitis
, J. Chem. Phys.
108
, 1552
(1998
).41.
G.
Hummer
, L. R.
Pratt
, and A. E.
Garcia
, J. Phys. Chem. A
102
, 7885
(1998
).42.
G.
Hummer
, L. R.
Pratt
, A. E.
Garcia
, S.
Garde
, B. J.
Berne
, and S. W.
Rick
, J. Phys. Chem. B
102
, 3841
(1998
).43.
H.
Resat
and J. A.
McCammon
, J. Chem. Phys.
104
, 7645
(1996
).44.
H.
Resat
and J. A.
McCammon
, J. Chem. Phys.
108
, 9617
(1998
).45.
S.
Sakane
, H. S.
Ashbaugh
, and R. H.
Wood
, J. Phys. Chem. B
102
, 5673
(1998
).46.
Y. Y.
Sham
and A.
Warshel
, J. Chem. Phys.
109
, 7940
(1998
).47.
P. H.
Hünenberger
and J. A.
McCammon
, J. Chem. Phys.
110
, 1856
(1999
).48.
Y. N.
Vorobjev
and J.
Hermans
, J. Phys. Chem. B
103
, 10234
(1999
).49.
M.
Baaden
, F.
Berny
, C.
Madic
, and G.
Wipff
, J. Phys. Chem. A
104
, 7659
(2000
).50.
C. S.
Babu
, P.-K.
Yang
, and C.
Lim
, J. Biol. Phys.
28
, 95
(2002
).51.
E. N.
Brodskaya
, Mol. Phys.
101
, 1495
(2003
).52.
A.
Grossfield
, P.
Ren
, and J. W.
Ponder
, J. Am. Chem. Soc.
125
, 15671
(2003
).53.
D. H.
Herce
, T.
Darden
, and C.
Sagui
, J. Chem. Phys.
119
, 7621
(2003
).54.
M.
Patra
and M.
Karttunen
, J. Comp. Chem.
25
, 678
(2004
).55.
M. A.
Kastenholz
and P. H.
Hünenberger
, J. Chem. Phys.
124
, 124106
(2006
).56.
M. A.
Kastenholz
and P. H.
Hünenberger
, J. Chem. Phys.
124
, 224501
(2006
).57.
G. L.
Warren
and S.
Patel
, J. Chem. Phys.
127
, 064509
(2007
).58.
G. L.
Warren
and S.
Patel
, J. Phys. Chem. C
113
, 7455
(2008
).59.
H. S.
Ashbaugh
and D.
Asthagiri
, J. Chem. Phys.
129
, 204501
(2008
).60.
61.
C. L.
Brooks
III, B. M.
Pettitt
, and M.
Karplus
, J. Chem. Phys.
83
, 5897
(1985
).62.
63.
N. A.
Baker
, P. H.
Hünenberger
, and J. A.
McCammon
, J. Chem. Phys.
110
, 10679
(1999
).64.
N. A.
Baker
, P. H.
Hünenberger
, and J. A.
McCammon
, J. Chem. Phys.
113
, 2510
(2000
).65.
S.
Boresch
and O.
Steinhauser
, J. Chem. Phys.
115
, 10780
(2001
).66.
S.
Boresch
and O.
Steinhauser
, J. Chem. Phys.
115
, 10793
(2001
).67.
M.
Bergdorf
, C.
Peter
, and P. H.
Hünenberger
, J. Chem. Phys.
119
, 9129
(2003
).68.
C.
Peter
, W. F.
van Gunsteren
, and P. H.
Hünenberger
, J. Chem. Phys.
119
, 12205
(2003
).69.
M. P.
Allen
and D. J.
Tildesley
, Computer Simulation of Liquids
(Oxford University Press
, New York, USA
, 1987
).70.
B. R.
Brooks
, R. E.
Bruccoleri
, B. D.
Olafson
, D. J.
States
, S.
Swaminathan
, and M.
Karplus
, J. Comput. Chem.
4
, 187
(1983
).71.
D. J.
Adams
and G. S.
Dubey
, J. Comput. Phys.
72
, 156
(1987
).72.
R. J.
Loncharich
and B. R.
Brooks
, Proteins: Struct., Funct., Genet.
6
, 32
(1989
).73.
K. S.
Kim
, Chem. Phys. Lett.
156
, 261
(1989
).74.
M.
Prevost
, D.
van Belle
, G.
Lippens
, and S.
Wodak
, Mol. Phys.
71
, 587
(1990
).75.
76.
P. J.
Steinbach
and B. R.
Brooks
, J. Comput. Chem.
15
, 667
(1994
).77.
G.
Hummer
and D. M.
Soumpasis
, Phys. Rev. E
49
, 591
(1994
).78.
G.
Hummer
and D. M.
Soumpasis
, J. Phys.: Condens. Matter
6
, A141
(1994
).79.
J.
Norberg
and L.
Nilsson
, Biophys. J.
79
, 1537
(2000
).80.
E.
Yakub
and C.
Ronchi
, J. Chem. Phys.
119
, 11556
(2003
).81.
D. A.C.
Beck
, R. S.
Armen
, and V.
Daggett
, Biochemistry
44
, 609
(2005
).82.
X.
Wu
and B. R.
Brooks
, J. Chem. Phys.
122
, 044107
(2005
).83.
E.
Yakub
and C.
Ronchi
, J. Low Temp. Phys.
139
, 633
(2005
).84.
85.
H.-Q.
Ding
, N.
Karasawa
, and W. A.
Goddard
III, Chem. Phys. Lett.
193
, 197
(1992
).86.
J.
Guenot
and P. A.
Kollman
, J. Comput. Chem.
14
, 295
(1993
).87.
J. A.
Barker
and R. O.
Watts
, Mol. Phys.
26
, 789
(1973
).88.
H.
Alper
and R. M.
Levy
, J. Chem. Phys.
99
, 9847
(1993
).89.
J. A.
Barker
, Mol. Phys.
83
, 1057
(1994
).90.
I. G.
Tironi
, R.
Sperb
, P. E.
Smith
, and W. F.
van Gunsteren
, J. Chem. Phys.
102
, 5451
(1995
).91.
P. H.
Hünenberger
and W. F.
van Gunsteren
, J. Chem. Phys.
108
, 6117
(1998
).92.
G.
Mathias
, B.
Egwolf
, M.
Nonella
, and P.
Tavan
, J. Chem. Phys.
118
, 10847
(2003
).93.
T. N.
Heinz
and P. H.
Hünenberger
, J. Chem. Phys.
123
, 034107
(2005
).94.
95.
R. W.
Hockney
and J. W.
Eastwood
, Computer Simulation Using Particles
(McGraw-Hill
, New York, USA
, 1981
).96.
T.
Darden
, D.
York
, and L.
Pedersen
, J. Chem. Phys.
98
, 10089
(1993
).97.
U.
Essmann
, L.
Perera
, M. L.
Berkowitz
, T.
Darden
, H.
Lee
, and L. G.
Pedersen
, J. Chem. Phys.
103
, 8577
(1995
).98.
P. H.
Hünenberger
, “Lattice-sum methods for computing electrostatic interactions in molecular simulations
,” in Simulation and Theory of Electrostatic Interactions in Solution: Computational Chemistry, Biophysics, and Aqueous Solution
; edited by G.
Hummer
and L. R.
Pratt
(American Institute of Physics
, New York, USA
, 1999
), pp. 17
–83
.99.
P. H.
Hünenberger
and J. A.
McCammon
, Biophys. Chem.
78
, 69
(1999
).100.
A.
Brünger
, C. L.
Brooks
III, and M.
Karplus
, Chem. Phys. Lett.
105
, 495
(1984
).101.
A.
Warshel
and G.
King
, Chem. Phys. Lett.
121
, 124
(1985
).102.
A. C.
Belch
and M.
Berkowitz
, Chem. Phys. Lett.
113
, 278
(1985
).103.
G.
King
and A.
Warshel
, J. Chem. Phys.
91
, 3647
(1989
).104.
A. H.
Juffer
and H. J. C.
Berendsen
, Mol. Phys.
79
, 623
(1993
).105.
A.
Wallqvist
, Mol. Simul.
10
, 13
(1993
).106.
L.
Wang
and J.
Hermans
, J. Phys. Chem.
99
, 12001
(1995
).107.
J. W.
Essex
and W. L.
Jorgensen
, J. Comput. Chem.
16
, 951
(1995
).108.
V.
Lounnas
, S. K.
Lüdemann
, Biophys. Chem.
78
, 157
(1999
).109.
R.
Sankararamakrishnan
, K.
Konvicka
, E. L.
Mehler
, and H.
Weinstein
, Int. J. Quantum Chem.
77
, 174
(2000
).110.
S. R.
Kimura
, R. C.
Brower
, C.
Zhang
, and M.
Sugimori
, J. Chem. Phys.
112
, 7723
(2000
).111.
W.
Im
, S.
Bernèche
, and B.
Roux
, J. Chem. Phys.
114
, 2924
(2001
).112.
Y.
Li
, G.
Krilov
, and B. J.
Berne
, J. Phys. Chem. B
109
, 463
(2005
).113.
G.
Petraglio
, M.
Ceccarelli
, and M.
Parrinello
, J. Chem. Phys.
123
, 044103
(2005
).114.
G.
Brancato
, A.
Di Nola
, V.
Barone
, and A.
Amadei
, J. Chem. Phys.
122
, 154109
(2005
).115.
G.
Brancato
, N.
Rega
, and V.
Barone
, J. Chem. Phys.
124
, 21405
(2006
).116.
H.
Bekker
, J. Comput. Chem.
18
, 1930
(1997
).117.
R. R.
Gabdoulline
and C.
Zheng
, J. Comput. Chem.
16
, 1428
(1995
).118.
R. R.
Gabdoulline
, C.
Zheng
, and G.
Vanderkooi
, J. Mol. Liq.
71
, 1
(1997
).119.
J.
Åqvist
and T.
Hansson
, J. Phys. Chem. B
102
, 3837
(1998
).120.
N. S.
Hush
, Aust. J. Sci. Res., Ser. A
1
, 480
(1948
).121.
G.
Passoth
, Z. Phys. Chem. (Leipzig)
203
, 275
(1954
).122.
J. E. B.
Randles
, Trans. Faraday Soc.
52
, 1573
(1956
).123.
P. H.
Hünenberger
and M. M.
Reif
, Single-Ion Solvation: Experimental and Theoretical Approaches to Elusive Thermodynamic Quantities
, Theoretical and Computational Chemistry Series
(Royal Society of Chemistry
, London, UK
, 2011
).124.
F. H.
Stillinger
, Jr., and A.
Ben-Naim
, J. Chem. Phys.
47
, 4431
(1967
).125.
N. H.
Fletcher
, Philos. Mag.
18
, 1287
(1968
).126.
N. I.
Christou
, J. S.
Whitehouse
, D.
Nicholson
, and N. G.
Parsonage
, Mol. Phys.
55
, 397
(1985
).127.
G.
Aloisi
, R.
Guidelli
, R. A.
Jackson
, S. M.
Clark
, and P.
Barnes
, J. Electroanal. Chem.
206
, 131
(1986
).128.
M. A.
Wilson
, A.
Pohorille
, and L. R.
Pratt
, J. Phys. Chem.
91
, 4873
(1987
).129.
E. N.
Brodskaya
, Mol. Phys.
62
, 251
(1987
).130.
M. A.
Wilson
, A.
Pohorille
, and L. R.
Pratt
, J. Chem. Phys.
88
, 3281
(1988
).131.
M.
Matsumoto
and Y.
Kataoka
, J. Chem. Phys.
88
, 3233
(1988
).132.
M. A.
Wilson
, A.
Pohorille
, and L. R.
Pratt
, J. Chem. Phys.
90
, 5211
(1989
).133.
M.
Matsumoto
and Y.
Kataoka
, J. Chem. Phys.
90
, 2398
(1989
).134.
M.
Matsumoto
and Y.
Kataoka
, J. Chem. Phys.
95
, 7782
(1991
).135.
J. S.
Bader
and D.
Chandler
, J. Phys. Chem.
96
, 6423
(1992
).136.
C. G.
Barraclough
, P. T.
McTigue
, and Y. L.
Ng
, J. Electroanal. Chem.
329
, 9
(1992
).137.
A.
Pohorille
and M. A.
Wilson
, J. Mol. Struct.: THEOCHEM
284
, 271
(1993
).138.
E. N.
Brodskaya
and V. V.
Zakharov
, J. Chem. Phys.
102
, 4595
(1995
).139.
V. L.
Kuzmin
, Colloid J.
57
, 776
(1995
).140.
S. E.
Feller
, R. W.
Pastor
, A.
Rojnuckarin
, S.
Bogusz
, and B. R.
Brooks
, Jr., J. Phys. Chem.
100
, 17011
(1996
).141.
E. N.
Brodskaya
, J. C.
Eriksson
, A.
Laaksonen
, and A. I.
Rusanov
, J. Colloid Interface Sci.
180
, 86
(1996
).142.
V. P.
Sokhan
and D. J.
Tildesley
, Mol. Phys.
92
, 625
(1997
).143.
H. S.
Ashbaugh
, Mol. Phys.
97
, 433
(1999
).144.
L. X.
Dang
and T.-M.
Chang
, J. Phys. Chem. B
106
, 235
(2002
).145.
V. I.
Parfenyuk
, Colloid J.
64
, 588
(2002
).146.
G.
Lamoureux
, A. D.
MacKerrel
, and B.
Roux
, J. Chem. Phys.
119
, 5185
(2003
).147.
K.
Jaqaman
, K.
Tuncay
, and P. J.
Ortoleva
, J. Chem. Phys.
120
, 926
(2004
).148.
S.
Patel
and C. L.
Brooks
III, J. Chem. Phys.
124
, 204706
(2006
).149.
C. D.
Wick
, L. X.
Dang
, and P.
Jungwirth
, J. Chem. Phys.
125
, 024706
(2006
).150.
E.
Harder
and B.
Roux
, J. Chem. Phys.
129
, 234706
(2008
).151.
S. M.
Kathmann
, W. K.
I-Feng
, and C. J.
Mundy
, J. Am. Chem. Soc.
130
, 16556
(2008
).152.
S. M.
Kathmann
, W. K.
I-Feng
, and C. J.
Mundy
, J. Am. Chem. Soc.
131
, 17522
(2009
).153.
154.
B. E.
Conway
and J. O’M.
Bockris
, Mod. Asp. Electrochem.
1
, 47
(1954
).155.
R. M.
Noyes
, J. Am. Chem. Soc.
84
, 513
(1962
).156.
H. F.
Halliwell
and S. C.
Nyburg
, Trans. Faraday Soc.
59
, 1126
(1963
).157.
R. M.
Noyes
, J. Am. Chem. Soc.
86
, 971
(1964
).158.
159.
B. E.
Conway
, R. E.
Verall
, and J. E.
Desnoyers
, Z. Phys. Chem. (Leipzig)
230
, 157
(1965
).160.
J. E.
Desnoyers
and C.
Jolicoeur
, Mod. Asp. Electrochem.
5
, 1
(1969
).161.
O.
Popovych
, Crit. Rev. Anal. Chem.
1
, 73
(1970
).162.
J. I.
Padova
, Mod. Asp. Electrochem.
7
, 1
(1972
).163.
H. L.
Friedman
and C. V.
Krishnan
, “Thermodynamics of ion hydration
,” in Water: A Comprehensive Treatise
edited by F.
Franks
(Plenum
, New York, USA
, 1973
), Vol. 3
, pp. 1
–118
.164.
P.
Kebarle
, Mod. Asp. Electrochem.
9
, 1
(1974
).165.
J. E.
Desnoyers
, Phys. Chem. Liq.
7
, 63
(1977
).166.
R.
Gomer
and G.
Tryson
, J. Chem. Phys.
66
, 4413
(1977
).167.
168.
169.
Y.
Marcus
, “Ion hydration
,” in Ion Solvation
(Wiley
, New York, USA
, 1985
), pp. 87
–129
).170.
Y.
Marcus
, J. Solution Chem.
37
, 1071
(2008
).171.
Y.
Marcus
, J. Phys. Chem. B
113
, 10285
(2009
).172.
J. D.
Bernal
and R. H.
Fowler
, J. Chem. Phys.
1
, 515
(1933
).173.
174.
L.
Benjamin
and V.
Gold
, Trans. Faraday Soc.
50
, 797
(1954
).175.
K. J.
Laidler
and C.
Pegis
, Proc. R. Soc.
248
, 80
(1957
).176.
177.
F.
Franks
and D. S.
Reid
, J. Phys. Chem.
73
, 3152
(1969
).178.
179.
M. W.
Lister
, S. C.
Nyburg
, and R. B.
Poyntz
, J. Chem. Soc. Faraday Trans. I
70
, 685
(1974
).180.
181.
D. F.C.
Morris
, Electrochim. Acta
27
, 1481
(1982
).182.
Y.
Marcus
, J. Chem. Soc. Faraday Trans. I
83
, 339
(1987
).183.
Y.
Marcus
, Pure Appl. Chem.
59
, 1093
(1987
).184.
Y.
Marcus
, J. Chem. Soc. Faraday Trans. I
83
, 2985
(1987
).185.
W. R.
Fawcett
and L.
Blum
, J. Electroanal. Chem.
328
, 333
(1992
).186.
J. V.
Coe
, Chem. Phys. Lett.
229
, 161
(1994
).187.
M. D.
Tissandier
, K. A.
Cowen
, W. Y.
Feng
, E.
Gundlach
, M. H.
Cohen
, A. D.
Earhart
, J. V.
Coe
, and T. R.
Tuttle
, Jr., J. Phys. Chem. A
102
, 7787
(1998
).188.
M. D.
Tissandier
, K. A.
Cowen
, W. Y.
Feng
, E.
Gundlach
, M. H.
Cohen
, A. D.
Earhart
, J. V.
Coe
, and T. R.
Tuttle
, Jr., J. Phys. Chem. A
102
, 9308
(1998
).189.
J. V.
Coe
, Int. Rev. Phys. Chem.
20
, 33
(2001
).190.
T. R.
Tuttle
, Jr., S.
Malaxos
, and J. V.
Coe
, J. Phys. Chem. A
106
, 925
(2002
).191.
S. C.
Lahiri
, Z. Phys. Chem.
217
, 13
(2003
).192.
C. P.
Kelly
, C. J.
Cramer
, and D. G.
Truhlar
, J. Phys. Chem. B
110
, 16066
(2006
).193.
194.
195.
J. E. B.
Randles
, Discuss. Faraday Soc.
24
, 194
(1957
).196.
B.
Kamieński
, Electrochim. Acta
1
, 272
(1959
).197.
J.
Llopis
, Mod. Asp. Electrochem.
6
, 91
(1971
).198.
J. E. B.
Randles
, Phys. Chem. Liq.
7
, 107
(1977
).199.
N. N.
Kochurova
and A. I.
Rusanov
, J. Colloid Interface Sci.
81
, 297
(1981
).200.
A.
Borazio
, J. R.
Farrell
, and P.
McTigue
, J. Electroanal. Chem.
193
, 103
(1985
).201.
L. I.
Krishtalik
, N. M.
Alpatova
, and E. V.
Ovsyannikova
, J. Electroanal. Chem.
329
, 1
(1992
).202.
Z.
Koczorowski
, Bull. Pol. Acad. Sci. Chem.
45
, 225
(1997
).203.
M.
Paluch
, Adv. Colloid Interface Sci.
84
, 27
(2000
).204.
V. I.
Parfenyuk
, Colloid J.
66
, 466
(2004
).205.
L. I.
Krishtalik
, Russ. J. Electrochem.
44
, 43
(2008
).206.
S.
Trasatti
, J. Electroanal. Chem.
52
, 313
(1974
).207.
A. N.
Frumkin
and B.
Damaskin
, J. Electroanal. Chem.
66
, 150
(1975
).208.
R.
Gomer
and G.
Tryson
, J. Chem. Phys.
69
, 2939
(1978
).209.
S.
Trasatti
, J. Electroanal. Chem.
139
, 1
(1982
).210.
H.
Reiss
and A.
Heller
, J. Phys. Chem.
89
, 4207
(1985
).211.
S.
Trasatti
, Mater. Chem. Phys.
15
, 427
(1986
).212.
S.
Trasatti
, Pure Appl. Chem.
58
, 955
(1986
).213.
A. L.
Rockwood
, Phys. Rev. A
33
, 554
(1986
).214.
Y. V.
Pleskov
, J. Phys. Chem.
91
, 1691
(1987
).215.
A. L.
Rockwood
, Phys. Rev. A
36
, 1525
(1987
).216.
H.
Reiss
, J. Electrochem. Soc.
135
, 247C
(1988
).217.
S.
Trasatti
, Electrochim. Acta
35
, 269
(1990
).218.
J.
Llano
and L. A.
Eriksson
, J. Chem. Phys.
117
, 10193
(2002
).219.
A. L.
Rockwood
, J. Chem. Phys.
122
, 087103
(2005
).220.
J.
Llano
and L. A.
Eriksson
, J. Chem. Phys.
122
, 087104
(2005
).221.
222.
223.
B. R.A.
Nijboer
and T. W.
Ruijgrok
, J. Stat. Phys.
53
, 361
(1988
).224.
G.
Hummer
, D. M.
Soumpasis
, and M.
Neumann
, Mol. Phys.
77
, 769
(1992
).225.
F.
Müller-Plathe
, Comput. Phys. Commun.
78
, 77
(1993
).226.
M.
Christen
, P. H.
Hünenberger
, D.
Bakowies
, R.
Baron
, R.
Bürgi
, D. P.
Geerke
, T. N.
Heinz
, M. A.
Kastenholz
, V.
Kräutler
, C.
Oostenbrink
, C.
Peter
, D.
Trzesniak
, and W. F.
van Gunsteren
, J. Comput. Chem.
26
, 1719
(2005
).227.
T.
Imai
, H.
Nomura
, M.
Kinoshita
, and F.
Hirata
, J. Phys. Chem. B
106
, 7308
(2002
).228.
229.
P. E.
Smith
and W. F.
van Gunsteren
, J. Chem. Phys.
100
, 3169
(1994
).230.
G.
Placzek
, B. R.A.
Nijboer
, and L.
van Hove
, Phys. Rev.
82
, 392
(1951
).231.
B.
Cichocki
, B. U.
Felderhof
, and K.
Hinsen
, Phys. Rev. A
39
, 5350
(1989
).232.
J.
Warwicker
and H. C.
Watson
, J. Mol. Biol.
157
, 671
(1982
).233.
M. E.
Davis
, J. D.
Madura
, B. A.
Luty
, and J. A.
McCammon
, Comput. Phys. Commun.
62
, 187
(1991
).234.
J. D.
Madura
, J. M.
Briggs
, R. C.
Wade
, M. E.
Davis
, B. A.
Luty
, A.
Ilin
, J.
Antosiewicz
, M. K.
Gilson
, B.
Bagheri
, L. R.
Scott
, and J. A.
McCammon
, Comput. Phys. Commun.
91
, 57
(1995
).235.
C.
Peter
, W. F.
van Gunsteren
, and P. H.
Hünenberger
, J. Chem. Phys.
116
, 7434
(2002
).236.
H. J. C.
Berendsen
, J. P.M.
Postma
, W. F.
van Gunsteren
, and J.
Hermans
, “Interaction models for water in relation to protein hydration
,” in Intermolecular Forces
, edited by B.
Pullman
(Reidel
, Dordrecht, The Netherlands
, 1981
), pp. 331
–342
.237.
M. M.
Reif
and P. H.
Hünenberger
, (unpublished).238.
Y.
Marcus
, J. Chem. Soc. Faraday Trans.
87
, 2995
(1991
).239.
Y.
Pak
and S.
Wang
, J. Phys. Chem. A
108
, 3692
(2004
).240.
D. M.
Camaioni
and C. A.
Schwerdtfeger
, J. Phys. Chem. A
109
, 10795
(2005
).241.
D. R.
Lide
, CRC Handbook of Chemistry and Physics
88th ed. (CRC
, Boca Raton, Florida
, 2008
).242.
T. J.
Webb
, J. Am. Chem. Soc.
48
, 2589
(1926
).243.
T. J.
Webb
, Proc. Natl. Acad. Sci. U.S.A.
8
, 524
(1926
).244.
W. M.
Latimer
and C.
Kasper
, J. Am. Chem. Soc.
51
, 2293
(1929
).245.
W. M.
Latimer
, K. S.
Pitzer
, and C. M.
Slansky
, J. Chem. Phys.
7
, 108
(1939
).246.
247.
248.
249.
A. D.
Buckingham
, Discuss. Faraday Soc.
24
, 151
(1957
).250.
R. H.
Stokes
, J. Am. Chem. Soc.
86
, 979
(1964
).251.
K. J.
Laidler
and J. S.
Muirhead-Gould
, Trans. Faraday Soc.
63
, 953
(1967
).252.
W. A.
Millen
and D. W.
Watts
, J. Am. Chem. Soc.
89
, 6051
(1967
).253.
S.
Goldman
and R. G.
Bates
, J. Am. Chem. Soc.
94
, 1476
(1972
).254.
M. H.
Abraham
and J.
Liszi
, J. Chem. Soc. Faraday Trans.
74
, 1604
(1978
).255.
M. H.
Abraham
and J.
Liszi
, J. Chem. Soc. Faraday Trans.
74
, 2858
(1978
).256.
M. H.
Abraham
, J.
Liszi
, and L.
Mészáros
, J. Chem. Phys.
70
, 2491
(1979
).257.
258.
259.
R. H.
Wood
, J. R.
Quint
, and J.-P.E.
Grolier
, J. Phys. Chem.
85
, 3944
(1981
).260.
M. H.
Abraham
, E.
Matteoli
, and J.
Liszi
, J. Chem. Soc. Faraday Trans. I
79
, 2781
(1983
).261.
A. A.
Rashin
and B.
Honig
, J. Phys. Chem.
89
, 5588
(1985
).262.
M.
Bucher
and T. L.
Porter
, J. Phys. Chem.
90
, 3406
(1986
).263.
264.
265.
F.
Hirata
, P.
Redfern
, and R. M.
Levy
, Int. J. Quantum Chem.
15
, 179
(1988
).266.
S.
Ehrenson
, J. Comput. Chem.
10
, 77
(1989
).267.
B.
Jayaryam
, R.
Fine
, K.
Sharp
, and B.
Honig
, J. Phys. Chem.
93
, 4320
(1989
).268.
B.
Roux
, H.-A.
Yu
, and M.
Karplus
, J. Phys. Chem.
94
, 4683
(1990
).269.
J. R.
Bontha
and P. N.
Pintauro
, J. Phys. Chem.
96
, 7778
(1992
).270.
A.
Kumar
, J. Phys. Chem. Soc. Jpn.
61
, 4247
(1992
).271.
J.-K.
Hyun
, C. S.
Babu
, and T.
Ichiye
, J. Phys. Chem.
99
, 5187
(1995
).272.
J.-K.
Hyun
and T.
Ichiye
, J. Chem. Phys.
109
, 1074
(1998
).273.
C. S.
Babu
and C.
Lim
, Chem. Phys. Lett.
310
, 225
(1999
).274.
275.
C. S.
Babu
and C.
Lim
, J. Phys. Chem. A
105
, 5030
(2001
).276.
B. E.
Conway
, “Factors limiting applications of the historically significant Born equation: A critical review
,” in Modern Aspects of Electrochemistry
, edited by B. E.
Conway
and R. E.
White
(Kluwer Academic/Plenum
, New York, USA
, 2002
), Vol. 35
, pp. 295
–323
.277.
L.
Sandberg
and O.
Edholm
, J. Chem. Phys.
116
, 2936
(2002
).278.
279.
H.
Gong
, G.
Hocky
, and K. F.
Freed
, Proc. Natl. Acad. Sci. U.S.A.
105
, 11146
(2008
).280.
M. M.
Reif
and P. H.
Hünenberger
, J. Chem. Phys.
134
, 144104
(2011
).281.
See supplementary material at http://dx.doi.org/10.1063/1.3567020 for additional information concerning the evaluation of the second derivatives of the correction terms with respect to their parameters and the numerical evaluation of the correction terms in the context of a Na+ ion in a (hypothetical) low-polarity solvent.
282.
283.
284.
285.
A.
Ben-Naim
, J. Solution Chem.
5
, 475
(2001
).286.
A.
Ben-Naim
, Molecular Theory of Solutions
(Oxford University Press
, Oxford, UK
, 2006
).287.
W. R.
Fawcett
, J. Phys. Chem. B
103
, 11181
(1999
).288.
A.
Loewenschuss
and Y.
Marcus
, Chem. Rev.
84
, 89
(1984
).289.
290.
A.
Loewenschuss
and Y.
Marcus
, J. Phys. Chem. Ref. Data
25
, 1495
(1996
).291.
D.
Horinek
, S. I.
Mamatkulov
, and R. R.
Netz
, J. Chem. Phys.
130
, 124507
(2009
).292.
M. M.
Reif
and P. H.
Hünenberger
, (unpublished).293.
N.
Bjerrum
and E.
Larsson
, Z. Phys. Chem., Stöchiom. Verwandtschaftsl.
127
, 358
(1927
).294.
A.
Voet
, Trans. Faraday Soc.
32
, 1301
(1936
).295.
E. J.W.
Verwey
, Recl. Trav. Chim. Pays-Bas
61
, 127
(1942
).296.
E.
Glueckauf
, Trans. Faraday Soc.
60
, 572
(1964
).297.
N. M.
Senozan
, J. Inorg. Nucl. Chem.
35
, 727
(1973
).298.
R.
Schmid
, A. M.
Miah
, and V. N.
Sapunov
, Phys. Chem. Chem. Phys.
2
, 97
(2000
).299.
I.
Danielewicz-Ferchmin
and A. R.
Ferchmin
, J. Solution Chem.
31
, 81
(2002
).300.
W. F.
van Gunsteren
, S. R.
Billeter
, A. A.
Eising
, P. H.
Hünenberger
, P.
Krüger
, A. E.
Mark
, W. R.P.
Scott
, and I. G.
Tironi
, Biomolecular Simulation: The GROMOS96 Manual and User Guide
(Verlag der Fachvereine
, Zürich, Switzerland
, 1996
).301.
D. P.
Fernández
, A. R.H.
Goodwin
, E. W.
Lemmon
, J. M.H.
Levelt Sengers
, and R. C.
Williams
, J. Phys. Chem. Ref. Data
26
, 1125
(1997
).302.
W. B.
Floriano
and M. A.C.
Nascimento
, Braz. J. Phys.
34
, 38
(2004
).303.
304.
305.
W. J.
Ellison
, K.
Lamkaouchi
, and J.-M.
Moreau
, J. Mol. Liq.
68
, 171
(1996
).306.
A. N.
Frumkin
, Z. A.
Iofa
, and M. A.
Gerovich
, Zh. Fiz. Khim.
10
, 1455
(1956
).307.
J. E. B.
Randles
and D. J.
Schiffrin
, J. Electroanal. Chem.
10
, 480
(1965
).308.
D. J.
Schiffrin
, Trans. Faraday Soc.
66
, 2464
(1970
).309.
J. R.
Farrell
and P.
McTigue
, J. Electroanal. Chem.
139
, 37
(1982
).310.
J. R.
Farrell
and P.
McTigue
, J. Electroanal. Chem.
163
, 129
(1984
).© 2011 American Institute of Physics.
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