We develop force field parameters for the divalent cations Mg2+, Ca2+, Sr2+, and Ba2+ for molecular dynamics simulations with the simple point charge-extended (SPC/E) water model. We follow an approach introduced recently for the optimization of monovalent ions, based on the simultaneous optimization of single-ion and ion-pair properties. We consider the solvation free energy of the divalent cations as the relevant single-ion property. As a probe for ion-pair properties we compute the activity derivatives of the salt solutions. The optimization of the ionic force fields is done in two consecutive steps. First, the cation solvation free energy is determined as a function of the Lennard-Jones (LJ) parameters. The peak in the ion-water radial distribution function (RDF) is used as a check of the structural properties of the ions. Second, the activity derivatives of the electrolytes MgY2, CaY2, BaY2, SrY2 are determined through Kirkwood-Buff solution theory, where Y = Cl, Br, I. The activity derivatives are determined for the restricted set of LJ parameters which reproduce the exact solvation free energy of the divalent cations. The optimal ion parameters are those that match the experimental activity data and therefore simultaneously reproduce single-ion and ion-pair thermodynamic properties. For Ca2+, Ba2+, and Sr2+ such LJ parameters exist. On the other hand, for Mg2+ the experimental activity derivatives can only be reproduced if we generalize the combination rule for the anion-cation LJ interaction and rescale the effective cation-anion LJ radius, which is a modification that leaves the cation solvation free energy invariant. The divalent cation force fields are transferable within acceptable accuracy, meaning the same cation force field is valid for all halide ions Cl, Br, I tested in this study.

1.
D. A.
Doyle
,
J. M.
Cabral
 et al,
Science
280
,
69
(
1998
).
2.
Y. X.
Jiang
,
A.
Lee
,
J. Y.
Chen
,
V.
Ruta
,
M.
Cadene
,
B. T.
Chait
, and
R.
MacKinnon
,
Nature (London)
423
,
33
(
2003
).
3.
R.
Dutzler
,
E. B.
Campbell
,
M.
Cadene
,
B. T.
Chait
, and
R.
MacKinnon
,
Nature (London)
415
,
287
(
2002
).
4.
A.
Malovikova
,
M.
Rinaudo
, and
M.
Milas
,
Biopolymers
34
,
1059
(
1994
).
5.
F. G.
Prendergast
and
K.
Mann
,
J. Biol. Chem.
252
,
840
(
1977
).
6.
S. X.
Wang
,
E.
Hur
,
C. A.
Sousa
,
L.
Brinen
,
E. J.
Slivka
, and
R. J.
Fletterick
,
Biochemistry
42
,
7959
(
2003
).
7.
G.
Kartha
,
K. I.
Varughese
, and
S.
Aimoto
,
Proc. Natl. Acad. Sci. U.S.A.
79
,
4519
4522
(
1982
).
8.
J.
Marra
and
J.
Israelachvili
,
Biochemistry
24
,
4608
4618
(
1985
).
9.
J.
Wilschut
,
M.
Holsappel
, and
R.
Jansen
,
Biochim. Biophys. Acta
690
,
297
301
(
1982
).
10.
T.
Dudev
and
L.
Carmay
,
Annu. Rev. Biophys.
37
,
97
(
2008
).
11.
T.
Dudev
and
L.
Carmay
,
Chem. Rev.
103
,
773
(
2003
).
12.
T. A.
Thomas
,
A.
Halgren
, and
W.
Damm
,
Curr. Opin. Struct. Biol.
11
,
236
242
(
2001
).
13.
W. L.
Ash
,
M. R.
Zlomislic
,
E. O.
Oloo
, and
D. P.
Tieleman
,
Biochim. Biophys. Acta
1666
,
158
189
(
2004
).
14.
P. G.
Kusalik
and
G. N.
Patey
,
J. Chem. Phys.
86
,
5110
(
1987
).
15.
F. P.
Kirkwood
and
J. G.
Buff
,
J. Chem. Phys.
19
,
774
(
1951
).
16.
A. P.
Lyubartsev
and
A.
Laaksonen
,
Phys. Rev. E
55
,
5689
(
1997
).
17.
D.
Beglov
and
B.
Roux
,
J. Chem. Phys.
100
,
9050
9063
(
1994
).
18.
J.
Åqvist
,
J. Phys. Chem.
94
,
8021
(
1990
).
19.
C. S.
Babu
and
C.
Lim
,
J. Phys. Chem.
110
,
691
699
(
2006
).
20.
D. A.
Pearlman
,
D. A.
Case
,
J. W.
Caldwell
,
W. S.
Ross
,
T. E.
Cheatham
,
S.
DeBolt
,
D.
Ferguson
,
G.
Seibel
, and
P.
Kollman
,
Comput. Phys. Commun.
91
,
1
41
(
1995
).
21.
T.
Bastug
and
S.
Kuyucak
,
Chem. Phys. Lett.
424
,
82
85
(
2006
).
22.
T.
Bastug
and
S.
Kuyucak
,
Biophys. J.
90
,
3941
3950
(
2006
).
23.
M.
Patra
and
M.
Karttunen
,
J. Comput. Chem.
25
,
678
(
2004
).
24.
M.
Fyta
and
R. R.
Netz
,
J. Chem. Phys.
136
,
124103
(
2012
).
25.
M. B.
Gee
 et al,
J. Chem. Theory Comput.
7
,
1369
(
2011
).
26.
B. R.
Brooks
,
R. E.
Bruccoleri
,
B. D.
Olafson
,
D. J.
States
,
S.
Swaminathan
, and
M.
Karplus
,
J. Comput. Chem.
4
,
187
(
1983
).
27.
J. R.
Grigera
,
H. J. C.
Berendsen
, and
T. P.
Straatsma
,
J. Phys. Chem.
91
,
6269
(
1987
).
28.
J. P.
Ryckaert
,
G.
Ciccotti
, and
H. J. C.
Berendsen
,
J. Comput. Phys.
23
,
327
341
(
1977
).
29.
T. P.
Straatsma
and
J. A.
Mccammon
,
Ann. Rev. Phys. Chem.
43
,
407
435
(
1992
).
30.
H. J. C.
Berendsen
,
D.
van der Spoel
, and
R.
van Drunen
,
Comput. Phys. Commun.
91
,
43
(
1995
).
31.
E.
Lindahl
,
B.
Hess
, and
D.
van der Spoel
,
J. Mol. Model.
7
,
306
(
2001
).
32.
T.
Darden
,
D.
York
, and
L.
Pedersen
,
J. Chem. Phys.
98
,
10089
10092
(
1993
).
33.
H. J. C.
Berendsen
,
J. P. M.
Postma
,
W. F.
van Gunsteren
,
A.
DiNola
, and
J. R.
Haak
,
J. Chem. Phys.
81
,
3684
(
1984
).
34.
M.
Fyta
,
I.
Kalcher
,
L.
Vrbka
,
J.
Dzubiella
, and
R. R.
Netz
,
J. Chem. Phys.
132
,
024911
(
2010
).
35.
D.
Horinek
,
S. I.
Mamatkulov
, and
R. R.
Netz
,
J. Chem. Phys.
130
,
124507
(
2009
).
36.
G.
Hummer
,
L.
Pratt
,
A.
Garcia
,
B.
Berne
, and
S.
Rick
,
J. Phys. Chem. B
101
,
3017
(
1997
).
37.
M.
Rami Reddy
and
M. L.
Berkowitz
,
Chem. Phys. Lett.
155
,
173
(
1989
).
38.
T.
Darden
,
D.
Pearlman
, and
L. G.
Pedersen
,
J. Chem. Phys.
109
,
10921
(
1998
).
39.
G.
Hummer
,
L.
Pratt
, and
A.
Garcia
,
J. Phys. Chem.
100
,
1206
(
1996
).
40.
G.
Lee Warren
and
S.
Patel
,
J. Chem. Phys.
127
,
064509
(
2007
).
41.
M. D.
Tissandier
,
K. A.
Cowen
 et al,
J. Chem. Phys.
102
,
7787
7794
(
1998
).
42.
Y.
Marcus
,
Ion Properties
(
Marcel Dekker
,
New York, Basel
,
1997
).
43.
L. X.
Dang
and
D. E.
Smith
,
J. Chem. Phys.
99
,
6950
6956
(
1993
).
44.
S.
Weerasinghe
and
P. E.
Smith
,
J. Chem. Phys.
119
,
11342
(
2003
).
45.
A.
Ben-Naim
,
Statistical Thermodynamics for Chemists and Biochemists
(
Plenum
,
New York
,
1992
).
46.
A. P.
Lyubartsev
and
S.
Marcelja
,
Phys. Rev. E
65
,
041202
(
2002
).
47.
B.
Hess
and
N. A. F.
van der Vegt
,
Proc. Natl. Acad. Sci. U.S.A.
106
,
13296
13300
(
2009
).
48.
K. D.
Collins
,
Biophys. J.
72
,
65
76
(
1997
).
49.
R. A.
Robinson
and
R. H.
Stokes
,
Electrolyte Solutions
, 2nd ed. (
Dover
,
New York
,
2002
).
50.
J. P.
Simonin
,
S.
Krebs
, and
W.
Kunz
,
Ind. Eng. Chem. Res.
45
,
4345
4354
(
2006
).
51.
W.
Kunz
,
Specific Ion Effects
, 1st ed. (
World Scientific
,
Singapore
,
2010
).
52.
N.
Schwierz
and
R. R.
Netz
,
Langmuir
28
,
3881
3886
(
2012
).
53.
R. G.
Pearson
,
J. Am. Chem. Soc
107
,
6801
6806
(
1985
).
54.
V. M.
Lobo
,
Pure Appl. Chem.
65
,
2613
2640
(
1993
).
55.
See supplementary material at http://dx.doi.org/10.1063/1.4772808 for Table of solvation free energies, corresponding correction terms and mean square displacement of ions.

Supplementary Material

You do not currently have access to this content.