A multistate empirical valence bond model for solvation and transport
simulations of OH?in aqueous solutions
Ivan S. Ufimtsev,waAndrey G. Kalinichev,*bTodd J. Martinezw*aand
R. James Kirkpatrickc
Received 20th April 2009, Accepted 12th August 2009
First published as an Advance Article on the web 27th August 2009
We describe a new multistate empirical valence bond (MS-EVB) model of OH?in aqueous
solutions. This model is based on the recently proposed ‘‘charged ring’’ parameterization for the
intermolecular interaction of hydroxyl ion with water [Ufimtsev, et al., Chem. Phys. Lett., 2007, 442, 128]
and is suitable for classical molecular simulations of OH?solvation and transport. The model
reproduces the hydration structure of OH?(aq) in good agreement with experimental data and the
results of ab initio molecular dynamics simulations. It also accurately captures the major
structural, energetic, and dynamic aspects of the proton transfer processes involving OH?(aq).
The model predicts an approximately two-fold increase of the OH?mobility due to proton
Proton exchange reactions are at the core of acid and base
chemistry and play crucial roles in aqueous processes involving
charged defect migration of hydronium (H3O+) and hydroxide
(OH?) ions. In biology, proton transport through protein
channels is a key element of cellular energetics.1–3In electro-
chemistry, cross-membrane proton diffusion is the principal
element of fuel cell operation.4–6In geochemistry and environ-
mental chemistry, proton exchange reactions at mineral–water
interfaces are important factors controlling mineral dissolution
and precipitation, binding and transport of contaminants in soil
and water.7–9The well known abnormally high diffusion rate of
these charge defects10,11is attributed to the so-called Grotthus-
type mechanism involving successive proton exchange events
between neighboring water molecules rather than simple
ion diffusion.12–17Numerous theoretical and experimental
investigations of H3O+diffusion in acidic solution provide a
consistent picture of this process,15–41in which the excess
proton diffuses through successive interconversions between
solvated H3O+(H2O)3 and (H2O???H???OH2)+structures,
known as Eigen42and Zundel43ions, respectively. This
mechanism is now reliably confirmed by both accurate ab initio
calculations and by less computationally demanding but larger
semi-classical molecular dynamics (MD) simulations.38In
striking contrast, the diffusion of the OH?ion in basic aqueous
solutions, which is of no less importance, has historically
attracted much less attention, because it is usually assumed
to be simply a ‘‘mirror representation’’ of the H3O+transport,
with the OH?ion having predominantly three H2O molecules
in the first solvation shell that donate hydrogen bonds to it.
A series of theoretical and experimental studies over the
last decade, however, have called this mechanism into
question14–17,44–65and have produced alternative mechanisms
involving a different OH?coordination scheme and a more
complex solvent reorganization around the ion as the system
approaches the transition state and the ion becomes capable of
recombining with one of the nearest water molecule’s protons
forming a different stable OH?ion.48,66,68Most of these studies
used ab initio molecular dynamics (AIMD) simulations,69,70with
the potential energy of the system calculated using density
functional theory (DFT)71,72with a plane-wave basis set.
In principle, this should lead to an exact solution of the
electronic structure problem, but, unfortunately, the exact
form of the exchange–correlation functional is not known,
and different approximations have been employed in these
calculations. For OH?(aq) systems, different functionals
provide somewhat different OH?solvation structures leading
to noticeably different diffusion mechanisms. For example, the
PW91 and PBE functionals result in mostly 3-coordinated
OH?(aq),67,68whereas the BLYP functional results in a higher
average coordination between 3 and 4,48and the HCTH
functional results in predominantly 4-coordination.48
In addition to the problem of exchange–correlation
computationally very demanding and, consequently, can handle
only relatively small systems on picosecond time scales. The
study of larger systems of biological and geochemical importance
still requires reliance on empirical force fields that can treat
proton exchange reactions in at least an approximate manner.
For H3O+in water, a series of such force fields involving
multistate, empirical valence bond (MS-EVB) potentials21,26–35
have been successful in reproducing solvation structures
simulations and in producing ion mobilities consistent with
aDepartment of Chemistry, University of Illinois at Urbana-Champaign,
Urbana, IL 61801. E-mail: Todd.Martinez@stanford.edu
bDepartment of Chemistry, Michigan State University, East Lansing,
MI 48824. E-mail: firstname.lastname@example.org
cCollege of Natural Science, Michigan State University,
East Lansing, MI 48824
w Present address: Department of Chemistry, Stanford University,
Stanford, CA 94305.
9420 | Phys. Chem. Chem. Phys., 2009, 11, 9420–9430This journal is ? c the Owner Societies 2009
PAPERwww.rsc.org/pccp | Physical Chemistry Chemical Physics
Following this methodology, we present here an MS-EVB
force field for solvation and transport simulations of OH?in
aqueous solution. The force field is built around our recently
proposed ‘‘charged ring’’ (CR) OH?model, which accurately
represents the three delocalized lone electron pairs14,38,49,50of
the oxygen atom.73The CR model corrects the major defect of
traditional point charge OH?(aq) models typically used in
classical molecular simulations, which inaccurately predict
that OH?accepts predominantly five to six hydrogen bonds.
Both neutron diffraction data54–58and AIMD calculations14,48
show much smaller coordination numbers. Although the
dielectric relaxation data for dilute NaOH solutions have been
earlier interpreted in terms of 5-6-coordinated OH?(aq),74
the dominance of four-coordinated OH?[H2O]4 species in
aqueous solutions is now convincingly supported by X-ray
diffraction,59X-ray adsorption,60FTIR,61and more recent
and photoelectron emission65
spectroscopic data. The ability of the CR model to correctly
reproduce the observable OH?solvation environment without
any unphysical charge scaling58,75makes it an especially good
foundation for the development of an MS-EVB force field
capable of treating the proton exchange reactions in basic
Multistate empirical valence bond model for hydrated
The EVB approach, proposed by Warshel and Weiss,76provides
a computationally efficient way to construct a potential energy
surface (PES) of an atomic system undergoing breaking or
formation of chemical bonds, where standard methods of
classical molecular mechanics (MM) fail to reliably describe
energetic and structural properties of the system.
In the MS-EVB model, the electronic structure of a
chemically reactive system is described by a superposition of
K orthogonal diabatic states |fki, k = 1,...,K:
where Q represents the coordinates of atomic nuclei at any
given moment of time. Each diabatic state |fki can be
completely identified by explicitly specifying all atoms constituting
the ion and the solvent water molecules, or in other words, the
After all relevant EVB states are identified, the Hamiltonian
is constructed as
and the ground state potential energy of the system, E0, is
determined as the smallest eigenvalue of the EVB Hamiltonian
HEVB(Q)c(Q) = Ec(Q).(3)
The corresponding normalized eigenvector c(Q) identifies the
MS-EVB electronic ground state |C0(Q)i (eqn (1)), and
the EVB contribution to the atomic energy gradient is given
by the Hellman–Feynman theorem:
FEVB(Q) = hC0(Q)|–rHEVB(Q)|C0(Q)i.(4)
This EVB method was originally applied to the migration of
an excess proton shared by two water molecules in a Zundel
ion, H5O2+, with only two EVB states used to construct the
2 ? 2 Hamiltonian matrix.30Later, the model was extended to
include an arbitrary number of different states, thereby allowing
the proton to diffuse across a three-dimensional hydrogen
bonding network in liquid water.26–29,31–35In addition, several
potentials were developed which included solvent polarization
effects induced by the excess proton.21,77
Fig. 1 illustrates how different EVB states are constructed
for the case of a hydrated OH?ion. State |1i represents the
initial state of the system. The other 5 states are then generated
through a series of virtual proton transfers to (state |2i) and
in the first solvation shell are included. This procedure can be
repeated recursively for the second, third, etc. H2O solvation
shells, until, ideally, all water molecules in the system
are considered as possible
corresponding diabatic states. In practice, however, the
computational costs grow rapidly with the number of
states under consideration, and only those states that make
significant contributions to the resulting potential energy
surface are usually taken into account. A set of heuristic
criteria can be applied to determine which states should be
included to the EVB Hamiltonian matrix. In many cases,
the criteria are essentially the same as those commonly
ions, generating the
accepting four H-bonds from the nearest water molecules and
donating one H-bond to another water molecule. Red balls—oxygen
atoms, blue balls—hydrogen atoms.
The first six possible diabatic EVB states for OH?(aq)
This journal is ? c the Owner Societies 2009 Phys. Chem. Chem. Phys., 2009, 11, 9420–9430 | 9421
58 S. E. McLain, S. Imberti, A. K. Soper, A. Botti, F. Bruni and
M. A. Ricci, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 74,
59 T. Megyes, S. Ba ´ lint, T. Gro ´ sz, T. Radnai, I. Bako ´ and P. Sipos,
J. Chem. Phys., 2008, 128, 044501.
60 C. D. Cappa, J. D. Smith, B. M. Messer, R. C. Cohen and
R. J. Saykally, J. Phys. Chem. A, 2007, 111, 4776–4785.
61 M. Smiechowski and J. Stangret, J. Phys. Chem. A, 2007, 111,
62 C. Petersen, J. Thogersen, S. K. Jensen and S. R. Keiding, J. Phys.
Chem. A, 2007, 111, 11410–11420.
63 W. H. Robertson, E. G. Diken, E. A. Price, J. -W. Shin and
M. A. Johnson, Science, 2003, 299, 1367–1372.
64 J. Thøgersen, S. K. Jensen, C. Petersen and S. R. Keiding, Chem.
Phys. Lett., 2008, 466, 1–5.
65 E. F. Aziz, N. Ottosson, M. Faubel, I. V. Hertel and B. Winter,
Nature, 2008, 455, 89–91.
66 N. Agmon, Chem. Phys. Lett., 2000, 319, 247–252.
67 D. D. Asthagiri, L. R. Pratt, J. D. Kress and M. A. Gomez, Chem.
Phys. Lett., 2003, 380, 530–535.
68 D. Asthagiri, L. R. Pratt, J. D. Kress and M. A. Gomez, Proc.
Natl. Acad. Sci. U. S. A., 2004, 101, 7229–7233.
69 R. Car and M. Parrinello, Phys. Rev. Lett., 1985, 55, 2471–2474.
70 W. Andreoni and A. Curioni, Parallel Computing, 2000, 26,
71 P. Hohenberg and W. Kohn, Phys. Rev., 1964, 136, B864–B871.
72 W. Kohn and L. J. Sham, Phys. Rev., 1965, 140, A1133–A1138.
73 I.S. Ufimtsev,A.G. Kalinichev,
R. J. Kirkpatrick, Chem. Phys. Lett., 2007, 442, 128–133.
74 R. Buchner, G. Hefter, P. M. May and P. Sipos, J. Phys. Chem. B,
1999, 103, 11186–11190.
75 M. G. Campo and J. R. Grigera, Mol. Simul., 2004, 30, 537–542.
76 A. Warshel and R. M. Weiss, J. Am. Chem. Soc., 1980, 102,
77 S. Walbran and A. A. Kornyshev, J. Chem. Phys., 2001, 114,
78 A. D. Becke, Phys. Rev. A: At., Mol., Opt. Phys., 1988, 38,
79 C. Lee, W. Yang and R. C. Parr, Phys. Rev. B: Condens. Matter
Mater. Phys., 1988, 37, 785–789.
80 H. S. Lee and M. E. Tuckerman, J. Chem. Phys., 2006, 125,
81 H. S. Lee and M. E. Tuckerman, J. Chem. Phys., 2007, 126,
82 M. Sprik, J. Hutter and M. Parrinello, J. Chem. Phys., 1996, 105,
83 D. Svozil and P. Jungwirth, J. Phys. Chem. A, 2006, 110,
84 L. X. Dang and B. M. Pettitt, J. Phys. Chem., 1987, 91, 3349–3354.
85 J. Anderson, J. J. Ullo and S. Yip, J. Chem. Phys., 1987, 87,
86 M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert,
M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga,
K. A. Nguyen, S. J. Su, T. L. Windus, M. Dupuis and
J. A. Montgomery, J. Comput. Chem., 1993, 14, 1347–1363.
87 CRC Handbook of Chemistry and Physics, ed. D. R. Lide,
CRC Press, Boca Raton, FL, 87th edn, 2006, pp. 8–71.
88 A. Luzar and D. Chandler, Phys. Rev. Lett., 1996, 76, 928–931.
89 CRC Handbook of Chemistry and Physics, ed. D. R. Lide,
CRC Press, Boca Raton, FL, 87th edn, 2006, pp. 5–77.
90 S. Meiboom, J. Chem. Phys., 1961, 34, 375–388.
91 Z. Luz and S. Meiboom, J. Am. Chem. Soc., 1964, 86, 4768–4769.
92 S. T. Roberts, P. B. Petersen, K. Ramasesha, A. Tokmakoff,
I. S. Ufimtsev and T. J. Martinez, Proc. Natl. Acad. Sci. U. S. A.,
2009, 106, 15154–15159.
93 C. D. Wick and L. X. Dang, J. Phys. Chem. A, 2009, 113, 6356–6364.
94 S. C. L. Kamerlin, J. Cao, E. Rosta and A. Warshel, J. Phys.
Chem. B, 2009, 113, 10905–10915.
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