MOLECULAR PHYSICS, 20 May 2003, VOL. 101, NO. 10, 1501–1510
Solvation properties of Li+ and Cl in water: molecular dynamics
simulation with a non-rigid model
ZHENHAO DUAN1,2* and ZHIGANG ZHANG1
1
Chinese Academy of Sciences, Institute of Geology and Geophysics,
Beijing 100029, China
2
Department of Chemistry, 0340, University of California, San Diego, La Jolla,
CA 92129, USA
(Received 18 December 2002; revised version accepted 5 February 2003)
Molecular dynamics (MD) simulations were carried out to investigate the solvation properties
of Li+ and Cl ions in water with a relatively accurate but rarely used non-rigid model,
RWK2, in this study. A new set of ion–water interaction parameters was evaluated from the
experimental data and first principles calculation results of stable clusters, Li+(H2O)n (n ¼
1–6) and Cl(H2O)n (n ¼ 1–4). With the ion–water potential parameters evaluated from the
data of the clusters and the water–water potential predetermined from the non-rigid RWK2
model, the structural (radial distribution functions, angular distribution functions, spatial
distribution functions, coordination number), dynamical (residence time) and energetic
properties of the ionic solvations in bulk water were studied through a comprehensive analysis
of our MD simulation outputs. These results not only agree well with experimental data and
first principles calculations, but also reveal some new insights into the microscopic ionic
solvation processes.
1. Introduction
Ionic solvation is a fundamental property of aqueous
electrolyte solutions associated with biological and
chemical processes. The knowledge of ionic solvation
structure, the dynamics of water molecules around ions
and the interaction energy of ions with water are of great
importance for the deep understanding of microscopic
mechanisms such as DNA stability [1] and the speciation
of ore-forming elements in hydrothermal processes [2].
There are generally three approaches to the study of ion
solvations: experimental measurements, first principles
molecular dynamics simulation and classical molecular
dynamics simulation.
Extensive experimental work (such as X-ray and
neutron diffraction) has been carried out to derive the
ionic solvation structure, the energy and the coordination number of water molecules around ions over the
past 30 years. These works were comprehensively
reviewed in [3]. However, experimental techniques
often yield an incomplete description of ionic solvation
or hydrogen bonding [4] because of such difficulties as
the lack of suitable isotope substitutions in neutron
diffraction, or the difficulties in separating the atomic
correlations of different species in diffraction tests.
Usually experiments are carried out in such high
*Author for correspondence. e-mail: duanzhenhao@yahoo.
com
concentration solutions that ion–ion interactions may
significantly alter the solvation structure [5]. Thus the
solvation mechanism of ions in dilute systems must be
an approximate extrapolation from concentrated solution measurements.
Recently first principles (FP) molecular dynamics
(MD) calculations have played an important role in the
study of microscopic properties [5–9]. These simulations
have led to a much better understanding of the solvation
mechanism. However, FP calculations are about 4000
times slower than the classical MD simulation. This
prevents many researchers from studying relatively large
systems. Most researchers still use a system size of less
than 100 water molecules with a less than 5 ps period of
molecular motions. Such a small system size may be too
small to reproduce meaningful properties in bulk. A few
picoseconds of molecular motion time may be insufficient for collecting dynamic data under the equilibrium
state. For example, the residence time of water molecules around an ion can be several dozens of picoseconds or longer; a time of a few picoseconds is obviously
too short to study the residence time and the equilibrium
process between the ion and the water molecules.
In addition, it is usually hard to estimate the quantitative
accuracy in the structural and thermodynamic properties calculated by FP calculations. In many cases,
the classical simulation can reproduce experimental
data with an accuracy not much different from FP
Molecular Physics ISSN 0026–8976 print/ISSN 1362–3028 online # 2003 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/0026897031000099907
1502
Z. Duan and Z. Zhang
calculations as long as the interaction potential is well
parameterized. Therefore, the simulations based on the
pairwise additive potentials are still justified.
In this study, we carry out MD simulations to
investigate the solvation properties of Li+ and Cl
ions in bulk water with a non-rigid model for water–
water interactions and an ion–water interaction model
evaluated from the data of ion–water clusters. In the
past, researchers employed rigid water molecule models
to simulate various bulk properties. However, some
results [10, 11] indicate that intramolecular forces
markedly modified the liquid structure and the liquid–
vapour equilibrium and that flexible potentials yield
better predictions. The non-rigid water potential model
RWK2 (Reiners, Watts and Klein, 1982) yields remarkably good predictions of steam, liquid water and ice, and
liquid–vapour phase equilibria but receives much less
attention [11]. Through this study, we should like to find
the Li+ and Cl solvation structure, the coordination
number of water molecules around the ions, the
solvation energy and the solvation dynamics at different
temperatures and pressures. We present this article as
follows. The predetermined water–water potential
RWK2 and the evaluation of the ion–water potential
will be introduced in Section 2. With the interaction
potentials determined, the ion solvation properties in
water clusters are investigated, as reported in Section 3.
The ion solvation properties in bulk water predicted by
MD simulation are discussed in Section 4. Finally,
conclusions are drawn in Section 5.
2. Interaction potential
The interaction potential plays a crucial role in the
results of MD simulations. There are three kinds of
interaction in the water–salt binary solutions: water–
water, water–ion and ion–ion interactions. Since our
objective in this study is to find the single-ion solvation
behaviour, the ion–ion interactions can be ignored here.
Over the past two decades, more than 30 water
potential models have been proposed to simulate water
properties. They can be approximately classified into
three categories [12]: pairwise two-body additive rigid
models (e.g. SPC/E [13, 14], TIP4P [15], ST2 [16]),
pairwise additive non-rigid models (e.g. RWK2 [17]),
and models which explicitly include the effects of polarization and many-body effects. Although the polarization
models are theoretically sound, they have in general not
led to more accurate predictions than the two-body
potentials in the prediction of such important properties
as liquid–vapour phase equilibria [11]. The rigid twobody potentials have found wide use in the study of
microscopic liquid structure and thermodynamic properties. However, some research results suggest that flexible
models, which allow intramolecular motions, are
Table 1.
Interaction
Li+–H2O
Cl–H2O
Parameters for the water–ion
interaction.
"IW
(kJ mol 1)
0.3108
0.5187
IW (Å)
2.72
3.635
superior in the prediction of mean force potential and
vapour–liquid equilibria [10, 11]. Therefore, we choose
RWK2, which predicts gas, liquid and ice properties with
remarkable accuracy for the water–water interactions in
this study. The RWK2 potential function and its
parameters can be found in the appendix of [18].
The ion–water interaction can be modelled in two
parts:
uIW ¼ uCoulomb
þ uShort
IW
IW ,
ð1Þ
where I denotes an ion, W stands for a water molecule,
uCoulomb
represents the Coulombic interaction and uShort
IW
IW
is the short-range interaction.
In the Coulombic interaction, the partial charges for
oxygen and hydrogen atoms are: 2qH ¼ qO ¼ 1.2,
which are consistent with the RWK2 model.
The pairwise potential function for the short-range
interaction is modelled as the Lennard-Jones (LJ) form:
"
12 6 #
IW
IW
LJ
uShort
,
ð2Þ
IW ¼ uIW ðrIW Þ ¼ 4"IW
rIW
rIW
where rIW is the distance between the centre of the ion
and the partial negative charge of the water molecule (its
position can be found on the bisector of the HOH angle,
see the appendix of [18]); "IW and IW are the energy and
size parameters, respectively.
Using a trial and reducing error procedure, the
parameters (table 1) for the Li+–H2O and Cl–H2O
interaction potentials are best obtained by reproducing
the binding energy of one ion associated with two- or
three-water-molecule clusters, since the multi-body
interactions need to be taken into account for the
study of bulk properties.
3. The solvation properties of clusters
The minimum energy structures of the clusters
Li+(H2O)n (n ¼ 1–6) and Cl(H2O)n (n ¼ 1–4), were
obtained from MD simulated annealing and the steepest
descent method [12]. The initial configuration was
generally taken from a previous simulation. The system
was annealed gradually with a scaling factor
(Ti+1/Ti ¼ 0.90). When the temperature reached a few
kelvins, we quenched the systems to 0 K with the
steepest descent method and obtained the minimum
Solvation properties of Li+ and Cl in water
energy structures. It is found from our simulation that
different initial configurations may generate several
stable isomers with little energy differences. These
isomers are all possible minimum energy structures
occurring in the real physical world and each contributes
to the probability distribution of the cluster according to
its Boltzmann factor [19].
The enthalpy (H ) of the formation of a cluster at a
specific temperature T can be calculated from:
H ¼ U þ pV ¼ Ucluster Uintra nRT,
ð3Þ
where Ucluster is the internal energy of the cluster, n is the
number of water molecules and R is the ideal gas
constant. Uintra is the intramolecular energy of water
molecules and is always a very small variable with a
magnitude of 104 kJ mol1 in the minimum energy
structure (in the rigid model, it is actually equal to zero),
so it can be ignored in the calculations.
-20
Energy (kcal/mol)
-40
-60
-80
-100
Simulated
Exp.
-120
-140
0
1
2
3
4
5
6
7
Number of water molecules
Figure 1. Simulated enthalpies of Li+(H2O)n and corresponding experimental data [20] (1 kcal ¼ 4.18 kJ).
Table 2.
1503
3.1. Li+–(H2O)n
Figure 1 and table 2 show the simulated enthalpies
and structures of stable Li+(H2O)n (n ¼ 1–6) clusters.
In general, our simulated results agree well with the
experimental data [20] with deviations of less than 5%,
except for the one-water cluster, Li+(H2O), with a
deviation of 15%. We could fit the potential parameters
to the one-water cluster data with an error of less than
5%. However, our objective is to find the ion solvation
properties in the bulk water, where more than one water
molecule surrounds the ion, and thus we fit the effective
pair potential to the multi-water cluster data. The
simulated distances between Li+ and oxygen in different
clusters, rLi–O, vary from 1.84 to 1.92 Å (table 2), except
for the long distance of rLi–O in Li+(H2O)5 or
Li+(H2O)6. These results are consistent with the results
of quantum calculations [9].
The stable minimum energy structures of Li+(H2O)n
clusters are displayed in table 2. Li+(H2O)2 is linear,
Li+(H2O)3 is triangular planar, Li+(H2O)4 is a tetrahedron, Li+(H2O)5 is a trigonal bipyramid, and
Li+(H2O)6 is an octahedron. These structures are
consistent with the results of prior workers [19] and
quantum mechanical calculations [9].
3.2. Cl(H2O)n
Table 3 shows the possible stable structures for
Cl(H2O)n (n ¼ 1–4) clusters. It can be seen that multiwater clusters, Cl (H2O)n (n > 2), generally have two
isomers: a symmetric ion-centred structure and an
asymmetric pyramidal structure. The symmetric ioncentred structures always have slightly higher energies
than the corresponding asymmetric pyramidal structures. These calculated energies are very close to the
experimental results [20]. The ion–oxygen distances,
rCl–O, for different clusters are also listed in table 3,
showing the close agreement with the quantum simulation results [9].
Structures and energies of Li+(H2O)n.
(a) n ¼ 1
(b) n ¼ 2
(c) n ¼ 3
(d) n ¼ 4
(e) n ¼ 5
(f ) n ¼ 6
120.8
142.2
1.84
1.86
235.5
250.1
1.84
1.87
339.7
336.7
1.87
1.90
426.7
405.3
1.91
1.94
485.6
463.5
1.92, 3.60
2.02
542.5
514.1
1.92, 3.63
2.08
Geometry
Enthalpy
(kJ mol 1)
rLi–O (Å)
Simulated
Exp. [20]
Simulated
FP [9]
1504
Z. Duan and Z. Zhang
Table 3.
Structures and energies of Cl (H2O)n.
(b) n ¼ 2
(c) n ¼ 3
(d) n ¼ 4
(a) n ¼ 1
I
II
I
II
I
II
51.9
54.8
3.24
3.30
108.3
107.9
3.24, 3.42
—
102.1
107.9
3.24
3.31
171.5
156.9
3.39
—
150.6
—
3.25
3.34
236.3
203.3
3.25, 3.44
—
210.4
203.3
3.23, 3.39, 4.08
3.37
Geometry
Enthalpy
(kJ mol 1)
rCl–O (Å)
Simulated
Exp. [20]
Simulated
FP [9]
I, pyramidal structure; II, symmetric ion-centred structure.
Compared with Li+(H2O)n, Cl(H2O)n clusters are
preferable to the asymmetric pyramidal structures.
According to the analysis in [19], the discrimination
between the ion-centred structure and the pyramidal
structure is directly related to the size of the ion. Smaller
ions tend to have stronger interactions with water
molecules and cause more distortions on the water
clusters. Therefore, a larger ion can accommodate
the pyramidal configuration more easily than a small
ion [19].
4.
The solvation properties of ions in bulk aqueous
solutions
With the interaction potentials determined above, the
solvation properties of Li+ and Cl in bulk water were
studied by canonical ensemble MD simulations. The
simulations were carried out at 298 K and 573 K,
respectively. A total of 230 water molecules and a single
ion are used in the cubic simulation box with a length
of 19.03 Å, which is equivalent to a volume of
18.0 cm3mol1. Another simulation was performed at
573 K and 22.0 cm3 mol1 for the study of pressure
impact on the solvation structure. The conventional
periodic boundary conditions and minimum image
conventions [21] were used in the simulations to treat
out-of-box atoms and to calculate interatom distances.
Long-range electrostatic forces and energies were
calculated with the Ewald sum. In all runs, the time
step was set as 31.25 au or 0.75 fs. Initial configurations
were selected from the final configurations of previous
simulations. Each simulation began with 10 000 step
pre-equilibrium runs followed by 40 000 subsequent
steps for data collection. However, for the study of the
residence time of water molecules around ions, a run of
400 000 steps is carried out for the data collection.
We did not notice an observable difference for the
solvation structure derived between the run of 40 000
steps and the run of 400 000 steps. The trajectories of the
particles were calculated using the Verlet algorithm [21]
and the intermediate configurations were saved at
certain intervals. Through the analysis of the trajectory
configurations as a function of time, the solvation
structures, the coordination number of water molecules
around ions, the solvation energy and the dynamics are
investigated.
4.1. Radial distribution functions and the coordination
number in the ionic solvation shell
Li–oxygen and Li–hydrogen radial distribution functions (rdfs) from our simulations and those from the FP
molecular simulations [7] are shown in figure 2. It is
remarkable that our results are in excellent agreement
with the corresponding FP calculation results. Two
prominent maxima can be found in the Li–oxygen rdf,
indicating that two solvation shells exist. The first
maximum is especially sharp, suggesting that the first
hydration shell is well established in the vicinity of the
lithium ion. The clearly delineated peaks in the Cl–O
and Cl–H radial distribution functions (figure 3) indicate
hydrogen bonding to the chlorine ion, as was found also
by Hanke et al. [22].
Table 4 lists the structural properties of the first
solvation shell from this study and compares them with
the corresponding results from some previously reported
simulations and experiments. Three parameters are used
to describe the characteristics of the first ionic hydration
shell: RIO, RIH and the coordination number. RIO is the
position of the first maximum in the ion–oxygen rdf and
RIH is the corresponding position in the ion–hydrogen
rdf. These two parameters calculated by our program
agree well with the experimental data [26–28].
Furthermore, our results are in good agreement with
the most recent quantum mechanical calculations and
experimental data [7, 29]. As for the coordination
number, various simulations have produced a range of
results from four to six for the lithium ion and from
Solvation properties of Li+ and Cl in water
Table 4.
12
g(r)
8
6
4
2
0
1
2
3
4
5
6
r(A)
Figure 2. Radial distribution functions of Li–O and Li–H
from our simulations and those from the FP simulations
[7] at 298 K.
5
Cl-O
Cl-H
4
Structural properties of the first solvation shell.
Li+
Cl
RIO (Å)
This work
Chandrasekhar et al. [23]
Heinzinger [24]
Mezei and Beveridge [25]
X-ray [26]
Neutron diffractiona
1.93
1.95
2.13
2.10
1.95–2.25
1.95
3.25
3.21
3.22
3.25
3.10–3.35
3.20–3.34
RIH (Å)
This work
Chandrasekhar et al. [23]
Heinzinger [24]
Mezei and Beveridge [25]
Neutron diffractiona
2.62
2.60
2.68
2.70
2.55
2.25
2.25
2.24
2.25
2.22–2.26
Coordination number
This workb
Chandrasekhar et al. [23]b
Heinzinger [24]
Mezei and Beveridge [25]
X-ray [26]
Neutron diffractiona
4.6 (9.2)
4.9 (10.6)
6.1
5.97
4–6
5.5
7.2 (7.4)
7.4 (7.0)
8.2
8.36
5–11
5.3–6.2
Source
Li-O: This work
Li-O: FP results
Li-H: This work
Li-H: FP results
10
1505
a
Reference [27] for lithium and reference [28] for chloride.
On the basis of ion–oxygen rdfs; values for ion–hydrogen
rdfs in parentheses.
b
g(r)
3
2
1
0
0
1
2
3
4
5
6
7
8
9
r(A)
Figure 3.
Radial distribution functions of Cl–O and Cl–H at
298 K.
seven to eleven for the chlorine ion [23–25, 30, 31]. There
also exists a discrepancy between different experiments
with different methods of measurement and different
definitions [32]. In this study the coordination number is
calculated with the most commonly used definition:
Z rmin
h ¼ 4p0
gðrÞr2 dr,
ð4Þ
0
where g(r) is the rdf of ion–oxygen or ion–hydrogen, 0
is the density of water molecules and rmin is the first
minimum position (after the first peak) of the rdf. Two
sets of coordination numbers are reported in table 4
on the basis of the ion–oxygen rdf as well as the
ion–hydrogen rdf (in the parentheses). These coordination numbers compare favourably with experiments
[26–28, 33]. They are also consistent with the MD
simulation results based on non-additive potentials
[34], polarizable model [35] and quasi-chemical organization of solution theory [36].
It can be seen from figures 4 and 5 that temperature
has a striking impact on the ion–oxygen rdf. As the
temperature increases, the first peak decreases significantly but accompanies a broadened width. At the
same time, the intensity of the first minimum increases
and the second peak almost vanishes to the average
bulk distributions at high temperatures. These features
indicate that the hydration shell around ions becomes
less prominent when the temperature increases, as
displayed by figures 4 and 5. However, the coordination number is almost unchanged. This is consistent
with the simulation results of [37] that suggest very
little temperature effect on the hydration number in the
Na+ solvation shell. The impact of pressure on the
solvation structures is found to be small as shown in
figures 6 and 7, which compare the ion–oxygen rdfs
under different pressures (corresponding to two different volumes and pressures: 18.0 cm3 mol1 (4966 bar)
and 22.0 cm3 mol1(714 bar)). In these two figures, the
curves of rdf remain almost unchanged for different
pressures except for a small difference in the intensities
of the first peaks. In fact, the calculated coordination
number (using equation (4)) remains the same when the
1506
Z. Duan and Z. Zhang
12
573K
298K
10
n(r)
30
4.0
25
3.5
3.0
20
6
15
4
10
2.5
g(r)
g(r)
n(r)
8
g(r)
18 cm3/mol
22 cm3/mol
2.0
1.5
2
0
0
1
2
3
4
5
6
7
8
5
1.0
0
0.5
9
r(A)
Figure 4.
0.0
Li–O radial distribution function and coordination
number at 298 K and 573 K.
0
1
2
3
4
5
6
7
8
9
r (A)
Figure 7. The Cl–O radial distribution functions at two
different volumes (18 cm3 mol1 and 22 cm3 mol1).
5
50
573K
298K
4
pressure increases (equivalent to the decreasing of the
volume).
40
n(r)
n(r)
30
g(r)
3
g(r)
2
20
1
10
0
0
0
1
2
3
4
5
6
7
8
9
r(A)
Figure 5.
Cl–O radial distribution function and coordination number at 298 K and 573 K.
10
18 cm3/mol
22 cm3/mol
8
g(r)
6
4
2
0
0
1
2
3
4
5
6
7
8
9
r(A)
Figure 6. The Li–O radial distribution functions at two
different volumes (18 cm3 mol1 and 22 cm3 mol1).
4.2. Angular structural properties in the ionic
hydration shell
Although the widely used radial distribution function
can provide useful insights into solvation structures,
it only reveals the two-body structural information
and the important properties involving orientations
and angular distributions may be lost by averaging.
A straightforward way to get more detailed structural
information of the ionic hydration shell is through the
study of the probability distributions of some angular
properties. These distributions reveal the rigorous
probability densities over the entire angular range.
As an example, figure 8 shows two kinds of angular
distributions in the first hydration shell of the lithium
ion. It can be seen that there are two maxima in the
O–Li–O angle distribution: the first is centred around
105 with a fluctuation of about 30 and the second
around 170 with a smaller fluctuation of about 10 . The
distribution of the dipole–ion angle, which is defined as
the angle between the HOH bisector and the direction
from oxygen to ion (as illustrated in figure 8), indicates
that the lithium ion lies around 160–165 away from the
HOH bisector with the most probability.
In order to present a more vivid image of the spatial
distribution of the hydration shell, we used a convenient
routine, the spatial distribution function (sdf ), which is
a three-dimensional function with a definition mentioned in [38]. This function can be visualized into
impressive graphics by some well-established software
such as the gOpenMol package [38, 39]. Figure 9 shows
the sdf of the lithium ion relative to a water molecule in
the first hydration shell. The origin of the local
Solvation properties of Li+ and Cl in water
1507
0.07
0.06
O-Li-O angle
Dipole-ion angle
Distribution
0.05
0.04
+
O
Li
H
0.03
Dip
H
ole
-io
n
0.02
an
gle
0.01
0.00
0
20
40
60
80
100
120
140
160
180
Angle
Figure 10. Spatial distribution of water molecules relative to
the Li+ ion in the first hydration shell. A coordinate
system is introduced where the ion defines the origin, one
oxygen of the hydration shell water molecules defines the
z-axis, and a second such oxygen defines the xz-plane.
Figure 8. Distribution of the O–Li–O angle and the dipole–
ion angle of Li–water in the first hydration shell at 298 K.
0.08
O-Cl-O Angle
Dipole-ion Angle
0.07
-
Cl
H
0.05
O
H
Di
n
-io
le
po gle
an
Distribution
0.06
0.04
0.03
0.02
0.01
þ
Figure 9. Spatial distribution of the Li ion relative to a
water molecule in the first hydration shell. The origin of
the local coordinate system lies on the centre of the
oxygen atom, the HOH bisector defines the x-axis and the
water molecule plane defines the xz-plane.
coordinate system lies on the centre of the oxygen atom,
the HOH bisector defines the x-axis and the water
molecule plane defines the xz-plane. In this figure, dark
shading indicates high intensity of the sdf and grey
corresponds to lower intensity. It can be found that the
maximum of the lithium ion distribution lies approximately on the plane perpendicular to the water molecule
plane.
Figure 10 shows the sdf of water molecules in the first
hydration shell relative to the Li+ ion. This figure
provides a more impressive image of the strucuture of
the first hydration shell of the lithium ion. Here is
introduced a coordinate system where the ion defines the
origin, one of the oxygens in the hydration shell defines
the z-axis, and a second oxygen the xz-plane. The two
water molecules defining the frame are plotted as two
oxygen atoms in this figure. We can easily find that four
water molecules in the first hydration shell of the lithium
ion lie around the vertices of a distorted tetrahedron,
which corresponds to the first peak of the O–Li–O
distribution in figure 8. In addition, we can also find
0.00
0
20
40
60
80
100
120
140
160
180
Angle
Figure 11. Distribution of the O–Cl–O angle and the dipole–
ion angle of Cl–water in the first hydration shell at 298 K.
another two smaller areas almost opposite the two axis
oxygen atoms and obviously these areas constitute the
second peak of the O–Li–O distribution in figure 8.
It can be noticed in figure 8 that the intensity of the
second peak is far smaller than that of the first peak,
indicating that these areas can be visited by water
molecules with lower probabilities or shorter residence
times. This will be further demonstrated in the following
analysis on the dynamical residence time of water
molecules.
Similar analysis is made on the hydration shell of
the Cl ion. Figure 11 shows the O–Cl–O angle and
the dipole–ion angle distributions. Compared with the
lithium ion, the hydration shell in the vicinity of the
chlorine ion is not so well featured, which is revealed by
the relatively flat distribution of the O–Cl–O angle.
However, a well-defined peak at around 60 can be
found in the dipole–ion angle distribution. This can
be interpreted from figure 12, which indicates that
the chlorine ion prefers positions approximately in the
1508
Z. Duan and Z. Zhang
Table 5. Average number of acceptors and donators of
hydrogen bonds per water molecule with different
distances from the ions (298 K).
Li+
Distance (Å)
Figure 12. Spatial distribution of Cl ion relative to a water
molecule in the first hydration shell. The local coordinate
system is defined as the same as figure 7.
0.10
+
Donator
Acceptor
Donator
0.118
0.374
1.586
1.785
1.756
1.793
1.765
1.743
1.707
1.707
1.717
1.744
1.763
1.737
0
1.786
1.685
1.723
1.767
1.678
1.706
0
0.863
0.934
1.714
1.739
1.724
1.731
4.0
3.5
0.06
Number of H-bonds
Distribution
Acceptor
0–2
2–3
3–4
4–5
5–6
6–7
7–8
Li
Cl
Bulk
0.08
Cl
0.04
0.02
3.0
2.5
+
Li
Cl
Pure water
0.00
2.0
80
90
100
110
120
130
Angle
1.5
Figure 13. The HOH angle distribution of water in the first
hydration shell of ions and that in the bulk.
direction of the O—H bond of a water molecule in
the first hydration shell, indicating hydrogen bonding to
the chlorine ion.
The use of such a flexible water model permits an
investigation of the influence of an ion on the geometry
of water molecules. Figure 13 demonstrates this
influence by a comparison between the HOH angle in
the first hydration shell of ions and the angle of bulk
water molecules. The effect turns out to be tiny but
measurable: the HOH angles of the water molecules
around the lithium ion are shrunk by about 0.5 while
the negative charge of chlorine increases the HOH angle
by about 1.0 .
4.3. Hydrogen bonding analysis
Hydrogen bonds were evaluated with the conventional geometric criteria: if a hydrogen atom of one
water molecule, A, is within the distance of 3.5 Å of the
oxygen atom of another water molecule, B, and the
H—O H angle is greater than 140.0 , a hydrogen bond
is assigned [5, 40]. We count an ‘acceptor’ for B and a
‘donator’ for A. According to our calculations, the
2
3
4
5
6
7
Distance(A)
Figure 14. Average number of hydrogen bonds per water
molecule with different distances from the ions.
average numbers of acceptors and donators per
molecule in pure water at 298 K have the same value
of 1.73.
Table 5 lists the average number of acceptors and
donators of hydrogen bonds per water molecule with
different distances from the ions at 298 K. From this
table, one can see that the acceptors and donators of
water molecules are distinctly affected by the ions: in the
vicinity of a Li+ ion, the acceptors are significantly
reduced while the donators keep an average value
around that of pure water. On the contrary, a Cl ion
reduces the donators of the water molecules around it.
This can be understood from the sdfs in figures 9 and 12,
which indicate that the position of a hydrogen bond
acceptor is firmly bonded by a positive ion (Li+) while
that of a donator is bonded with a negative ion (Cl).
Figure 14 displays the number of hydrogen bonds as a
function of distances from the ions. The horizontal dot–
dashed line is the average number of hydrogen bonds
per molecule in pure water with a value of 3.47. The
solute ions reduce the number of hydrogen bonds in the
Solvation properties of Li+ and Cl in water
areas close to them. Nevertheless, this influence is only
noticeable when the distance is less than 4.5 Å. Beyond
this distance the numbers of hydrogen bonds remain at
about the same value as in the pure water (3.47), which
indicates that the ions have almost negligible effects on
the hydrogen bonds of water molecules in this region.
4.4. Dynamical residence time
The question of how long a water molecule stays in
the hydration shell is interesting, but is very difficult to
answer with experimental approaches [3] or with short
ab initio simulations. An approximate measurement
with the nuclear magnetic resonance (NMR) spectroscopy technique reveals that the residence time of water
molecules in the first hydration shell of the Li+ ion
should be a little greater than 30 ps [3].
Such a long residence time is obviously originated
from the well-established hydration shell around the
lithium ion. It seems that a water molecule inside the
shell has to overcome a strong energy barrier to
exchange with outside molecules. An analysis of the
dynamical residence time of water molecules in the first
hydration shell over a long (300 ps) MD simulation
shows consistent but somewhat surprising behaviour of
the water molecules. The four water molecules at the
vertices of the distorted tetrahedron (see figure 10) have
a relatively long residence time of 15–57 ps, while
another two molecules in the hydration shell are always
exchanging with the outside molecules frequently, with a
residence time of 1–8 ps.
The chlorine ion has much less influence on water
molecules and in its first hydration shell there are more
residents but none dwells there for a long time. The
lifetime of the water molecule in the first hydration shell
of the chlorine ion varies from 1.0 to 12.0 ps, which is
consistent with the data in [3].
The lifetimes of hydrogen bonds are even shorter. The
average lifetime of a hydrogen bond is less than 0.4 ps.
Occasionally there exists a hydrogen bond that lasts for
a relatively long time of several picoseconds.
4.5. Solvation energies
Solvation energy is defined as the energy for the
process of transferring the solute from the ideal gas
phase into the solvent. It can be obtained from
the simulations on the pure solvent and the dilute
solution [23]:
Esol ¼ Esolution Epure ,
ð5Þ
where Esolution is the configurational energy in the dilute
solution and Epure is the energy of pure water under the
same conditions. Our calculated solvation energies of
lithium ions and chlorine ions in water are
1509
486.5 kJ mol1 and 358.1 kJ mol1, respectively.
These results are in good agreement with the experimental data [41].
5. Conclusion
In this study, the RWK2 model is proven to be able to
predict the solvation structures and dynamical properties of Li+ and Cl ions in water with an accuracy close
to experiments and the first principles calculation
results.
A new set of parameters for ion–water short-range
interaction potentials has been evaluated by fitting
binding energies and geometries of gas-phase clusters
to experimental data. Several stable structures for the
clusters Li+(H2O)n (n ¼ 1–6) and Cl(H2O)n (n ¼ 1–4)
have been obtained. These structures and their corresponding energies are generally in good agreement with
experimental data and quantum mechanical calculation
results.
On the basis of the obtained parameters for the
interaction potentials, the solvations of Li+ and Cl
ions in bulk water have been extensively investigated
with molecular dynamics simulations in this study. The
detailed solvation structures of lithium and chlorine ions
in water have been revealed through the analysis of our
simulation results. These structures are strikingly
influenced by temperature but not much by pressure.
Dynamical properties of water molecules in the hydration shell and the solvation energies have also been
investigated. These results not only agree well with
experimental data and first principles calculation results,
but also disclose some new insights into the microscopic
ionic solvation processes.
We thank Dr Ruth Lynden-Bell and a reviewer for
their constructive suggestions. This work is supported
by Zhenhao Duan’s ‘Hundred Scientists Project’ funds
awarded by the Chinese Academy of Sciences and his
Outstanding Young Scientist funds (#40225008)
awarded by the National Science Foundation of
China. This work is also partially supported by the
National Science Foundation (USA): Ear-0126331.
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