JOURNAL OF CHEMICAL PHYSICS
VOLUME 118, NUMBER 23
15 JUNE 2003
Kirkwood–Buff derived force field for mixtures of acetone and water
Samantha Weerasinghea) and Paul E. Smithb)
Department of Biochemistry, Kansas State University, Manhattan, Kansas 66506-3702
共Received 24 January 2003; accepted 24 March 2003兲
A united atom nonpolarizable force field for the simulation of mixtures of acetone and water is
described. The force field is designed to reproduce the thermodynamics and aggregation behavior of
acetone–water mixtures over the full composition range at 300 K and 1 atm using the enhanced
simple point charge water model. The Kirkwood–Buff theory of solutions is used to relate
molecular distributions obtained from the simulations to the appropriate experimental
thermodynamic data. The model provides a very good description of the solution behavior at low
(x a ⬍0.2) and high (x a ⬎0.8) acetone concentrations. Intermediate compositions display a small
systematic error in the region of highest water self-aggregation, which is removed on using larger
system sizes. In either case, the activity of the solution is well reproduced over the full range of
compositions. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1574773兴
I. INTRODUCTION
The ability to accurately reproduce the properties of different solutes in water using computer simulation will provide an increased understanding of the thermodynamics and
properties of these systems. Acetone 共propanone兲 and water
represent one of the simplest examples of two solvents which
are completely miscible at all mole fractions. Previous experimental studies of mixtures of acetone and water indicate
that water molecules tend to self-aggregate, and that the degree of aggregation displays a maximum around compositions of 0.5 mole fraction.1,2 However, most simulations of
acetone and water mixtures have focused on describing spectroscopic data or characterizing the distribution of hydrogen
bonds within the system.3–5 None have described the aggregation of acetone or water in any detail. Unfortunately, our
preliminary studies with currently available acetone force
fields3,6 suggested that this behavior was poorly reproduced.
Hence, an improved force field for the description of
acetone–water mixtures has been developed and is presented
here. The model is specifically designed to reproduce the
molecular aggregation and thermodynamic properties, in particular, the activity of these mixtures as described by the
Kirkwood–Buff 共KB兲 theory. Other properties are then examined to determine if they are consistent with the experimental data.
The KB theory has been used by many researchers to
investigate the properties of liquid mixtures.7,8 The majority
of these studies extracted the appropriate KB integrals from
the experimental data. Some studies have determined KB
integrals from computer simulations.8 However, to our
knowledge, calculated KB integrals have not been used in
the development of force fields for solution mixtures. The
KB approach is used here, as our previous studies have indicated that the corresponding KB integrals and activity dea兲
Permanent address: Department of Chemistry, University of Ruhuna, Matara, Sri Lanka.
b兲
Electronic mail: [email protected]
0021-9606/2003/118(23)/10663/8/$20.00
rivatives provide a very sensitive test of a particular model,
and the charge distribution, in particular.9,10 This is especially significant as we have found that many of the usual
physical properties which characterize a solution mixture
共densities, diffusion constants, dielectric constants, compressibilities, etc.兲 can be relatively insensitive to changes in
model parameters.10 In addition, the KB integrals also provide a route to the solution activities which are not normally
available during force field development. Using this type of
KB approach, a model for urea/water mixtures was developed which reproduces both the KB data and the usual
physical properties.11 The model correctly describes the experimental degree of urea aggregation,11 which has been
shown to vary significantly between different force
fields.10,12 In contrast to many other force field approaches,
the partial atomic charges were varied during the parameterization to obtain the correct solution thermodynamics as described by the KB theory, rather than determining the appropriate charge distributions from ab initio calculations. The
same KB derived force field 共KBFF兲 approach is used here
for mixtures of acetone and water.
II. METHODS
A. Molecular dynamics simulations
The different acetone solutions were simulated using
classical molecular-dynamics techniques. Several water
models were used 关enhanced simple point charge 共SPC/E兲,13
simple point charge 共SPC兲,14 transferable intermolecular potentials 共TIP3P兲兴,15 although the majority of simulations involved the SPC/E model. All simulations were performed in
the isothermal isobaric 共NpT兲 ensemble at 300 K and 1 atm.
The weak coupling technique16 was used to modulate the
temperature and pressure with relaxation times of 0.1 and 0.5
ps, respectively. All bonds were constrained using SHAKE17
and a relative tolerance of 10⫺4 nm, allowing a 2 fs time
step for the integration of the equations of motion. The particle mesh Ewald technique was used to evaluate electrostatic interactions.18,19 A real space convergence parameter of
10663
© 2003 American Institute of Physics
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10664
J. Chem. Phys., Vol. 118, No. 23, 15 June 2003
S. Weerasinghe and P. E. Smith
3.5 nm⫺1 was used in combination with twin range cutoffs of
0.8 and 1.2 nm, and a nonbonded update frequency of 10
steps. The reciprocal space sum was evaluated on a 403 grid
with ⬇0.1 nm resolution. Initial configurations of the different solutions were generated from a cubic box (L⬇4.0 nm)
of equilibrated water molecules by randomly replacing water
with acetone until the required concentration was attained.
The steepest descent method was then used to perform 100
steps of minimization. This was followed by extensive
equilibration which was continued until all interspecies potential energy contributions displayed no drift with time. Total simulation times were in the 2– 4 ns range, and the final
2–3 ns were used for calculating ensemble averages. Configurations were saved every 0.1 ps for the calculation of
various properties. Diffusion constants were determined using the mean-square fluctuation approach,20 relative permittivities from the dipole moment fluctuations,21 and finite difference compressibilities by performing additional
simulations of 250 ps at 1000 atm. Relaxation times were
obtained after fitting the appropriate correlation function
共first-order Legendre polynomial兲 to a single exponential decay model.22 The excess enthalpy of mixing (H E ) was determined using an established procedure,23,24 with values for the
pure SPC/E water and pure acetone configurational energies
of ⫺46.45 and ⫺25.73 kJ/mol, respectively. Errors 共⫾1␴兲 in
the simulation data were estimated by using two or three
block averages.
B. Kirkwood–Buff theory
The development of the KB theory is described in detail
elsewhere.7,25 The thermodynamic properties of a solution
mixture can be expressed in terms of the KB integrals between the different solution components,25
G i j ⫽4 ␲
冕
⬁
0
关 g ␮i j VT 共 r 兲 ⫺1 兴 r 2 dr.
共1兲
Here, G i j is the KB integral between species i and j, g ␮i j VT (r)
is the corresponding radial distribution function 共RDF兲 in the
grand canonical 共␮VT兲 ensemble, and r is the corresponding
center of mass-to-center of mass distance. The KB integrals
were determined from the simulation data 共NpT ensemble兲
by assuming that,7,24,26
G i j ⫽4 ␲
冕
R
0
2
关 g NpT
i j 共 r 兲 ⫺1 兴 r
dr,
共2兲
where R represents a correlation region within which the
solution composition differs from the bulk composition.7 All
RDFs are assumed to be unity beyond R. Excess coordination numbers are defined as N i j ⫽ ␳ j G i j , where ␳ j ⫽N j /V is
the number density of j particles. A value of N i j greater than
zero indicates an excess of species j in the vicinity of species
i 共over a random distribution兲, while a negative value corresponds to a depletion of species j surrounding i.
For a binary solution consisting of water 共w兲 and acetone
共a兲, a variety of thermodynamic quantities can be defined in
terms of the integrals G ww , G aa , and G aw , and the number
densities 共or molar concentrations兲 ␳ w and ␳ a . The partial
molar volumes of the two components, V̄; the isothermal
compressibility of the solution, ␬ T ; derivatives of the chemi-
cal potential, ␮; derivatives of the acetone molar activity,
a a ⫽y a ␳ a ; and derivatives of the acetone mole fraction (x a )
scale activity coefficients f a , at a pressure 共p兲 and a temperature 共T兲 are given by7
V̄ w ⫽
V̄ a ⫽
1⫹ ␳ a 共 G aa ⫺G aw 兲
␩
,
1⫹ ␳ w 共 G ww ⫺G aw 兲
␩
a aa ⫽
f aa ⫽
冉 冊
⳵ ln a a
⳵ ln ␳ a
冉 冊
⳵ ln f a
⳵ ln x a
⫽1⫹
p,T
⫽⫺
p,T
,
␬ T⫽
冉 冊
⳵ ln y a
⳵ ln ␳ a
␤␨
,
␩
⫽
p,T
共3兲
1
,
1⫹ ␳ a 共 G aa ⫺G aw 兲
␳ w x a 共 G ww ⫹G aa ⫺2G aw 兲
,
1⫹ ␳ w x a 共 G ww ⫹G aa ⫺2G aw 兲
共4兲
共5兲
where
␩ ⫽ ␳ w ⫹ ␳ a ⫹ ␳ w ␳ a (G ww ⫹G aa ⫺2G aw ),
␨ ⫽1
2
), ␤ ⫽1/(RT), and
⫹ ␳ w G ww ⫹ ␳ a G aa ⫹ ␳ w ␳ a (G ww G aa ⫺G aw
R is the gas constant. For real 共stable兲 solutions, the values of
␩, ␨, and a aa must be positive, while f aa must be ⬎⫺1.7
There are no approximations made during the derivation.25
Hence, the KB theory provides a direct relationship between
acetone self-aggregation (N aa ) and acetone activity derivatives through Eqs. 共4兲 and 共5兲, and should provide a good test
of a particular force field. Our previous simulations and others have indicated that a combination of the KB theory and
NpT simulations can provide quantitative information concerning the thermodynamics of solutions.8,9,24,27
Two sets of experimental data exist describing the KB
integrals for acetone–water mixtures.1,2 The two studies used
independent determinations of the solution activities or excess molar Gibbs energies. As the activities are typically the
largest source of error in the KB analysis,1 we have included
both sets of data in our comparison to provide an estimate of
the degree of uncertainty in the experimental data. As a further consistency check, we have also reproduced the data of
Blandamer et al.2 Both sets of experimental data are consistent in their description of the KB integrals for this system
and suggest smaller errors in the integrals than originally
estimated by Matteoli and Lepori.1
C. Parameter development
The experimental geometry for acetone was used to determine equilibrium bond lengths and angles.28 Force constants for the bonded terms were taken from the GROMOS96
force field.29 Nonbonded interactions were described by the
commonly used Lennard-Jones 6-12 potential combined with
a Coulomb potential. Geometric combination rules were
used for both the 6-12 ␴ and ⑀ parameters. The ␴ and ⑀
parameters for the united atom methyl group were taken
from a recent reparametrization of the GROMOS hydrocarbon
force field.30 The remaining ␴ and ⑀ parameters were determined by using the correlation between atomic size and
of
molecular
atomic
hydrid
components
( ␶ i)
polarizabilities,31 as described previously.11 Values of ␶ depend on hybridization and not connectivity. Furthermore, it
was assumed that the form of the dispersion interaction followed the London equation.32 Hence, our values of ␴ ii and
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J. Chem. Phys., Vol. 118, No. 23, 15 June 2003
Force field for acetone-water mixtures
TABLE I. Bonded parameters for KBFF acetone. Potential functions are:
Angles, V ␪ ⫽1/2k ␪ ( ␪ ⫺ ␪ 0 ) 2 and impropers, V ␻ ⫽1/2k ␻ ( ␻ ⫺ ␻ 0 ) 2 . Energies
共force constants兲 are in kJ/mol/rad2, angles in degrees, and distances in nm.
Bond lengths (r 0 ) were constrained.
TABLE II. Nonbonded parameters. Lennard-Jones 6-12 plus Coulomb potential. Geometric mean combination rules were used for both ␴ i j and ⑀ i j .
Model
Bonds
r0
Angles
k␪
␪0
Impropers
k␻
␻0
C—O
0.1222
OuCuCH3
730.0
121.44
CuOuCH3 uCH3
167.36
0.0
CuCH3
0.1507
CH3 uCuCH3
670.0
117.12
Acetone
KBFF
Water
SPC/E
⑀ ii were taken to be proportional to ␶ 1/2
and ␶ i I i , respeci
tively. The scaling factor for ⑀ 共0.0207兲 was determined by
reference to the value of the SPC/E water oxygen, with hybridization dependent ionization potentials (I i ) taken from
Hinze and Jaffe.33 The scaling factor for ␴ 共0.281兲 was taken
from our previous work.11 No charge was assigned to the
united atom methyl group so as to be consistent with the
hydrocarbon reparametrization, and because trial simulations
suggested the KB results were relatively insensitive to small
methyl charges. Consequently, only one parameter, the
carbon/oxygen charge, was varied to obtain the correct density for an acetone/water mixture of 0.5 mole fraction. The
final force field parameters are displayed in Tables I and II,
and a summary of the simulations performed is presented in
Table III. The final dipole moment of acetone was 3.32 D for
the current model compared to the gas phase experimental
value of 2.88.34
III. RESULTS
The final acetone force field is described in Tables I and
II and was used to perform a series of simulations of acetone
and water mixtures covering the full mole fraction concentration range 共Table III兲. It was important to study these mixtures using reasonably large simulation volumes to ensure
that the RDFs displayed no long-range structure 共beyond 1.5
nm or so兲, and that the KB integrals converged to a reasonable plateau value. In addition, a significant simulation time
was required 共1 ns or so兲 to ensure full equilibration of the
10665
Atom
⑀
共kJ/mol兲
␴
共nm兲
C
O
CH3
0.330
0.560
0.8672
0.336
0.310
0.3748
0.565
⫺0.565
0.0
O
H
0.6506
0.0000
0.3166
0.0000
⫺0.8476
0.4238
q
(兩e兩)
systems 共no systematic changes in the RDFs兲, followed by
several ns of simulation to precisely determine the value of
the slowly fluctuating KB integrals.
The RDFs obtained from the x a ⫽0.5 mixture of acetone
and water are displayed in Fig. 1, together with the corresponding KB integrals as a function of integration distance.
The large first peak in the water–water RDF illustrates the
high degree of water self-association observed using the
model. This is further highlighted by the large positive KB
integral for water–water, contrasted by the negative values
for the acetone–acetone and acetone–water KB integrals.
The latter two integrals were well converged at large distances, displaying only small oscillations around their average values. The water–water KB integral was not fully converged for the mixtures with a large degree of water selfaggregation. However, we feel reasonable estimates of the
appropriate values were obtained with the current system
sizes after averaging the KB integrals obtained between R
⫽0.85 and 1.25 nm, which represented approximately one
oscillation in the KB integrals 共see Fig. 1兲. Significant contributions to the water–water KB integral were observed
from the second- and third-solvation shells, as observed in
other systems.8,27 First-shell coordination numbers, as a
function of acetone mole fraction, are presented in Table IV,
and displayed the expected systematic changes with no observed maxima or minima.
The simulated and experimental KB integrals are displayed in Fig. 2 in the form of excess coordination numbers
(N i j ⫽ ␳ j G i j ). The trends in the experimental data were very
well reproduced. Acetone self-association decreased as the
TABLE III. Summary of the molecular-dynamics simulations of acetone/water mixtures. All simulations were
performed at 300 K and 1 atm in the NpT ensemble. Symbols are N i , number of i molecules; x a , acetone mole
fraction; ␳ a , acetone molarity; V, average simulation volume; ␳, mass density; and T sim, total simulation time.
Na
Nw
xa
␳a
共M兲
V
共nm3兲
␳
共g/cm3兲
T sim
共ns兲
0
168
275
396
432
462
500
513
520
2170
1512
1100
594
432
308
125
57
0
0.00
0.10
0.20
0.40
0.50
0.60
0.80
0.90
1.00
0.00
4.34
7.08
10.23
11.19
11.91
12.93
13.29
13.64
65.265
64.333
64.507
64.282
64.114
64.383
64.223
64.066
63.303
0.995
0.954
0.921
0.870
0.851
0.835
0.809
0.799
0.792
2
4
4
4
4
4
4
4
2
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10666
J. Chem. Phys., Vol. 118, No. 23, 15 June 2003
S. Weerasinghe and P. E. Smith
FIG. 1. Radial distribution functions (g i j ) and KB integrals (G i j ) as a
function of distance for the x a ⫽0.5 simulation.
mole fraction of acetone increased. The observed maximum
in the degree of water self-association was reproduced, but
the quantitative agreement was not so good for mole fractions of 0.5 or so. An underestimation of the degree of water
aggregation was observed in this region. The model displayed good agreement with experiment in the low (x a
⬇0.2) and high (x a ⬎0.8) composition regions. In between,
the degree of self-aggregation was underestimated, while the
degree of acetone solvation was overestimated. Further efforts were unable to produce a model which reproduced both
the solution density and KB integrals in the region of x a
⫽0.5 by variation of just the carbon/oxygen charge. Simultaneous variations of the charge and ␴ scale factor for
carbon/oxygen were not investigated here. The reason for the
disagreement observed for the x a ⫽0.1 composition was unclear, but may be related to the poor sampling for G aa at low
acetone mole fractions.
The partial molar volumes, isothermal compressibilities,
and densities as a function of composition are displayed in
Fig. 3. The simulated density was in excellent agreement
with experiment over the whole concentration range, although this appeared to be due to a slight underestimation of
the acetone partial molar volume, in combination with an
overestimation of the water partial molar volumes. The KB
derived compressibility was in excellent agreement with experiment except for some deviation at high acetone mole
fractions. However, lower finite difference compressibilities
were obtained for the same compositions. It is not immedi-
FIG. 2. Excess coordination numbers (N i j ) as a function of acetone mole
fraction (x a ). Lines represent the two sets of experimental data 共from Refs.
1 and 2兲 and crosses correspond to the KBFF model.
ately clear why the two values differ. The KB derived compressibility is difficult to obtain as it is very sensitive to the
value of R for all but very large systems 共see later兲. Alternatively, the finite difference approximation may also lead to
some error for more compressible solvents than water. Nevertheless, the trends in all the properties were very well reproduced.
The solution activity derivatives and corresponding activities are displayed in Fig. 4. The simulated acetone mole
fraction activity coefficient ( f a ) was obtained by assuming
that the excess molar Gibbs energy (G E ) follows a Wilson
equation form,36
␤ G E ⫽⫺x a ln共 x a ⫹c w x w 兲 ⫺x w ln共 x w ⫹c a x a 兲 ,
共6兲
and using the thermodynamic relationship,
f aa ⫽
冉 冊
⳵ ln f a
⳵ ln x a
⫽x a x w ␤
p,T
冉 冊
⳵ 2G E
⳵ x 2a
.
共7兲
p,T
Equation 共6兲 satisfies the Gibbs–Duhem condition (N a d ␮ a
⫹N w d ␮ w ⫽0, at constant p and T兲 and should be accurate
enough for the current purposes considering the estimated
errors in the simulated derivatives. On fitting the derived
equation for f aa to the corresponding simulated activity derivatives, the constants c a and c w were determined to be
0.263 and 0.372, respectively. The value of f a was then obtained by numerical integration, and the value of y a was
obtained from f a by using standard conversion rules.37
TABLE IV. First-shell coordination numbers (n i j ) for acetone/water mixtures. The distance to the first minimum of the RDF was 0.725 nm for acetone–acetone, 0.425 nm for acetone–water, and 0.345 nm for water–
water. Typical errors were ⫾0.1.
xa
n aa
n aw
n ww
0.0
0.1
0.2
0.4
0.5
0.6
0.8
0.9
1.0
6.9
3.3
3.8
9.6
2.0
3.0
10.4
1.5
2.7
11.1
1.3
2.3
11.9
0.6
1.5
12.3
0.3
1.0
12.6
4.7
4.7
4.2
4.4
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J. Chem. Phys., Vol. 118, No. 23, 15 June 2003
FIG. 3. Partial molar volumes (V̄ i ), isothermal compressibilities ( ␬ T ), and
solution density as a function of acetone mole fraction (x a ). Lines represent
the experimental data 共from Ref. 35兲 and crosses correspond to the KBFF
model. Finite difference compressibilities are displayed as triangles.
The experimental mole fraction activity derivatives proceed through a minimum around x a ⫽0.5, which corresponds
to the point of highest self-aggregation. A value of f aa ⬍
⫺1 indicates an unstable solution. Hence, acetone–water
mixtures approach, but do not reach, immiscibility in this
region. This trend was reproduced by the current model although not in a quantitative manner. Even so, the corresponding acetone activities show good agreement with experiment, although they are consistently higher than
experiment as a direct result of the underestimation in the
degree of water 共and acetone兲 aggregation, which led to
smaller values of the activity derivatives. The Gibbs–Duhem
condition ensures that the water activities must also be well
reproduced if the densities and acetone activity derivatives
are accurate.
Some solution properties not directly used in the parameterization are displayed in Fig. 5 and Table V. It was en-
FIG. 4. Activity derivatives (a aa and f aa ) and activity coefficients (y a and
f a ) as a function of acetone concentration ( ␳ a or x a ). Lines represent the
experimental data 共from Refs. 1 and 2兲 and crosses correspond to the KBFF
model.
Force field for acetone-water mixtures
10667
FIG. 5. Diffusion constants (D i ), relative permittivities 共⑀兲, excess Gibbs
energy (G E —upper curves兲, excess enthalpy (H E —lower curves兲 as a function of acetone mole fraction (x a ). Lines represent the experimental data
共from Refs. 38 – 41兲 and crosses correspond to the KBFF model.
couraging that the trends in the acetone and water diffusion
constants, the relative permittivity, excess Gibbs energy, and
excess enthalpy were reproduced with quantitative agreement in many cases. The diffusion of acetone was in excellent agreement with experiment. Water diffusion displayed
the experimentally observed minimum, but shifted to larger
acetone concentrations. Additional calculations of the diffusion constants under microcanonical NVE and canonical NVT
conditions indicated that they were insensitive, within the
observed errors, to the ensemble used. The relative permittivity decreased monotonically with acetone mole fraction, in
agreement with experiment, but remained consistently lower
than the experimental data. The excess Gibbs energy 关obtained from Eq. 共6兲兴 was in excellent agreement with experiment. The excess enthalpy displayed the correct sinusoidal
shape but was slightly too negative 共favorable兲 beyond x a
⫽0.2. Hence, the model resulted in a larger solvation enthalpy than observed experimentally for x a ⬎0.2. Obviously,
the excess entropy of solution must compensate for the deviations in excess enthalpy in order to generate the correct
excess Gibbs energy. It is unclear how this imbalance may
affect the temperature dependent solution activities. A maximum in the single molecule and total dipole moment relaxation times was observed 共Table V兲 which appeared to coincide with the water aggregation maximum 共Fig. 2兲.
Some selected atom–atom RDFs are displayed in Fig. 6
for the x a ⫽0.5 simulation. Significant solvation of acetone
by water was observed with the most solvation occurring
between the acetone oxygen and water, probably due to the
higher degree of solvent exposure compared to the central
carbon. The first-shell coordination number for water around
the carbonyl oxygen was 0.8 at 0.345 nm. The pair interaction energy histograms and average pair interaction energies
are displayed in Fig. 7. They indicate a diffuse acetone–
water pair interaction energy distribution, and an average
water pair interaction energy of ⫺23 kJ/mol at 0.27 nm,
which favored water aggregation. The dipole–dipole spatial
correlation functions are also displayed in Fig. 7 and indicate
that acetone pairs in very close contact 共0.32 nm兲 tended to
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10668
J. Chem. Phys., Vol. 118, No. 23, 15 June 2003
S. Weerasinghe and P. E. Smith
TABLE V. Relaxation times and relative permittivities of acetone/water mixtures. Symbols are ␶ a and ␶ w , are
single molecule rotational relaxation times for the acetone and water dipoles, respectively; ␶ M , total dipole
relaxation time; ⑀, relative permittivity. Errors were typically ⫾1 ps for the relaxation times and ⫾5 for the
permittivities.
xa
0.0
0.1
0.2
0.4
0.5
0.6
0.8
0.9
1.0
␶ a (ps)
␶ w (ps)
␶ M (ps)
⑀
10
10
18
50
13
14
18
39
14
20
24
25
11
22
22
28
12
26
27
23
8
22
9
18
7
17
6
16
3
6
9
72
favor antiparallel stacked dimers with an average interaction
energy of ⫺17 kJ/mol. However, the average angle between
acetone molecules at the first maximum in the acetone–
acetone RDF 共0.5 nm兲 was 84°, i.e., either perpendicular or
almost random, and possessed an average interaction energy
of only ⫺2 kJ/mol.
As the KB integrals obtained for the x a ⫽0.5 simulation
did not appear to converge completely, and the degree of
water aggregation was also underestimated, a larger system
was simulated to investigate possible system size effects. The
larger system contained 1500 acetone and 1500 water molecules in a box approximately 6.0 nm in length. Some of the
results are displayed in Table VI and Fig. 8 共all of the other
properties were insensitive to the system size兲. The major
differences between the two systems were manifested in the
longer-range correlations with the shorter-range distributions
(n i j ) remaining unaffected. The data clearly showed that a
larger system permitted a larger degree of water aggregation
(N ww ⫽5.3) to occur by extending the correlation region to
distances of 1.5–2.0 nm. Consequently, the results were in
better agreement with experiment than the smaller system,
although the changes did not significantly affect the calculated activities.
The acetone force field described here was developed for
use with the SPC/E water model. In Table VI, we also
present the corresponding data for the acetone force field
with both the SPC and TIP3P water models. As might be
FIG. 6. Intermolecular atom–atom radial distribution functions obtained
from the x a ⫽0.5 simulation using the KBFF model.
3
15
expected, the simulations with the SPC and TIP3P water
models produced data which were in slightly worse agreement with experiment than the SPC/E model. Hence, the
choice of water model can influence the results, although this
was not the case for our previous study of urea and water
mixtures.11 The direction of the deviations was consistent
with the trend in water–water interaction energies. Consequently, the SPC/E model, which has the largest partial
atomic charges, produced a larger water–water interaction
energy and hence a larger degree of water aggregation. The
diffusion results suggested that the SPC model might work
best with the KBFF acetone force field. However, pure SPC
water displays a high diffusion constant 共almost twice the
experimental value兲9 and so this agreement was probably
somewhat fortuitous.
Also displayed in Table VI are the results obtained for
the optimized parameters for liquid simulations 共OPLS兲 acetone force field6 and TIP3P water system. OPLS acetone is
known to exhibit a low density for pure acetone under NpT
conditions, or high pressures under NVT conditions.43 Water
FIG. 7. Pair interaction energy probabilities 共top兲, distance dependent average pair interaction energies 共middle兲, and dipole–dipole spatial correlation
functions 共bottom兲, obtained from the x a ⫽0.5 simulation using the KBFF
model.
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J. Chem. Phys., Vol. 118, No. 23, 15 June 2003
Force field for acetone-water mixtures
10669
TABLE VI. Comparison of the properties of different acetone and water models. All data correspond to an acetone mole fraction of x a ⫽0.5. Typical errors
are shown in Figs. 2–5. Experimental data: Density from Ref. 35, diffusion coefficients from Ref. 39, and KB integrals from Refs. 1 and 2. The KB integrals
for the larger (N a ⫽1500) system were obtained after averaging between R⫽2.0 and 2.4 nm.
KBFF
Na
␳
Da
Dw
n aa
n ww
n aw
V̄ a
V̄ w
G aa
G ww
G aw
a aa
f aa
OPLS
SPC/E
SPC/E
SPC
TIP3P
TIP3P
432
0.851
2.1
1.5
10.4
2.7
1.5
72.6
16.8
⫺66
293
⫺85
0.9
⫺0.7
1500
0.851
2.2
1.6
10.4
2.7
1.6
72.3
17.1
⫺56
472
⫺130
0.6
⫺0.8
432
0.843
2.3
2.1
10.3
2.5
1.7
73.1
17.2
⫺73
177
⫺59
1.2
⫺0.5
432
0.838
2.9
2.7
10.2
2.5
1.6
73.3
17.4
⫺73
170
⫺58
1.2
⫺0.5
432
0.776
4.5
4.8
10.5
3.7
0.7
79.1
19.0
136
3870
⫺952
0.09
⫺0.97
aggregation (G ww ) for the OPLS model was over an order of
magnitude larger than the KBFF model, and more than five
times the experimental value. In addition, the magnitude of
f aa indicated that the solution was very close to the stability
limit ( f aa ⫽⫺1). The reason for this behavior appeared to be
the relatively low OPLS acetone charges (q O⫽⫺0.424, q C
⫽⫺0.300, and q CH3 ⫽⫺0.062), which led to a lower solvation energy and hence a high degree of water aggregation.
However, as the oxygen atom size 共␴ value兲 is also smaller
for the OPLS force field, this type of analysis may be too
simplistic. Furthermore, it is clear that many models using ab
initio derived charge distributions might not necessarily reproduce the correct solution thermodynamics, especially as
the use of different basis sets can generate very different
charge distributions which significantly affect the molecular
distributions in solution.10,11
Expt.
Units
0.852
2.14
2.20
g/cm3
10⫺9 m2 /s
10⫺9 m2 /s
73.2
16.0
⫺50/⫺55
564/688
⫺175/⫺140
0.51/0.42
⫺0.85/⫺0.82
cm3/mol
cm3/mol
cm3/mol
cm3/mol
cm3/mol
The parameters derived here were obtained from simulations of acetone–water mixtures. The results for pure acetone are presented in Table VII. The data are in reasonable
agreement with the available experimental values, especially
the density and relative permittivity. The diffusion constant
was slightly low, as was the compressibility. The configurational energy was less negative than the experimental data,38
although the data have not been corrected for polarization or
quantum-mechanical effects which are often significant.13,46
The dipole moment of liquid acetone (3.32 D) is larger than
the gas phase value (2.88 D), as expected for effective
charge models which include polarization effects implicitly.
The compressibilities obtained from the KB and finite difference approaches were in agreement for pure water, but deviated significantly for pure acetone 共see also Fig. 3兲. Hence,
the difference between the two approaches appears to be
TABLE VII. Properties of the pure acetone and pure SPC/E water models.
Compressibilities determined from the KB integrals 共KB兲 and finite difference calculations. Experimental data: Densities from Refs. 35 and 44, diffusion constants from Refs. 39 and 45, permitivities from Refs. 42 and 44,
and compressibilities from Ref. 42.
FIG. 8. The KB integrals (cm3 /mol) obtained for simulations of x a ⫽0.5
mole fraction. The solid lines are the smaller 共432 acetone兲 simulation,
while the dashed lines correspond to the larger 共1500 acetone兲 simulation.
Thin lines indicate the average of the two experimental values.
Molecular dynamics
Expt.
Units
KBFF acetone
␳
Da
⑀
␬ T -KB
␬ T -finite difference
E pot
0.792
4.1
15
20.4
8.0
⫺25.73
0.784
4.94
19.1
12.39
g/cm3
10⫺9 m2 /s
SPC/E Water
␳
Dw
⑀
␬ T -KB
␬ T -finite difference
E pot
0.995
2.9
72
4.5
4.5
⫺46.45
0.997
2.35
78
4.6
10⫺5 atm⫺1
kJ/mol
g/cm3
10⫺9 m2 /s
10⫺5 atm⫺1
kJ/mol
Downloaded 05 Feb 2009 to 128.210.126.199. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp
10670
J. Chem. Phys., Vol. 118, No. 23, 15 June 2003
more evident for larger solutes and/or more compressible
solutions.
IV. CONCLUSIONS
A model for acetone–water mixtures has been developed
using the KB theory of solution thermodynamics. The model
performs very well for all acetone mole fractions. However,
the degree of water self-aggregation is slightly underestimated for mole fractions of around 0.5 due to the need for
very large systems to fully capture the aggregation behavior
in this region. This is a general problem which relates to the
extent of the correlation region. The exact value of R at
which all the RDFs are essentially unity is unknown and
varies from system to system. It will be dependent on the
sizes of the molecules under study and the properties of the
solution itself. Large solutes 共or solvents兲 and highly aggregating systems will tend to display larger correlation volumes. Clearly, the data presented here indicate that large 共6.0
nm box length兲 systems may often be required when any of
the KB integrals (G i j ) become much greater in magnitude
than the corresponding partial molar volumes (V̄ i ).
In our opinion, the current model represents a significant
improvement in describing the relative distribution of molecules in solutions of acetone and water, and accurately reproduces the solution activities. The degree of water aggregation appeared to be sensitive to the partial charge on the
carbonyl atoms. The larger the charge, the higher the solvation, and the lower the water self-aggregation. Changing the
water model to a less polar charge distribution results in less
water self-aggregation due to decreases in the water–water
interaction energy. Results obtained for other properties not
included in the original parameterization, and for pure acetone, were encouraging and suggest that obtaining force
fields via a combination of simulation and KB theory yields
realistic liquid state models. The ability to easily calculate
the solution activities using simple NpT simulations provides
additional data for parameter determination and represents a
significant step in the development and characterization of
force fields for liquid mixtures.
ACKNOWLEDGMENTS
This project was partially supported by the Kansas Agricultural Experimental Station 共Contribution No. 03-268-J兲.
This material is based upon work supported by DOE Grant
No. DE-FG02-99ER45764, the NSF, and matching support
from the State of Kansas. Acknowledgment is made to the
donors of The Petroleum Research Fund, administered by the
ACS, for partial support of the research.
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