Kirkwood Buff derived force field for mixtures of acetone and water

Transcription

1 JOURNAL OF CHEMICAL PHYSICS VOLUME 118, NUMBER JUNE 2003 Kirkwood Buff derived force field for mixtures of acetone and water Samantha Weerasinghe a) and Paul E. Smith b) Department of Biochemistry, Kansas State University, Manhattan, Kansas Received 24 January 2003; accepted 24 March 2003 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 American Institute of Physics. DOI: / 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 propanone 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 fields 3,6 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 KB 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 de- a Permanent address: Department of Chemistry, University of Ruhuna, Matara, Sri Lanka. b Electronic mail: pesmith@ksu.edu 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 densities, diffusion constants, dielectric constants, compressibilities, etc. 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 KBFF 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 enhanced simple point charge SPC/E, 13 simple point charge SPC, 14 transferable intermolecular potentials TIP3P, 15 although the majority of simulations involved the SPC/E model. All simulations were performed in the isothermal isobaric NpT ensemble at 300 K and 1 atm. The weak coupling technique 16 was used to modulate the temperature and pressure with relaxation times of 0.1 and 0.5 ps, respectively. All bonds were constrained using SHAKE 17 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 /2003/118(23)/10663/8/$ American Institute of Physics

2 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 40 3 grid with 0.1 nm resolution. Initial configurations of the different solutions were generated from a cubic box (L4.0 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 first-order Legendre polynomial 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 and kj/mol, respectively. Errors 1 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 ij 4 g VT ij r1r 2 dr. 0 Here, G ij is the KB integral between species i and j, g VT ij (r) is the corresponding radial distribution function RDF in the grand canonical VT ensemble, and r is the corresponding center of mass-to-center of mass distance. The KB integrals were determined from the simulation data NpT ensemble by assuming that, 7,24,26 G ij 4 Rg NpT ij r1r 2 dr, 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 ij j G ij, where j N j /V is the number density of j particles. A value of N ij greater than zero indicates an excess of species j in the vicinity of species i over a random distribution, while a negative value corresponds to a depletion of species j surrounding i. For a binary solution consisting of water w and acetone a, a variety of thermodynamic quantities can be defined in terms of the integrals G ww, G aa, and G aw, and the number densities or molar concentrations w and a. The partial molar volumes of the two components, V ; the isothermal compressibility of the solution, T ; derivatives of the chemical 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 p and a temperature T are given by 7 V w 1 ag aa G aw, V a 1 wg ww G aw, T, a aa ln a a ln a f aa ln f a ln x a 1 ln y a ln a a G aa G aw, 4 wx a G ww G aa 2G aw 1 w x a G ww G aa 2G aw, where w a w a (G ww G aa 2G aw ), 1 w G ww a G aa w a (G ww G aa G 2 aw ), 1/(RT), and R is the gas constant. For real stable 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. 4 and 5, 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 atomic hydrid components ( i ) of molecular 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 5

3 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 force constants are in kj/mol/rad 2, angles in degrees, and distances in nm. Bond lengths (r 0 ) were constrained. Bonds C O CuCH 3 r Angles OuCuCH 3 CH 3 ucuch 3 k Impropers CuOuCH 3 uch 3 k TABLE II. Nonbonded parameters. Lennard-Jones 6-12 plus Coulomb potential. Geometric mean combination rules were used for both ij and ij. Model Atom kj/mol nm q (e) Acetone KBFF C O CH Water SPC/E O H ii were taken to be proportional to i 1/2 and i I i, respectively. The scaling factor for 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 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 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 Table III. It was important to study these mixtures using reasonably large simulation volumes to ensure that the RDFs displayed no long-range structure beyond 1.5 nm or so, and that the KB integrals converged to a reasonable plateau value. In addition, a significant simulation time was required 1 nsorso to ensure full equilibration of the systems no systematic changes in the RDFs, 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 see Fig. 1. 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 ij j G ij ). 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. N a N w x a M a V nm 3 g/cm 3 T sim ns

4 10666 J. Chem. Phys., Vol. 118, No. 23, 15 June 2003 S. Weerasinghe and P. E. Smith FIG. 1. Radial distribution functions (g ij ) and KB integrals (G ij ) as a function of distance for the x a 0.5 simulation. FIG. 2. Excess coordination numbers (N ij ) as a function of acetone mole fraction (x a ). Lines represent the two sets of experimental data from Refs. 1 and 2 and crosses correspond to the KBFF model. 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 immediately 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 see later. 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 lnx a c w x w x w lnx w c a x a, and using the thermodynamic relationship, f aa 2 G E 2 x a ln f a ln x a x a x w 6. 7 Equation 6 satisfies the Gibbs Duhem condition (N a d a N w d w 0, at constant p and T 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 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 ij ) for acetone/water mixtures. The distance to the first minimum of the RDF was nm for acetone acetone, nm for acetone water, and nm for water water. Typical errors were 0.1. x a n aa n aw n ww

5 J. Chem. Phys., Vol. 118, No. 23, 15 June 2003 Force field for acetone-water mixtures FIG. 3. Partial molar volumes (V i), isothermal compressibilities ( T ), and solution density as a function of acetone mole fraction (x a ). Lines represent the experimental data from Ref. 35 and crosses correspond to the KBFF model. Finite difference compressibilities are displayed as triangles. FIG. 5. Diffusion constants (D i ), relative permittivities, excess Gibbs energy (G E upper curves, excess enthalpy (H E lower curves as a function of acetone mole fraction (x a ). Lines represent the experimental data from Refs and crosses correspond to the KBFF model. 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 from Refs. 1 and 2 and crosses correspond to the KBFF model. 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 and acetone 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 encouraging 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 obtained from Eq. 6 was in excellent agreement with experiment. The excess enthalpy displayed the correct sinusoidal shape but was slightly too negative favorable 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 Table V which appeared to coincide with the water aggregation maximum Fig. 2. 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 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 0.32 nm tended to

6 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. x a a (ps) w (ps) M (ps) 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 0.5 nm 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 all of the other properties were insensitive to the system size. The major differences between the two systems were manifested in the longer-range correlations with the shorter-range distributions (n ij ) 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 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 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 almost twice the experimental value 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 OPLS acetone force field 6 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. 6. Intermolecular atom atom radial distribution functions obtained from the x a 0.5 simulation using the KBFF model. FIG. 7. Pair interaction energy probabilities top, distance dependent average pair interaction energies middle, and dipole dipole spatial correlation functions bottom, obtained from the x a 0.5 simulation using the KBFF model.

7 J. Chem. Phys., Vol. 118, No. 23, 15 June 2003 Force field for acetone-water mixtures 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 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 R2.0 and 2.4 nm. KBFF OPLS SPC/E SPC/E SPC TIP3P TIP3P Expt. Units N a g/cm 3 D a m 2 /s D w m 2 /s n aa n ww n aw V a cm 3 /mol V w cm 3 /mol G aa /55 cm 3 /mol G ww /688 cm 3 /mol G aw /140 cm 3 /mol a aa /0.42 f aa /0.82 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 CH ), which led to a lower solvation energy and hence a high degree of water aggregation. However, as the oxygen atom size value 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 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 see also Fig. 3. 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 KB 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. Molecular dynamics Expt. Units KBFF acetone g/cm 3 D a m 2 /s T -KB atm 1 T -finite difference 8.0 E pot kj/mol FIG. 8. The KB integrals (cm 3 /mol) obtained for simulations of x a 0.5 mole fraction. The solid lines are the smaller 432 acetone simulation, while the dashed lines correspond to the larger 1500 acetone simulation. Thin lines indicate the average of the two experimental values. SPC/E Water g/cm 3 D w m 2 /s T -KB atm 1 T -finite difference 4.5 E pot kj/mol

8 10670 J. Chem. Phys., Vol. 118, No. 23, 15 June 2003 S. Weerasinghe and P. E. Smith 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 or solvents and highly aggregating systems will tend to display larger correlation volumes. Clearly, the data presented here indicate that large 6.0 nm box length systems may often be required when any of the KB integrals (G ij ) become much greater in magnitude than the corresponding partial molar volumes (V 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 Contribution No J. 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. 1 E. Matteoli and L. Lepori, J. Chem. Phys. 80, M. J. Blandamer, J. Burgess, A. Cooney, H. J. Cowles, I. M. 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