Evaluation and Refinement of the General AMBER Force Field for

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Evaluation and Refinement of the General AMBER Force Field for Nineteen Pure Organic Electrolyte Solvents Yushan Zhang, Yong Zhang, Mark J. McCready, and Edward J. Maginn* Department of Chemical and Biomolecular Engineering, University of Notre Dame, 182 Fitzpatrick Hall, Notre Dame, Indiana 46556, United States

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 08/27/18. For personal use only.

S Supporting Information *

ABSTRACT: The performance of the general AMBER force field (GAFF) was evaluated by computing the density (ρ), dielectric constant (ε), viscosity (η), and enthalpy of vaporization (ΔHvap) for 19 different organic solvents at 298 K and 1 atm. The force field performed very well for liquid densities, with deviations from experiment averaging around 3%. The performance of the force field was much worse for the other properties, with average absolute deviations of 10% for ΔHvap, 35% for ε, and 132% for η. A set of modified GAFF parameters were developed for each fluid using an optimization procedure to uniformly scale the Lennard-Jones parameters and partial charges. The modified parameters generally yielded more accurate properties than the original GAFF model, though discrepancies still remained for some liquids. Since these properties depend on the parameters of this class of force field in a complex and nonadditive manner, it is unlikely that any combination of parameters will yield a very high accuracy for all four properties. In particular, obtaining accurate dielectric constants and viscosities without compromising the liquid density or enthalpy of vaporization may require the use of a polarizable force field.

1. INTRODUCTION Better energy storage technologies are needed to fully exploit renewable energy sources such as wind and solar.1−3 Rechargeable batteries are particularly desirable because they directly produce dispatchable electricity. Since the 1990s, lithium-ion batteries have become widely used due to their high energy density and variety of cell types.4−6 New battery technologies with even better performance characteristics are under development, including sodium−sulfur, lithium−sulfur, metal air, and multivalent (i.e., calcium and magnesium) ion batteries. These different battery technologies often require the use of an organic liquid electrolyte that acts as a conductive pathway for cation movement during discharging and charging.7 The physical properties of the electrolyte are crucial in governing the performance, stability, and safety of batteries.8 While many different organic liquids and liquid mixtures have been evaluated as electrolytes, there are a vast number of other potential liquid electrolytes that have not been examined. Experimentally measuring the properties of an electrolyte is accurate but also expensive and time-consuming. Molecular simulations can be used to rapidly compute a range of important properties for liquid electrolytes and mixtures of electrolytes, thereby ruling out those that have unfavorable properties and identifying new promising compounds. Such simulations also provide a detailed molecular-level understanding of how the physical properties of an electrolyte are related to its chemical structure and composition, thereby providing guidance in © XXXX American Chemical Society

the search for optimal electrolytes in new types of batteries. Key electrolyte properties of interest to us include the liquid density ρ, the static dielectric constant ε, the shear viscosity η, and the enthalpy of vaporization ΔHvap. The accuracy of these and other properties obtained from a molecular simulation depends on the quality of the intermolecular potential (“force field”) used to represent the molecular interactions in the liquid. The optimized potentials for liquid simulations (OPLS) force field9,10 has been used to simulate a variety of organic electrolytes. For example, the static dielectric constants of ethylene carbonate and propylene carbonate were simulated using the OPLS force field; the simulated dielectric constants differed from experiment by around 30%.11 Modifications of OPLS have been proposed by adjusting the parameters to match experimental data. Böckmann and co-workers optimized the OPLS force field to better match the properties of long hydrocarbons.12 Umebayashi and co-workers used ab initio calculations to modify the OPLS force field for tetraglyme. They validated the modified force field by comparing computed density and X-ray structure factors with experiment.13 The transferable potentials for phase equilibria (TraPPE) force field is another widely used force field.14,15 TraPPE has Received: May 10, 2018 Accepted: August 7, 2018

A

DOI: 10.1021/acs.jced.8b00382 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. List of the 19 solvents studied in the present work. Molecule number, abbreviation, formal name, and Chemical Abstracts Service Registry number are provided.

candidate electrolytes being investigated by experimental collaborators. The names, structures, and abbreviations of the molecules are shown in Figure 1. We then try to achieve better agreement between these computed properties and available experimental data by modifying the parameters of the GAFF force field. We note that there are gaps in the published experimental data for some of these solvents. We therefore only used 15 of the solvents in our optimization procedures but still computed all properties for the 19 solvents using the GAFF force field and a modified GAFF force field, described below. Several different procedures have been suggested for optimizing force field parameters. One is the ForceBalance method developed by Wang and co-workers,23−25 which has been used to parametrize two rigid water models and extended to develop a protein force field. The method can automatically derive force field parameters by updating the parameters to minimize the differences between MD results and reference data. The procedure we use is in the spirit of the approach used by Fennell and co-workers,26,27 and is similar to what we did in previous work to develop a better force field for glymes.22 One starts with a base force field (in this case GAFF) and then uniformly scales the force field parameters by a constant in order to optimize the properties, where the scales are chosen manually. This method has also been used to optimize potentials or tested for a number of other systems.28−30 It has been found that obtaining an accurate liquid density and dielectric constant often results in greater accuracy for other properties without the need to add more sophistication to a force field.26 This work provides a test of this approach for a diverse set of compounds. We stress that modification of the parameters of a given force field technically results in a “new” force field. That is, the new parameters we propose here are no longer the “GAFF” force field.

parameters for a range of molecular classes, including alkanes, ethers, glycols, ketones, and aldehydes. It has been found to be accurate for properties such as Hildebrand solubility parameters, liquid-phase densities, and enthalpies of vaporization for a range of organic solvents.16 TraPPE was developed for computing thermodynamic properties and phase equilibria, but it has also been used successfully to compute transport properties.17 Several groups have proposed modifications to the TraPPE parameters to improve the estimation of certain properties. For example, Sadowski and co-workers reparameterized the dihedral potentials of the united atom form of TraPPE and obtained better results describing conformer equilibria for dimethoxyethane as well as other poly(oxyethylene) oligomers.18 The AMBER force field19 and the general AMBER force field (GAFF)20 are also widely used in simulations of organic molecules. van der Spoel and co-workers have computed density, enthalpy of vaporization, heat capacity, surface tension, isothermal compressibility, volumetric expansion coefficient, and dielectric constant of 146 organic liquids with GAFF as well as OPLS.21 They found that, although OPLS performed better than GAFF on some properties, both have significant difficulty reproducing the dielectric constant, which is a crucial property for electrochemical applications. We proposed modified GAFF parameters to obtain more accurate dielectric constants for three different poly(ethylene glycol) ethers (glymes).22 The modified parameters also yielded reasonable values for the liquid density, thermal expansivity, enthalpy of vaporization, self-diffusion coefficient, and shear viscosity. In this work, we assess the accuracy of GAFF for determining the liquid density, static dielectric constant, shear viscosity, and enthalpy of vaporization for 19 different small molecule solvents that could potentially be used as electrolytes. The solvents represent a range of compounds with chemical and structural diversity and were chosen from a list of B



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2. COMPUTATIONAL METHODS 2.1. Simulation Details. Molecular dynamics (MD) simulations were used to calculate ρ, ε, η, and ΔHvap for all 19 solvents at 298 K using the GAFF functional form for the potential20 Etot =

∑ bonds

kr(r − r0)2 +

∑

details associated with the calculation of each property are described in the next section. 2.2. Calculation of Organic Solvent Properties. 2.2.1. Density. As noted above, densities were computed over the final 0.6 ns of a 1 ns NPT simulation via a block average procedure.38 The 0.6 ns production runs were divided into six 0.1 ns blocks. The density was computed from the average of the individual block values, and the uncertainty was estimated as the standard deviation. Density is a rapidly converging quantity and the dynamics of the organic solvents are fast, so relatively short simulations were sufficient. 2.2.2. Static Dielectric Constant. The static dielectric constant, ε, is given by39

kθ(θ − θ0)2

angles

v + ∑ n [1 + cos(nϕ − γ )] dihedrals 2 ÄÅ É | ÅÅi y12 i y6ÑÑÑ N−1 N l o qiqj o o o Å σ σ o o jj ij zz ÑÑÑ ÅÅjjj ij zzz o o + ∑ ∑m 4ϵijÅÅÅjj zz − jjj zzz ÑÑÑ + } o o o o j z j z Å Ñ πϵ r r 4 r o ÅÅk ij { o ij 0 ij Ñ i=1 i 1.0). For a given value of fq, we need to choose from a list of fσ or fϵ to keep the value of ρ to within 3% of the experimental value according to eqs 5 and 6. As an example of how we apply this approach to the scaling of qi and σii, we take as a trial for PC fq = 1.1; the experimental density of PC is 1.200.49 We obtain a range of acceptable values for fσ from eq 8: 1.2 × (1 − 3%) ≤ (2.58 ± 0.03) − (1.75 ± 0.03) × f σ + (0.246 ± 0.009) × 1 + (0.16 ± 0.01) × 1.1 ≤ 1.2 × (1 + 3%) (9)

The resulting fσ range is (1.01 ± 0.04) to (1.05 ± 0.04). We then calculate ρ with fq = 1.1 and fσ from (1.01−0.04) to (1.05 + 0.04) in increments of 0.02, resulting in seven simulations. If the simulated density is within 3% of the experimental value, we then calculate ε. Similarly, when scaling qi and ϵii parameters, if we select fq = 1.1, the resulting fϵ range is (0.62 ± 0.04) to (0.92 ± 0.04). We calculate ρ with fq as 1.1 and fϵ from 0.50 to 1.00 with an increment of 0.1, resulting in six simulations. The increment is larger for fϵ than fσ because the density is much more sensitive to σii than ϵii. Once we have found the optimum scaling parameters for ρ and ε according to the two procedures described by eqs 5 and 6, we then proceed to compute η and ΔHvap using the optimum scaling parameters. That is, η and ΔHvap are not used in the optimization procedure.

(7)

The fitted regression coefficients (a, b, c, and d) for all 19 liquids are provided in the Supporting Information. As expected, we observe that ρ increases with decreasing fσ and increasing fϵ and fq, which corresponds to negative b and positive c and d in the linear regression equation. In general, fσ has the most significant effect on ρ, while fϵ and fq have a much more modest effect on ρ. All of the coefficients of determination are close to or larger than 0.9, indicating a good linear fit. The fitted linear regression equation can be used to narrow the selection range of fϵ and fσ when constraining the deviation in ρ, thereby reducing the number of simulations needed to G



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Figure 6. Parity plots for (a) density ρ, (b) static dielectric constant ε, (c) viscosity η, and (d) enthalpy of vaporization ΔHvap at 298 K when qi and ϵii are scaled.

3.4. Optimized Parameter Performance for Dielectric Constant, Shear Viscosity, and Enthalpy of Vaporization. The parity plots and results from scaling fq and fϵ are shown in Figure 6 and Table 3. In Figure 6, the simulated ρ, ε, and ΔHvap values are clustered around the experimental values, showing that the simulations overestimate experiments for some of the liquids and underestimate in others. The simulated η overestimates the experimental η in most systems except DMSO and EDA. The MAPD of ρ, ε, η, and ΔHvap are 1.1, 12.9, 69.5, and 13.6%, respectively. MAPDs for ρ, ε, and η from the force field parameters in which fq and fϵ were scaled are smaller than those obtained with the original GAFF force field, while the MAPD for ΔHvap is slightly larger than the result from the original GAFF force field. Except for EDA, fq is greater than 1 and fϵ is smaller than 1, suggesting that the original GAFF tends to overestimate the Lennard-Jones energy parameters and underestimate Coulombic interactions. Note that, in our previous work with ionic liquids,50 we showed that

reducing partial charges was necessary to obtain better agreement with experimental transport properties; it has been argued that reducing partial charges accounts for polarization and charge transfer effects in ionic liquids. For these neutral molecular liquids, however, partial charges generally need to be increased to account for polarization effects in the condensed phase. The actual static dielectric constant is related to the atomic motion and electronic polarization of the molecule.51 In our simulations, since we neglect electronic polarization, ε is related only to fluctuations in the (static) dipole moment of the molecule (vide supra, eq 2). That means that ε tends to be underestimated (as is observed with the original GAFF force field parameters) and that, to increase the computed value of ε, larger partial charges are needed (fq > 1). Of course, the sensitivity of ε to partial charge scaling is not the same for all liquids. For small polar molecules with relatively large dipole moments such as THF and ACN, increasing the partial charges H



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Table 3. Results from Optimal fϵ, fq Values Where fσ = 1a ρ (g/cm3)

ε

η (mPa·s)

ΔHvap (kJ/mol)

num

solvent

sim

diff (%)

sim

diff (%)

sim

diff (%)

sim

diff (%)

fϵ

fq

1

DMC

1.042 ± 0.002

1.342 ± 0.001

−17.1

0.5

1.3

42.1 ± 2.9 64.2 ± 1.9

1.5 1

PC

−1.2

66.8 ± 0.6

2.96 ± 0.07

0.7

1.1

DME

0.859 ± 0.001

7.23 ± 0.07

0.7 ± 0.2

0.84

1.02

6

THF

0.875 ± 0.003

−0.4 −0.3 −0.8

17.0 17.7 56.4

57.4 ± 1.3

5

2.9 3.0 2.3

8.13 ± 0.08

3.2

0.6 ± 0.1

29.1

28.8 ± 1.3

0.9

1.3

7 9 12 14

ACN DMSO FEC EA

0.773 1.091 1.493 0.901

± ± ± ±

0.001 0.001 0.003 0.002

−5.3 5.6 0.4 −6.6 −19.5 −13.3 −12.6 −10.5 −10.1 13.8 −23.5

0.5 1

4

0.979 1.346 1.352 1.185

29.7 39.4 186.9 160.7

31.5 ± 2.6

DEC EC

−58.1 −56.7 −45.6 −6.0

0.82 ± 0.06

2 3

−2.0 −2.1 1.0 1.0

−6.1

0.6 0.7 0.5 0.7

1.3 1.1 1.3 1.3

15 16 17 18

DMF DMA TMP ACE

0.936 0.953 1.222 0.798

± ± ± ±

0.001 0.001 0.002 0.004

19

EDA MAPD

± ± ± ±

0.003 0.002b 0.001 0.002

0.890 ± 0.003

−0.5 −0.5 2.7 0.3 0.7 −0.9 1.7 0.7 1.2 1.8 −0.6 1.1

1.542 ± 0.002 89.6 ± 7.9

36.0 48.5 116.0 4.42

± ± ± ±

0.7 0.8 9.2 0.02

37.1 38.4 18.7 19.8

± ± ± ±

0.2 0.2 0.7 0.4

2.1 ± 0.2 5.9 ± 0.3

0.0 4.5 5.5 −29.5 −26.2 0.3 1.6 −9.3 −2.8 −7.9 −21.3 12.9

10.6 ± 0.3

0.49 0.7 7.7 0.69

± ± ± ±

0.03 0.1 0.5 0.02

36.1 −65.8

0.83 2.24 3.5 0.49

± ± ± ±

0.02 0.07 0.1 0.03

4.8 143.2

0.72 ± 0.05

−48.2 69.5

60.4

59.6

31.9 ± 2.7

37.5 40.4 63.1 33.5

± ± ± ±

3.2 3.1 1.4 1.6

45.6 53.4 58.9 37.1

± ± ± ±

3.5 3.1 3.1 2.3

−2.2 5.4 24.1 18.8

0.6 0.9 0.5 0.6

1.3 1.3 1.4 1.5

30.0 ± 3.4

−34.8 13.6

0.6 0.68

0.9 1.24

fq

a

All temperatures are 298 K unless otherwise noted. bCalculated at 308.15 K.

Table 4. Results from Optimal fσ, fq Values Where fϵ = 1a ρ (g/cm3)

ε

η (mPa·s)

num

solvent

sim

diff (%)

sim

diff (%)

1

DMC

1.048 ± 0.001

2.00 ± 0.05

2 3

DEC EC

−37.6 −35.6 −5.5 −6.0

4

PC

0.970 1.346 1.352 1.218

−1.4 −1.5 0.1 1.0

5

DME

6

± ± ± ±

0.001 0.002b 0.001 0.001

2.7 ± 0.1 89.6 ± 7.9

1.5

65.1 ± 1.3

0.874 ± 0.001

1.4

7.1 ± 0.1

THF

0.901 ± 0.001

2.1

7.61 ± 0.05

−3.5

7 9 12 14

ACN DMSO FEC EA

0.785 1.100 1.421 0.899

± ± ± ±

0.002 0.001 0.001 0.001

35.8 46.4 80.0 6.3

± ± ± ±

0.2 2.1 9.2 0.3

15 16 17 18

DMF DMA TMP ACE

0.945 0.932 1.237 0.770

± ± ± ±

0.001 0.001 0.001 0.001

36.1 36.8 11.8 20.7

± ± ± ±

1.7 2.1 0.5 0.3

19

EDA MAPD

−0.6 0.0 −27.3 −0.1 4.6 −2.4 −2.5 −42.5 1.9 −3.4 −7.2 9.3

0.910 ± 0.001

1.1 0.4 −2.2 0.1 0.5 0.1 −0.5 1.9 −2.4 −1.8 1.7 1.1

12.5 ± 0.2

0.2 0.3 0.0

sim

ΔHvap (kJ/mol)

diff (%)

N/A N/A 5.9 ± 0.3 20.8 ± 2.2

160.7

1.1 ± 0.1

721.2 726.1 157.6

1.1 ± 0.2

120.0

1.25 ± 0.03 1.9 ± 0.1 N/A N/A

245.3 −2.8

2.8 ± 0.1 4.5 ± 0.3 N/A 1.0 ± 0.3

250.6 387.7

2.1 ± 0.2

51.3 232.8

228.3

sim

diff (%)

fσ

92.6 ± 4.3

143.8

1.1

2

100.8 ± 1.4 64.2 ± 1.9

127.1 5.6 0.4 24.9 7.7 17.6 18.5 1.9 2.4 40.2 −8.2

1.1 1

2 1

1.02

1.1

1.03

1.07

1

1.25

106.2

1.03 1.02 1.06 1.1

1.28 1.04 1.3 1.8

76.8 ± 1.0 43.2 ± 1.5 46.1 ± 2.6 32.8 ± 3.1 46.3 48.5 87.2 73.6

± ± ± ±

3.4 2.7 1.4 1.4

61.2 65.1 87.9 42.5

± ± ± ±

1.9 2.4 1.2 0.8

31.1 28.6 85.0 36.0

1.04 1.03 1.04 1.06

1.25 1.35 1.4 1.35

197.9 ± 3.6

330.3 69.7

1.04 1.04

0.95 1.34

a

All temperatures are 298 K unless otherwise noted. N/A: unable to compute due to the extremely high viscosity. bCalculated at 308.15 K.

partial charges greatly increase the magnitude of ε. For PC, a value of fq = 1.1 increases ε from 51 to 67, while, for FEC, a value of fq = 1.3 increased ε from 47 to 116. For relatively nonpolar and/or symmetric molecules, however, uniform scaling of partial charges has a much more modest

a modest amount increases dipole moment fluctuations significantly and results in a large increase in ε. For example, by scaling the partial charges by fq = 1.3, ε for THF increases from 4.8 to 8.1 and ε for ACN increases from 23.8 to 36. Similarly, for aromatic molecules such as PC and FEC, small increases in I



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Figure 7. Parity plots for (a) density ρ, (b) static dielectric constant ε, (c) viscosity η, and (d) enthalpy of vaporization ΔHvap at 298 K when qi and σii are scaled. Note that the ranges of values in parts c and d are expanded relative to Figures 4 and 6.

effect on ε. For DMC and DEC, ε increased from 1.224 to 1.342 and from 1.324 to 1.524 with fq values of 1.3 and 1.5, respectively, resulting in computed static dielectric constants that are about 50% too low. Dill and co-workers observed similar behavior when trying to scale the partial charges of CCl4 to improve the calculated ε.26 All “reasonable” values of scaled partial charges resulted in calculated values of ε between 1.0 and 1.05, while the experimentally observed value is 2.2. These differences are small in terms of the absolute value of ε but large on a percentage basis. Inclusion of electronic polarizability in the force field would provide an alternative and physically appealing way of further improving the accuracy of the calculated static dielectric constant. The first optimization procedure (simultaneously adjusting qi and ϵii) restricts the value of fq to be not larger than 1.5 for most of the liquids. This is because the regression coefficients of fq and fϵ have opposite signs and similar magnitudes (see the Supporting Information). As fq increases above 1.5, the value of fϵ drops below the lower physical limit we set of 0.5 for many liquids. As a result, we were unable to increase ε any further.

As an alternative, the second optimization procedure (simultaneously adjusting qi and σii) enables us to achieve values of fq as high as 2.0 while maintaining the constraint on density and the bounds on fσ. This is because the regression coefficients of fσ are much larger than those of fq, as shown in the Supporting Information. The optimal fq and fσ values obtained by the second optimization procedure as well as the corresponding results are shown in Table 4 and Figure 7. The MAPD for ρ and ε are 1.1 and 9.3%, respectively, which are smaller than the original GAFF force field and the modified GAFF force field obtained by scaling qi and ϵii. However, the MAPD for η and ΔHvap are 232.8 and 69.7%, respectively, which are much higher than both the original GAFF force field and the modified GAFF force field with fq and fϵ. In all systems except EDA, fq and fσ are larger than 1. The new parameter set results in much more viscous liquids than either the original GAFF parameters or those obtained using the first fitting procedure. This is driven by the fact that the scaling factors used for partial charges tend to be large with the second optimization procedure in order to J



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Table 5. Results Obtained Using fϵ = 0.7 and fq = 1.25 for All Systemsa ρ (g/cm3) num

solvent

sim

1

DMC

1.091 ± 0.002

2 3

DEC EC

4

PC

0.972 1.346 1.352 1.229

5

DME

0.847 ± 0.001

6

THF

0.789 ± 0.004

7 8 9 10 11 12 13 14

ACN 26CO DMSO VC VEC FEC TFPC EA

0.780 0.832 1.155 1.355 1.208 1.516 1.533 0.884

± ± ± ± ± ± ± ±

0.002 0.002 0.003 0.002 0.003 0.002 0.002 0.002

15 16 17 18

DMF DMA TMP ACE

0.949 0.895 1.230 0.754

± ± ± ±

0.002 0.001 0.001 0.003

19

EDA MAPD

± ± ± ±

0.002 0.002b 0.003 0.002

1.111 ± 0.003

ε diff (%)

diff (%)

1.340 ± 0.009

−58.1 −56.8 −51.1 81.4

2.6 2.5 0.3 1.0

1.386 ± 0.005 172.9 ± 7.3

2.4

91.3 ± 18.5

−1.8 −1.7 −10.6 0.4 −7.8 5.3 0.0 2.1 4.3 −4.2 −1.6 −1.2 0.4 −4.4 1.4 −4.4 −3.9 24.2 4.1

η (mPa·s)

sim

40.6 40.7 41.8

10.0 ± 0.1 6.67 ± 0.04

−15.4

35.1 7.4 64.5 235.9 75.6 98.3 55.3 4.35

± ± ± ± ± ± ± ±

1.0 0.1 5.9 28.1 5.7 12.2 2.3 0.08

−2.4

35.5 32.3 14.1 16.7

± ± ± ±

1.3 1.4 0.6 0.3

38.9

−10.6 −30.6 −27.4 −4.1 −14.4 −31.7 −18.0 −22.2 −47.3 32.4

7.1 ± 0.9

sim 1.47 ± 0.01 1.6 ± 0.2 5.8 ± 0.7 11.7 ± 0.6

ΔHvap (kJ/mol) diff (%)

sim

diff (%)

133.3 150.8 110.2 155.2

38.1 ± 3.1

0.1

42.2 ± 0.8 68.1 ± 1.4

−4.9 12.0 6.4 15.7 −0.3 −15.2 −14.5 −41.9 −41.6 13.3

71.1 ± 0.8

0.45 ± 0.04

364.0 366.7 7.6

31.2 ± 2.6

0.267 ± 0.004

−44.6

18.7 ± 0.6

0.57 ± 0.09 0.9 ± 0.2 2.14 ± 0.06 2.1 ± 0.2 5.7 ± 0.8 15.2 ± 1.3 13.4 ± 1.1 0.55 ± 0.04 1.01 ± 0.07 0.9 ± 0.1 3.3 ± 0.2 0.28 ± 0.04

57.0 9.9

29.1 26.9 −3.8 −9.5

N/A 80.1

37.4 31.8 50.7 47.1 71.5 66.3 66.1 28.9

± ± ± ± ± ± ± ±

1.9 1.5 0.9 1.4 1.6 2.3 1.2 2.1

−19.1

44.4 40.6 59.1 29.4

± ± ± ±

3.6 2.0 1.4 1.8

−4.8 −19.8 24.4 −6.1

84.8 ± 1.5

84.3 17.9

−4.1 14.1

a

All temperatures are 298 K unless otherwise noted. N/A: unable to compute due to the extremely high viscosity. bCalculated at 308.15 K.

get more accurate values of ε. It has been reported23 that stronger intermolecular Coulombic interactions increase viscosity, which is observed here as well. For example, the viscosities of DMC, DEC, and EA (which have charge scaling factors fq of 2, 2, and 1.8, respectively) are significantly higher than when the original GAFF force field was used. In fact, the viscosities for DMC, DEC, FEC, TMP, and EA are so high that we were unable to compute the viscosity of these liquids, even when we increased the simulation length time (30 ns versus 5 ns). On the basis of the above results, we find that, although scaling qi and σii results in smaller MAPDs in ρ and ε, the modifications result in unreasonably high viscosities caused by the overscaled partial charges. Since combinations of fq and fϵ generate better overall results regarding η and ΔHvap, we recommend using those parameters (see Table 3). 3.5. Performance of a Single Set of Averaged Scaled GAFF Parameters. Above, the results were obtained by using a unique scaling of parameters for each liquid and optimizing against known experimental data. To test if the proposed modifications are more generally accurate, we computed the average values of fq and fϵ determined in the first optimization procedure (Table 3). The result is fq = 1.25 and fϵ = 0.7. We applied these scaling factors to each liquid and computed the four properties. The results are shown in Table 5, and Figure 8 shows a parity plot. The MAPDs for ρ and ΔHvap are 4.1 and 17.9%, which are slightly worse than the original GAFF model. The large MAPDs for ρ and ΔHvap are heavily influenced by THF and EDA. On the other hand, the MAPDs for ε and η are 32.4 and 80.1%, which are better than the original GAFF model. Thus, for this class of liquids (and

related compounds), the current results suggest that a very simple way of improving the accuracy of the GAFF model is to uniformly scale all partial charges by a factor of 1.25 and all Lennard-Jones energy parameters by a factor of 0.7 while keeping the Lennard-Jones size parameters the same when the GAFF model underestimates the dielectric constant. This procedure should yield improvements in the ability of the model to estimate the static dielectric constant and shear viscosity while maintaining reasonable accuracy for density and enthalpy of vaporization. 3.6. Are Polarizable Force Fields Needed? The results of this work show that there are limitations to the accuracy of a conventional “class I” force field such as GAFF. It is very difficult to get a range of thermodynamic and transport properties “correct” with a simple model, and there are often tradeoffs such that one property can be obtained with good accuracy but at the expense of another property. In particular, the neglect of electronic polarizability can result in the need to use large partial charges (especially for molecules with small dipole moments), which can adversely affect other properties such as shear viscosity. For example, Park and co-workers52 used a polarizable force field to model DMC and calculated ε = 2.03 ± 0.04. This agrees better with the experimental value of ε = 3.2 reported by Naejus et al.53 than any of the values we computed. For comparison, the original GAFF model for DMC yielded a value of ε = 1.224 ± 0.002, while scaling the charges by fq = 1.3 yielded ε = 1.342 ± 0.001 and a scaling factor of fq = 2.0 still only gave a value of ε = 2.00 ± 0.05. Regarding the viscosity and enthalpy of vaporization of DMC, the percentage deviations from the original GAFF model are 127.4 and 13%, K



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Figure 8. Parity plots for (a) density ρ, (b) static dielectric constant ε, (c) viscosity η, and (d) enthalpy of vaporization ΔHvap at 298 K when fq = 1.25 and fϵ = 0.7. Note that the range of values in part b is expanded relative to Figures 4, 6, and 7.

respectively; the percentage deviations when fq = 1.3 are 29.7 and −17.1%, respectively; when fq = 2.0, the viscosity is so high that it cannot be calculated and the enthalpy of vaporization percentage deviation is 143.8%. It has been found in other work, in which a many-body polarizable force field was used, that the deviation for shear viscosity of DMC is 16% and that for enthalpy of vaporization is 3%.54 This suggests that polarizable force fields may be more accurate for dynamic properties while maintaining the same accuracy for the dielectric constant. On the other hand, for a highly polar molecule like DMSO, it is possible to adjust the dielectric constant a considerable amount using very modest charge scaling. The original GAFF model predicts that ε = 42.5 ± 0.2, which is only slightly below the experimental value of 46.4.55 A modest scaling of the partial charges by fq = 1.1 yields ε = 48.5 ± 0.8. For comparison, van Gunsteren and co-workers have simulated DMSO using a polarizable force field and calculated ε to be 44.7,56 suggesting that the need for including polarizability in a strongly polar molecule like DMSO is ironically not as critical as it is for a weakly polar molecule like DMC. This is because a

greater fraction of the dielectric constant for a molecule like DMC arises from electronic polarizability than for a polar molecule like DMSO.

4. CONCLUSIONS A procedure is described in which we systematically search for force field parameters that yield improved property predictions for density (ρ), dielectric constant (ε), viscosity (η), and enthalpy of vaporization (ΔHvap). We do this by first computing the density and static dielectric constant for 19 different organic liquids using the GAFF force field. The mean absolute percent deviation (MAPD) between the simulations and experiment for ρ was 3.1%, but for ε, it was 34.6%. We sought to improve the accuracy of the force field for obtaining ε while still retaining acceptable accuracy in the density through two approaches. The first approach involved uniform scaling of the magnitudes of the partial charges and Lennard-Jones energy parameters, while the second approach involved uniform scaling of the magnitudes of the partial charges and LennardJones size parameters. We minimized the error in ε with a L



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constraint that densities must stay within 3% of the experimental value. Using the optimized parameters from these two methods, we proceeded to compute η and ΔHvap and found that the first approach gave overall better results. The MAPD for ρ, ε, and η were all better than that with the original GAFF model, while the accuracy of ΔHvap was about the same. We then proposed a single partial charge and Lennard-Jones energy scaling factor based on the average values. We showed that, by slightly increasing the magnitudes of the partial charges used by GAFF and decreasing the Lennard-Jones energy parameters, slightly better overall property estimations were obtained relative to GAFF. Our results suggest that the use of a polarizable force field might be most important for molecules with small dipole moments, while modest charge scaling can likely yield accurate static dielectric constants for more polar molecules without negatively impacting other properties. To further test the modified GAFF parameters, we plan to compute additional properties, including coexisting densities, vapor pressures, and critical points.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00382.

■

List of calculated dipole moments; fitted linear regression coefficients of density for each molecule; a link to the LAMMPS postprocessing codes to calculate dielectric constant and viscosity; sample LAMMPS input files for 1,2-dimethoxyethane (DME) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1-574-631-5687. Fax: +1-574631-8366. ORCID

Yushan Zhang: 0000-0002-6507-5738 Yong Zhang: 0000-0003-3988-5961 Edward J. Maginn: 0000-0002-6309-1347 Funding

Yo.Z. and E.J.M. acknowledge the support of the U.S. Department of Energy, Basic Energy Science, Joint Center for Energy Storage Research under Contract No. DE-AC0206CH11357. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Computational resources were provided by Notre Dame’s Center for Research Computing. REFERENCES

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Evaluation and Refinement of the General AMBER Force Field for

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