Toward a Molecular Dynamics Force Field for Simulations of 40

Article pubs.acs.org/JPCB

Toward a Molecular Dynamics Force Field for Simulations of 40% Trifluoroethanol−Water J. T. Gerig* Department of Chemistry and Biochemistry, University of California, Santa Barbara, Santa Barbara, California 93106, United States S Supporting Information *

ABSTRACT: Various computational models of trifluoroethanol (TFE) and water have been explored with the goal of finding a system for molecular dynamics (MD) simulations that reliably predict properties of 40% TFE−water (v/v) and can be used in studies of peptide−solvent nuclear cross-relaxation. Models derived by modification of TFE parameters developed by Fioroni et al. (J. Phys. Chem. B 2000, 104, 12347), in combination with either TIP4P-Ew or TIP5P-E water, were most successful. Simulations of 40% TFE−TIP4P-Ew water evidenced separation of the system into large TFE-rich and water-rich domains. With TIP5P-E water, simulations showed aggregation of each solvent component into small clusters. Nuclear spin dipolar interactions between solvent fluorines and the methyl hydrogens of acetate ion dissolved in 40% TFE−water were calculated. The crossrelaxation parameter σHF reckoned for the TFE−TIP5P-E system agreed with experiment while the value calculated using the TFE−TIP4P-Ew system was too low. While the TFE−TIP5P-E model of 40% TFE−water leads to good predictions of the system density, translational diffusion coefficients, and a solvent−solute cross-relaxation parameter, this model performs poorly in predicting the enthalpy of mixing. Preliminary studies of 20% TFE−water and 50% TFE−water suggest that the model will perform with the same characteristics for mixtures that have compositions near 40% TFE−water.

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conformations in TFE−water mixtures.14 Chitra and Smith15,16 have examined six sets of force field parameters for TFE, showing that none of them reliably predict all of the properties of neat TFE or of TFE−water mixtures. Most recent studies of TFE and TFE−water mixtures have tended to rely on the force fields considered by these authors.17−21 We desired a parameter set for TFE−water mixtures that leads to reasonable predictions of intermolecular solvent fluorine−solute hydrogen NMR cross-relaxation terms. Experimental values for these terms are obtainable from studies of solvent−solute nuclear Overhauser effects (NOEs). Comparison of predicted and experimental NOEs could help validate the parameter set used for a simulation while providing a basis for interpretation of unusual solute−solvent cross-relaxation terms. In exploring force field parameters for TFE in water, we looked primarily at agreement of predicted densities and enthalpies of vaporization and mixing with experimental data. Reasonable agreement of calculated translational diffusion coefficients with experiment was also desired since intermolecular NMR cross-relaxation phenomena depend on diffusion of mixture components. Lastly, we wanted to retain compatibility with the AMBER force fields for peptides since these perform well in replicating peptide conformational dynamics.22,23

INTRODUCTION Addition of trifluoroethanol (TFE) or other highly fluorinated aliphatic alcohols to an aqueous solution of a biological material can provoke a change in the dominant conformation(s) of the material and may alter its association with itself or other species.1 Typically, the presence of TFE favors the formation of helical conformations of peptides2−4 and proteins.5 Changes in conformational preference potentially can open new routes to oligomerization or aggregation.3,6,7 A number of mechanisms have been proposed to account for the effects of TFE, and developing an understanding of these continues to be of interest.8−12 Insight at the molecular level into factors that produce the observed effects of fluoroalcohols can potentially be obtained by molecular dynamics (MD) simulations. Simple force fields with a minimal set of adjustable parameters are preferred for MD simulations in order to keep the computational expense of the calculations under control. However, it is often the case that a single set of force field parameters does not lead to reliable predictions of all experimentally observable quantities. Thus, it is no surprise that there appear to be few universally applicable force fields for MD simulations of materials dissolved in trifluoroethanol− water mixtures. Fioroni et al.13 have parametrized a seven-atom model of TFE that provides predictions of several properties of neat TFE that agree with experiment and, in combination with the SPC model of water, properties of TFE−water mixtures as well. This model has been used in explorations of peptide © 2014 American Chemical Society

Received: September 4, 2013 Revised: January 22, 2014 Published: January 24, 2014 1471

dx.doi.org/10.1021/jp408879g | J. Phys. Chem. B 2014, 118, 1471−1480

The Journal of Physical Chemistry B

Article

relaxation contributions to the cross-relaxation parameter σHF describing relaxation of a solute hydrogen by a group of identical solvent F spins is given by

In this work, small adjustments to a set of TFE parameters provided by Fioroni et al.13 led to simulations of neat TFE, 40% TFE−water, and a solution of acetate in 40% TFE−water that afforded predictions of system densities and translational diffusion coefficients close to experimental values. Use of TIP5P-E water generally gave the best results although no model of the TFE−water system led to good predictions of the enthalpy of mixing TFE and water.

σHF =

3 2 2 2 1 3 γH γF ℏ − J 0 (ωH − ωF) + J 2 (ωH + ωF) 4 12 4

{

}

(1)

where γH and γF are gyromagnetic ratios and ωH and ωF are Larmor frequencies. The spectral density functions Jm (ω) are written in terms of the components (x, y, z) of the vector r which connects H−F spin pairs37

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EXPERIMENTAL SECTION Molecular Dynamics Simulations. All simulations were done with GROMACS24 packages running locally on a SUN SunFire X4600 or on the Lonestar, Stampede, and Kraken systems operated by the National Science Foundation (NSF)sponsored XSEDE consortium at the University of Texas and the University of Tennessee. Force field parameters used for TFE are described below, while parameters for the SPC, TIP3P, TIP4P-Ew, and TIP5P-E water models used were taken from the GROMACS distribution. Most parameters for acetate were from the AMBER99SB-ILDN force field.25 Calculations were made using the OPLS26 or REDDB27 charges for acetate. The REDDB atom charges from the literature were adjusted slightly so that they summed to −1.0. In all cases, the combination rule for σ nonbonded parameters was the arithmetic mean (σij = 1 /2(σii + σjj) as used in the AMBER force fields. The combination rule for ε nonbonded parameters was the geometric mean (εij = (εiiεjj)1/2). For simulations of neat TFE, a cubic simulation cell approximately 6.5 nm on a side and containing 2440 TFE molecules was used. Simulations of TFE−water mixtures used 2440 trifluoroethanol molecules and 14,828 water molecules, giving a mole fraction of TFE (0.141) that corresponds to 40% TFE−water (v/v). The cubic simulation box for TFE−water was approximately 9 nm on an edge. For simulations of acetate in 40% TFE−/water, the simulation box contained an acetate ion and a sodium ion. The integration time step was 0.002 ps. The particle mesh Ewald (PME) method for long-range electrostatics was applied,28 as was the long-range correction for the van der Waals interaction described by Allen and Tildesley.29 Cutoffs for electrostatic and van der Waals terms were 1.4 nm. The nonbonded interaction list was updated every 5 steps. Periodic boundary conditions were applied. Motion of the model center of mass was corrected at every step. Covalent bonds of TFE and acetate were constrained to constant length by the LINCS procedure30 while the SETTLE algorithm was used for water.31 Systems were regulated at 298 K and a pressure of 1 bar by use of the Berendsen temperature (velocity rescaling) and pressure coupling methods with relaxation time constants of 0.1 and 1 ps, respectively.32 Simulations to produce trajectories of up to 95 ns duration were carried out after initial equilibration for at least 1 ns. Snapshots of the system coordinates were taken at 0.5, 2.5, or 5 ps intervals. Analyses of Trajectories. Programs contained within the GROMACS package were used to compute the system density, radial distribution functions (RDFs), and self-diffusion coefficients of solvent components via the Einstein relationship.33 The RDFs were calculated as histograms with the distance r incremented by 0.002 nm. Computation of dipolar correlation functions for TFE− acetate (fluorine−hydrogen) dipolar interactions followed the procedure described previously.34 To summarize, assuming that cross-correlation effects are negligible,35,36 the collective

J m (ω) = 2 =2

∫0 ∫0

∞

∞

Gm(t ) e−iωt dt Ncut

⟨{∑ Fijm(0) Fijm(t )}⟩e−iωt dt (2)

j≠i

with r 2 − 3z 2 r5 (x − iy)2 F2 = r5

F0 =

F1 =

z(x − iy) r5

The summation in eq 2 collects all pairwise interactions with the target H spin; these are then averaged over the sample. The strong internuclear distance dependence of Gm(t) dictates that σHF is dominated by interactions of the solute hydrogen with near-neighbor F spins in the solvent. To reduce the computational effort required to evaluate Jm(ω), it is advantageous to limit the number of F spins considered to those that lie within a cutoff distance (rcut) from the H spin. There will be Ncut F spins within this sphere. For the present work, we considered all interactions with trifluoroethanol fluorines that were within 3 nm of a solute hydrogen. It has been shown that a 3 nm cutoff will capture greater than 99.9% of the interactions that contribute to relaxation.38 For isotropic liquids, normalized correlation functions (Gm(t)/Gm(0)) are independent of m and have the same time dependence.39 Following Feller et al.,40 we assumed that normalized functions can be represented by a collection of n exponentially decaying functions: G m (t ) ≅ Gm(0)

t⎞ ⎟ ⎝ τn ⎠ ⎛

∑ an exp⎜− n

(3)

By approximating the decay of Gm(t)/Gm(0) in this way, the Fourier transform of Gm(t) becomes J m (ω) = 2Gm(0) τm(ω)

(4)

with τm(ω) =

∑ n

anτn (1 + (ωτn)2 )

(5)

where ∑nan = 1. Collecting terms, σHF arising from trifluoromethyl fluorines interacting with a solute hydrogen is given by σHF = −6.3086 × 10−8G 0(0) τ0(ωH − ωF) + 5.6777 × 10−7G2(0) τ2(ωH + ωF)

(6)

The units for τ0(ωH − ωF) and τ2(ωH + ωF) are picoseconds. 1472



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Table 1. Properties of Trifluoroethanol Models model

I

II

III

IV

V

Charges

a

C(F) F C(H) H(C) O H

0.699 −0.214 0.041 0.038 −0.525 0.354

0.510 −0.19 0.030 0.090 −0.550 0.400

C−F

0.136

F−C−F C−C−F

109.5 (920.5) 109.5 (920.5)

σF, nm εF, kJ/mol

0.262 0.590

0.503 −0.179 0.048 0.071 −0.586 0.431 Bond Length (nm) 0.135 0.135 Bond Angles (Θ, deg (kΘ, kJ/mol)) 107.6 (644.3) 109.1 (644.3) 111.4 (418.4) 109.0 (418.4) Lennard-Jones Parameters 0.262 0.312 0.590 0.255

0.452 −0.170 0.273a −0.625 0.410

0.452 −0.170 0.135 0.069 −0.625 0.410

0.136

0.135

107.6 (460.2) 111.4 (460.2)

107.6 (460.2) 111.4 (460.2)

0.308 0.347

0.315 0.417

The CH2 group of trifluoroethanol in model IV is treated as a united atom; the parameter given is for the united atom.

Table 2. Calculated Properties of Neat Trifluoroethanol at 298 K TFE model a

I −3

density, kg m ΔHvap, kJ mol−1 DTFE × 109, m2 s−1

a

b

1410, 1376 26.2,a 26.5b 2.3,a 2.5b

II

IIIa

IVc

Va

expt

1703.4 48.1 0.55

1353.5 37.8 1.1

1383. 42.7 0.40

1383.9 44.0 0.70

1382.247 43.9748 0.6849,50

a Value(s) obtained in this work at 298 K with simulations of 2440 TFE molecules. bValue reported by Chitra and Smith at 300 K obtained with simulations of 225 TFE molecules.15 cResults reported by Fioroni et al.13

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To compute Gm(t) for acetate methyl hydrogens, TFE fluorines within the cutoff distance of an acetate hydrogen in the simulation box were determined for a MD trajectory snapshot taken at a time defined as t = 0. Diffusion of the selected solvent fluorines was followed in subsequent snapshots with the quantities F0, F1, and F2 evaluated at each subsequent time step (t). The quantity Fmij (0) Fmij (t) was evaluated and stored so that it was associated with t. The snapshot chosen to represent t = 0 was then advanced along the trajectory and the process repeated. Resulting Fmij (0) Fmij (t) values at a given time were averaged. In the present work, the correlation function typically was represented by 500 points obtained in calculations that averaged about 18,500 evaluations of each time point. The number of TFE fluorines (Ncut) within a 3 nm radius selection sphere of a homogeneous 40% TFE−TIP5P-E water mixture at 298 K is 1140. The number of fluorines observed over the trajectories used for calculation of the acetate hydrogen−solvent fluorine correlation function in this system ranged from 998 to 1360, with an average of 1167. The density of the 40% TFE−TIP4P-Ew water system is slightly different, and, in this case, 1124 TFE fluorines are expected in a 3 nm sphere if the system is homogeneous. Reflecting the higher inhomogeneity of this system compared to the TFE−TIP5P-E system, the number observed over the course of trajectories ranged from 76 to 1894 fluorines, with an average of 724. Fitting of Gm(t)/Gm(0) computed from a MD trajectory to a sum of exponential functions used a local version of Provencher’s program DISCRETE. 41 (See http://sprovencher.com/index.shtml.) The optimum fit to the decay of Gm(t)/Gm(0) typically used four exponential terms.

RESULTS Pure Trifluoroethanol. Table 1 gives five sets of force field parameters for TFE that were evaluated for their abilities to model the neat liquid and a 40% mixture of TFE with water. Model I was proposed by Bodkin and Goodfellow42 and was used by them in a study of a peptide dissolved in 30% TFE− water. Parameters for model I not shown in the table in the original work were taken from an early AMBER force field.43 This model is equivalent to model 4 examined by Chitra and Smith.15 Model II was proposed by Scharge et al.19 and was used in studies of TFE aggregation in the gas and solution phases. The parm99 AMBER force field of Wang et al. formed the basic parameter set.44 Atomic charges for the model were derived by RHF/6-31G* calculations using the RESP approach. Several sets of fluorine Lennard-Jones parameters were considered by these authors. Those of Bodkin and Goodfellow (model M2 of Scharge et al.) were used for the present work. Remaining Lennard-Jones parameters were those of the AMBER99SBILDN force field provided with the GROMACS 4.5.5 distribution.22 Model III is an AMBER force field that includes atomic charges for TFE made available at q4md-forcefieldtools.org/ REDDB/Projects/W-96.45 The remainder of the parameters used were those of the AMBER99SB-ILDN force field provided with the GROMACS 4.6 distribution.22 Model IV, developed by Fioroni et al.,13 is equivalent to model 6 of Chitra and Smith.15 Initial atomic charges and molecular geometries for the Fioroni et al. model were based on the results of ab initio calculations while starting LennardJones parameters were taken from GROMOS96 force field.46 Optimization of parameters was done with the goal of producing accurate predictions of density, enthalpy of vapor1473



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ization, and tracer diffusion coefficients. Model IV includes a united-atom representation of the TFE methylene group and uses geometric averages as the combining rule for LennardJones σij nonbonded parameters. Model V was developed in this work by empirically adjusting parameters for model IV slightly while using AMBER parameters for intramolecular interactions not specifically indicated in Table 1 and the AMBER Lennard-Jones combining rules. The parameters shown in Table 1 for this model were not the result of an optimization. Rather, small improvements in the calculated diffusion constants and system density were sought. Properties of neat TFE at 25 °C were calculated using the five models described. Results are given in Table 2. It was found that models IV and V gave densities, heats of vaporization, and translational diffusion coefficients that agreed well with experimental data while the remaining models gave predictions that were close to one of these data but not all three. Center-of-mass TFE−TFE radial distribution functions calculated for TFE models I, II, III, and V are shown in Figure 1. These are similar to distribution functions obtained with

Table 3. Calculated Properties of 40% Trifluoroethanol− TIP3P Water at 298 K TFE model density, kg m−3 ΔHmix, kJ mol−1 DTFE × 109, m2 s−1 DH2O × 109, m2 s−1

I

II

III

V

expt

1158.2 0.23 1.63 4.01

1228.8 0.53 1.00 4.14

1127.4 −1.30 1.57 3.78

1139.3 0.43 1.04 3.88

1176a 0.06456,57 0.7249,50 ∼1.358,59

a

The experimental density given is the average of interpolations of the data of Gente and La Mesa,47 Palepu and Clarke,60 and Harris et al.49

several additional water models in an attempt to gain improved predictions of the experimental properties of 40% TFE−water. Results of these efforts are shown in Table 4. Table 4. Calculated Properties of 40% Trifluoroethanol− Water at 298 K Using Several Water Models water model −3

density, kg m ΔHmix, kJ mol−1 DTFE × 109, m2 s−1 DH2O × 109, m2 s−1 GTFE−TFE,b cm3 mol−1 GTFE−H2O,b cm3 mol−1 GH2O−H2O,b cm3 mol−1

SPC

TIP3P

TIP4P-Ew

TIP5P-E

expt

1136.4 0.38 0.81

1139.3 0.43 1.04

1152.5 0.27 0.65

1169.5 −0.78 0.66

1176a 0.06456 0.7249,50

3.01

3.88

1.85

1.68

∼1.358,59

5458

4944

6126

226

335c

−3694

−3387

−4174

−270

−333c

2372

2194

2759

155

179c

a

The experimental density given is the average of interpolations of the data of Gente and La Mesa,47 Palepu and Clarke60 and Harris et al.49 b Kirkwood−Buff integrals obtained by numerical integration of 4π∫ [gij(r) − 1]r2 dr from r = 0 to 1.4 nm. The RDFs (gij(r)) were calculated using the center of mass of each solution component. c Estimated from graphs provided by Chitra and Smith.61 Figure 1. TFE center-of-mass radial distribution functions for TFE model I (black), model II (red), model III (green), and model V (blue). These results can be compared to similar plots given by Chitra and Smith,15 Fioroni et al.,13 and Jia et al.51

Calculations done using TFE model V with the TIP4P-Ew62 and TIP5P-E63 models of water gave values for the system density and the translational diffusion coefficients of TFE and water that agreed fairly well with experimental data. The enthalpy of mixing, predicted using the TIP4P-Ew water model, is too large but has the correct (positive) sign while the prediction obtained using TIP5P-E water was negative. Chitra and Smith observed that some simulations of TFE− water mixtures can feature extensive separation of the system components into TFE-rich and water-rich domains.15,16 X-ray scattering data suggest that TFE and water are inhomogeneously mixed with each other, with the extent of TFE and water cluster formation being at a maximum at a TFE mole fraction (∼0.15) that is close to the composition of 40% TFE− water (v/v).54 Dynamic light scattering data from 40 to 60% solutions of TFE in water are consistent with formation of TFE clusters with radii of ∼0.6 nm,64 a result in line with the presence of TFE dimers and trimers.54 We found that simulations of systems at 298 K using model V TFE and SPC, TIP3P, and TIP4P-Ew water models eventually produced large subvolumes within the simulation box that contained high concentrations of TFE or water

model IV,13 with models considered by Chitra and Smith15 and with the GAFF representation of TFE.51 The radius of a sphere representing the TFE molecule has been estimated to be 0.246 nm,52 and the first peaks near ∼0.5 nm in these distribution functions presumably arise from direct interaction of two TFE molecules. In all cases, there are indications of long-range structural order in the liquid that likely are the result of formation of clusters of TFE molecules.18,53,54 Trifluoroethanol−Water (40% (v/v)). Mixtures of 40% TFE in water were modeled using the five sets of TFE parameters given in Table 1 and TIP3P water.55 Results obtained with these systems are in Table 3. The enthalpy of mixing trifluoroethanol and water has a small, positive value at the mole fraction corresponding to 40% TFE−water (v/v).56 None of the TFE models considered in combination with TIP3P water produced values for the density of 40% TFE−water or the diffusion coefficients of the mixture components that agreed with experimental values. TFE model V gave the best accounting of experimental quantities for neat TFE (Table 2). This model was used with 1474



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molecules. Typically the TFE-rich and water-rich volumes emerged after about 10 ns of simulation. Figure 2 shows slices taken through the center of various simulation boxes that illustrate these observations. All water−

Figure 2. Views of a 1 nm slice of the simulation box for simulations of (A) 2440 model V TFE molecules plus 14,828 TIP4P-Ew water molecules equilibrated at 500 K, (B) 2440 TFE molecules plus 14,828 TIP4P-Ew water molecules after cooling to 298 K over 16 ns of simulation, and (C) 2440 TFE molecules plus 14,828 TIP5P-E water molecules at 298 K after 18 ns of simulation. The cubic simulation boxes were approximately 9 nm on a side. Oxygen and hydrogen atoms of water are red and white, respectively, while fluorine and carbon atoms of trifluoroethanol are, respectively, cyan and green. Simulations with model V TFE molecules and SPC or TIP3P water molecules gave results similar to those observed with TIP4P-Ew water (B).

TFE models appeared to be reasonably well-mixed at a sample temperature of 500 K. There were small clusters of TFE molecules under these conditions, but the clusters remained about the same size and were distributed throughout the simulation box over simulation times as long as 10 ns (Figure 2A). When systems initially at 500 K were cooled to 298 K, large TFE-rich domains became apparent after the system had been at this temperature for long times (Figure 2B). After the large, TFE-rich and water-rich regions had formed, the system energy was constant. In contrast, calculations involving model V TFE molecules and TIP5P-E water at 298 K showed small clusters of TFE that remained evenly distributed throughout the simulation box for simulation times in excess of 70 ns (Figure 2C). Heterogeneity within a TFE−-water simulation box was explored by dividing the box into 216 cubes and counting the number of TFE and water molecules in each cube. The ratio of the number of TFE (or water molecules) present to the number expected for a homogeneously mixed system (TFE0, water0) was calculated and the value binned. Ratios calculated for several hundred snapshots of the MD trajectory were averaged. Typical results of such analysis are shown in Figure 3. It was found that after equilibration at 500 K a few cubes contained up to twice the number of TFE or water molecules that would be present if the solvent molecules were homogeneously distributed throughout the simulation box (Figure 3A). However, the most likely numbers of TFE or water molecules present in a cube were clustered around the number of each expected for homogeneous distribution of these components. After equilibration at 298 K, simulations of 40% TFE−water that used SPC, TIP3P, or TIP4P-Ew water models gave results similar to those shown in Figure 3B. In these cases, around 30% of the 216 cubes contained nearly the number of molecules expected for pure water or for pure TFE. In contrast, simulations of 40% TFE−water at 298 K that used the TIP5P-E water model gave results (Figure 3C) that were similar to those found for systems at 500 K, with the

Figure 3. Analysis of the volume homogeneity in simulations of 40% mixtures of TFE and water. The simulation box was divided into 216 equal volume cubes, and the numbers of TFE and water molecules in each cube were determined. The number of a given species was compared to the number expected (TFE0, water0) to be in a cube if the system were homogeneous. The percent of the 216 cubes with a given TFE/TFE0 or water/water0 ratio are shown. Results for (A) 2440 TFE molecules + 14,828 TIP4P-Ew water molecules at 500 K, (B) the same system as in A but at 298 K, and (C) 2440 TFE molecules + 14,828 TIP5P-E water molecules at 298 K. The data in panel B indicate that about 30% of the simulation box was empty or nearly empty of water but contained mostly TFE while about 30% of the box contains mostly water and little TFE. The red data points are for TFE while the black data points represent results for water.

composition of the cubes distributed around the TFE/TFE0 and water/water0 ratios expected for a homogeneous mixture of system components. Center-of-mass TFE−TFE radial distribution functions calculated for the TFE−TIP4P-Ew and TFE−TIP5PE models of 40% TFE−water at 298 K are shown in the Supporting Information. These RDFs are similar to those found for neat TFE (Figure 1) with maxima at ∼0.5 and ∼1.0 nm, consistent with the association of TFE molecules into clusters. Radial distribution functions for the TFE oxygen atoms (go−o(r)) in neat TFE and in these TFE−water mixtures are shown in Figure 4. Neat TFE shows a first maximum at r = 0.278 nm, consistent with formation of O−H···O hydrogen bonds between TFE molecules. The TFE O−O radial 1475



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diffusion coefficients of the mixtures but fails in prediction of heats of mixing over this concentration range. Solvent Spin−Solute Spin Cross-Relaxation. Intermolecular nuclear spin dipolar interactions between spins of solvent molecules and those of solute molecules can lead to detectable intermolecular nuclear Overhauser effects.69 The intermolecular cross-relaxation parameter σsolute,solvent characterizing such interactions depends on the concentrations of the solvent and solute spins, and the details of how the solvent and solute molecules interact with one another, including their relative translational diffusion.39,70 Since simulations using model V of TFE and TIP4P-Ew or TIP5P-E water models did the best in reproducing the diffusion coefficients of the components of TFE−water mixtures (Table 4), calculations using these models were used to explore solute hydrogen− solvent fluorine interactions in solutions of sodium acetate in 40% TFE−water. As shown in the Supporting Information, simulations of the acetate-containing systems gave essentially the same values for the density and translational diffusion coefficients of the solvent components as those reported in Table 4. The translational diffusion coefficient of acetate from the simulations was 0.7 × 109 and 0.8 × 109 m2s−1, respectively, for calculations with TIP4P-Ew and TIP5P-E water. The experimental value is 0.5 × 109 m2 s−1.52 Figure 5 shows how the solvent composition varies within a 3 nm sphere centered on an acetate methyl hydrogen in a

Figure 4. Trifluoroethanol oxygen−oxygen radial distributions functions (go−o(r)) computed from simulations of neat TFE (2440 molecules, black line), 2440 TFE molecules and 14,828 molecules of TIP4P-Ew water molecules (blue line), and 2440 TFE molecules and 14,828 molecules of TIP5P-E water molecules (red line).

distribution calculated for TFE in the TFE−TIP4P-Ew water simulation likewise exhibits a maxima at r = 0.278 nm, confirming the conclusion from the analysis shown in Figure 3 that at least part of the simulated system is similar to neat TFE. A minor feature at 0.278 nm was present in go−o(r) calculated for the TFE−TIP5PE water simulations, but a more intense collection of features from r = 0.37 to 0.45 nm was also present. The latter is consistent with the formation of water-separated hydrogen bonds between TFE molecules in this system. All radial distribution functions calculated for the TFE-SPC, TFE-TIP3P, and TFE-TIP4P-Ew systems show distorted baselines (Figure 4 and Supporting Information). These RDFs are reminiscent of the RDFs found with simulations of poorly mixed (inhomogeneous) systems.65−67 The Kirkwood−Buff (KB) theory of binary solutions relates the radial distribution functions (gij(r)) for solution components i and j to various thermodynamic properties through Kirkwood−Buff integrals of the form Gij = 4π

∫0

∞

[gij(r ) − 1]r 2 dr

(7)

Rigorously, KB integrals are computed from radial distribution functions taken from calculations with grand canonical (μVT) ensembles. However, Chitra and Smith have shown how these can be approximated by data from NpT ensembles by truncating the integration at a distance over which intermolecular interactions are dominant.16,68 For the present work, this distance was set to be 1.4 nm, corresponding to the cutoff distance for electrostatic and nonbonded interactions in the MD force field. Values for the KB integrals calculated with these assumptions are given in Table 3. It was found that KB integrals calculated from the TFE (model V)−TIP5P-E water system are fairly close to experimental values, but, consistent with what has been reported previously,16 other water models lead to KB integrals that are much larger. The generality of the TFE−TIP5P-E model of trifluoroethanol−water developed here was explored in some preliminary simulations of mixtures with compositions ranging from 20% (v/v) to 50% (v/v) TFE in water. The results, shown in the Supporting Information, suggest that the model provides a reasonable accounting of the density and translational

Figure 5. Variation of the ratio of water molecules to TFE molecules present in a sphere of 3 nm radius centered on an acetate methyl hydrogen in a simulation of sodium acetate in 40% TFE−TIP4P-Ew water. The simulation used the OPLS charges for acetate. The red line is at the expected water/TFE ratio for the homogeneous solvent.

simulation of acetate in a 40% (v/v) mixture of model V TFE and TIP4P-Ew water. If TFE and water molecules in the mixture were homogeneously distributed throughout this system, the ratio of the number of water molecules to the number of TFE molecules in a given solvent volume would be 14,848/2440 = 6.08. Figure 5 indicates that acetate ion in this system transitions between the water-rich and TFE-rich environments mentioned previously but that the anion preferentially resides in the water-rich regions of the system. Variations of the water/TFE ratio within a 3 nm sphere centered on an acetate methyl hydrogen in simulations in 40% model V TFE and TIP5P-E water, shown in Figure 6, contrast with these results. While the solvent composition within the 3 1476



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Figure 6. Variation of the ratio of water molecules to TFE molecules present in a sphere of 3 nm radius centered on an acetate methyl hydrogen in a simulation of sodium acetate in 40% TFE−TIP5P-E water. The OPLS charges for acetate were used. The red line is at 6.08, the expected water/TFE ratio if the solvent were homogeneous throughout the sample.

nm sphere in this system again fluctuates rapidly, these fluctuations appear superimposed on more gradual changes of the solvent composition. For time periods of the order of 10 ns, the local environment of an acetate methyl hydrogen tends to be water-rich and then TFE-rich, but, over long times, the average water/TFE ratio tends toward the expected value. Figure 7 shows the normalized correlation function (Gm(t)/ m G (0)) for TFE (fluorine)−acetate (methy1 hydrogen) dipolar interactions, computed for a magnetic field strength of 11.74 T from simulations of acetate in 40% TFE−TIP4P-Ew water. A similar normalized correlation function obtained from simulations that used the TIP5P-E water model is given in the Supporting Information. The correlation function initially decays rapidly with a time constant of ∼0.2 ps to a value of (∼0.5) and then changes more slowly. The rapid initial decay of Gm(t)/Gm(0) is presumably due to rotation and libration of the CF3 groups.34,71 The initial rapid decay contributes little to τm(ω) (eq 5) and was ignored. The slowly decaying part of the correlation function was well-represented by a sum of four exponential terms (Figure 7). Results of analysis of trajectories for systems containing acetate, model V TFE and either TIP4PEw or TIP5P-E water for the parameters shown in eq 6 are given in Table 5. The TFE−fluorine−acetate−methyl hydrogen cross-relaxation parameter σHF estimated for acetate in 40% TFE−water using the hard-spheres treatment of Ayant et al.,70 as has been described for related systems,34,71,72 is 4.5 × 10−3 s−1, in agreement with the results of simulations using the TIP5P-E water model (Table 5). The experimental value for σHF in 40% TFE−water at 298 K is 4 ± 1 × 10−3 s−1,52 consonant with both the Ayant et al. predictions and the simulations using the TIP5P-E water model, and suggesting that model V TFE with TIP5P-E water provides a reliable representation of the 40% TFE−water mixture.

Figure 7. Behavior of the normalized correlation function G(t)/G(0) for interactions of TFE fluorines with acetate methyl hydrogens calculated from a simulation of acetate in 40% TFE−TIP4P-Ew water. OPLS charges for acetate were used. The top panel shows the rapid initial decay, presumably due to the rapid rotation of solvent trifluoromethyl groups. The remaining panels show the fits of the data (red lines) to a sum of four exponential terms which give the τ0 and τ2 values in Table 5. Points were calculated every 0.5 ps for the top panel and every 5 ps for the others.

tional diffusion of pure TFE. The model of Fioroni et al. (model IV, Table 2) features a united-atom representation of the methylene group of TFE and uses the OPLS combination rules for Lennard-Jones parameters. In the present work, model V of TFE is an all-atom model that uses the same combination rules for parameters as the AMBER force field. Three other TFE models, taken from the recent literature, are less successful in predicting the properties mentioned (Table 2). We are ultimately interested in simulations of peptides in 40% TFE−water mixtures. Although commonly used in simulations of materials dissolved in TFE−water mixtures,20 the performance of each TFE model with TIP3P water molecules was generally disappointing. We found that predicted system densities were too low while translational diffusion coefficients for TFE and water were too high no matter which of the TFE models was used. Other models of water were explored. Simulations using TIP4P-Ew and TIP5P-E water afforded predictions of the

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DISCUSSION A model of trifluoroethanol (model V, Table 2), largely based on a parameter set developed by Fioroni et al.,13 gives a good accounting of the density, heat of vaporization, and transla1477



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Table 5. Fluorine−Hydrogen Dipolar Correlation Functions at 11.74 Ta

a

water model

acetate charges

trajectory duration, ns

G0(0) × 10−3

τ0(ωH − ωF), ps

G2(0) × 10−3

τ2(ωH + ωF), ps

σHF ×x 103, s−1

TIP4P-Ew TIP4P-Ew TIP5P-E TIP5P-E TIP5P-E TIP5P-E

OPLS RESP OPLS OPLS RESP RESP

95 24 33 67 35 50

0.3914 0.4082 1.615 1.617 1.356 1.328

19.942 17.903 16.411 16.411 16.428 16.866

0.3065 0.2948 1.015 1.068 0.9007 0.8838

12.529 11.788 11.637 11.726 11.932 11.893

1.7 1.5 5.2 5.4 4.7 4.6

The systems simulated included a single sodium acetate, 2440 molecules of TFE-d2, and 14,828 molecules of water.

(additional) adjustable parameters, might lead to better performance. Further refinement of the force field(s) for TFE−water mixtures is probably needed before MD simulations of biological materials dissolved in these mixtures provide compelling insight into the reasons for the conformational effects produced. A mixture composed of 40% TFE−TIP5P-E water molecules, while exhibiting the formation of TFE and water clusters, is more homogeneous than a mixture of TFE and TIP4P-Ew water in simulations. A solute such as acetate experiences more encounters with TFE in the first system, and this is reflected in the larger fluorine−acetate−methyl hydrogen cross-relaxation parameter (σHF) calculated for this system (Table 5). The agreement of this cross-relaxation parameter with the experimental value provides some evidence that simulations of 40% TFE−water systems using TIP5P-E water are more likely to give results in accord with experimental data in studies of cross-relaxation parameters of other solutes. We are presently exploring this possibility in simulations of small peptides in TFE−water.

density of 40% TFE−water that were close to the experimental value, as were the translation diffusion coefficients of the mixture components. However, no water−TFE model considered was very successful in reproducing the heat of mixing of TFE and water at this composition. The formation of large TFE-rich and water-rich domains during simulations of TFE−water mixtures appears to depend sensitively on the parameter sets, and possibly the parameter combining rules, used for the calculations. Chitra and Smith observed such separations in calculations using all-atom and united-atom models of TFE in conjunction with SPC and TIP3P water. The geometric mean was used for combining Lennard-Jones σ parameters in their work.15,16 Jalili and Akhavan report simulations that employed TFE model I described above, TIP3P water, and the AMBER combining rules that apparently did not show the formation of large TFErich domains although their results did indicate formation of large TFE clusters at TFE mole fractions near that of 40% TFE−water.20 Similarly, simulations of a peptide in 30−40% TFE−water that used TFE model I and SPC/E water and in which the peptide was represented by an AMBER force field did not show this behavior.21 The generally well-performing TFE model IV developed by Fioroni et al.13 shows TFE clustering in simulations done using SPC water and the geometric mean combination rule, but not the incipient phase separation illustrated in Figure 2B. One notes that the heats of vaporization of pure water and pure TFE are essentially identical (∼44 kJmol−1),48,73 implying that intermolecular interactions within each liquid, while not identical in nature, are, in net effect, isoenergetic. The heats of vaporization are generally well-predicted by force fields used for the neat liquids. The enthalpy change when mixing TFE and water is highly dependent on the mole fraction of TFE present, changing sign near the 40% TFE−water composition considered in the present work. None of the TFE−water models encountered in the literature provide a good accounting of the heat of mixing at 40% TFE, suggesting that simple combination of force field parameters for neat TFE and neat water are inadequate for characterizing the new interactions that develop in a TFE−water mixture. It has been found that significant adjustments to the usual treatment of fluorine−hydrogen dispersive interactions in the OPLS-AA force field are required to improve calculated enthalpies of mixing for trifluoroethanol−ethanol mixtures74 and perfluoroalkane−alkane mixtures.75 Such an approach might be fruitfully applied to TFE−water simulations. The explicit inclusion of electronic polarization (ignored by the force fields used in the present work) may offer an avenue for improving agreement of observed and calculated properties of TFE−water mixtures. A number of weak, highly directional interactions with covalent fluorine have come to light,76 and incorporation of these into a force field, such as through

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ASSOCIATED CONTENT

S Supporting Information *

Figures showing center-of-mass TFE−TFE radial distribution functions calculated from simulations of TFE in TIP4P-Ew and TIP5P-E water and plots of the normalized H−F dipolar correlation function for acetate in TFE-TIP5P-E water and tables listing results of simulations of 20% (v/v) and 50% (v/v) mixtures of TFE and water, calculated properties of solutions of sodium acetate in TFE−water, and GROMACS files for implementing the five TFE and two acetate models described herein. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 805-893-2113. Fax: 805893-4120. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

We thank the National Science Foundation (Grant CHE0408415) and the UCSB Committee on Research for supporting the initial phases of this work. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant OCI-1053575. Staff members at the XSEDE supercomputer facilities are thanked for valuable information and guidance. Dr. Kadir Diri of the UCSB Office of Information 1478



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Technology was helpful in facilitating our use of these national facilities.

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