Molecular Force Field for Ionic Liquids V: Hydroxyethylimidazolium

Feb 22, 2010 - Maria A. Tesa-Serrate , Eric J. Smoll , Jr. , Lucía D'Andrea , Simon M. ..... Kiki A. Kurnia , Tânia E. Sintra , Catarina M. S. S. Neve...
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J. Phys. Chem. B 2010, 114, 3592–3600

Molecular Force Field for Ionic Liquids V: Hydroxyethylimidazolium, Dimethoxy-2Methylimidazolium, and Fluoroalkylimidazolium Cations and Bis(Fluorosulfonyl)Amide, Perfluoroalkanesulfonylamide, and Fluoroalkylfluorophosphate Anions Karina Shimizu,†,‡ Dimitrios Almantariotis,§,⊥ Margarida F. Costa Gomes,§,⊥ Agı´lio. A. H. Pa´dua,*,§,⊥ and Jose´ N. Canongia Lopes*,†,‡ Centro de Quı´mica Estrutural, Instituto Superior Te´cnico, 1049 001 Lisboa, Portugal, Instituto de Tecnologia Quı´mica e Biolo´gica, UNL, AV. Repu´blica Ap. 127, 2780 901 Oeiras, Portugal, UniVersite´ Blaise Pascal, Laboratoire Thermodynamique et Interactions Mole´culaires, Clermont UniVersite´, BP 10448, F-63000 Clermont-Ferrand, France, and CNRS, UMR 6272, LTIM, F-63177 Aubière, France ReceiVed: December 21, 2009; ReVised Manuscript ReceiVed: February 2, 2010

In this article, the fifth of a series that describes the parametrization of a force field for the molecular simulation of ionic liquids within the framework of statistical mechanics, we have modeled cations belonging to the hydroxyethylimidazolium, dimethoxy-2-methylimidazolium, and fluoroalkylimidazolium families and anions of the bis(fluorosulfonyl)amide, perfluoroalkanesulfonylamide, and fluoroalkylfluorophosphate families. The development of the force field, created in the spirit of the OPLS-AA model in a stepwise manner and oriented toward the calculation of equilibrium thermodynamic and structural properties in the liquid and crystalline phases, is discussed in detail. Because of the transferability of the present force field, the ions studied here can be combined with those reported in our four previous publications to create a large variety of ionic liquids that can be studied by molecular simulation. The present extension of the force field was validated by comparison of simulation results with experimental crystal structure and liquid density data. Introduction 1–4

In a series of previous publications, we have described the development of a transferable all-atom molecular force field and its application to the simulation of different families of ionic liquids. Molecular simulations are important predictive and interpretative tools in the field of ionic liquid research, for a number of reasons. One is that the field is relatively new, and experimental information is still scarce. Another is that molecular simulation provides fundamental insights into the physical chemistry of these liquids. The situation is complicated by the enormous variety of ionic liquids, which poses difficulties for systematic study. The alternative is to establish structure-property relationships from sound physicochemical bases, and here, the contribution of atomistic simulation has been major. Different types of simulations have been reported in the literature, raging from quantum descriptions (Car-Parrinello)5 to coarse-grained mesoscopic models.6 Our approach lies between these extremes and is based on an atomistic description since we think that it is important to retain a level of detail in the models; ionic liquids are defined by a balance between van der Waals and Coulomb forces and by their flexible, asymmetric molecular architectures. However, with present-day resources, it is impossible to attain the time and space scales necessary to describe ionic liquid systems due to the number of atoms involved and their slow dynamics. The molecular force field model is here extended to families of cations and anions that have emerged recently as new and useful constituents of ionic liquids, following two directions. * To whom correspondence should be addressed. † Instituto Superior Te´cnico. ‡ Instituto de Tecnologia Quı´mica e Biolo´gica. § Clermont Universite´. ⊥ CNRS.

One direction is related to the concept of task-specific ionic liquids,7 in which “traditional” ions are modified by the introduction of chemical functional groups in view of specific applications. These functional groups either bring new chemical or physical properties to the ionic liquid or improve its performance when used in a device or process. One of the most common homologous series of cations that compose ionic liquids is that of dialkylimidazolium ions, and these cations can form the basis of such task-specific ionic liquids. Alkylimidazolium cations are already described by the present force field,1,3,4 and the molecular model is now extended to include functionalized alkyl side chains of different types, hydroxyalkylimidazolium, dimethoxy-2-methylimidazolium, and fluoroalkylimidazolium. The first cation differs from other imidazolium-based cations by a hydroxy group directly linked to the second carbon of the alkyl side chain (cf. Chart 1 below). The second cation includes two methoxy groups directly linked to the nitrogen atoms of the imidazolium ring and a methyl group linked to the C2 carbon of the same ring. The third constitutes a series of imidazolium cations in which the alkyl side chain is perfluorinated beyond the second carbon since it would be difficult to synthesize imidazolium cations in which the first and second carbon atoms of the chain are also perfluorinated. Alkylimidazolium cations with side chains functionalized by an amine group have already been described as an extension to the present force field;8 therefore, we have not repeated that work here. As the present force field model was designed with transferability in mind, some of the parameters for the new functionalized cations could be transferred from other previously studied imidazolium-based cation families. This is possible if introduction of a substituent or functional group has negligible effects on distant parts of a molecule, and has to be checked. Inevitably,

10.1021/jp9120468  2010 American Chemical Society Published on Web 02/22/2010

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CHART 1: Adopted Nomenclature for the Interaction Sites in the (i) 1-(2-Hydroxyethyl)-3-methylimidazolium Cation, [C2OHmim]+; (ii) 1,3-Dimethoxy-2-methylimidazolium Cation, [(OMe)2mim)]+; (iii) 1-(2-Perfluoroalkyl)-ethyl-3methylimidazolium, [CnF2(n-2)+1H4mim]+; (iv) Bis(fluorosulfonyl)amide Anion, [N(SO2F)2]-; (v) Perfluoroalkanesulfonylamide Anions, [(CmFnSO2)N(SO2CxFy)]-; and (vi) Fluoroalkylfluorophosphate Anions, [PFy(CmFn)x]-

these parameters that are transferable have to be completed with calculations specifically performed to describe the functional groups introduced in the ions studied here and neighboring atoms whose properties are modified. The present study also addresses the bis(fluorosulfonyl)amide, perfluoroalkanesulfonylamide, and fluoroalkylfluorophosphate classes of anions. The success of the bistriflamide ([N(SO2CF3)2]- or [NTf2]-) anion as a constituent of very stable, hydrophobic ionic liquids prompted the investigation of new anions with similar molecular structures. The trifluoromethanesulfonate, or triflate, anion ([CF3SO3]-) is widely used and has already been parametrized in the present force field.2 It can be regarded as one rigid “half” of a bistriflamide anion. In this work, the force field is generalized to bis(perfluoroalkanesulfonyl)amides of any chain length, including the shortest bis(fluorosulfonyl)amide anion9 ([N(SO2F)2]-). Tsuzuki et al.10 have published force field parameters for the bis(pentafluoroethylsulfonyl)amide, or BETI, anion ([N(SO2C2F5)2]-), basing their work on our own force field with some modifications that include the reparameterization of certain parameters in order to improve the prediction of liquid densities. In the interest of consistency and transferability, we recalculated here the parameters for the entire series of anions. Finally, the fluoroalkylfluorophosphate anions, which contain a varying number of fluoroalkyl chains linked to a fluorophosphate core, have been associated with ionic liquids capable of solubilizing large amounts of CO2.11 Similarly to the case of the bistrisflamide derivatives mentioned in the previous paragraph, the fluoroalkylfluorophosphate anions can be consideraded as long-chain versions of the commonly used hexafluorophosphate anion, [PF6]-. We found in the literature one computational study on a member of the fluoroalkylfluorophosphate family of anions11 ([PF3(C2F5)3]-) described at the unitedatom level and with no detailed conformational analysis describing the attachment of the fluoroalkyl chains to the phosphorus atom.

In order to develop a new set of parameters for the ions under discussion that is fully compatible with the previously established force field,1–4 the following steps were carried out: (i) ab initio quantum mechanical calculations to determine the geometrical and conformational parameters (bond lengths, valence angles, torsion energy profiles) that are not yet included in the OPLS-AA12 or AMBER13 force fields; (ii) quantum mechanical calculations of electrostatic charge distributions; and (iii) validation of the obtained parametrization by molecular dynamics simulations to calculate condensed-phase properties of the ionic liquids and compare the results with crystal structure and liquid density experimental data. A more detailed description of the complete methodology can be found elsewhere.1 Results and Discussion Force Field Development. The present force field has the same functional form as the widely used OPLS-AA molecular force field bonds

uR,β )

∑

kij (r - r0,ij)2 + 2 ij

ij dihedrals

angles

∑ ijk

θij (θ - θ0,ijk)2 2 ijk

4

Vm,ijkl [1 - (-1)m cos(mφijkl)] + 2 m)1

∑ ∑

ijkl nonbounded

∑ ij

{ [( ) ( ) ] 4εij

σij rij

12

-

σij rij

6

+

1 qiqj 4πε0 rij

}

(1)

with the traditional decomposition of the potential energy, uRβ, into covalent bond stretching, valence angle bending, torsion barriers around dihedral angles, and atom-atom pairwise repulsive, dispersive, and electrostatic contributions. The Coulomb interactions are defined in terms of atomic point charges, while the (12-6) Lennard-Jones potential describes the repulsive

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and dispersive terms. Together, they act either between sites in different molecules or between sites in the same molecule separated by three or more bonds. A scaling factor of 0.5 is applied to the Lennard-Jones and Coulombic interactions when sites in the same molecule are exactly three bonds apart. It is important to stress that the function represented in eq 1 is slightly different from that adopted by the OPLS-AA convention; in our case, some of the bonded interactions (bonds and angles) are described by harmonic potentials that have their force constants divided by a factor of 2 (in the OPLS-AA/AMBER function,12,13 only the coefficients of the dihedral cosine series are divided by 2). Bond and Angle Parameterization. The OPLS-AA/AMBER force field includes parameters describing covalent bonds and valence angles for a wide variety of chemical structures. Although the transferability of such parameters can usually be performed in a reliable and straightforward manner, it must not be taken for granted. In other words, it is important to compare the bond and angle parameters to be transferred with available experimental structural data such as X-ray diffraction data for the target molecules and apply corrective measures whenever necessary. In general, for the purpose of using the force field to simulate equilibrium thermodynamics properties in condensed phases, it is easier to transfer bond and angle force constants values, kr and kθ, than the corresponding equilibrium distances and angles, r0 and θ0, which affect directly the geometry and conformations of the molecules. For the cations presented in this work, the bond and angle parameters were taken from one of our previous studies on imidazolium cations.1 For the methoxy groups linked to the imidazolium ring and the hydroxy group present in the side chain, parameters were taken from the OPLS-AA/AMBER force field12 (cf. Table 1). For perfluoroalkyl chains, whether in fluoroalkylimidazolium cations, in bis(fluoroalkylsulfonyl)amides, or in fluoroalkylfluorophosphates, the parameters were taken from the OPLS-AA force field for perfluoroalkanes.14 It is expected that these parameters describe the perfluoroalkyl chains beyond a certain distance from their attaching points to the ions, as will be discussed below. For the anions, bond and angle parameters were directly transferred from the OPLS-AA/AMBER force field whenever possible. However, in the case of [N(SO2F)2]-, some bonds and angles, such as the N-S and S-O bonds and the O-S-O, O-S-N, and S-N-S angles, which had already been parametrized by us for the bistriflamide anion,2 were taken from our own force field. The same applies to the perfluoroalkanesulfonylamide ions, where all bonds and almost all angles had been previously parametrized for the bistriflamide ion and the perfluoroalkane class of compounds, and to the fluoroalkylfluorophosphate ions, where all bonds and most angles had already been parametrized for the hexafluorophosphate ion.1 The correct transferability of most of the previously obtained parameters was confirmed by calculating ab initio the equilibrium distances and angles in bistriflamide, hexafluorophosphate, and perfluoroalkane compounds and in the present ions. The differences were always less than 2 pm or 1 degree of arc. In cases where the parameters from the OPLS-AA/AMBER force field could not be transferred, ab initio calculations were performed using the Gaussian package.16 The missing equilibrium distances and angles were estimated by geometry optimization at the RHF level with 6-31G(d) basis sets, as recommended by Friesner et al.15 Missing stretching and bending force constant were obtained by frequency calculations. In some cases, this type of calculation is ineffective due to the ill-conditioning

Shimizu et al. of the transformation matrices that convert normal modes to internal molecular coordinates. Whenever this occurred, the correlation proposed by Halgren17 was used to assign the corresponding angle bending force constants. All values obtained are presented in Table 1. The comparison between X-ray diffraction data available in the literature and the equilibrium bond lengths and angles calculated ab initio yields in most cases differences lower than 1 pm or 3 degrees of arc, respectively. These differences are due not only to the uncertainty associated with the experimental determinations and to the approximations performed during the ab initio calculations (geometry optimization) but also to the simple fact that the ions are experiencing completely different environments in each case s a crystalline ionic lattice in the case of the X-ray experiments and vacuum in the case of the ab initio calculations. In fact, the small differences (of the same magnitude as that observed in the earlier works1–4) warrant the use of ab initio calculations and the existing OPLS geometrical parameters to model the ions of an ionic liquid. One remarkable exception to this tendency is the difference between the angle PX-CX-CX in the [FEP]- anion obtained by ab initio calculations and the experimental X-ray data. Ab initio calculations tend to overestimate this value by 4.5 arc degrees. This large difference seems to indicate that in this case, the intermolecular interactions in the crystalline phase, not considered in the single-ion calculations, play a significant role in the definition of the intramolecular geometry of the anions. After much deliberation, we decided to use the ab initio result for two reasons; first, there is only one available X-ray structure, which means that we do not know how the geometry will evolve for other members of the family; second, we do not know if this distortion caused by the “packing” interactions in the crystalline phase will also play a similar role in the liquid state (where most simulations for this type of compounds will occur). Partial Charge Parameterization. In agreement with the philosophy behind OPLS-AA force field development, the Coulomb interactions were modeled by partial charges positioned at the center of mass of each atom. These interactions that describe the electrostatic forces acting on each ion are calculated ab initio at the MP2 theoretical level using a quite large basis set, cc-pVTZ(-f). An electrostatic surface potential methodology (ChelpG)24 was used to determine the point charges from the corresponding electronic density functions. Since electrostatic surface potential fits yield charges that vary with the molecular conformation, in the case of ions with multiple stable conformers, the charges in each atom were assigned using a weighted averaging process. On the other hand, and for the sake of simplicity, the chosen set of charges should form a scheme that is transferable between similar molecules, for example, along a homologous series or family of ions. Furthermore, the charge scheme should be consistent with other molecular residues described within the OPLS-AA framework. As a result, the overall electrostatic charge of a given functional group can be constrained in some cases and present deviations from the values obtained ab initio. In other words, there is a compromise between the accuracy of the point charge definition for a given ion and the transferability of point charges within families of ionic liquids. In order to minimize errors and make educated choices, different sets of charges were calculated for different members of a selected ionic liquid family and the resulting trends analyzed and incorporated in the charge assignment process.1–4 For the cations, only few atoms had their charges reparameterized. The atoms in question are C2O in the case of the 1-(2-

Molecular Force Field for Ionic Liquids

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TABLE 1: Force Field Parameters for Ionic Liquids Containing 1-(2-Hydroxyethyl)-3-methylimidazolium, 1,3-Dimethoxy-2-methylimidazolium, 1-(2-Perfluoroalkyl)-ethyl-3-methylimidazolium, Fluoroalkylimidazolium, Bis(fluorosulfonyl)amide, Perfluoroalkanesulfonylamide, and Fluoroalkylfluorophosphate ionsa 1-(2-Hydroxyethyl)-3-methylimidazolium, [C2OHmim]+ atoms

q (au)

ε (kJ mol-1)

σ (Å)

dihedralangles

V1(kJmol-1)

V2(kJmol-1)

V3(kJmol-1)

C2O

0.275

0.27614

3.50

NA-C1-C2O-OH

-3.5787

-1.6564

4.9154

1,3-Dimethoxy-2-methylimidazolium, [(OMe)2mim]

+

atoms

q (au)

ε (kJ mol-1)

σ (Å)

bonds

r0 (Å)

kr (kJ mol-1 Å-2)

r0 (Å) XR18

CRO CON ONA

-0.11 -0.07 -0.18

0.27614 0.27614 0.58615

3.50 3.50 2.90

CT-ONA NA-ONA

1.410 1.341

2678.0 3768.0

1.447 1.361

angles CR-NA-ONA CW-NA-ONA NA-ONA-CT

θ0 (deg) Kθ (kJ mol-1 rad-2) θ0 (deg) XR 123.4 124.8 113.1

703.8 672.5 801.8

dihedral angles

V1 (kJ mol-1) V2 (kJ mol-1) V3 (kJ mol-1) V4 (kJ mol-1)

CW-NA-ONA-CT CR-NA-ONA-CT NA-ONA-CT-HC

121.5 124.3 110.1

7.2779 0 0

6.2995 0 0

3.1427 0 7.9460

4.9123 0 0

1-(2-Perfluoroalkyl)-ethyl-3-methylimidazolium, [CnF2(n-2)+1H4mim]+ atoms

q (au)

ε (kJ mol-1)

σ (Å)

dihedral angles

V1 (kJ mol-1)

V2 (kJ mol-1)

V3 (kJ mol-1)

C1H C3F

-0.05 +0.12

0.27614 0.27614

3.50 3.50

C3F-C2H-C1H-NA

-4.0582

-3.6527

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Bis(fluorosulfonyl)amide, [N(SO2F)2]atoms

q (au)

ε (kJ mol-1)

σ (Å)

bonds

r0 (Å)

kr (kJ mol-1 Å-2)

r0 (Å) XR19

F

-0.130

0.222

2.95

F-S

1.575

1879.0

1.563

angles

θ0 (deg)

Kθ (kJ mol-1 rad-2)

θ0 (deg) XR

F-S-N F-S-O

103.0 104.1

902.0 1077.0

103.9 104.2

dihedral angles

V1 (kJ mol-1)

V2 (kJ mol-1)

V3 (kJ mol-1)

0 11.445

0 -15.186

-0.015 -3.212

O-S-N-S F-S-N-S

Perfluoroalkanesulfonylamide, [(CmFnSO2)N(SO2CxFy)]atoms

q (au)

ε (kJ mol-1)

σ (Å)

angles

θ0 (deg)

kθ (kJ mol-1 rad-2)

θ0 (deg) XR20

C1F

0.19

0.27614

3.50

SBT-C1F-CS/T

115.9

418.4

116.1

dihedral angles

V1 (kJ mol-1)

V2 (kJ mol-1)

V3 (kJ mol-1)

dihedral angles

V1 (kJ mol-1)

V2 (kJ mol-1)

V3 (kJ mol-1)

V4 (kJ mol-1)

SBT-C1F-CS/T-FA OBT-SBT-C1F-CF

0 0

0 0

1.4530 -0.7400

NBT-SBT-C1F-CF SBT-C1F-CSF-CF

-3.0940 50.0900

0 0

0 -4.6260

0 -4.0080

Fluoroalkylfluorophosphate, [PFy(CmFn)x]atoms

q (au)

ε (kJ mol-1)

σ (Å)

angles

θ0 (deg)

kθ (kJ mol-1 rad-2)

θ0 (deg) XR18

P5 P4 P3 CD3 F3D CF2 F2C CF3 F3C

1.10 0.86 0.62 0.51 -0.22 0.24 -0.12 0.42 -0.19

0.83680 0.83680 0.83680 0.27614 0.25520 0.27614 0.25520 0.27614 0.25520

3.74 3.74 3.74 3.50 3.12 3.50 3.12 3.50 3.12

FX-PX-CFX PX-CX-FX PX-CX-CX CX-PX-CX

90.0 112.3 119.5 90.0

982.9 523.3 422.7 858.5

90.0 109.5 124.0 89.99

dihedral angles

V1 (kJ mol-1)

V2 (kJ mol-1)

V3 (kJ mol-1)

dihedral angles

V1 (kJ mol-1)

V2 (kJ mol-1)

V3 (kJ mol-1)

V4 (kJ mol-1)

FX-PX-CX-FX PX-CX-CX-FX PX-CX-CX-CX

0 -0.5685 28.9568

0 1.2678 10.7287

0 7.5851 -19.3573

FX-PX-CX-CX CX-PX-CX-CX CX-PX-CX-FX

-0.0862 31.6107 -0.1218

-0.1015 -2.3396 -0.2699

0.0888 -2.9449 -3.2203

4.3994 -8.3914 0

a Values in bold refer to parameter values taken from OPLS-AA/AMBER.12 Also included for comparison purposes are experimental values obtained by X-ray diffraction (XR) of equilibrium bond lengths and angles of crystals containing the ions under discussion.

hydroxyethyl)-3-methylimidazolium and CRO, CON, and ONA in the case of the 1,3-dimethoxy-2-methylimidazolium, that is, most are atoms directly attached to the new residues. In fact, in

the case of the latter cation, there is a rather unexpected result since the introduction of the methoxy groups directly linked to the nitrogen atoms of the imidazolium ring does not change

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significantly the point charges of the atoms of the ring. It is important to stress that the charge on the CRO carbon atom linked to the CRM atom of the imidazolium ring (cf. Chart 1) suffers a significantly change from -0.26 au in the analogous 1,2,3trialkylimidazolium ion4 to -0.11 au in the 1,3-dimethoxy-2methylimidazolium ion, whereas the charge on CRM is not affected. On the other hand, the point charges on the methoxy group, CON and ONA, are rather different from the OPLS-AA values for ether groups.12 In the fluorinated chain imidazolium cations, only two atoms need to be modified, the first fluorinated carbon C3F and also the first atom of the chain, C1H, which is bonded to the NA of the imidazolium ring. The proposed new charges in [CnF2(n-2)+1H4mim]+ are q(C1H) ) -0.05 au, and q(C3F) ) +0.12 au. For all of the remaining atoms, only minor deviations (i.e., smaller than (0.1 au) from the charges of a perfluorinated alkane or an alkylimidazolium cation were obtained, and the original partial charges could be transferred to the new cations. For example, the second hydrogenated carbon, connected to the perfluorinated segment, has a partial charge of q(C2H) ) +0.01 au as in alkylimidazolium cations. In the case of the [N(SO2F)2]- anion, it was possible to keep all of the atomic point charges that modeled the bistriflamide anion,2 except the charge on the fluorine atom that changed from -0.16 au in bistriflamide2 to -0.13 au in [N(SO2F)2]-. This kind of tranfereability between analogous ions is one of the hallmarks of the present force field. In the case of perfluoroalkanesulfonylamide, some of the point charges (CBT, NBT, SBT, and OBT) were taken once more from bistriflamide,2 whereas other point charges (CSF, CTF, and F) were assumed to be perfluoroalkane values.14 The only exception to this trend was the first carbon of the fluoroalkyl chain, C1F, with an assigned charge of +0.19 au. For the fluoroalkylfluorophosphate, only the point charges assigned to the fluorine atoms directly attached to the phosphorus atom were transferred from the hexafluorophosphate anion.1 It was found during the ab initio calculations that the atomic point charges of all of the atoms contained in the new residues (P5, P4, P3, CD3, F3D, CF3, F3C, CF2, and F2C) vary quite considerably according to the number and relative position of the fluoroalkyl chains present in the anion. In this case, it was necessary to find a point charge scheme that would encompass in a transferable manner the different series of analogous compounds (mono-, bi-, and trisubstituted fluorophosphates). Such a scheme is implicit in the values reported in Table 1. Dihedral Angle Parameterization. The conformational energy and structure of the flexible ions that compose most ionic liquids are determined by the force field terms describing the dihedral angles. Accordingly, particular attention was given to the calculation of those terms, and the same procedures as those described elsewhere1–4 were applied here. It should be noted that the parameters for torsion energy profiles depend on the partial charges previously calculated since, when undergoing internal rotations, the potential energy is affected not only by the dihedral terms (described by a cosine series with appropriate parameters) but also by van der Waals and Coulomb interactions between atoms of the same molecule, whose positions change during the internal rotation. Therefore, it is more correct to obtain first the partial charges and only then to calculate the dihedral terms. Several ab initio calculations using constrained configurations of the dihedral angle under analysis were implemented and the corresponding torsion energy profile obtained. These calculations include geometry optimizations at the RHF/6.31G(d) level, followed by energy calculations at the MP2/cc-pVTZ(-f) level.

Shimizu et al.

Figure 1. Torsion potential energy profiles (TPEP) for two selected dihedral angles, (a) NA-C1-C2O-OH in the 1-(2-hydroxyethyl)-3methylimidazolium cation and (b) FX-PX-CX-CX in the fluoroalkylfluorophosphate anion. Total TPEP (filled squares and full line), nonbonded TPEP obtained by MD (empty circles and dotted line), and total TPEP obtained by MD with the fitted dihedral parameters (dashed line).

Second, a series of molecular dynamics runs using the DL_POLY package21 were performed under similar constraint conditions and with the parameters of the selected dihedral set to zero (only nonbonded interactions were considered). These two procedures allow the separation of the dihedral angle interactions into bonded and nonbonded contributions. Finally, the difference between the two torsion potential energy profiles obtained in the two steps was fitted to an appropriate function (generally a cosine series), and the dihedral angle parameters (V1 to V4 in eq 1) were obtained. Further details concerning this methodology and its successful application can be found in previous publications about the present force field.1–4 The torsion potential energy profiles of selected dihedral angles of two of the ions under study can be appreciated in Figure 1a and b. In the case of 1-(2-hydroxyethyl)-3-methylimidazolium, only one dihedral angle parameter had to be calculated; all others had been previously calculated for ions with similar dihedral angle structures. The dihedral angle in question is NA-C1-C2O-OH, and it models the movement of the hydroxy group linked at the end of the alkyl side chain. The calculated parameters are given in Table 1, and the corresponding torsion potential energy profile is illustrated in Figure 1a. In this case, a three-term cosine series yields an excellent fit between the ab initio values and those obtained by MD simulation using the complete force field, with a difference of just 1.4 kJ mol-1 at 127° (one of the energy maxima) For 1,3-dimethoxy-2-methylimidazolium, three new dihedral angles had to be computed, corresponding to the CW-NA-ONA-CT,

Molecular Force Field for Ionic Liquids

Figure 2. Torsion energy profile around the C3F-C2H-C1H-NA dihedral of the region where the fluorinated alkyl chain is attached to the imidazolium head group.

CR-NA-ONA-CT, and NA-ONA-CT-HC sequences. The last of these dihedral angles has a three-fold symmetry, and only the V3 term is non-null. In contrast, the first dihedral angle (CW-NA-ONA-CT) is rather complex, and a cosine series with four terms was required to represent the torsion energies with an average deviation of 2.3 kJ mol-1 from the ab initio values. The largest difference was observed at 180° (the energy maximum), corresponding to a deviation of 6.3 kJ mol-1. The complexity of the energy profile reflects the possibility of the ion to adopt different stable conformations by rotation of the CW-NA-ONA-CT dihedral angle, a situation analogous to that of the previously studied 1-ethyl-3-methyimidazolium cation.22 In imidazolium cations with a fluorinated alkyl side chain, specific force field parameters were developed here concerning the atoms and bonds near the junction of the fluorinated chain with the imidazolium ring. The two carbon atoms of the chain near the imidazolium ring were left hydrogenated since this spacer facilitates the synthesis of the cations. The perfluorinated segment of the chain is represented by existing OPLS-AA parameters for perfluoroalkanes,14 and the junction with the hydrogenated spacer is represented by a specific parameter for semifluorinated alkanes (or perfluoroalkane-alkane diblocs).23 In order to describe the conformations of fluorinated chain imidazolium cations, only the torsion energy profile corresponding to the C3F-C2H-C1H-NA dihedral angle need to be calculated. With these parameters, the torsion energy profile is reproduced as shown in Figure 2. The parameters calculated in this work to describe torsion energy profiles are given in Table 1. For the bis(fluorosulfonyl)amide and perfluoroalkane-sulfonylamide anions, many of the dihedral angle parameters were taken from the specific force field for bistriflamide previously developed by us.2 However, two and four new dihedral angles had to be calculated for bis(fluorosulfonyl)amide and perfluoroalkanesulfonylamide, respectively. These are the O-S-N-S and F-S-N-S dihedral angles for the first anion and the SBT-C1F-CS/T-FA, OBT-SBT-C1F-CF, NBT-SBT-C1F-CF, and SBT-C1F-CSF-CF dihedral angles for the second anion, which are given in Table 1. The F-S-N-S dihedral angle was fitted by a three-term cosine series with an average deviation of 1.3 kJ mol-1 from the ab initio values. On the other hand, the dihedrals O-S-N-S, SBT-C1F-CS/T-FA, and OBT-SBT-C1F-CF have a three-fold symmetry (similar to the previously mentioned NA-ONA-CT-HC dihedral in the 1,3-dimethoxy-2-methylimi-

J. Phys. Chem. B, Vol. 114, No. 10, 2010 3597 dazolium cation), and once more, only the V3 term is non-null. Finally, the dihedral NBT-SBT-C1F-CF has a two-fold symmetry, and only the V1 term is non-null. In these cases, the fitting process was simple and accurate. Finally, the SBT-C1F-CSF-CF dihedral angle represented a more complex situation and had to be fitted to a four-term cosine series. For fluoroalkylfluorophosphate, the entire set of dihedral angle parameters had to be calculated in order to model the conformations of the alkyl side chains around the central phosphorus atom. The six new dihedrals are FX-PX-CX-FX, PX-CX-CX-FX, PX-CX-CX-CX, FX-PX-CX-CX, CX-PX-CX-CX, and CX-PX-CX-FX, presented in Table 1. The first dihedral was set to zero since the difference in the energy between the conformations in the entire torsion potential energy profile is very small (0.02 kJ mol-1). For dihedrals PX-CX-CX-FX, PX-CX-CX-CX, and CX-PX-CX-FX,a cosine series with three terms could represent the torsion potential energy profiles with average deviations of 0.6, 1.7, and 0.8 kJ mol-1 from the ab initio values, respectively. Finally, the last two dihedrals (FX-PX-CX-CX and CX-PX-CX-CX) had to be adjusted with a cosine series with four terms. The average deviations found for these dihedrals are 0.4 and 1.0 kJ mol-1, respectively. An illustration of the excellent fit between the force field (MD) and ab initio values for the FX-PX-CX-CX dihedral angle is shown in Figure 1b. Lennard-Jones Parameters. The Lennard-Jones (12-6) potential function represents the repulsion-dispersion terms in the OPLS-AA force field. For cations, the Lennard-Jones parameters for each type of atom were taken from the OPLSAA model of heterocyclic aromatic ring compounds12 and from perfluoroalkanes.14 An analogous methodology was employed for the anions, where most OPLS-AA nonbonded parameters had already been adapted to similar molecules.12,14,25 The repulsive-dispersive unlike interactions between atoms of different types were computed using combining rules with geometric means for both σ and ε. Validation. As far as the equilibrium thermodynamic properties of ionic liquids are concerned, volumetric properties (still) represent the most reliable and extensive set of experimental data. Therefore, and as in previous works concerning this force field,1–4 the performance of the extended parametrization was tested by comparing simulated molar densities and structural parameters with experimental ones. The comparisons included volumetric data both in the liquid and/or crystalline phases of ionic liquids where at least one of the ions was one of the new species under discussion. It must be stressed that other thermophysical properties of ionic liquids that can assist in the validation of molecular force fields (e.g., vapor-liquid equilibrium data) started to emerge in the literature in recent years.26 However, these results are still limited to a few selected ionic liquid families (notably, 1-alkyl-3-methylimidazolium bistriflamide ionic liquids), which means that a new refinement and validation strategy is not applicable to most of the ions modeled so far by the present force field and is applicabel to none of the new ions under discussion. In fact, and if one wants to keep the transferability of parameters between families of ionic liquids and the integration with the OPLS-AA framework, the only valid route continues to be to (re)parametrize of those parts of the force field that can be quantified through ab initio or MD calculations (geometrical parameters, torsion profiles, electron density, and point charge distribution) and leave the empirical nonbonded parameters (Lennard-Jones coefficients) unchanged from their

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OPLS-AA values. Validation should be performed using structural and volumetric data. This does not mean that particular ionic liquids or ionic liquid systems cannot be modeled using other methodologies when some specific, subtler effects are under analysis. Indeed, a number of diverse publications aimed to improve the predictive power of the present and other force fields (either by tackling the question of electron polarization27 and charge transfer28 or by adjustments of the OPLS nonbonded interaction parameters29,30) were published very recently. These are important developments that do not interfere or compete with the existence of the present, more general force field that is suitable for predicting with a good degree of confidence many of the available static thermodynamic properties (and even some transport properties31) and access important information related to the complex structure of ionic liquids.22,32 The main improvement in the description of molecular interactions that could be brought to general, classic force fields is the explicit inclusion of electronic polarization. It is in systems containing charged species interacting with polarizable ones that these nonadditive contributions are expected to have the largest impact, and ionic liquids containing delocalized π-electrons are one such case. Different methods of including explicit electronic polarization have been proposed, namely, fluctuating charge models, induced dipoles, or Drude oscillators (also called “core-shell” models).33 They are more difficult to implement in simulation codes and are more computationally demanding when compared to fixed charge simulations. Technically, some methods of treating polarization can be added to existing force field parameter sets. However, results have not always been better than when using fixed charged versions, for example, in the prediction of thermodynamic or structural properties. It is likely that an overall optimization of the intermolecular terms is required in order to attain good predictions of dynamic and equilibrium properties using polarizable models. Recent reviews of the state of the art33,34 tell us that there is still no agreed upon methodology to develop a general and transferable, polarizable force field. Crystal Structure and Density Simulations. Four crystalline structures containing the anions, bis(fluorosulfonyl)amide, perfluoroalkanesulfonylamide, or fluoroalkyl-fluorophosphate, and the cation, 1,3-dimethoxy-2-methylimidazolium, were selected from the Cambridge Crystallographic Database, CSD.35 Unfortunately, no crystalline structure containing the 1-(2-hydroxyethyl)-3-methylimidazolium cation with a suitable anion was found in the database. The crystalline structures studied by MD simulation were those of triphenylphosphonium bis(fluorosulfonyl)amide ([PH(C6H5)3][N(SO2F)2]19), sodium trans-bis(perfluoro-n-butylsulfonyl)amide ([Na][N(SO2C2F5)2]20), potassium cis-bis(perfluoro-n-butylsulfonyl)amide, and potassium trans-bis(perfluoron-butylsulfonyl)amide ([K][N(SO2C2F5)2]20) and 1,3-dimethoxy2-methylimidazolium tris(pentafluoroethyl)trifluorophosphate ([(OMe)2mim][(PF3(C2F5)3]18) salts. These particular choices are the outcome of two types of constraint, (i) the reduced number of structures containing the desired cations and/or anions and (ii) the pairing of those ions with counterions that were already part of our own force field or of the OPLS framework, such as the triphenylphosphonium, potassium, or sodium cations. The simulations in the crystalline phase tested the performance of the force field in predicting both the density and the structural properties of the crystal, such as the dimensions and director angles of the unit cell. The simulation boxes and initial configurations were set up by taking into account the dimensions

Shimizu et al. and occupancy of the unit cells of each crystalline structure given by the CSD data. In most cases, the unit cells of the crystals were too small to accommodate a sufficiently large cutoff distance. To overcome this problem, several cells were stacked together to form a sufficiently large simulation box that allows cutoff distances larger than 10 Å. Long-range corrections were applied to the Lennard-Jones interactions beyond those distances, and the Ewald methodology was implemented to take into account the long-range character of the electrostatic interactions. Since the overall size of the simulation box is defined by the dimension and director angles of the unit cell of each crystal, simulations with different box sizes and cutoff distances (up to 16 Å) were run to check that the dimensions of the simulation box and the cutoff were sufficiently large to avoid any finite-size effects. The results presented in Table 2 correspond to simulations performed with the larger cutoff distances. The runs were performed using a Nose´-Hoover thermostat coupled with an anisotropic Hoover barostat that allowed the simulation box to change volume and shape under constant (N, p, T) conditions. The temperatures were fixed to match those used during the crystallographic experiments, and the pressure was set to the null value. All runs were allowed to equilibrate for a period of 0.2 ns, followed by production times of at least 0.4 ns. These simulation times were found appropriate since the runs are started from a known, “equilibrated”, initial configuration (the experimental equilibrium crystalline structure), and it was observed, by inspection of the corresponding thermodynamic properties, that the relaxation was complete well before the end of the equilibration period. In some cases, the simulation runs were performed under more stringent conditions that tested the ergodicity of the trajectories; the initial simulation boxes were constructed in order to represent distorted crystal structures that were then allowed to evolve to the reported experimental values. The simulation results for each crystal are given in Table 2. The densities of all crystals except those based on the 1,3dimethoxy-2-methylimidazolium cation are predicted with an accuracy better than 2%. It is important to notice that (i) the deviations are of the same order of magnitude as those obtained by us or by other authors when comparing the performance of their IL models against experimental density data; (ii) the level of agreement is very good considering that the calculations are purely predictive as all parameters used were either taken as such from the OLPS-AA force field or calculated ab initio (no direct fit to experimental data was performed); and (iii) in some cases, experimental IL density results from different sources also exhibit deviations in the 2-4% range, reflecting in some cases the difficulty of using consistently pure ionic liquids or the existence of different crystalline phases of similar stability (polymorphism). The exception to these 2-4% deviations (the [(OMe)2mim][PF3(C2F5)3] crystal with a deviation of almost 8%) can be explained by the fact that we have found that in the case of the [PF3(C2F5)3]- anion, there is an inconsistency in the value of the PX-CX-CX angle between crystallographic and ab initio results (cf. the section concerning the bond and angle parametrization). Since this is the only known structure containing this anion and since the liquid density results do not show such large deviations (see below), we can assume that for this particular salt, the packing of the ions in the crystalline lattice causes large distortions that are not correctly modeled by the force field (based on the ab initio geometries). The wrong density and structure predictions in the crystalline phase (and

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TABLE 2: Comparison of Simulated Crystal Structures with Experimental Data from the Cambridge Structural Database (CSD) [PH(C6H5)3][N(SO2F)2] 35

ZUWCAV P21/n 144 4×3×3 16.0 143.15 4 9.94 10.35 15.98 15.04 12.34 12.19 90 90.05 97.02 98.51 90 89.97 1944.3 1915.4 3.416 3.471 1.6

CSD code space group ions/box stacked cells cutoff/Å T/K ions/cell aexp/Å asim/Å bexp/Å bsim/Å cexp/Å csim/Å Rexp/(deg) Rsim/(deg) βexp/(deg) βsim/(deg) γexp/(deg) γsim/(deg) Vexp/Å3 Vsim/Å3 Fexp mol dm-3 Fsim mol dm-3 δF/%

[Na][N(SO2C2F5)2]

19

[K][N(SO2C2F5)2]

20

[(OMe)2mim][(PF3(C2F5)3]

20

NEHCEI P2/c 96 2×6×4 16.0 298 2 16.469 16.423 6.492 6.633 8.637 8.655 90 90.02 99.62 99.65 90 89.95 910.5 929.4 3.648 3.573 -2.1

VIBNAW18 P21/n 144 4×3×3 16.0 233 4 9.4101 9.6475 13.8039 14.1521 16.2881 16.6990 90 90.00 102.951 102.951 90 90.00 2061.9 2222.1 3.221 2.989 -7.8

NEHCIM P21/n 128 2×2×2 16.0 203 16 19.31 19.003 17.999 18.292 22.8 22.781 90 90.02 110.34 109.78 90 89.89 7430.3 7488.8 3.576 3.548 -0.8

TABLE 3: Comparison of Simulated Liquid Densities with Experimental Data [C2OHmim] [C2OHmim] [BF4] [NTf2] T/K Fexp/mol dm-3 Fsim/mol dm-3 δF/%

298 6.22 6.16 -0.9

303 3.85 3.98 3.2

[C4mim] [N(SO2C2F5)2]

[C2mim] [C4mim] [mC2pyr] [C2mim] [C4mim] [C8F13H4mim] [N(SO2C2F5)2] [C4F9SO3] [C4F9SO3] [PF3(C2F5)3] [PF3(C2F5)3] [NTf2]

293 333 393 2.90 2.82 2.71 3.04 2.96 2.85 4.4 4.7 5.2

the much better results in the liquid phase) are just a consequence of this fact. Liquid Densities. Eight ionic liquids with known density and containing at least one of the cations or anions under discussion were selected from the literature. These include 1-(2-hydroxyethyl)-3-methylimidazolium tetrafluoroborate and bistriflamide ([C2OHmim][BF4]36 and [C2OHmim][NTf2]37), 1-butyl-3-methylimidazolium and 1-ethyl-3-methylimidazolium bis(pentafluoroethyl)amide ([C4mim][N(SO2C2F5)2]38 and [C2mim][N(SO2C2F5)2]39), 1-butyl-3-methylimidazolium and 1-ethyl-3-methylpyridiniumnonafluorobutanesulfonate([C4mim][C4F9SO3]40 and [mC2pyr][C4F9SO3]41), and 1-ethyl-3-methylimidazolium and 1-butyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate ([C2mim][PF3(C2F5)3]41 and [C4mim][PF3(C2F5)3]41), and 1-(3,3,4,4,5,5,6,6,7,7,8,8,8-tridecafluorooctyl)-3-methylimidazolium bis[trifluoromethylsulfonyl]amide ([C8F13H4mim][NTf2]). All simulations contained 250 ion pairs. Cutoff distances were taken at 16 Å for the short-range Lennard-Jones interactions (with appropriate tail corrections above that threshold) and also for the long-range Coulomb forces (with long-range corrections handled by the Ewald method with R ) 0.1 and k ) 4). The Nose´-Hoover thermostat and Hoover barostat were activated to maintain the desired temperature and pressure, with time constants of 0.1 and 0.5 ps, respectively. The equilibration period in the liquid-phase simulation runs is very important. Like in previous publications, different approaches were used to ensure that the ergodicity of the simulation was properly attained. Initially, the ions are placed at random in the simulation box, at very low density, and the equilibration starts by a short relaxation of a few picoseconds

298 3.24 3.35 3.3

295 3.36 3.42 1.8

293 3.61 3.67 1.7

293 3.07 3.18 3.2

293 2.79 2.85 2.1

373 2.29 2.38 4.1

at 1 K in the microcanonical ensemble to allow internal modes to relax. Then, an equilibration period is imposed at the final temperature of the simulation, followed by the activation of the thermostat and barostat (isobaric-isothermal ensemble). Alternatively, other simulations of the same system were allowed to evolve from initial configurations based on the expanded structure of an analogous ionic crystal. Another method to ensure the ergodicity of the simulation is to perform several temperature annealing cycles or to scramble/unscramble the two components (ions) of the system by switching off and on their electrostatic charges. The equilibration was considered successful only after stable and consistent results over periods of at least 100 ps were obtained. The production runs took at least 400 ps and were made in (N, p, T) conditions, under a pressure of 1 bar and at a temperature matching that of a liquid density reported in the literature. Simulation results are compared with relevant experimental data in Table 3. In all cases except that involving the 1-butyl-3-methylimidazolium bis(pentafluoroethyl)amide ionic liquid, the liquid densities were predicted with within 3% uncertainty. It is hard to pinpoint the cause of discrepancy in the above-mentioned system since coincidently it contains two ions parametrized in the present force field that when combined with other ions yielded densities with much lower deviations relative to the experimental values. As stressed above, the agreement of simulated densities with the experiment could eventually be improved by fine-tuning some of the parameters on a case-by-case basis. In our previous reports on force field development for ILs, we concluded that it was difficult to attribute the sign of the deviations to a certain cation family or anion and could not devise a strategy to improve the results in a general and transferable manner.

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