Magnitude and Directionality of Interaction in Ion Pairs of Ionic Liquids

Aug 10, 2005 - The magnitude of the interaction energies of 1-ethyl-3-methylimidazolium (emim) complexes follows the trend CF3CO2- > BF4- > CF3SO3- ...
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16474

J. Phys. Chem. B 2005, 109, 16474-16481

Magnitude and Directionality of Interaction in Ion Pairs of Ionic Liquids: Relationship with Ionic Conductivity Seiji Tsuzuki,*,†,‡ Hiroyuki Tokuda,§ Kikuko Hayamizu,† and Masayoshi Watanabe§ National Institute of AdVanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan, and 305-8565, Japan, Department of Chemistry and Biotechnology, Yokohama National UniVersity, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan, and CREST-JST ReceiVed: June 21, 2005

The intermolecular interaction energies of nine ion pairs of room temperature ionic liquids were studied by MP2/6-311G** level ab initio calculations. The magnitude of the interaction energies of 1-ethyl-3methylimidazolium (emim) complexes follows the trend CF3CO2- > BF4- > CF3SO3- > (CF3SO2)2N- ∼ PF6- (-89.8, -85.2, -82.6, -78.8, and -78.4 kcal/mol, respectively). The interaction energies of BF4complexes with emim, ethylpyridinium (epy), N-ethyl-N,N,N-trimethylammonium ((C2H5)(CH3)3N), and N-ethyl-N-methylpyrrolidinium (empro) are not very different (-85.2, -82.8, -84.6, and -84.4 kcal/mol, respectively), while the size of the orientation dependence of the interaction energies follows the trend emim > epy ∼ (C2H5)(CH3)3N > empro. Comparison with the experimental ionic conductivities shows that the magnitude and directionality of the interaction energy of the ion pairs play a crucial role in determining the ionic dissociation/association dynamics in the ionic liquids. The electrostatic interaction is the major source of attraction between ions. The induction contribution is small but not negligible. The hydrogen bonding with the C2-H of imidazolium is not essential for the attraction in the ion pair. The interaction energy of the BF4- complex with 1-ethyl-2,3-dimethylimidazolium (em2im) (-81.8 kcal/mol) is only 4% smaller than that of the emim complex.

Introduction Room temperature ionic liquids (RTILs) are a class of compounds composed of organic cations and inorganic and organic anions, which are liquid at ambient temperature or even far below ambient temperature. RTILs have attracted increasing interest in many fields of chemistry. RTILs have the potential to become important industrial solvents for synthesis, catalysis, extraction, and purification, as they have a low vapor pressure and unusual catalytic properties.1-19 RTILs also show the potential for applications to electrochemical devices including batteries and solar cells due to their high ionic conductivity and electrochemical stability.20-25 Physical properties such as melting point, density, viscosity, and ionic conductivity can be adjusted through variation of both the cation and the anion. In recent years, the number of possible cation and anion combinations has increased significantly.2,3 Therefore it is essential to develop a systematic method to select an ion pair to rationally design new RTILs. The properties of RTILs have been studied extensively in the past decade, both by experimental1-25 and theoretical methods.26-48 However, the relationship between the properties of RTILs and the structures of ions is still not clear. The physical properties of RTILs are controlled by the intermolecular interaction between ions. Recently, ab initio molecular orbital calculation has been becoming a powerful tool * Corresponding author. E-mail: [email protected]. † National Institute of Advanced Industrial Science and Technology (AIST). ‡ Member of Research Consortium for Synthetic Nano-Function Materials Project (SYNAF), National Institute of Advanced Industrial Science and Technology (AIST). § Yokohama National University and CREST-JST.

for studying intermolecular interaction.49-51 Recent ab initio calculations of small molecular clusters show that ab initio calculations provide sufficiently accurate interaction energies, if a reasonably large basis set is used and electron correlation is properly corrected.52-54 A few ab initio calculations of ion pairs of RTILs were reported.26-31 Meng et al. reported HF and B3LYP calculations of the 1-butyl-3-methylimidazolium (bmim) complex with PF6-.26 Paulechka et al. reported HF/6-31G* calculations of the bmim complex with PF6-.28 Katsyuba et al. reported B3LYP calculations of the 1-ethyl-3-methylimidazolium (emim) complex with BF4-.29 These calculations mainly focus on the molecular structures and vibrational frequencies. Turner et al. reported ab initio calculations (mainly HF/STO3G calculations) of 1-alkyl-3-methylimidazolium complexes with halides (F-, Cl-, Br-, and I-).27 Heimer et al. reported B3LYP/6-311+G(2d,p) calculations of BF4- complexes with emim and 1-propyl-3-methylimidazolium (pmim).30 They reported the structures and interaction energies of the complexes. Very recently, Liu reported HF/6-31+G* calculations of the structures and interaction energies of BF4- complexes with emim and PF6- complexes with 1,3-dimethylimidazolium (mmim) and bmim.31 Despite the extensive studies on the structures and physical properties of RTILs, unsettled fundamental important issues still remain: (1) The magnitude of the interaction energy between ions is important for understanding the physical properties of RTILs, as the intermolecular interaction controls the properties of RTILs. However, very little is known on the magnitude of the interaction energy. Especially its dependence on the ions is not revealed. (2) Although the orientation dependence of the interaction energy is important for the dynamic properties of RTILs, the directionality of the interaction energy is not clear.

10.1021/jp0533628 CCC: $30.25 © 2005 American Chemical Society Published on Web 08/10/2005

Interaction in Ion Pairs of Ionic Liquids

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Figure 1. Atomic charges obtained by electrostatic potential fitting using Kollman’s scheme from the MP2/6-311G** wave functions. Atomic charges with hydrogens were summed into heavy atoms.

(3) The electrostatic interaction is believed to be the major source of attraction. However, the strong electric field produced by an ion polarizes the counterion and therefore induced polarization (induction) also contributes to the attraction. The magnitude of induction contribution is not known. Quantitative analysis of the induction energy is necessary for the evaluation of its importance. (4) In the RTILs composed of 1-alkyl-3methyl imidazolium, the importance of the hydrogen bond between the C2-H of imidazolium and an anion was stressed repeatedly.29,55,56 However, the role of the hydrogen bond on the attraction is not clear. (5) The selection of the cation and anion considerably changes the properties of RTILs. However, the relationship between the interaction of ions (magnitude and directionality) and the properties of RTILs is not clearly understood. A comparison of the interaction energies of a series of ion pairs with the properties of RTILs is essential for improving our understanding of the relationship. In this paper, we have calculated the intermolecular interaction energies of nine ion pairs in RTILs by the high level ab inito method. We have discussed these issues on the basis of the calculated interaction energies. Computational Method The Gaussian 98 program57 was used for the ab initio molecular orbital calculations. The basis sets implemented in the Gaussian program were used. Electron correlation was accounted for at the MP258,59 and CCSD(T)60 levels. The geometries of complexes were fully optimized at the HF/6311G** level. The geometries of complexes were optimized from 20 to 64 initial geometries. The MP2 level interaction energy (EMP2) was calculated by the supermolecule method. The basis set superposition error (BSSE)61 was corrected for all calculations using the counterpoise method.62 The total interaction energy (Eint) was calculated as the sum of EMP2 and the deformation energy (Edef), which is the increase of the energies of monomers by the deformation of geometries in complex formation. The electrostatic energy of the dimer was calculated using the ORIENT program, version 3.2.63 The electrostatic energy of the dimer was calculated as interactions between distributed multipoles of monomers. Distributed multipoles50,64

up to hexadecapole on all atoms were obtained from the MP2/ 6-311G** wave functions of an isolated ion using the CADPAC program, version 6.65 The induction energy was calculated as the interactions of polarizable sites with the electric field produced by the multipoles of monomers.66 The atomic polarizabilities of carbon (R ) 10 au), nitrogen (R ) 8 au), oxygen (R ) 6 au), boron (R ) 8 au), fluorine (R ) 3 au), phosphorus (R ) 10 au), and sulfur (R ) 20 au) were used for the calculations.67 Distributed multipoles were used only to estimate the electrostatic and induction energies. Results and Discussion Charge Distributions. The atomic charge distributions of cations and anions were calculated by electrostatic potential fitting using the Merz-Singh-Kollman scheme68,69 from the MP2/6-311G** wave functions of isolated ions, as summarized in Figure 1. The calculated atomic charge distributions of emim and ethylpyridinium (epy) show that the positive charge does not localize on aromatic rings. The methyl and methylene groups also have a substantial positive charge. The methyl and methylene groups of aliphatic ammonium ions ((C2H5)(CH3)3N and N-ethyl-N-methylpyrrolidinium (empro)) also have a substantial positive charge. The size of the negative charge on a fluorine atom of PF6- is not very different from that of BF4-. The oxygen atoms of CF3CO2- and CF3SO3- have larger negative charges than the fluorine atoms. The nitrogen and oxygen atoms of (CF3SO2)2N- have a large negative charge. Effect of Basis Set and Electron Correlation Correction on the Calculated Interaction Energy. HF and MP2 interaction energies of the emim complex with BF4- (Figure 2, 1a) were calculated using several basis sets, as summarized in Table 1. The basis set effect on the calculated interaction energy is negligible. The HF interaction energies lie between -83.8 and -85.3 kcal/mol. The MP2 interaction energies lie between -86.1 and -89.6 kcal/mol. Electron correlation increases the attraction. The effect of electron correlation is enhanced, if large basis sets are used for the calculation. The MP2/cc-pVQZ interaction energy is 5.0 kcal/mol larger (more negative) than the HF/cc-pVQZ one. The effect of electron correlation indicates that dispersion is not negligible for the attraction.

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Figure 3. Optimized structures and interaction energies of four epy complexes with BF4-. The geometries of other orientation complexes are shown in Supporting Information Figure 2S. See the caption of Figure 2. Figure 2. HF/6-311G** level optimized geometries and interaction energies of four emim complexes with BF4-. The geometries of other orientation complexes are shown in Supporting Information Figure 1S. Total interaction energies (Eint ) EMP2 + Edef) are shown. BSSE corrected interaction energies at the MP2/6-311G* level (EMP2) are shown in parentheses. Edef is the increase of the energies of monomers by deformation of geometries in complex formation. See text.

TABLE 1: HF and MP2 Interaction Energies for the emim Complex with BF4- a basis set

bfb

EHFc

EMP2c

6-31G* 6-311G* 6-311G** 6-311++G** 6-311G(2d,2p) 6-311G(3d,3p) cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ

217 267 300 363 398 496 237 544 1045 398 851

-85.3 -84.8 -84.9 -83.8 -84.8 -85.0 -85.0 -84.3 -84.0 -84.2 -83.9

-87.5 -86.6 -87.2 -86.1 -88.8 -89.6 -87.1 -88.5 -89.0 -88.3 -88.9

a Energies in kcal/mol. The geometry is shown in Figure 2 (1a). Number of base functions used in the calculation. c BSSE corrected interaction energies.

b

TABLE 2: Interaction Energies for the emim Complex with BF4- with Electron Correlation Correction by Several Methodsa

b

basis set

HFb

MP2b

MP3b

CCSDb

CCSD(T)b

6-31G* 6-311G*

-85.3 -84.8

-87.5 -86.6

-87.5 -86.8

-87.6 -86.9

-88.0 -87.3

a Energies in kcal/mol. The geometry is shown in Figure 2 (1a). BSSE corrected interaction energies.

The HF, MP2, MP3, CCSD, and CCSD(T) interaction energies of 1a using the 6-31G* and 6-311G* basis sets are shown in Table 2. The MP3, CCSD, and CCSD(T) interaction energies are not very different from the MP2 interaction energies. The effect of electron correlation beyond MP2 is not large. Due to the good performance of the MP2 level electron correlation correction and the 6-311G** basis set, we have decided to study the interaction energies of other complexes using the MP2/6-311G** level calculations. The choice of the basis set and electron correlation procedure sometimes considerably changes the calculated intermolecular interaction energies of hydrogen-bonded systems and van der Waals clusters.52-54 However, the major source of attraction in an ion pair is the monopole-monopole (charge-charge) interaction, as we will discuss later. The choice of the basis set

and electron correlation procedure does not change the monopole-monopole interaction. Therefore, the choice of the basis set and electron correlation procedure does not largely change the calculated interaction energy of the ion pair. 1-Ethyl-3-methylimidazolium (emim) Complex with BF4-. The nine local minima shown in Figure 2 and Supporting Information Figure 1S (1a-1i) were found by the geometry optimization. Five complexes (1a-1e) have larger (more negative) Eint values (-84.4 to -85.2 kcal/mol) than 1f-1i (-72.6 to -77.3 kcal/mol). The structures of 1a-1e are nearly identical except for the conformation of the ethyl group and the orientation of the B-F bonds. The BF4- is above or below the plane of the imidazolium ring in these complexes. The BF4has close contact with the C2-H of imidazolium in these complexes. The C2-H‚ ‚ ‚B distance is 2.46 Å in the most stable complex 1a. Those in 1b-1e are 2.45-2.49 Å. On the other hand, the BF4- has close contact with other hydrogen atoms of the imidazolium ring (C4-H and C5-H) in 1f-1i. The BF4- is close to the imidazolium plane in these complexes. The Eint values of 1a-1e are substantially larger than those of 1f-1i, which shows that the BF4- prefers to have close contact with the C2-H. The difference between the Eint values of the most stable 1a and the least stable 1i (Ediff) is 12.6 kcal/mol. A few ab initio calculations of the emim complex with BF4have been reported. These calculations also show that the BF4has close contact with the C2-H.29-31 Similar geometries were calculated for pmim and bmim complexes with BF4-.29,30 The BF4- locates above the plane of the imidazolium ring of emim,29 as for the optimized geometry of 1a. Molecular dynamics simulations also show that anions prefer to locate around the C2-H, both above and below the plane of the imidazolium ring.31,32,43,47 The C2-H group has a larger positive charge than the C4-H and C5-H groups, as shown in Figure 1, which would be a cause of this preference. Although the C2-H has close contact with two fluorine atoms in 1a (the C2-H‚ ‚ ‚F distances are 2.12 and 2.26 Å), the C2-H‚ ‚ ‚F angles (134.3 and 120.9°) are not close to 180°. The small C2-H‚ ‚ ‚F angles suggest that the H‚ ‚ ‚F interaction is not hydrogen bonding and that hydrogen bonding is not essential for the attraction. Liu et al. reported that the interaction energy of the emim complex with BF4- calculated at the HF/6-31+G* level is -82.6 kcal/mol. This value is slightly smaller than the MP2/6-311G** level interaction energy of the complex 1a (-85.2 kcal/mol) in this work. 1-Ethylpyridinium (epy) Complex with BF4-. The 12 local minima shown in Figure 3 and Supporting Information Figure 2S (2a-2l) were found by the geometry optimization. Ten complexes (2a-2j) have substantially larger Eint values (-79.4

Interaction in Ion Pairs of Ionic Liquids

Figure 4. Optimized structures and interaction energies of four (C2H5)(CH3)3N complexes with BF4-. The geometries of other orientation complexes are shown in Supporting Information Figure 3S. See the caption of Figure 2.

to -82.8 kcal/mol) than 2k and 2l (-73.1 and -72.9 kcal/mol, respectively). The BF4- has close contact with the nitrogen atom of pyridinium in 2a, 2f, 2i, and 2j. The N‚ ‚ ‚B distance is 3.213.62 Å in these complexes. The most stable complex 2a has Cs symmetry. The BF4- is close to the C2-H in 2b, 2c, 2d, 2e, 2g, and 2h. The N‚ ‚ ‚B distance is 3.73-4.16 Å, and the C2H‚ ‚ ‚B distance is 2.45-2.82 Å in these complexes. The BF4is close to C3-H and C4-H in 2k and 2l. The C3‚ ‚ ‚B and C4‚ ‚ ‚B distances are 2.64 and 2.84 Å in 2k. Those in 2l are 2.63 and 2.79 Å. The calculated Eint values of the complexes show that the BF4- prefers to have close contact with the nitrogen atom and the C2-H. The positive charge of epy is distributed mainly on the nitrogen atom, C2-H, C4-H, C6-H, and methylene groups, as shown in Figure 1. This charge distribution would be the cause of the stability of 2a-2j. The Ediff value of 2 (9.9 kcal/mol) is smaller than that of 1. N-Ethyl-N,N,N-trimethylammonium ((C2H5)(CH3)3N) Complex with BF4-. The eight local minima shown in Figure 4 and Supporting Information Figure 3S (3a-3h) were found by the geometry optimization. The Eint values of 3a and 3b are -84.6 and -83.9 kcal/mol, respectively. The N‚ ‚ ‚B distance is 3.92 and 3.94 Å in these complexes. The Eint values of 3c3g (-79.7 to -81.9 kcal/mol) are smaller than those of 3a and 3b. The N‚ ‚ ‚B distances in these complexes (4.12-4.28 Å) are larger than those in 3a and 3b. The Eint value of 3h (-74.7 kcal/mol) is substantially smaller than those of the other complexes. The N‚ ‚ ‚B distance (4.42 Å) is very large in this complex. The comparison of Eint with N‚ ‚ ‚B distances in the complexes suggests that the cation-anion distance mainly determines the magnitude of the Eint value of complex 3. The Ediff value of 3 (9.9 kcal/mol) is smaller than that of 1. N-Ethyl-N-methylpyrrolidinium (empro) Complex with BF4-. The 19 local minima shown in Figure 5 and Supporting Information Figure 4S (4a-4s) were found by the geometry optimization. Complex 4 has large numbers of nearly isoenergetic local minima. The Eint values of 11 local minima (4a4k) lie between -81.5 and -84.4 kcal/mol. The difference is less than 3 kcal/mol. The calculated Eint values of the 19 complexes are -76.4 to -84.4 kcal/mol. The N‚ ‚ ‚B distances lie between 3.87 and 4.36 Å in these complexes. The orientation dependence of the Eint value of 4 is small. The Ediff value of 4 (8.0 kcal/mol) is smaller than those of complexes 1-3.

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Figure 5. Optimized structures and interaction energies of four empro complexes with BF4-. The geometries of other orientation complexes are shown in Supporting Information Figure 4S. See the caption of Figure 2.

Figure 6. Optimized structures and interaction energies of four emim complexes with PF6-. The geometries of other orientation complexes are shown in Supporting Information Figure 5S. See the caption of Figure 2.

emim Complex with PF6-. The eight local minima shown in Figure 6 and Supporting Information Figure 5S (5a-5h) were found by the geometry optimization. The Eint values of 5a-5d (-76.6 to -78.4 kcal/mol) are substantially larger than those of 5e-5h (-67.9 to -70.8 kcal/mol). The PF6-, which has close contact with the C2-H, is above or below the plane of the imidazolium ring in 5a-5c, while the PF6- is close to the plane in 5d. The C2-H‚ ‚ ‚P distance is 2.81-2.91 Å, and the shortest C2-H‚ ‚ ‚F distance is 2.09-2.21 Å in these complexes. On the other hand, the PF6- has close contact with other hydrogen atoms of the imidazolium ring in 5e-5h. The large Eint values of 5a-5d show that the PF6- prefers to have close contact with the C2-H, as for BF4-. The hydrogen-fluorine radial distribution functions obtained from molecular dynamics simulations of RTIL composed of bmim and PF6- show that the first maximum location of C2-H‚ ‚ ‚F (2.23 Å) is shorter than those of C4-H‚ ‚ ‚F and C5-H‚ ‚ ‚F (2.53 Å).31 Recently reported ab initio calculations of mmim and bmim complexes with PF6also show that PF6- has close contact with the C2-H.26,28,31 The PF6- locates above the plane of the imidazolium ring of bmim.28 Paulechka et al. reported that the MP2/6-31+G* level interaction energy of the bmim complex with PF6- is -88.3 kcal/mol. Liu et al. reported that the HF/6-31+G* level interaction energy of the complex is -76.7 kcal/mol.

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Figure 7. Optimized structures and interaction energies of four emim complexes with CF3CO2-. The goemetries of other orientation complexes are shown in Supporting Information Figure 6S. See the caption of Figure 2.

Tsuzuki et al.

Figure 9. Optimized structures and interaction energies of four emim complexes with (CF3SO2)2N-. The geometries of other orientation complexes are shown in Supporting Information Figure 8S. See the caption of Figure 2.

Figure 10. Optimized structures and interaction energies of BF4complexes with emim and em2im. See the caption of Figure 2. Figure 8. Optimized structures and interaction energies of four emim complexes with CF3SO3-. The geometries of other orientation complexes are shown in Supporting Information Figure 7S. See the caption of Figure 2.

emim Complex with CF3CO2-. The 10 local minima shown in Figure 7 and Supporting Information Figure 6S (6a-6j) were found by the geometry optimization. The Eint values of 6a-6e (-84.7 to -89.8 kcal/mol) are considerably larger than those of 6f-6j (-79.9 to -82.1 kcal/mol). The CF3CO2- is close to the C2-H in 6a-6e, while the CF3CO2- is close to other hydrogen atoms in 6f-6j. The CF3CO2- prefers to have close contact with the C2-H, as for BF4- and PF6-. The CO2 group of CF3CO2- has close contact with the C2-H in 6a-6c. Both CF3 and CO2 groups are close to the C2-H in 6d and 6e. The larger interaction energies of 6a-6c (-89.7 to -89.8 kcal/mol) than those of 6d and 6e (-85.0 and -84.7, respectively) show that the C2-H prefers to have close contact with the CO2 group of CF3CO2-. This preference is explained by the larger negative charge on the CO2 group (-0.78 e) than that on the CF3 group (-0.22 e). The nearly identical Eint values of 6a-6c show that the potential energy surface is very flat with respect to the tilting. emim Complex with CF3SO3-. The six local minima shown in Figure 8 and Supporting Information Figure 7S (7a-7f) were found by the geometry optimization. The Eint values of 7a-7c (-82.4 to -82.6 kcal/mol) are considerably larger than those of 7d-7f (-72.5 to -75.4 kcal/mol). The SO3 group of CF3SO3- is close to the C2-H in 7a-7c. The CF3SO3- is close to other hydrogen atoms of the pyridinium ring in 7d-7f. The CF3SO3- also prefers to have close contact with the C2-H, as for the CF3CO2-. Two oxygen atoms of the SO3 group have

close contact with the C2-H in 7a-7c. This preference is explained by the calculated charge distributions of CF3SO3-, as for CF3CO2-. The SO3 group has a much larger negative charge (-0.82) than the CF3 group. emim Complex with (CF3SO2)2N-. The 24 local minima shown in Figure 9 and Supporting Information Figure 8S (8a8x) were found by the geometry optimization. Complex 8 has large numbers of nearly isoenergetic local minima. The Eint values of 18 local minima (8a-8r) lie between -77.4 and -78.8 kcal/mol. The difference is less than 1.5 kcal/mol. The C2-H has close contact with the N or SO2 group of the anion in these complexes. The Eint value of 8s (-75.3 kcal/mol) is smaller than those of 8a-8r. One SO2 group is above the imidazolium ring in 8s. The Eint values of 8t-8x (-67.4 to -70.7 kcal/mol) are further smaller. The anion has close contact with the C4-H or C5-H in these complexes. 1-Ethyl-2,3-dimethylimidazolium (em2im) Complex with BF4-. The optimized geometry of the em2im complex with BF4- (9) is compared with that of 1a, as shown in Figure 10. The BF4- is above the plane of the imidazolium ring in both complexes. However, the BF4- is closer to the center of the ring in 9. The C2‚ ‚ ‚B distances in 1a and 9 are 3.12 and 3.48 Å, respectively. The CMe-C2‚ ‚ ‚B angle in 9 (86.8°) is considerably larger than the H-C2‚ ‚ ‚B angle in 1a (43.4°). Although 9 does not have the C2-H‚ ‚ ‚F hydrogen bond, the Eint value of 9 (-81.8 kcal/mol) is only 4% smaller than that of 1a (-85.2 kcal/mol). The small difference of Eint shows that the hydrogen bonding with the C2-H of imidazolium is not essential for the attraction between the imidazolium ring and the anion.

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TABLE 3: Interaction Energies for Complexesa complex [emim][BF4] (1a) [emim][BF4] (1e) [epy][BF4] (2a) [(C2H5)(CH3)3N][BF4] (3a) [empro][BF4] (4a) [emim][PF6] (5a) [emim][CF3CO2] (6a) [emim][CF3SO3] (7a) [emim][(CF3SO2)2N] (8a) [em2im][BF4] (9)

EMP2b Edefc Eintd -87.2 -78.2 -84.5 -86.3 -86.0 -80.6 -91.5 -84.5 -80.5 -83.6

2.0 1.6 1.7 1.7 1.6 2.2 1.7 1.9 1.7 1.8

-85.2 -76.6 -82.8 -84.6 -84.4 -78.4 -89.8 -82.6 -78.8 -81.8

Eese -83.4 -74.5 -80.5 -82.5 -81.0 -77.2 -86.0 -79.7 -75.3 -79.3

Eindf Eotherg -10.0 -7.8 -11.4 -8.1 -9.8 -8.3 -11.9 -11.1 -11.1 -11.3

6.1 4.1 7.4 4.4 4.8 4.8 6.4 6.3 5.9 7.0

a Energies in kcal/mol. The geometries are shown in Figures 2-10. BSSE corrected interaction energies of complexes calculated at the MP2/6-311G** level. c Increase of the energies of monomers by the deformation of geometries in complex formation. Edef was calculated at the MP2/6-311G** level. d Total interaction energy of the complex, which is the sum of EMP2 and Edef. e Electrostatic energy. f Induction energy. g Eother ) EMP2 - Ees - Eind. Eother is mainly exchange-repulsion and dispersion energies.

b

Roles of Electrostatics and Induction. The electrostatic and induction energies of complexes 1-9 (the most stable orientation of each complex) are summarized in Table 3. The electrostatic energies (Ees) lie between -77.2 and -86.0 kcal/mol. The inductions energies (Eind) lie between -8.1 and -11.9 kcal/ mol. The electrostatic interaction is mainly responsible for the attraction and mainly determines the size of the total interaction energy (Eint). However, the contribution of induction is not negligible, which suggests that nonadditivity of the interactions between ions may influence the properties of ionic liquid, as induction is the major source of many-body effects of intermolecular interaction. The electrostatic interaction mainly determines the stable structure of complexes. The Eint value of complex 1a, where the BF4- has close contact with the C2-H, is 8.6 kcal/mol larger (more negative) than 1e, where the BF4has contact with the C5-H. The Ees value of 1a (-83.4 kcal/ mol) is 8.9 kcal/mol more negative than that of 1e (-74.5 kcal/ mol). In contrast to the significant directionality of a hydrogen bond between neutral molecules such as the water dimer, the orientation dependence of the Eint values of 1-8 is not very large. The Ediff values of 1-8 (8.0-12.6 kcal/mol) are less than 15% of the Eint values. The electrostatic interaction is the major source of attraction in the hydrogen-bonded systems and ion pairs. The electrostatic interaction between two species (Ees) can be described as shown in eq 1 by multipole expansion50

Ees ) Echarge-charge + Echarge-dipole + Echarge-quadrupole + Edipole-dipole + Edipole-quadrupole + Equadrupole-quadruople + ... (1) For neutral species, the charges are zero, and the leading term is the highly orientation dependent dipole-dipole interaction. Therefore, the electrostatic interaction in hydrogen-bonded neutral molecules has significant directionality. On the other hand, for the ion pairs, the isotropic charge-charge interaction is the leading term and therefore the orientation dependence of electrostatic interaction is not very large. Comparison with Crystal and Liquid Structures. The crystal structure of the salt [emim][PF6] shown in Figure 11 indicates that an emim is surrounded by four PF6-.70 The crystals of the salt [emim]X (X ) Cl, Br, or I) also have similar structures.71-73 Three PF6- (A, B, and C in Figure 11) are close to the plane of the imidazolium ring, while one PF6- (D) is above the plane in the crystal.70 The PF6- (A, B, C, and D) have close contacts with the C2-H, C4-H, C5-H, and C2. The

Figure 11. Crystal structure of the salt [emim][PF6]. The C‚ ‚ ‚P distances are shown in angstroms.

C2‚ ‚ ‚PA, C4‚ ‚ ‚PB, C5‚ ‚ ‚PC, and C2‚ ‚ ‚PD distances are 4.01, 4.22, 4.23, and 4.08 Å. The position of PF6- (D) is close to that in 5a. The C2‚ ‚ ‚PD distance in the crystal is larger than that in 5a (3.58 Å). The PF6- (D) exhibits a smaller parallel offset than that in 5a. The repulsion with PF6- (A) and interactions with other ions in the crystal would be the cause of these differences. Very recently, Hardacre et al. reported neutron diffraction measurements of liquid [mmim]Cl and [mmim][PF6].74,75 They found a close relationship between the crystal structures and liquid structures from the analysis of probability distributions for the anions around the imidazolium ring. The position of PF6- with respect to the cation is predominantly in a position facing the imidazolium ring, although there is some density axial to the C2-H.75 The position of PF6- in the emim complex with PF6- (1a) coincides with the high probability region of PF6- in liquid [mmim][PF6]. Effects of the Anion and Cation on the Interaction Energy and Properties of Ionic Liquid. The Eint values of emim complexes depend on the counteranion. The magnitude of the interaction energy in the most stable orientation (Emax) follows the trend CF3CO2- > BF4- > CF3SO3- > (CF3SO2)2N- ∼ PF6-, as summarized in Table 4. This order coincides with the order of Ees shown in Table 3. The large negative charge on oxygen atoms (-0.68 e) of CF3CO2- would be the cause of the large Ees value (-86.0 kcal/mol) of the CF3CO2- complex (6a). The Ees value (-79.7 kcal/mol) of the CF3SO3- complex (7a) is substantially smaller than that of 6a. The C2-H‚ ‚ ‚O distances in 6a (2.02 and 2.10 Å) are shorter than those in 7a (2.15 and 2.17 Å). The larger separation due to the steric repulsion of the sulfur atom in 7a is the cause of the smaller Ees value . The Eint value of the PF6- complex (5a) is much smaller than that of the BF4- complex (1a). The smaller electrostatic energy due to the larger intermolecular separation in 5a is the cause of the smaller interaction energy of 5a. The negative charge was distributed to one nitrogen atom and four oxygen atoms in (CF3SO2)2N-, while the nitrogen atom alone has close contact with the C2-H in the most stable (CF3SO2)2Ncomplex (8a). Other oxygen atoms are not close to the C2-H due to steric repulsion. This structural feature would be the cause of the small Ees value (-75.3 kcal/mol) of 8a. The calculated interaction energies of emim complexes are compared with the experimental properties (melting point, density, self-diffusion coefficient, and molar conductivity) of RTILs composed of emim or bmim, as shown in Table 4. A close relationship between the size of the calculated interaction energies with these properties is not found, which indicates that these properties are not determined only by the size of the interaction energy. The molar conductivity is an important property of RTILs for their application as electrolytes for electrochemical devices.

16480 J. Phys. Chem. B, Vol. 109, No. 34, 2005

Tsuzuki et al.

TABLE 4: Interaction Energies for Complexes and Physical Properties of Ionic Liquida complex

Emaxb

Eminc

[emim][CF3CO2] (6) [emim][BF4] (1) [emim][CF3SO3] (7) [emim][(CF3SO2)2N] (8) [emim][PF6] (5)

-89.8 -85.2 -82.6 -78.8 -78.4

-79.9 -72.6 -72.5 -67.4 -67.9

Ediffd

mpe

9.9 12.6 10.1 11.4 10.5

-14 11 -9 -15 62

Ff

Dg k

1.22 1.20l 1.30m 1.44n 1.37o

Λimph k

3.23 2.72l 3.02m 4.75n 1.21o

k

0.63 0.69l 0.64m 1.10n 0.31o

ΛNMRi k

1.25 1.04l 1.10m 1.82n 0.46o

Λimp/ΛNMRj 0.51 0.66 0.58 0.60 0.68

a Energies in kcal/mol. The geometries are shown in Figures 2 and 6-9. b The calculated interaction energy (E ) of the most stable complex. int The calculated interaction energy (Eint) of the least stable complex. d The difference between Emax and Emin. e Melting point (°C) (refs 78 and 79). f Density (g cm-3) at 298 K (obtained from the equation in ref 76). g Self-diffusion coefficient (cation + anion) at 298 K (10-7 cm2 s-1) (obtained from the equation in ref 76). h Molar conductivity obtained from impedance measurement (S cm2 mol-1) at 298 K (obtained from the equation in ref 76). i Molar conductivity obtained from ion diffusivity measurement by NMR (S cm2 mol-1) at 298 K (obtained from the equation in ref 76). j Ratio of Λ k l m [bmim][CF SO ]. n [bmim][(CF SO ) N]. o [bmim][PF ]. imp and ΛNMR. [bmim][CF3CO2]. [bmim][BF4]. 3 3 3 2 2 6 c

TABLE 5: Interaction Energies for Complexes and Physical Properties of Ionic Liquida complex

Emaxb

Eminc

Ediffd

mpe

Ff

Dg

Λimph

ΛNMRi

Λimp/ΛNMRj

[emim][BF4] (1) [epy][BF4] (2) [(C2H5)(CH3)3N][BF4] (3) [empro][BF4] (4)

-85.2 -82.8 -84.6 -84.4

-72.6 -72.9 -74.7 -76.4

12.6 9.9 9.9 8.0

-3k 26l 19m -15n

1.44k 1.44l 1.39m 1.40n

4.75k 3.91l 2.34m 3.12n

1.10k 0.94l 0.61m 0.82n

1.82k 1.44l 0.91m 1.19n

0.60 0.66 0.67 0.69

a Energies in kcal/mol. The geometries are shown in Figures 2-5. b The calculated interaction energy (E ) of the most stable complex. c The int calculated interaction energy (Eint) of the least stable complex. d The difference between Emax and Emin. e Melting point (°C) (ref 77). f Density (g cm-3) at 298 K (obtained from the equation in ref 77). g Self-diffusion coefficient (cation + anion) at 298 K (10-7 cm2 s-1) (obtained from the equation in ref 77). h Molar conductivity obtained from impedance measurement (S cm2 mol-1) at 298 K (obtained from the equation in ref 77). i Molar conductivity obtained from ion diffusivity measurement by NMR (S cm2 mol-1) at 298 K (obtained from the equation in ref 77). j Ratio of Λimp and ΛNMR. k [bmim][(CF3SO2)2N]. l [bpy][(CF3SO2)2N]. m [(n-C4H9)(CH3)3N][(CF3SO2)2N]. n [bmpro][(CF3SO2)2N].

Tokuda et al. reported the measurement of the molar conductivity of RTILs composed of bmim and several anions.76 They showed that the molar conductivity obtained from impedance measurement (Λimp) is smaller than that obtained from ion diffusivity measurement by NMR (ΛNMR). They pointed out that the Λimp/ΛNMR value provides useful information on the ionic dissociation/association dynamics in the ionic liquid.76 They reported that the Λimp/ΛNMR values of RTILs composed of bmim follow the order PF6- > BF4- > (CF3SO2)2N- > CF3SO3- > CF3CO2-. A small Λimp/ΛNMR value shows that an ion prefers to move with a counterion. Λimp/ΛNMR is an important parameter for designing highly conductive ionic liquid. The RTILs composed of round-shaped anions (PF6- and BF4-) have larger Λimp/ΛNMR values than those composed of the other rod-shaped anions. The round-shaped anions dissociate and associate with cations more easily in the RTILs. The Eint value of the emim complex with PF6- (-78.4 kcal/mol) is smaller than that of the BF4- complex (-85.2 kcal/mol). The BF4- binds with emim stronger than the PF6-, which well explains the smaller Λimp/ΛNMR value for [bmim][BF4] than that for [bmim][PF6]. The Eint values of emim complexes with (CF3SO2)2N-, CF3SO3-, and CF3CO2- are -78.8, -82.6, and -89.8 kcal/mol, respectively. The order of Λimp/ΛNMR of three RTILs composed of bmim and the rod-shaped anions coincides with the reverse order of the magnitude of the interaction energies of the emim complexes. The BF4- complexes with four cations (emim, epy, (C2H5)(CH3)3N, and empro) have nearly identical Emax values (-82.8 to -85.2 kcal/mol), as shown in Table 5. The calculated interaction energies are compared with the properties of RTILs, as shown in Table 5. A close relationship between the calculated interaction energies (Emax) and the properties is not found. However, the Ediff value of the complexes, which shows the size of the orientation dependence of the interaction energy, has a close relationship with the experimental Λimp/ΛNMR value of the RTILs. The Ediff values of RTILs follow the trend emim > epy ∼ (C2H5)(CH3)3N > empro, as summarized in Table 5. The experimental Λimp/ΛNMR values of the RTILs composed of (CF3SO2)2N with bmim, butylpyridinium (bpy), N-butyl-

N,N,N-trimethylammonimu ((n-C4H9)(CH3)3N), and N-butyl-Nmethylpyrrolidinium (bmpro) follow the order bmpro > (nC4H9)(CH3)3N > bpy > bmim.77 These cations have a butyl group instead of an ethyl group in emim, epy, (C2H5)(CH3)3N, and empro. The order of Ediff coincides with the reverse order of Λimp/ΛNMR. This agreement shows that not only the magnitude of the interaction energy but also its orientation dependence play a crucial role in determining the ionic dissociation/ association dynamics in RTILs. The comparison of the calculated interaction energies of the ion pairs and experimental Λimp/ΛNMR values of RTILs suggests that three factors play important roles in determining the Λimp/ ΛNMR value: (1) RTILs have large Λimp/ΛNMR values if the interaction between the cation and the anion is small. (2) RTILs that consist of round-shaped ions have large Λimp/ΛNMR values. Probably, the round shape of the ions enables a high mobility of the ions in RTILs. (3) RTILs have large Λimp/ΛNMR values if the orientation dependence of the interaction is small. Probably, a large anisotropy of the interaction would decrease the mobility of the ions. Conclusions We have calculated the intermolecular interaction energies of nine ion pairs of RTILs by the high level ab initio method. The calculated interaction energies lie between -78.4 and -89.8 kcal/mol. The electrostatic interaction is mainly responsible for the attraction. However, the contribution of induction is not negligible. Anions prefer to have close contact with the C2-H of the imidazolium ring in emim complexes. The electrostatic interaction is responsible for this preference. The comparison of the interaction energies of BF4- complexes with emim and em2im shows that the hydrogen bonding between the C2-H of the imidazolium and anion is not essential for the attraction. The magnitude of the interaction energies of emim complexes follows the trend CF3CO2- > BF4- > CF3SO3- > (CF3SO2)2N∼ PF6-. The interaction energies of BF4- complexes with emim, epy, (C2H5)(CH3)3N, and empro are nearly equal, while the size of the orientation dependence of the interaction energies follows

Interaction in Ion Pairs of Ionic Liquids the trend emim > epy ∼ (C2H5)(CH3)3N > empro. Comparison with experimental ion conductivities shows that the magnitude and directionality of the interaction energy between ions play a crucial role in determining the ionic dissociation/association dynamics in the ionic liquid. Acknowledgment. This work was partly supported by NEDO under the Nanotechnology Materials Program, by NAREGI Nanoscience Project, Ministry of Education, Culture, Sports, Science and Technology, Japan, and by KAKENHI 14209022. We thank Tsukuba Advanced Computing Center for the provision of the computational facilities. Supporting Information Available: Complete ref 57, tables showing the Cartesian coordinates of optimized structures and calculated energies of nine ion pairs of RTILs, and figures showing the optimized structures and interaction energies of eight ion pairs of RTILs. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Welton, T. Chem. ReV. 1999, 99, 2071. (2) Holbrey, J. D.; Seddon, K. R. Clean Prod. Processes 1999, 1, 223. (3) Wasserscheid, P.; Keim, W. Angew. Chem., Int. Ed. 2000, 39, 3772. (4) Huddleston, J. G.; Visser, A. E.; Reichert, W. M.; Willauer, H. D.; Broker, G. A.; Rogers, R. D. Green Chem. 2001, 3, 156. (5) Earle, M. J.; Seddon, K. R. Pure Appl. Chem. 2000, 72, 1391. (6) Chiappe, C.; Capraro, D.; Conte, V.; Pieraccini, D. Org. Lett. 2001, 3, 1061. (7) Stark, A.; MacLean, B.; Singer, R. D. J. Chem. Soc., Dalton Trans. 1999, 63. (8) Sheldon, R. J. Chem. Soc., Chem. Commun. 2001, 2399. (9) Carmichael, A. J.; Earle, M. J.: Holbrey, J. D.; McCormac, P. B.; Seddon, K. R. Org. Lett. 1999, 1, 997. (10) Chun, S.; Dzyba, S. V.; Bartsch, R. A. Anal. Chem. 2001, 73, 3737. (11) Fadeev, A. G.; Meagher, M. M. J. Chem. Soc., Chem. Commun. 2001, 295. (12) Scafer, T.; Rodrigues, C. M.; Afonso, A. M.; Crespo, J. G. J. Chem. Soc., Chem. Commun. 2001, 1622. (13) Bates, E. D.; Mayton, R. D.; Ntai, I.; Davis, J. H. J. Am. Chem. Soc. 2002, 124, 926. (14) Gutowski, K. E.; Broker, G. A.; Willauer, H. D.; Huddleston, J. G.; Swatloski, R. P.; Holbrey, J. D.; Rogers, R. D. J. Am. Chem. Soc. 2003, 125, 6632. (15) Audic, N.; Clavier, H.; Mauduit, M.; Guillemin, J.-C. J. Am. Chem. Soc. 2003, 125, 9248. (16) Geldbach, T. J.; Dyson, P. J. J. Am. Chem. Soc. 2004, 126, 8114. (17) Zhao, D.; Fei, Z.; Geldbach, T. J.; Scopelliti, R.; Dyson, P. J. J. Am. Chem. Soc. 2004, 126, 15876. (18) Solinas, M.; Pfaltz, A.; Cozzi, P. G.; Leitner, W. J. Am. Chem. Soc. 2004, 126, 16142. (19) Mo, J.; Xu, L.; Xiao, J. J. Am. Chem. Soc. 2005, 127, 751. (20) Lagrost, C.; Carrie, D.; Vaultier, M.; Hapiot, P J. Phys. Chem. A 2003, 107, 745. (21) Ryan, D. M.; Reichel, T. L.; Welton, T. J. Electrochem. Soc. 2002, 149, A371. (22) Wikes, J. S.; Levisky, J. A.; Wilson, R. A.; Hussey, C. L. Inorg. Chem. 1982, 21, 1263. (23) Chum, H. L.; Koch, V. R.; Miller, L. L.; Oesteryoung, R. A. J. Am. Chem. Soc. 1975, 97, 3264. (24) Wang, P.; Zakeeruddin, S. M.; Comte, P.; Exnar, I.; Gratzel, M. J. Am. Chem. Soc. 2003, 125, 1166. (25) Wang, P.; Zakeeruddin, S. M.; Moser, J.-E.; Humphry-Baker, R.; Gratzel, M. J. Am. Chem. Soc. 2004, 126, 7164. (26) Meng, Z.; Dolle, A.; Carper, W. R. THEOCHEM 2002, 585, 119. (27) Turner E. A.; Pye, C. C.; Singer, R. D. J. Phys. Chem. A 2003, 107, 2277. (28) Paulechka, Y. U.; Kabo, G. J.; Blokhin, A. V.; Vydrov, O. A.; Magee, J. W.; Frenkel, M. J. Chem. Eng. Data 2003, 48, 457. (29) Katsyuba, S. A.; Dyson, P. J.; Vandyukova, E. E.; Chernova, A.; Vidis, A. HelV. Chim. Acta 2004, 87, 2556. (30) Heimer, N. E.; Del Sesto, R. E.; Carper, W. R. Magn. Reson. Chem. 2004, 42, 71. (31) Liu, Z.; Huang, S.; Wang, W. J. Phys. Chem. B 2004, 108, 12978. (32) Hanke, C. G.; Price, S. L.; Lynden-Bell, R. M. Mol. Phys. 2001, 99, 801. (33) Morrow, T. I.; Maginn, E. J. J. Phys. Chem. B 2002, 106, 12807.

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