Conformational Analysis of 1-Butyl-3-methylimidazolium by CCSD (T

Jun 5, 2008 - C2rH, are 0.0, r1.61 and r0.25 kcal/mol, respectively. The GT rotamer is favored by the strong attractive electrostatic interaction betw...
0 downloads 0 Views 277KB Size
Download PDF
J. Phys. Chem. B 2008, 112, 7739–7747

7739

Conformational Analysis of 1-Butyl-3-methylimidazolium by CCSD(T) Level Ab Initio Calculations: Effects of Neighboring Anions Seiji Tsuzuki,*,† Asako Ayusawa Arai,‡ and Keiko Nishikawa‡ National Institute of AdVanced Industrial Science and Technology, Tsukuba Center, Tsukuba, Ibaraki 305-8568, Japan, and Graduate School of AdVanced Integration Science, Chiba UniVersity, Inage-ku, Chiba 263-8522, Japan ReceiVed: March 11, 2008

Conformational energies for the butyl group of 1-butyl-3-methylimidazolium (bmim) were calculated by highlevel ab initio methods. Estimated relative energies for the TT, GT and G′T rotamers of an isolated bmim cation at the CCSD(T)/cc-pVTZ level are 0.0 -0.02 and -0.50 kcal/mol, respectively. The close contact of a Cl anion to the C2-H of imidazolium considerably increases the relative stability of the GT rotamer. Estimated relative energies for the three rotamers of the [bmim]Cl complex, in which the Cl anion exists close to the C2-H, are 0.0, -1.61 and -0.25 kcal/mol, respectively. The GT rotamer is favored by the strong attractive electrostatic interaction between the bmim cation and Cl anion. The C2-H group in the GT rotamer has a larger positive charge compared with those in the TT and G′T rotamers. The contact of a Br anion to the C2-H also stabilizes the GT rotamer. The effects of the Cl anion close to the C4-H and C5-H are small. The anion effects suggest that the GT rotamer is the most stable in ionic liquids. The positive charge on imidazolium ring does not largely change the conformational energies. Estimated relative energies for the three rotamers of N-butylimidazole (0.0, -0.29 and -0.75 kcal/mol, respectively) are not largely different from those for isolated bmim. Calculated MP2/cc-pVTZ level torsional potential for the Cim-Nim-C-C bond has a minimum when the torsional angle is close to 90°. Coplanar conformation is not a stable structure. Calculated torsional barrier height between the two nonplanar minima is less than 1 kcal/mol. Introduction Ionic liquids attract considerable interest due to the potential to use them as low-volatite solvents for green chemistry and as liquid electrolytes for batteries.1–9 1-Butyl-3-metylimidazolium (bmim, 1) is one of the commonly used cations for ionic liquids.5,10,11 The conformation of the butyl group in bmim has been studied extensively both by experimental12–20 and by theoretical methods.18,21–24 The conformation of the alkyl chain attached to the imidazolium ring is important for understanding the roles of the alkyl chain for the structures and physicochemical properties of ionic liquids. Typical ionic liquids have alkyl group(s) attached to the cationic structures such as imidazolium and pyridinium rings. A change in the alkyl chain length has been reported to cause changes in the melting points and other physicochemical properties such as viscosity, self-diffusion coefficient, and ionic conductivity.25 The crystal structures of two polymorphs of [bmim]Cl have been reported.14 In an orthorhombic form, bmim has the gauche C(7)-C(8) bond and trans C(8)-C(9) bond (Figure 1) when the C(2)-N(1)-C(7)-C(8) torsional angle is positive (GT rotamer, 1b).26 In a monoclinic form, both the C(7)-C(8) and the C(8)-C(9) bonds are trans (TT rotamer, 1a). In the crystals of [bmim]Br and [bmim]I, the C(7)-C(8)-C(9) conformation is GT.14,15,19 Ozawa et al. reported that both trans and gauche C(7)-C(8) bonds coexist in liquid [bmim][BF4] using Raman spectra and vibrational analysis by DFT calculations.15 The existence of the two rotamers in liquid [bmim]Cl and [bmim][PF6] were also reported.16–18 Turner et al. calculated * Corresponding author. E-mail [email protected]. † National Institute of Advanced Industrial Science and Technology. ‡ Chiba University.

relative energies for 10 rotamers of an isolated bmim cation (1) by HF and MP2 methods using several basis sets up to the 6-31+G* basis set.21 The calculated relative energies depend strongly on the basis set and electron correlation correction. The MP2/6-31+G* level calculations show that the G′T rotamer (1c) is the most stable and that the TT and GT rotamers (1a and 1b) are 0.90 and 0.46 kcal/mol above the G′T rotamer, respectively. More recently, Lopes et al. calculated torsional potential around the C(7)-C(8) bond of an isolated bmim cation at the MP2/cc-pVTZ(-f)//HF/6-31G(d) level.23 Their calculations indicate that this bond prefers gauche conformation. Anions exist close to the C-H bonds of imidazolium in condensed phase. Neutron diffraction measurements and ab initio molecular dynamics (MD) simulations show that anions exist close to the C-H bonds of imidazolium in ionic liquids.27,28 The C2-H bond of imidazolium has a close contact with an anion in many crystals of ionic liquids.12,14,15,19,29–31 Turner et al. reported ab initio calculations for the [bmim]X complexes (X ) F, Cl, Br, and I).21 Wang et al. reported density-functional theory (DFT) calculations for the [bmim]X complexes.22 The anion has close contact with a C-H bond of imidazolium in the optimized structures for these complexes. These studies mainly focused on the positions of the anion in the stable structures. Although the interaction between the imidazolium and an anion is very strong, the effects of anion on the conformation of bmim are not clearly understood. The interaction between the C2-H bond and an anion is often regarded as a hydrogen bond.27,31 Although the structures of the C2-H contacts with anions in the crystals are similar to those of conventional hydrogen bonds, the nature of the interaction between the imidazolium and an anion is completely different from that of conventional hydrogen bonds.32 Conven-

10.1021/jp802107m CCC: $40.75  2008 American Chemical Society Published on Web 06/05/2008

7740 J. Phys. Chem. B, Vol. 112, No. 26, 2008

Tsuzuki et al.

Figure 1. MP2/6-311G** level optimized geometries and estimated CCSD(T)/cc-pVTZ level relative energies for nine rotamers of bmim cation (1).

TABLE 1: HF and MP2 Level Relative Energies for Rotamers of Isolated bmim Cation (1)a ∆EHFc

∆EMP2d

basis set

bfb

GTe

G′Tf

GTe

G′T f

6-31G 6-31G* 6-311G* 6-311G** 6-311++G** cc-pVDZ cc-pVTZ cc-pVQZ

120 180 225 270 325 215 510 1000

1.06 1.17 1.17 1.18 1.21 1.21 1.40 1.46

0.57 0.62 0.58 0.60 0.61 0.63 0.80 0.84

0.29 -0.16 -0.44 -0.43 -0.57 -0.23 -0.25 -0.19

-0.04 -0.56 -0.88 -0.88 -1.05 -0.66 -0.70 -0.65

a Energy in kilocalories per mole. b Number of basis functions. HF level relative energy. d MP2 level relative energy. e Relative energy for GT rotamer (1b) from TT rotamer (1a). f Relative energy for G′T rotamer (1c) from TT rotamer (1a). c

tional hydrogen bonds (hydrogen bonds between neutral molecules) are highly directional.33 The X-H bond (X ) O or N) strongly prefers to point toward a negative atom. The interaction energies of conventional hydrogen bonds are usually around -5 kcal/mol.34 On the other hand, the size of interaction energy between the imidazolium and an anion (Cl-, Br-, BF4-, or PF6-) is mainly determined by the distance between the imidazolium ring and the anion. The mutual orientation of the C2-H bond and anion is not important.32 The interaction energy is significantly greater than those for conventional hydrogen bonds. Ab initio calculations show that the interaction energy of an imidazolium with an anion is about -80 kcal/mol.35 The electrostatic interaction is the major source of the attraction both in conventional hydrogen bonds and in interaction between

TABLE 2: Relative Energies for Rotamers of Isolated bmim Cation (1) Calculated with Several Electron Correlation Correction Methodsa ∆E basis set

f CCSD(T)

∆∆ CCSD(T)g

0.21 0.00 0.04 0.20

0.07 -0.17 -0.14 0.05

0.23 0.27 0.29 0.28

-0.25 -0.50 -0.46 -0.28

-0.36 -0.64 -0.62 -0.41

0.20 0.24 0.26 0.25

∆EHFb ∆EMP2c ∆EMP3d ∆ECCSDe

6-31G* 6-311G* 6-311G** cc-pVDZ

1.17 1.17 1.18 1.21

-0.16 -0.44 -0.43 -0.23

6-31G* 6-311G* 6-311G** cc-pVDZ

0.62 0.58 0.60 0.63

-0.56 -0.88 -0.88 -0.66

GT h 0.24 0.03 0.07 0.24 G′T i -0.19 -0.44 -0.40 -0.21

a Energy in kilocalories per mole. b HF level relative energy. MP2 level relative energy. d MP3 level relative energy. e CCSD level relative energy. f CCSD(T) level relative energy. g CCSD(T) correction term. ∆∆CCSD(T) ) ∆ECCSD(T) - ∆EMP2. h Relative energy for GT rotamer (1b) from TT rotamer (1a). i Relative energy for G′T rotamer (1c) from TT rotamer (1a). c

ions.35,36 The electrostatic interaction between ions is not highly orientation dependent, because the dominant term of the electrostatic interaction is the isotropic charge-charge interaction. On the other hand, the highly orientation dependent dipole-dipole interaction is the leading term in the electrostatic interaction between neutral species. Therefore, conventional hydrogen bonds are highly orientation dependent. Despite broad interests on the conformation of the butyl group in bmim, many unsettled fundamental important issues still remain. (1) The relative energies for the TT, GT, and G′T

Analysis of 1-Butyl-3-methylimidazolium by CCSD(T)

J. Phys. Chem. B, Vol. 112, No. 26, 2008 7741

TABLE 3: Effects of Optimized Geometries on the Calculated MP2/cc-pVTZ Level Relative Energies for Rotamers of Isolated Bmim Cation (1)a optimizationb

GTc

G′Td

MP2/6-31G* MP2/6-311G* MP2/6-311G** MP2/cc-pVDZ MP2/cc-pVTZ

-0.24 -0.25 -0.25 -0.25 -0.25

-0.69 -0.70 -0.70 -0.69 -0.70

a Energy in kilocalories per mole. b Level of geometry optimization. Relative energy for GT rotamer (1b) from TT rotamer (1a). d Relative energy for G′T rotamer (1c) from TT rotamer (1a). c

Figure 2. Torsional potential for C(2)-N(1)-C(7)-C(8) bond in bmim cation (1).

Figure 4. Torsional potential for C(8)-C(9) bond in bmim cation (1). The C(7)-C(8) bond is trans in (A) and gauche′ in (B).

Figure 3. Torsional potential for C(7)-C(8) bond in bmim cation (1).

phase, the effects of anions on the conformational energies were not well understood. In this paper, we carried out detailed evaluation of the basis set effects using several basis sets up to the cc-pVQZ and the effects of electron correlation beyond MP2 for an accurate estimation of the conformational energies. We calculated conformational energies for an isolated bmim cation (1) and those for the [bmim]Cl (2) and [bmim]Br (3) complexes by highlevel ab initio methods. In addition, we compared conformational energies for 1-butlylimidazole (bim, 4) with those for 1 for understanding the effects of positive charge of the imidazolium ring. Computational Method

rotamers are still unclear. The calculated conformational energies strongly depend on basis set and electron correlation correction. Similar dependence is observed in calculations for small organic molecules. Sufficiently large basis set and proper electron correlation correction are necessary for an accurate evaluation of the conformational energies. Unfortunately, a detailed evaluation of the basis set and electron correlation effects on the conformational energies of the butyl group was not reported. (2) Although the torsional potentials for the N(1)-C(7) and C(8)-C(9) bonds are also important for understanding the conformation of bmim, an accurate evaluation of the torsional potentials for these bonds was not reported. (3) Although anions exist close to the C-H bonds of imidazolium in condensed

The Gaussian 03 program37 was used for the ab initio molecular orbital calculations. The basis sets implemented in the program were used for the calculations. Electron correlation was accounted for by the second-order Moeller-Plesset perturbation (MP2) method38,39 and by coupled cluster calculations with single and double substitutions with noniterative triple excitations [CCSD(T)].40 Geometries of molecules were optimized at the MP2/6-311G** level. Torsional potentials were calculated at the MP2/cc-pVTZ level. A tortional angle was fixed and other geometrical parameters were fully optimized in the calculations of torsional potentials. The CCSD(T)/cc-pVTZ level relative energies (∆ECCSD(T)/cc-pVTZ) for rotamers of bmim cation (1) and bim (4) were estimated as the sum of the MP2/

7742 J. Phys. Chem. B, Vol. 112, No. 26, 2008

Tsuzuki et al.

Figure 5. MP2/6-311G** level optimized geometries and estimated CCSD(T)/cc-pVTZ level formation energies for three rotamers of [bmim]Cl complex (2a-2c). Relative energies are shown in parentheses. The Cl anion has a close contact with the C2-H of imidazolium.

TABLE 4: MP2 and CCSD(T) Level Interaction Energies and Formation Energies for Rotamers of [bmim]Cl (2) and [bmim]Br (3) Complexesa EMP2/cc-pVTZ

EMP2/6-31G*

ECCSD(T)/6-31G*

∆CCSD(T)b

ECCSD(T)/cc-pVTZc

Edefd

Eforme

-0.09 -0.01 -0.08 0.68 0.70 0.71 0.82 0.85 0.84 0.82 0.84 0.80

-96.61 -98.46 -96.41 -80.56 -80.81 -80.99 -87.25 -87.49 -87.53 -88.75 -88.38 -87.70

2.50 3.06 1.74 1.50 1.51 1.11 1.85 1.83 1.37 1.72 1.56 1.16

-94.11 -95.39 -94.66 -79.06 -79.30 -79.88 -85.40 -85.66 -86.16 -87.03 -86.82 -86.55

0.31 0.36 0.27

-90.75 -92.47 -90.31

2.03 2.61 1.30

-88.72 -89.86 -89.01

[bmim]Cl f

TT 2a GT 2bf G′T 2cf TT 2dg GT 2eg G′T2fg TT 2gh GT 2hh G′T2ih TT 2ji GT 2ki G′T2 Li

-96.52 -98.44 -96.33 -81.24 -81.51 -81.70 -88.07 -88.34 -88.37 -89.57 -89.22 -88.50

-91.10 -92.85 -91.31 -78.24 -78.36 -78.62 -83.71 -83.96 -83.98 -84.09 -84.20 -83.49

-91.19 -92.86 -91.39 -77.56 -77.66 -77.92 -82.89 -83.10 -83.14 -83.27 -83.37 -82.69 [bmim]Br

TT 3a GT 3b G′T3c

-91.05 -92.83 -90.58

-89.00 -90.47 -89.13

-88.69 -90.11 -88.86

a Energy in kilocalories per mole. MP2/6-311G** optimized geometries were used. Geometries are shown in Figures 5, 7, 8, 9, and 12. CCSD(T) correction term [) ECCSD(T)/6-31G* - EMP2/6-31G*]. c Estimated CCSD(T)/cc-pVTZ level interaction energy [) EMP2/cc-pVTZ + ∆CCSD(T)]. d Deformation energy. e Formation energy of complex from isolated ions. f Cl anion has a contact with C2-H of imidazolium in the complex. g Cl anion has contacts with C4-H and C5-H of imidazolium in the complex (Structure A in Figure 6). h Cl anion has contacts with C4-H and a hydrogen atom of the methyl group of imidazolium in the complex (Structure B in Figure 6). i Cl anion has contacts with C5-H and a hydrogen atom of the C7 methylene group of imidazolium in the complex (Structure C in Figure 6). b

Figure 6. Stable Cl anion positions close to C4-H and C5-H.

calculated by the supermolecule method. The basis set superposition error (BSSE)41 was corrected using the counterpoise method.42 The CCSD(T)/cc-pVTZ level interaction energy (ECCSD(T)/cc-pVTZ) was estimated as the sum of the MP2/cc-pVTZ level interaction energy and the CCSD(T) correction term.43 Formation energy of the complex from isolated ions (Eform) was obtained as the sum of the ECCSD(T)/cc-pVTZ and deformation energy (Edef). The Edef is the increase of the energy of bmim by the deformation of geometry in complex formation. The Edef at the CCSD(T)/cc-pVTZ level was estimated.44 Relative energies for rotamers of 2 and 3 were obtained from the calculated Eform. Electrostatic energy was calculated as the interactions between a charge of the anion and distributed multipoles45,46 of the bmim cation using the Orient version 3.2.47 Distributed multipoles up to hexadecapole on all atoms were obtained from MP2/cc-pVTZ wave functions of an isolated bmim cation using the GDMA program.48 The distributed multipoles were used only to estimate the electrostatic energies. Results and Discussion

cc-pVTZ level relative energies (∆EMP2/cc-pVTZ) and the CCSD(T) correction terms [∆∆CCSD(T) ) ∆ECCSD(T) - ∆EMP2, ∆ECCSD(T), and ∆EMP2 denote CCSD(T) and MP2 level relative energies] calculated using the 6-31G* basis set. Interaction energies for the [bmim]Cl (2) and [bmim]Br (3) complexes were

Effects of Basis Set and Electron Correlation Correction. Relative energies for the TT, GT, and G′T rotamers of an isolated bmim cation (Figure 1) were calculated using several basis sets. Calculated HF and MP2 level relative energies (∆EHF and ∆EMP2) for the GT and G′T rotamers (1b and 1c) from the TT

Analysis of 1-Butyl-3-methylimidazolium by CCSD(T)

J. Phys. Chem. B, Vol. 112, No. 26, 2008 7743

Figure 7. MP2/6-311G** level optimized geometries and estimated CCSD(T)/cc-pVTZ level formation energies for three rotamers of [bmim]Cl (2d-2f). Relative energies are shown in parentheses. The Cl cation has close contacts with the C4-H and C5-H of imidazolium.

Figure 8. MP2/6-311G** level optimized geometries and estimated CCSD(T)/cc-pVTZ level formation energies for three rotamers of [bmim]Cl (2g-2i). Relative energies are shown in parentheses. The Cl cation has close contacts with the C4-H of imidazolium and a hydrogen atom of the methyl group. See text.

Figure 9. MP2/6-311G** level optimized geometries and estimated CCSD(T)/cc-pVTZ level formation energies for three rotamers of [bmim]Cl (2j-2l). Relative energies are shown in parentheses. The Cl cation has close contacts with the C5-H of imidazolium and a hydrogen atom of the C7 methylene group. See text.

Figure 10. Electrostatic potential at Y was calculated. X is the midpoint of two nitrogen atoms of imidazolium. The X. . . H2 points toward Y. R is the distance between X and Y.

rotamer (1a) are summarized in Table 1. The calculated ∆EMP2 using the large cc-pVTZ and cc-pVQZ basis sets show that the G′T rotamer (1c) is the most stable among the three rotamers and that the TT rotamer (1a) is slightly above the GT rotamer (1b). The HF calculations overestimate the relative stability of the TT rotamer compared with the MP2 calculations. The calculated ∆EMP2 substantially depend on the basis set. The small 6-31G basis set overestimates the ∆EMP2 for the GT and G′T rotamers compared with the large basis sets. On the other hand the medium-size 6-311G** basis set underestimates the

∆EMP2 for the two rotamers. The ∆EMP2 for GT and G′T rotamers obtained using the cc-pVTZ basis set are close to those obtained using the very large cc-pVQZ basis set. The relative energies for the three rotamers were calculated with electron correlation correction by several methods using the 6-31G*, 6-311G*, 6-311G**, and cc-pVDZ basis sets as shown in Table 2. The effects of electron correlation correction beyond MP2 are not negligible. The MP2 method underestimates the relative stability of the TT rotamer (1a) compared with the more reliable CCSD(T) method. The ∆∆CCSD(T) [)∆ECCSD(T) - ∆EMP2] for the GT rotamer (1b) relative to the TT rotamer (1a) is 0.23-0.29 kcal/mol. That for the G′T rotamer (1c) is 0.20-0.26 kcal/mol. Although ∆EMP2 and ∆ECCSD(T) substantially depend on basis set, the basis set dependence of ∆∆CCSD(T) is small.49 Optimized Geometry Effects. The relative energies for the three rotmaers (1a-1c) were calculated at the MP2/cc-pVTZ level using geometries obtained by five levels of optimizations for evaluating the optimized geometry effects. The geometries optimized at the MP2 levels with the 6-31G*, 6-311G*, 6-311G**, cc-pVDZ, and cc-pVTZ basis sets were used for

7744 J. Phys. Chem. B, Vol. 112, No. 26, 2008

Tsuzuki et al.

TABLE 5: Calculated Electrostatic Interaction between bmim Cation and Positive Point Charge (1.0 e)a R(Å)b

TTc

GTd

differencee

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

124.08 97.70 83.38 73.47 65.93 59.90 54.92 50.74 47.15 44.05 41.33 38.93 36.79 34.87 33.15

123.99 97.63 83.34 73.44 65.91 59.89 54.92 50.73 47.15 44.04 41.32 38.92 36.78 34.86 33.13

-0.08 -0.07 -0.04 -0.03 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01

a

Energy in kilocalories per mole. MP2/6-311G**//HF/ 6-311G** level wave functions for isolated bmim (TT and GT forms) were used for the calculations of electrostatic potentials. Calculated electrostatic potential corresponds to the electrostatic interaction energy between the imidazolium and the positive point charge. b The distance between the bmim and the positive charge. The position of the positive charge is shown in Figure 10. c Electrostatic interaction with TT form of bmim (1a). d Electrostatic interaction with GT form of bmim (1b). e Difference between the calculated electrostatic interactions with GT and those with TT forms of bmim.

the calculations. The calculated relative energies (Table 3) show that the optimized geometry effects are very small. The differences are only 0.01 kcal/mol. Estimation of CCSD(T)/cc-pVTZ Level Relative Energies for Rotamers of bmim (1). The calculated relative energies for the rotamers (1a-1c) of an isolated bmim cation summarized in Tables 1 and 2 show that CCSD(T) level calculations using a large basis set such as the cc-pVTZ are necessary for an accurate evaluation of the relative energies. Unfortunately, computationally demanding CCSD(T)/cc-pVTZ level calculations of 1, which require more than 500 basis functions, are not practical at present. Therefore, we estimated the ∆ECCSD(T)/ cc-pVTZ from the ∆EMP2/cc-pVTZ and the ∆∆CCSD(T) obtained using the 6-31G* basis set. The ∆EMP2/cc-pVTZ and ∆∆CCSD(T) are summarized in Table 1S in Supporting Information. Errors of the estimated ∆ECCSD(T)/cc-pVTZ will not be large, because the basis set dependence of the ∆∆CCSD(T) is small as shown in Table 2.49 Estimated relative energies (∆ECCSD(T)/cc-pVTZ) for nine rotamers of bmim cation (Figure 1) show that the G′T rotamer (1c) is the most stable. The G′G′ rotamer (1i) is the second most stable rotamer. The TT and GT rotamers (1a and 1b) are 0.50 and 0.48 kcal/mol above the G′T rotamer, respectively. The TT and GT rotamers are nearly isoenergetic. Torsional Potentials for bmim Cation (1). Calculated torsional potential for the C(2)-N(1)-C(7)-C(8) bond has a minimum near 90° (The conformation of C(7)-C(8)-C(9) bond is TT in the calculations) as shown in Figure 2. The preference of the nonplanar form agrees well with the observed structures in the crystals.13–15,19 Although the MP2/cc-pVTZ level potential has another shallow minimum when the C(2)-N(1)-C(7)-C(8) torsional angle is 0°, the torsional barrier from this minimum is very small (less than 0.1 kcal/mol), which shows that the planar form is not a stable structure. Calculated torsional barrier height between the two nonplanar minima is less than 1 kcal/ mol. A similar torsional potential was also calculated for the

ethyl group of 1-ethyl-3-methylimidazolium.50 The HF calculations substantially overestimate the torsional barrier height at 180° compared with the MP2 calculations. Calculated torsional potential for the C(7)-C(8) bond (the C(2)-N(1)-C(7)-C(8) torsional angle is around 90° and the C(8)-C(9) bond is trans conformation in the calculations) shows that the gauche and gauche′ conformations are more stable than the trans conformation (Figure 3) in contrast to the torsional potentials for n-alkanes. The gauche′ conformation is slightly more stable than the gauche conformation. The HF calculations overestimate the stability of the trans conformation. Calculated torsional potentials for the C(8)-C(9) bond (the C(2)-N(1)-C(7)-C(8) torsional angle is around 90°) are shown in Figure 4. The C(7)-C(8) bond is trans conformation in the calculations for the torsional potential (A). The C(8)-C(9) bond prefers trans conformation as in the cases of torsional potentials for n-alkanes. The calculated energy difference between the gauche and the trans conformations (0.49 kcal/ mol) is close to that of n-hexane (0.55 kcal/mol) calculated at the same level. The C(7)-C(8) bond is gauche′ conformation in the calculations for the torsional potential (B). The gauche′ conformation of the C(8)-C(9) bond is only slightly less stable than the trans conformation (0.23 kcal/mol), while the gauche conformation is 1.38 kcal/mol less stable than the trans conformation due to the steric repulsion. Relative Energies for Rotamers of [bmim]Cl (2). The Cl anion close to the C2-H of imidazolium significantly increases the relative stability of the GT rotamer. Formation energies (Eform) for three rotamers (2a-2c) of the [bmim]Cl complex are shown in Figure 5. The ECCSD(T)/cc-pVTZ and Edef are summarized in Table 4. The Cl anion has a close contact with the C2-H in these structures. The GT rotamer (2b) is the most stable among the three rotamers in contrast to an isolated bmim cation (1), which prefers the G′T rotamer (1c). The G′T rotamer (2c) is 0.73 kcal/mol above 2b, while the G′T rotamer of an isolated bmim cation (1c) is 0.48 kcal/mol below the GT rotamer (1b). The TT rotamer (2a) is 0.55 kcal/mol above the G′T rotamer (2c). This energy difference is close to that between the TT and the G′T rotamers (1a and 1c) of isolated bmim cation (0.50 kcal/mol). The effects of Cl anions close to the C4-H and C5-H were also studied. Calculated stable structures for the [bmim]Cl complex by DFT method show that there are three positions (A-C in Figure 6) of the Cl anion close to the C4-H and C5-H. The Cl anion has close contacts with the C4-H and C5-H in the structure A (2d-2f in Figure 7). The Cl anion has close contacts with the C4-H and a hydrogen atom of the methyl group in the structure B (2g-2i in Figure 8). The Cl anion has close contacts with C5-H and a hydrogen atom of the C7 methylene group in the structure C (2j-2l in Figure 9). The Cl anion in the structures A and B does not largely change the relative stability of the rotamers. Calculated formation energies for the TT, GT, and G′T rotamers of the [bmim]Cl complex (2d-2f, structure A) are shown in Figure 7. The relative energies for the three rotamers (0.0, -0.24, and -0.82 kcal/mol) are not largely different from those for the three rotamers (1a-1c) of an isolated bmim cation (0.0, -0.02, and -0.50 kcal/mol). The relative energies for three rotamers (2g-2i, structure B) shown in Figure 8 (0.0, -0.26, and -0.33 kcal/mol) are also not largely different from those for the three rotamers of an isolated bmim cation. The Cl anion in the structure C increases the relative stabilities for the TT and GT rotamers compared with that for the G′T rotamer. The relative

Analysis of 1-Butyl-3-methylimidazolium by CCSD(T)

J. Phys. Chem. B, Vol. 112, No. 26, 2008 7745

Figure 11. Calculated charge distributions for three rotamers (1a-1c) of bmim cation. Atomic charges with hydrogen atoms summed into heavy atoms.

Figure 12. MP2/6-311G** level optimized geometries and estimated CCSD(T)/cc-pVTZ level formation energies for three rotamers of [bmim]Br complex (3a-3c). Relative energies are shown in parentheses. The Br anion has a close contact with the C2-H of imidazolium.

Figure 13. MP2/6-311G** level optimized geometries and estimated CCSD(T)/cc-pVTZ level relative energies for three rotamers of bim (4a-4c).

energies for the three rotamers (2j-2 L) are 0.0, 0.21, and 0.48 kcal/mol, respectively (Figure 9). In order to evaluate the effects of distant charges, the electrostatic potentials around isolated TT and GT bmim cations were calculated as summarized in Table 5. The calculated electrostatic potential corresponds to the electrostatic energy (Ees) between the bmim cation and a positive point charge (1.0e ) 1.602 × 10-9 C). The position of the positive charge is shown in Figure 10. R is the distance between the midpoint of the two nitrogen atoms of imidazolium and the positive charge. The calculated Ees is significant, even if the positive charge is wellseparated. The Ees values for the TT and GT rotamers are about 33 kcal/mol when R ) 10.0 Å. Although the Ees values are significant, the difference between the Ees values for the two rotamers [Ees(diff)] decreases rapidly with distance. The Ees(diff) is about 0.01 kcal/mol, when R is 5.0-10.0 Å. Molecular dynamics simulations show the formation of charge ordering in ionic liquids, which indicates that each ion has close contacts with counterions.51–53 The charge ordering in ionic liquids suggests that the electrostatic interactions of long distant charges are largely screened by neighboring counterions.

Calculated cation-anion radial distribution functions for the ionic liquids have the first peak around 5 Å, which corresponds to the neighboring anions around the imidazolium. The radial distribution functions have the second peak around 10 Å. Calculated cation-cation radial distribution functions have the first peak around 7 Å. Our calculations suggest that the GT rotamer of bmim is the most stable in ionic liquids. Recently reported neutron diffraction measurements and ab initio MD simulations of imidazoliumbased ionic liquids show that anions have close contacts with the hydrogen atoms of imidazolium ring.27,28 Our calculations show that the neighboring anions increase the relative stability of the GT rotamer. The Cl anion close to the C2-H significantly stabilizes the GT rotamer. The neighboring anions play important roles in determining the stable conformation of the butyl group in ionic liquid. Anions also have close contacts with hydrogen atoms of imidazolium in crystals, which suggests that the anions also play important roles in determining the conformation of the butyl group in the crystals. The GT rotamer (2b) is favored by the strong attraction between the bmim cation and the Cl anion. Greater electrostatic

7746 J. Phys. Chem. B, Vol. 112, No. 26, 2008 interaction in 2b is responsible for the strong attraction. Calculated electrostatic energies for the complexes 2a-2c are -91.25, -92.14, and -90.72 kcal/mol, respectively. The charge distributions on the imidazolium ring, which depend on conformation of the butyl group, explain the dependence of the electrostatic energy on the conformation of the butyl group. Atomic charge distributions for three rotamers (1a-1c) of an isolated bmim cation calculated by electrostatic potential fitting using Merz-Singh-Kollman scheme from the MP2/6-311G** wave functions54,55 are shown in Figure 11. The C2-H group in the GT rotamer has a substantial positive charge (+0.08 e), while the charges on the C2-H group in the TT and G′T rotamers are small (+0.03 and -0.03 e). The Cl anion close to the C2-H increases the relative stability of the GT rotamer due to the large attractive electrostatic interaction with the GT rotamer. The sum of the charges on the C4-H and C5-H groups in the three rotamers (+0.07, +0.09, and +0.09, respectively) are nearly identical. Therefore, the anion close to the C4-H and C5-H bonds does not largely change the relative stability of the three rotamers (2d-2f). Relative Energies for Rotamers of [bmim]Br (3). The Br anion close to the C2-H significantly increases the relative stability of the GT rotamer (3b) compared with an isolated bmim cation as in the case of the Cl anion close to the C2-H (2b). Formation energies for three rotamers (3a-3c) of the [bmim]Br complex are shown in Figure 12. The Br anion has a close contact with the C2-H in these structures. The GT rotamer (3b) is the most stable among the three rotamers. The relative energies for the TT, GT, and G′T rotamers for the [bmim]Br complex (3a-3c) are 0.0, -1.14, and -0.29 kcal/mol, resepectively. These values are close to those for the [bmim]Cl complex (2a-2c, 0.0, -1.28, and -0.55 kcal/mol, respectively). Relative Energies for Rotamers of N-Buthylimidazole (bim, 4). Estimated relative energies (∆E CCSD(T)/cc-pVTZ) for three rotamers of bim (Figure 13) show that the positive charge on the imidazolium ring of bmim cation (1) does not largely change the conformational energies. The G′T rotamer (4c) is the most stable as in the case of an isolated bmim cation (1). The GT rotamer (4b) is 0.46 kcal/mol above the G′T rotamer (4c). This energy difference is close to that between the GT and the G′T rotamers (1b and 1c) of bmim cation (0.48 kcal/mol). The energy difference between the TT (4a) and the G′T (4c) rotamer (0.75 kcal/mol) is slightly larger than that between the TT and the G′T rotamers (1a and 1c) of an isolated bmim cation (0.50 kcal/mol). Conclusion An isolated bmim cation favors the G′T rotamer, while the neighboring anions increase the relative stability of the GT rotamer. The GT rotamer is the most stable when the Cl anion is close with the C2-H of imidazolium. The Br anion close to the C2-H also increases the relative stability of the GT rotamer. The anion close to the C2-H plays an important role in determining the stable conformation of the butyl group in condensed phase. The GT rotamer is favored by the greater electrostatic interaction between the bmim cation and the anion. Charge distributions of imidazolium ring in the bmim cation depend on the conformation of the butyl group. The C2-H group in the GT rotamer has a larger positive charge compared with the TT and G′T rotamers. Recently reported neutron diffraction measurements and ab initio MD simulations of imidazoliumbased ionic liquids show that anions exist near the hydrogen atoms of imidazolium ring. Our calculations suggest that the GT rotamer of bmim is the most stable in ionic liquids. The

Tsuzuki et al. comparison with the conformational energies for N-butylimidazole shows that the positive charge on the imidazolium ring does not largely change the conformational energies. The calculated torsional potential for the N(1)-C(7) bond in an isolated bmim shows that the coplanar conformation is not a stable conformation. The C(7)-C(8) bond prefers the gauche conformation, while the C(8)-C(9) bond favors the trans conformaion. Acknowledgment. This work was partly supported by MEXT Japan through Project No. 18045032 involving Grants-in-Aid. We thank Tsukuba Advanced Computing Center for the provision of the computational facilities. Supporting Information Available: Relative energies for rotamers of bmim (1) and bim (4). 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, 2071–2083. (2) Holbrey, J. D.; Seddon, K. R. Clean Products Processes 1999, 1, 223–236. (3) Wasserscheid, P.; Keim, W. Angew. Chem., Int. Ed. 2000, 39, 3772– 3789. (4) Huddleston, J. G.; Visser, A. E.; Reichert, W. M.; Willauer, H. D.; Broker, G. A.; Rogers, R. D Green Chem. 2001, 3, 156–164. (5) Earle, M. J.; McCormac, P. B.; Seddon, K. R. Chem. Commun. 1998, 2245–2246. (6) Wasserscheid, P.; van Hal, R.; Bosmann, A Green Chem. 2002, 4, 400–4004. (7) Fuller, J.; Carlin, R. T.; Osteryoung, R. A. J. Electrochem. Soc. 1997, 144, 3881–3886. (8) Noda, A.; Hayamizu, K.; Watanabe, M. J. Phys. Chem. B 2001, 105, 4603–4610. (9) Wang, P.; Zakeeruddin, S. M.; Comte, P.; Exnar, I.; Gratzel, M. J. Am. Chem. Soc. 2003, 125, 1166–1167. (10) Morrow, T. I.; Maginn, E. J. J. Phys. Chem. B 2002, 106, 12807– 12813. (11) Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. J. Phys. Chem. B 2004, 108, 16593–16600. (12) Saha, S.; Hayashi, S.; Kobayashi, A.; Hamaguchi, H. Chem. Lett. 2003, 32, 740–741. (13) Hayashi, S.; Ozawa, R.; Hamaguchi, H. Chem. Lett. 2003, 32, 498– 499. (14) Holbray, J. D.; Reichert, W. M.; Nieuwenhuyzen, M.; Johnston, S.; Sedon, K. R.; Roger, R. D. Chem. Commun. 2003, 1636–1637. (15) Ozawa, R.; Hayashi, S.; Saha, S.; Kobayashi, A.; Hamaguchi, H. Chem. Lett. 2003, 32, 948–949. (16) Katayanagi, H.; Hayashi, S.; Hamaguchi, H.; Nishikawa, K. Chem. Phys. Lett. 2004, 392, 460–464. (17) Hamaguchi, H.; Saha, S.; Ozawa, R.; Hayashi, S. ACS Symp. Ser. 2005, 901, 68–78. (18) Berg, R. W.; Deetlefs, M.; Seddon, R.; Shim, I.; Thompson, J. M. J. Phys. Chem. B 2005, 109, 19018–19025. (19) Nakakoshi, M.; Shiro, M; Fujimoto, T.; Machinami, T.; Seki, H.; Tashiro, M.; Nishikawa, K. Chem. Lett. 2006, 35, 1400–1401. (20) Nishikawa, K.; Wang, S.; Katayanagi, H.; Hayashi, S.; Hamaguchi, H.; Koga, Y.; Tozaki, K. J. Phys. Chem. B 2007, 111, 4894–4900. (21) Turner, E. A.; Pye, C. C.; Singer, R. D. J. Phys. Chem. A 2003, 107, 2277–2288. (22) Wang, Y.; Li, H.; Han, S. J. Chem. Phys. 2005, 123, 174501. (23) Lopes, J. N. C.; Deschamps, J.; Padua, A. A. H. J. Phys. Chem. B 2004, 108, 2038–2047. (24) Lopes, J. N. C.; Padua, A. A. H. J. Phys. Chem. B 2006, 110, 7485– 7489. (25) Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. J. Phys. Chem. B 2005, 109, 6103–6110. (26) The crystal has four bmim cations in a unit cell. One bmim cation in the unit cell is crystallographically independent. Two bmim cations in the unit cell are mirror image isomers, in which the C(7)-C(8) bond is gauche′ and the C(2)-N(3)-C(7)-C(8) torsional angle is negative. (27) Hardacre, C.; McMath, S. E. J.; Bowron, D. T.; Soper, A. K. J. Chem. Phys. 2003, 118, 273–278. (28) Del Popolo, M. G.; Lynden-Bell, R. M.; Kohanoff, J. J. Phys. Chem. B 2005, 109, 5895–5902.

Analysis of 1-Butyl-3-methylimidazolium by CCSD(T) (29) Abdul-Sada, A. K.; Greenway, A M.; Hitchcok, P. B.; Mohammed, T. J.; Seddon, K. R.; Zora, J. A J. Chem. Soc., Chem. Commun. 1986, 1753–1754. (30) Dymek, C. M., Jr; Grossie, D. A.; Fratini, A. V.; Adams, W. W J. Mol. Struct. 1989, 213, 25–34. (31) Elaiwi, A.; Hitchcock, P. B.; Seddon, K. R.; Srinivasan, N.; Tan, Y.-M.; Welton, T.; Zora, J. A. J. Chem. Soc., Dolton Trans. 1995, 3467– 3472. (32) Tsuzuki, S.; Tokuda, H.; Mikami, M. Phys. Chem. Chem. Phys. 2007, 9, 4780–4784. (33) Desiraju, G. R.; Steiner, T. The Weak Hydrogen Bond; Oxford University Press: New York, 1999. (34) Curtiess, L. A.; Frurip, D. J.; Blander, M. J. Chem. Phys. 1979, 71, 2703–2711. (35) Tsuzuki, S.; Tokuda, H.; Hayamizu, K.; Watanabe, M. J. Phys. Chem. B 2005, 109, 16474–16481. (36) Stone, A. J. Chem. Phys. Lett. 1993, 211, 101–109. (37) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, ReVision D.01; Gaussian, Inc.: Wallingford, CT, 2004. (38) Mφller, C,; Plesset, M. S. Phys. ReV. 1934, 46, 618–622. (39) Head-Gordon, M.; Pople, J. A.; Frisch, M. J. Chem. Phys. Lett. 1988, 153, 503–506. (40) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968–5975.

J. Phys. Chem. B, Vol. 112, No. 26, 2008 7747 (41) Ransil, B. J. J. Chem. Phys. 1961, 34, 2109–2118. (42) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553–566. (43) The CCSD(T) correction term is the difference between the CCSD(T) and the MP2 level interaction energies. The CCSD(T) correction term was calculated using the 6-31G* basis set. (44) The CCSD(T)/cc-pVTZ level Edef was estimated from the MP2/ccpVTZ level Edef and the CCSD(T) correction term using the same method for the estimation of the CCSD(T)/cc-pVTZ level relative energies (∆ECCSD(T)/ccpVTZ) for rotamers. (45) Stone, A. J.; Alderton, M. Mol. Phys. 1985, 56, 1047–1064. (46) Stone, A. J. The theory of intermolecular forces; Clarendon Press: Oxford, 1996. (47) Stone, A. J.; Dullweber, A.; Hodges, M. P.; Popelier, P. L. A.; Wales, D. J. Orient: a program for studying interactions between molecules, Version 3.2; University of Cambridge, 1995. (48) Stone, A. J. J. Chem. Theory Comput. 2005, 1, 1128–1132. (49) The basis set effects on the∆∆CCSD(T) is usually very small, if the basis set effects on the MP2 level relative energy [∆EMP2] is small. Table 1 shows that the calculated∆EMP2 values using the cc-pVDZ basis set are very close to those obtained using the very large cc-pVTZ and ccpVQZ basis sets. The differences are less than 0.05 kcal/mol. Therefore, we can expect that the calculated∆∆CCSD(T) values using the cc-pVDZ basis set are very close to those obtained using the cc-pVTZ and cc-pVQZ basis sets. (50) Umebayashi, Y.; Fujimori, T.; Sukizaki, T.; Asada, M.; Fujii, K.; Kanzaki, R.; Ishiguro, S. J. Phys. Chem. A 2005, 109, 8976–8982. (51) Hanke, C. G.; Price, S. L.; Lynden-Bell, R. M. Mol. Phys. 2001, 99, 801–809. (52) Urahata, S. M.; Ribeiro, M. C. C. J. Chem. Phys. 2004, 120, 1855– 1863. (53) Lopes, J. N. A. C.; Padua, A. A. H. J. Phys. Chem. B 2006, 110, 3330–3335. (54) Singh, U. C.; Kollman, P. A. J. Comput. Chem. 1984, 5, 129–145. (55) Besler, B. H.; Merz, K. M.; Kollman, P. A J. Comput. Chem. 1990, 11, 431–439.

JP802107M