Characterizing the Structural Properties of N,N-Dimethylformamide

Amide-based ionic liquids are receiving great enthusiasm recently. In this work, the structures of a kind of N,N-dimethylformamide-based (DMF-based) i...
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11016

J. Phys. Chem. B 2007, 111, 11016-11020

Characterizing the Structural Properties of N,N-Dimethylformamide-Based Ionic Liquid: Density-Functional Study Lei Zhang, Haoran Li,* Yong Wang, and Xingbang Hu Department of Chemistry, Zhejiang UniVersity, Hangzhou 310027, People’s Repblic of China ReceiVed: June 23, 2007; In Final Form: July 20, 2007

Amide-based ionic liquids are receiving great enthusiasm recently. In this work, the structures of a kind of N,N-dimethylformamide-based (DMF-based) ionic liquid are investigated theoretically by means of densityfunctional theory methods. Enol and keto forms of the cation with anions are optimized. The enol form of the DMFH+ cation can form three stable configurations of ion pairs with the anion, while the cation of the keto form is unstable and the proton transfer occurs to form three kinds of neutral molecule pairs. Moreover, the neutral pairs are more stable than the ion pairs, and the ion pairs tend to tautomerize to neutral pairs without barriers. It is suggested that the transformation from the ion pairs to neutral pairs may be the first step for decomposition of DMF-based ionic liquids.

1. Introduction Ionic liquids (ILs) are receiving an upsurge of interest in multidisciplinary areas.1-5 Despite the successful design of various task-specific ILs such as guanidinium-based ILs for SO2 absorption6,7 and the amine-appending ILs for CO2 capture,8,9 the lack of knowledge on the link between microscopic structures and specific physical and chemical properties of ILs is restricting the exploitation and application of ILs. Hence, research on the microscopic structures as well as the interaction between cations and anions of ILs is of key importance. Since studies by experiments are time consuming and cost intensive, a range of theoretical methods have now been used to explore ILs. Classical molecular dynamics (MD),10-14 Monte Carlo,15,16 and ab initio MD17-20 methods have been applied to ILs to obtain useful information on ILs. However, accurate structural and energetic properties could not be obtained from molecular simulation. The quantum chemical (QM) calculation is an efficient and indispensable approach to simulate the exact microscopic structural and electronic properties of ILs. The past few years have witnessed enormous growth in this area, and more attention has been paid to imidazolium melts. For example, Carper et al. calculated the structures of bmim+ (1-butyl-3methyl imidazolium)-PF6- employing semiempirical and ab initio methods.21 Later, the interaction energy of 1-alkyl-3imidazolium halides was reported by Singer et al.22 Tsuzuki et al. calculated the relationship between the interaction and ionic conductivity in several ion pairs of ILs.23 A computational approach for predicting the formation and stability of a variety of imidazolium-based salts has been described by Dixon and co-workers.24 In their pioneering studies focusing on the multiple stable conformers of the 1-butyl-3-methylimidazolium ion pair, Hunt and co-workers25 studied the vibrational spectrum of each conformer. The electronic structures were also analyzed by them,26 and the cooperativity was researched by Kossmann et al.27 Besides, hydrogen bonds in imidazolium ILs have been explored by Zhang et al.28 Moreover, infrared, Raman, and X-ray diffraction (XRD) studies have recently been combined with * To whom correspondence should be addressed. Fax: +86-571-87951895. E-mail: [email protected].

the QM calculations to analyze ILs.29-34 Our research team has been also involved in studying the imidazolium salt by QM calculations.35 However, the past research has focused mainly on imidazolium-based ILs. Currently a great enthusiasm has been seen for amide-based ILs. Novel ammonium ILs [Me3NH][HSO4] and [Et3NH][HSO4] have been used both as a catalyst and as an environmentally benign solvent for the hydrolytic reaction, and they have been applied in industry.36 The conversion and selectivity in these ILs are significantly increased in comparison with those reported in traditional organic solvents.37,38 Recently, a new family of Brønsted-acidic room-temperature ionic liquids (RTILs) derived from N,N-dimethylformamide (DMF) has been synthesized, and they are demonstrated to be proton conductive.39 However, the detailed structures and conformations of these amide-based ILs, which are of vital importance to understanding their physical properties and reaction mechanism, are still unknown. Before solvation in these ILs can be understood, we need to have an awareness of the gas-phase structural properties and interactions between the cations and anions. Therefore, this work reports on an analysis of the structure of a kind of DMF-based ionic liquid using the quantum chemical calculations. The theoretical results here will help to understand the fundamental properties of these ILs. The anion selected is NO3- as reported in ref 39, which is the anion of common acid and with low cost. This paper is organized as follows: Structures of the cation are first optimized, and then the ion pairs initiated from the optimized cation with the anion at different binding sites are discussed. Geometries parameters, energies, as well as the harmonic frequencies and charge population analysis of them are explored. Finally, discussions are carried out for the above results. 2. Methodology The density-functional theory (DFT) method is one of the most widely used tools for studying the geometric and electronic structures of molecules, has been shown to produce more reliable geometries and vibrational frequencies for hydrogen-bond

10.1021/jp0749064 CCC: $37.00 © 2007 American Chemical Society Published on Web 08/24/2007

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Figure 1. Optimized structures of the keto (a) and enol (b) forms of the DMFH+ cation.

systems than Hartree-Fock (HF) methods,40-42 and has the advantage of a much lower computational cost than the secondorder Møller-Plesset perturbation MP2 methods. DFT has also been successfully employed to calculate the structural properties of some of the ionic liquids.21-35 Therefore, DFT is also employed here to predict the structures of the DMF-based ionic liquids. In fact, when the MP2 methods are employed to check the reliability of the DFT methods, the results of the two methods match well as described in the main text. All calculations reported here were performed with the Gaussian 03 program package.43 The density-functional method B3LYP, i.e., Becke’s three-parameter nonlocal exchange functional44 with the nonlocal correlation functional of Lee et al.45,46 as implemented in the Gaussian 03 program, was used in this study. The medium-size 6-31G* basis set with the B3LYP functional was employed to preoptimize the geometries and fully characterized as minima by frequency analysis. Subsequent geometry optimizations were performed at the more sophisticated 6-311++G** basis set starting from the B3LYP/6-31G* geometries. No restrictions on symmetries were imposed on the initial structures; therefore, geometry optimization for the saddle points occurred with all degrees of freedom. A vibrational analysis was performed on all DFT structures to ensure the absence of negative vibrational frequencies and verify the existence of a true minimum.47,48 Besides, the interaction energy is defined as the difference between the energy of the ion pairs system (EAX) and the sum of the energies of the purely cationic (EA+) and anionic (EX-) species22

∆E (kJ/mol) ) 2625.5 [EAX(au) - (EA+(au) + EX-(au))] Since the results of the two theoretical methods agree well, the values discussed below are mainly those from the B3LYP/ 6-311++G** method. Basis set superposition error (BSSE) corrections and NBO analysis were calculated at the same theoretical level. 3. Results and Discussion 3.1. Geometry of the DMFH+ Cation. The cation DMFH+ may exist in two forms, namely, the keto form and the enol form. Optimized structures of these two forms are depicted as a and b in Figure 1, respectively. The energies of them are calculated, and the enol form of DMFH+ lies approximately 73.1 kJ/mol at the B3LYP/6-311++G** method and 67.3 kJ/ mol at the B3LYP/6-31G* method lower in energy than the

Figure 2. Possible structures of ion pairs of [DMFH+][NO3-]. 1a and 1b structures are not stable at B3LYP/6-311++G**, and the values at this level are described in parentheses.

keto form. It suggests that the enol form of the DMFH+ cation is more stable than the keto form. When the MP2/6-311++G** method is applied to check the reliability of the DFT methods, the geometries obtained from MP2 agree well with that of Figure 1. The energies of the two kinds of cations here are both higher than that of the DFT methods. However, the keto form is 52.5 kJ/mol higher in energy than the enol form of the cation, also coinciding with the results of the DFT methods. Therefore, the DFT methods are adequate for determining the geometries and energies for the system here. 3.2. Structures of Ion Pairs. Ion pairs of the cation with the enol and keto forms are optimized, respectively, with DFT methods using the B3LYP/6-31G* method first and then the 6-311++G** basis set. There are some differences between the results of these two methods, and it will be discussed in detail below. 3.2.1. Enol Form of the DMFH+ Cation. The NO3- anions are then initially put at all possible sites near the enol forms of the DMFH+ cation (Figure 1b) and optimized. As can be seen, the enol forms of the cation form stable ionic pairs with the anions, reinforcing the result of Dai et al.39 that reaction of neutral amides with H+ occurs on O rather than on N. Hence, the optimized structures of the ionic pairs are discussed below. Five possible conformations of [DMFH+][NO3-] have been obtained after optimization at the B3LYP/6-31G* method (Figure 2). However, when these geometries are reoptimized at the higher B3LYP/6-311++G** level, structures 1a and 1b are not stable at all, and the reason will be discussed in the next section. Therefore, structures 1c-e are mainly explored here. The detailed geometrical parameters and interaction energies for 1c-e are listed in Table 1. Structures 1c and 1d are stabilized

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TABLE 1: Geometrical Parameters and Interaction Energies of [DMFH+][NO3-] at B3LYP/6-311++G** (bond lengths in Angstroms and angles in degrees) structures

cation (enol)

1c

1d

1e

C1-N2 C1-O5 O5-H13 C1-H6 O5-C1-N2 H6-C1-N2 H13-O5-C1 C1-N2-C3 H13-O5-C1-N2 H6-C1-N2-C3 O5-C1-N2-C3 interaction energiesa (kJ/mol)

1.291 1.306 0.969 1.087 120.78 119.27 112.85 120.64 179.98 0.00 179.99

1.302 1.324 0.972 1.081 119.64 118.49 107.03 119.63 -146.25 -12.64 -177.14 -395.642 (-755.007)

1.302 1.324 0.972 1.081 119.63 118.49 107.04 119.63 146.40 12.71 177.13 -395.705 (-755.008)

1.281 1.323 0.965 1.085 121.27 119.52 111.28 120.34 -179.72 -3.34 176.67 -301.418 (-593.100)

a

The values in parentheses are the BSSE-corrected interaction energies.

TABLE 2: Vibrational Frequencies (cm-1) of [DMFH+][NO3-] Using B3LYP/6-311++G** structures

1ca

1da

1ea

νa(C4H)1 νa(C3H)1 νa(C3H)2 νa(C4H)2 νs(C4H) νs(C3H) ν(C1N2)

3180 (-10) 3146 (-14) 3125 (-15) 3122 (-15) 3054 (-12) 3049 (-11) 1714 (-53)

3180 (-10) 3145 (-15) 3124 (-16) 3122 (-15) 3054 (-12) 3049 (-11) 1714 (-53)

3190 (0) 3158 (-2) 3113 (-27) 3132 (-5) 3024 (-42) 3005 (-55) 1786 (19)

a The values in parentheses are the differences with the frequencies of the enol form of the cation.

by O-H‚‚‚O and C-H‚‚‚O hydrogen bonds. Significant changes have been observed for the cation of 1c and 1d when comparing with the cation. The planar geometries of DMFH+ in 1c and 1d are distorted (Figure 2), and dihedral angles of H13-O5C1-N2 and H6-C1-N2-C3 change greatly, which indicates the strong interaction between the cation and the anion. Remarkable alteration of vibrational frequencies (Table 2) and distinct charge transfer (Table 3) also confirm formation of hydrogen bonds between the cations and the anions for these ionic pairs. Structure 1e is maintained by C-H‚‚‚O hydrogen bonds. Since 1e is 68.3 kJ/mol less favorable and has a smaller interaction energy than 1c and 1d, it is less stable than 1c and 1d.

Figure 3. Optimized structures and energies at B3LYP/6-311++G** for proton-transferred structures that result from optimization of initial geometries of a DMFH+ cation (keto form) paired with a NO3- anion.

3.2.2. Proton Transfer in the Keto Form of the DMFH+ Cation. The case for the keto form of the cation (Figure 1a) is completely different from the enol form above, that is, when the NO3- anions are put aside the keto form of the DMFH+ cations and optimized all the keto forms of the DMFH+ cation with the anions nearby are not stable and the H+ ions on DMFH+ cations transfer onto the anions and bind with the anions to form neutral molecular pairs, namely, DMF and HNO3 molecules, after optimization. The results here indicate the instability of the keto form of the cation and also the stability of the enol form of the DMFH+ cation as discussed above. The proton-transferred structures are shown in Figure 3. Hydrogen bonding is also important in the stabilization of the neutral molecular pairs. Hydrogen-bond lengths are 1.936, 1.670, and 1.590 Å, and the three kinds of neutral pairs have almost linear hydrogen bonds. The H atom of HNO3 in 2a forms a hydrogen bond with the N atom of DMF, while in 2b and 2c HNO3 molecules form hydrogen bonds with the carbonyl oxygen atoms. Maybe due to the larger electronegativity of the O atom than the N atom, the O-H‚‚‚N hydrogen bond (1.936 Å) in 2a is longer than the O-H‚‚‚O hydrogen bonds in 2b (1.670 Å) and 2c (1.590 Å). Meanwhile, the reason why the keto form of the DMFH+ cations are not stable in [DMFH+][NO3-] ion pairs may also be the larger electronegativity of the HNO3 O atom which attracts the H+ ion from the keto form of the DMFH+ cation. An energy scan has been further carried out for 2a-c with a step size of 0.05 Å (Figure 4) to investigate the stabilities of these neutral molecule pairs. The minima of the three curves are 1.95, 1.65, and 1.60 Å. They are coinciding well with the hydrogen bond lengths of 2a (1.936 Å), 2b (1.670 Å), and 2c (1.590 Å) as shown in Figure 3, which manifests the stability of 2a-c well. The corresponding ionic pairs as depicted in Figure 4 are not the stable extreme on the curves and therefore would not be stable and will transform to the neutral pairs of 2a-c without barriers. It is not surprising that ion pairs of ionic liquids are not stable and proton transfer take places in the gas phase. Proton transfer in the gas phase may be a critical step when ionic liquids evaporate, sublimate, or chemically decompose.49 Morokuma et al.50 found that [NH3][trans-HONO] is the most stable isomer for NH4NO2. The stable configurations for gas-phase hydroxylammonium nitrate (HAN) and ammonium dinitramide (ADN) have been observed by Alavi et al.51,52 to involve strong hydrogen bonding between hydroxylamine (hydrogen dinitramide) and nitric acid (ammonia) molecules. Proton transfer from the cation to the anion in triazolium53-, tetrazolium54-, and pentazole55-based ionic liquids have also been reported by Gordon et al. Moreover, a recent thermal decomposition study

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TABLE 3: (A) Mulliken and (B) NBO Charge (in units of electrons) Distribution for the Ion Pairs Using B3LYP/6-311++G** C1 structures DMFH+ (enol) 1c 1d 1e a

A

N2 Ba

0.0821 0.5557

A

O5 Ba

-0.0540 -0.3520

A

H13 Ba

-0.1648 -0.5950

A 0.3371 0.5234

H6 Ba

A

Ba

0.2284 0.2024

-0.0922 0.5874 (0.0317)

0.0148 -0.4008 (-0.0488) -0.1828 -0.6683 (-0.0733) 0.3320 0.5229 (-0.0005) 0.2298 0.1966 (-0.0058 ) -0.0927 0.5874 (0.0317) 0.0152 -0.4009 (-0.0489) -0.1832 -0.6682 (-0.0732) 0.3320 0.5228 (-0.0006) 0.2298 0.1966 (-0.0058) 0.0566 0.5159 (-0.0398) -0.0244 -0.3119 (0.0401) -0.1719 -0.6208 (-0.0258) 0.3116 0.5022 (-0.0212) 0.1948 0.1833 (-0.0191)

The values in parentheses are the differences with the charges of the enol form of the cation.

Figure 4. Variation of energies with hydrogen-bond lengths of 2a-c calculated at B3LYP/6-311++G**.

of 1-H-4-amino-1,2,4-triazolium nitrate by infrared laser heating from Litzinger et al. also reveals that the most probable route to initiate decomposition of this ionic liquid is through proton transfer from the N1 site of the cation to the nitrate forming a neutral pair.56 Our result that the ionic pairs of [DMFH+][NO3-] are not stable and tend to tautomerize to the neutral molecule pairs also indicates that the initiating step for decomposition of DMF-based ionic liquid may also be the proton transfer from the cation to the anion to form neutral products. The nonbarrier conversion from the ionic pairs to the neutral molecular pairs results in the lower stability of DMF-based ionic liquid (decompose at about 190 °C39) than the imidazolium-based ILs (decompose at about 380 °C57). Besides, all ionic structures are higher in energy than the neutral hydrogen-bonded complexes of DMF and HNO3 from which they are formed. Both the 1a and 1b structures which are stable at B3LYP/6-31G* transform to form the 2c molecular pair at B3LYP/6-311++G**. The reason why 1c-e are stable may be that formation of hydrogen bonds between the anions

and the methyl groups of the cation reduces the electronegativity of the anions. However, when the ionic liquid is heated and the anions of 1c-e are delocalized, proton transfer may take place to form neutral pairs, and thus, decomposition of the ionic liquid may occur. 4. Conclusions In summary, the structures and interaction patterns of a kind of DMF-based ionic liquid, namely, [DMFH+][NO3-], have been investigated using DFT methods. The DMFH+ cation may exist in the enol or keto form, and the enol form is more stable and 73.1 kJ/mol lower in energy than the keto form at B3LYP/ 6-311++G**. Further optimizations of the cation with the anions suggest that stable ion pairs of [DMFH+][NO3-] exist with H+ on O rather than on N of the cation, which is in good accordance with the spectrum results of the reference. H+ on N of the cation is not stable, and it transfers to the anion to form neutral molecule pairs maybe due to the larger electronegativity of the O atom of HNO3 than the N atom of the cation.

11020 J. Phys. Chem. B, Vol. 111, No. 37, 2007 Moreover, an energy scan shows that the ionic pairs are less stable and protons on the cations tend to transfer to the anion to form the corresponding neutral molecule pairs. It indicates that proton transfer from the cation to the anion may be the initiating step for decomposition of DMF-based ionic liquids as in many other cases such as NH4NO2 as reported. The nonbarrier proton-transfer processes may further express the less thermal stability of DMF-based ILs than other ILs such as the imidazolium-based ILs. Besides, the geometrical and energetic results here may also contribute to the force-field development of amide-based ILs. Acknowledgment. This work was supported by the National Natural Science Foundation of China (20573093 and 20434020). References and Notes (1) Welton, T. Chem. ReV. 1999, 99, 2071. (2) Wasserscheid, P.; Keim, W. Angew. Chem., Int. Ed. 2000, 39, 3772. (3) Shobukawa, H.; Tokuda, H.; Tabata, S.-i.; Wantanabe, M. Electrochim. Acta 2004, 50, 1. (4) Wang, P.; Zakeeruddin, S. M.; Shaik, M.; Humphry-Baker, R.; Gratzel, M. Chem. Mater. 2004, 16, 2694. (5) Angell, C. A.; Xu, W. Science 2003, 302, 422. (6) Wu, W.; Han, B.; Gao, H.; Liu, Z.; Jiang, T.; Huang, J. Angew. Chem., Int. Ed. 2004, 43, 2415. (7) Huang, J.; Riisager, A.; Wasserscheid, P.; Fehrmann, R. Chem. Commun. 2006, 38, 4027. (8) Bates, E. D.; Mayton, R. D.; Ntai, I.; Davis, J. H. J. Am. Chem. Soc. 2002, 124, 926. (9) Zhang, J. M.; Zhang, S. J.; Dun, K.; Zhang, Y. Q.; Shen, Y. Q.; Lv, X. M. Chem. Eur. J. 2006, 12, 4021. (10) Hanke, C. G.; Price, S. L.; Lynden-Bell, R. M. Mol. Phys. 2001, 99, 801. (11) Morrow, T. I.; Maginn, E. J. J. Phys. Chem. B 2002, 106, 12807. (12) Chaumont, A.; Wipff, G. Phys. Chem. Chem. Phys. 2003, 5, 3481. (13) Liu, Z.; Huang, S.; Wang, W. J. Phys. Chem. B 2004, 108, 12978. (14) Lopes, J. N. C.; Deschamps, J.; Padua, A. A. H. J. Phys. Chem. B 2004, 108, 2038. (15) Shah, J. K.; Brennecke, J. F.; Maginn, E. J. Green Chem. 2002, 4, 112. (16) Shah, J. K.; Maginn, E. J. J. Phys. Chem. B 2005, 109, 10395. (17) Del Po´polo, M. G.; Lynden-Bell, R. M.; Kohanoff, J. J. Phys. Chem. B 2005, 109, 5895. (18) Bu¨hl, M.; Chaumont, A.; Schurhammer, R.; Wipff, G. J. Phys. Chem. B 2005, 109, 18591. (19) Bhargava, B. L.; Balasubramanian, S. Chem. Phys. Lett. 2006, 417, 486. (20) Kirchner, B.; Seitsonen, A. P. Inorg. Chem. 2007, 46, 2751. (21) Meng, Z.; Do¨lle, A.; Carper, W. R. J. Mol. Struct. (Theochem) 2002, 585, 119. (22) Turner, E. A.; Pye, C. C.; Singer, R. D. J. Phys. Chem. A 2003, 107, 2277. (23) Tsuzuki, S.; Tokuda, H.; Hayamizu, K.; Watanabe, M. J. Phys. Chem. B 2005, 109, 16474. (24) Gutowski, K. E.; Holbrey, J. D.; Rogers, R. D.; Dixon, D. A. J. Phys. Chem. B 2005, 109, 23196. (25) Hunt, P. A; Gould, I. R. J. Phys. Chem. A 2006, 110, 2269. (26) Hunt, P. A.; Kirchner, B.; Welton, T. Chem. Eur. J. 2006, 12, 6762. (27) Kossmann, S.; Thar, J.; Kirchner, B.; Hunt, P. A.; Welton, T. J. Chem. Phys. 2006, 124, 174506. (28) Dong, K.; Zhang, S.; Wang, D.; Yao, X. J. Phys. Chem. A 2006, 110, 9775.

Zhang et al. (29) Talaty, E. R.; Raja, S.; Storhaug, V. J.; Do¨lle, A.; Carper, W. R. J. Phys. Chem. B 2004, 108, 13177. (30) Drake, G. W.; Hawkins, T. W.; Boatz, J.; Hall, L.; Vij, A. Propell. Explos. Pyrot. 2005, 30, 156. (31) Berg, R. W.; Deetlefs, M.; Seddon, K. R.; Shim, I.; Thompson, J. M. J. Phys. Chem. B 2005, 109, 19018. (32) Ko¨ddermann, T.; Wertz, C.; Heintz, A.; Ludwig, R. ChemPhysChem 2006, 7, 1944. (33) Fujii, K.; Fujimori, T.; Takamuku, T.; Kanzaki, R.; Umebayashi, Y.; Ishiguro, S. J. Phys. Chem. B 2006, 110, 8179. (34) Heimer, N. E.; Del Sesto, R. E.; Meng, Z.; Wilkes, J. S.; Carper, W. R. J. Mol. Liq. 2006, 124, 84. (35) (a) Wang, Y.; Li, H.; Han, S. J. Chem. Phys. 2005, 123, 174501. (b) Wang, Y.; Li, H.; Han, S. J. Chem. Phys. 2006, 124, 044504. (c) Wang, Y.; Li, H.; Han, S. J. Phys. Chem. B 2006, 110, 24646. (d) Wang, Y.; Li, H.; Wu, T.; Wang, C.; Han, S. Acta Phys.-Chim. Sin. 2005, 21, 517. (36) Weng, J.; Wang, C.; Li, H.; Wang, Y. Green Chem. 2006, 8, 96. (37) Wang, C.; Guo, L.; Li, H.; Wang, Y.; Weng, J.; Wu, L. Green Chem. 2006, 8, 603. (38) Jiang, H.; Wang, C.; Li, H.; Wang, Y. Green Chem. 2006, 8, 1076. (39) Huang, J. F.; Baker, G. A.; Luo, H.; Hong, K.; Li, Q. F.; Bjerrum, N. J.; Dai, S. Green Chem. 2006, 8, 599. (40) Clhorda, M. J. Chem. Commun. 2000, 10, 801. (41) Li, X.; Sevilla, M. D.; Sanche, L. J. Am. Chem. Soc. 2003, 125, 8916. (42) Dkhissis, A.; Houben, L.; Adamowicz, J.; Maes, G. J. Phys. Chem. A 2000, 104, 9785. (43) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Jr.; 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.; 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 B.01; Gaussian, Inc.: Pittsburgh, PA, 2003. (44) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (45) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (46) Gordon, M. S.; Binkley, J. S.; Pietro, W. J.; Hehre, W. J. J. Am. Chem. Soc. 1982, 104, 2797. (47) David, K.; Malick, D. K.; Petersson, G. A. J. Chem. Phys. 1998, 108, 5704. (48) Peiro´-Garcı´a, J.; Nebot-Gil, I. ChemPhysChem 2003, 4, 843. (49) Galwey, A. K.; Brown, M. E. Thermal Decomposition of Ionic Solids; Elsevier: Amsterdam, 1999; pp 415-435. (50) Mebel, A. M.; Lin, M. C.; Morokuma, K.; Melius, C. F. J. Phys. Chem. 1995, 99, 6842. (51) Alavi, S.; Thompson, D. J. Chem. Phys. 2003, 118, 2599. (52) Alavi, S.; Thompson, D. J. Chem. Phys. 2003, 119, 4274. (53) Schmidt, M. W.; Gordon, M. S.; Boatz, J. A. J. Phys. Chem. A 2005, 109, 7285. (54) Zorn, D. D.; Boatz, J. A.; Gordon, M. S. J. Phys. Chem. B 2006, 110, 11110. (55) Pimienta, I. S. O.; Elzey, S.; Boatz, J. A.; Gordon, M. S. J. Phys. Chem. A 2007, 111, 691. (56) Li, J.; Litzinger, T. A. Thermochim. Acta 2007, 454, 116. (57) Noda, A.; Susan, M. A. B. H.; Kudo, K.; Mitsushima, S.; Hayamizu, K.; Watanabe, M. J. Phys. Chem. B 2003, 107, 4024.