Prediction of the Formation and Stabilities of Energetic Salts and Ionic

Nov 16, 2005 - Even stronger alkylating agents should be considered to enhance the chances of synthetic success. When using the enthalpies of reaction...
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J. Phys. Chem. B 2005, 109, 23196-23208

Prediction of the Formation and Stabilities of Energetic Salts and Ionic Liquids Based on ab Initio Electronic Structure Calculations Keith E. Gutowski, John D. Holbrey,† Robin D. Rogers, and David A. Dixon* Department of Chemistry and Center for Green Manufacturing, Shelby Hall, Box 870336, The UniVersity of Alabama, Tuscaloosa, Alabama 35487 ReceiVed: July 19, 2005; In Final Form: September 20, 2005

A computational approach to predict the thermodynamics for forming a variety of imidazolium-based salts and ionic liquids from typical starting materials is described. The gas-phase proton and methyl cation acidities of several protonating and methylating agents, as well as the proton and methyl cation affinities of many important methyl-, nitro-, and cyano-substituted imidazoles, have been calculated reliably by using the computationally feasible DFT (B3LYP) and MP2 (extrapolated to the complete basis set limit) methods. These accurately calculated proton and methyl cation affinities of neutrals and anions are used in conjunction with an empirical approach based on molecular volumes to estimate the lattice enthalpies and entropies of ionic liquids, organic solids, and organic liquids. These quantities were used to construct a thermodynamic cycle for salt formation to reliably predict the ability to synthesize a variety of salts including ones with potentially high energetic densities. An adjustment of the gas phase thermodynamic cycle to account for solid- and liquid-phase chemistries provides the best overall assessment of salt formation and stability. This has been applied to imidazoles (the cation to be formed) with alkyl, nitro, and cyano substituents. The proton and methyl cation donors studied were as follows: HCl, HBr, HI, (HO)2SO2, HSO3CF3 (TfOH), and HSO3(C6H4)CH3 (TsOH); CH3Cl, CH3Br, CH3I, (CH3O)2SO2, CH3SO3CF3 (TfOCH3), and CH3SO3(C6H4)CH3 (TsOCH3). As substitution of the cation with electron-withdrawing groups increases, the triflate reagents appear to be the best overall choice as protonating and methylating agents. Even stronger alkylating agents should be considered to enhance the chances of synthetic success. When using the enthalpies of reaction for the gas-phase reactants (eq 6) to form a salt, a cutoff value of -13 kcal mol-1 or lower (more negative) should be used as the minimum value for predicting whether a salt can be synthesized.

Introduction There is significant interest in the development of new energetic compounds for use as aerospace propellants and fuels to explosives.1 Examples of compounds that have been widely used by the aerospace community are hydrazine and its methylated derivatives.2 These high-energy compounds are liquid at normal temperatures and formulated mixtures of hydrazine and monomethyl hydrazine or unsymmetrical dimethyl hydrazine can serve as monopropellants, the decomposition of which is easily facilitated by the use of metal and metal oxide catalysts. However, hydrazine has been classified by the U.S. Environmental Protection Agency as a Group B2, probable human carcinogen.3 Occupational exposure occurs primarily through inhalation or skin exposure, thus posing a potential health risk in the workplace. Not surprisingly, there is interest in developing energetic materials with reduced impacts on the environment and on human health. Salts are important systems for the development of highenergy density materials as salts are intrinsically nonvolatile and typically are thermally stable under normal conditions. Energetic salts have several advantages over nonionic materials, including negligible volatility, which improves ease of handling, as well as higher density due to their ordered, close-packed * To whom correspondence may be addressed. E-mail: [email protected]. † Current address: The QUILL Research Centre, Queen’s University of Belfast Belfast BT9 5AG, Northern Ireland, U.K.

nature.4,5 Ionic liquids (ILs) are a class of low-melting (conventionally defined as below 100 °C) salts that can be both thermally stable (commonly up to several hundred degrees Celsius) and nonvolatile in the liquid state, thus potentially combining the useful characteristics of solid salt systems with the advantages of handling liquid systems. In addition, ILs are easily prepared via simple synthetic routes and their physical properties (i.e., hydrophobicity, density, viscosity) are readily tuned through modifications to either the cationic or anionic component.6,7 Synthetically modified ILs with energetic substituents that are both thermally stable and nonvolatile have been suggested as potential frameworks from which to develop new classes of liquid energetic materials. Drake and co-workers4,8,9 have demonstrated that energetic ILs can readily be prepared by combining energetic cations, such as 1H-1,2,4-triazolium, 4-amino-1,2,4-triazolium, and 1H1,2,3-triazolium, with relatively energetic anions, such as nitrate, perchlorate, and dinitramide. All of Drake’s materials possess high densities and low melting points, and it was suggested that these materials could potentially find practical use as energetic materials. Ogihara et al.10 and Katritzky et al.11 have recently described the preparation of potential energetic ILs based on the widely adopted imidazolium cation shown below. Ogihara et al.10 combined 1-ethyl-3-methylimidazolium cations with simple triazolate and tetrazolate anions, while Katritzky et al.11 prepared a novel IL with the 1-butyl-3-methylimidazolium cation and the rigid, planar 3,5-dinitro-1,2,4-triazolate anion. Both types

10.1021/jp053985l CCC: $30.25 © 2005 American Chemical Society Published on Web 11/16/2005

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of compounds exhibit unusually low melting points, thus making them true ILs; however, their energetic qualities were not evaluated. Xue et al. have reported the synthesis of energetic salts comprised of substituted imidazolium and 1,2,4-triazolium cations with 4,5-dinitroimidazolate and 5-nitrotetrazolate anions.12

The heterocyclic compound, 1-methylimidazole, is a versatile and widely used starting material in the synthesis of a wide range of organic salts and has become the ubiquitous core for formation of ILs. Substitution of the imidazole ring, at the 2-, 4-, and 5-positions with nitro or other energetic groups has been suggested as a way to produce imidazolium cations with energetic properties.4,13 Adding methyl groups to the ring can provide more robust imidazolium cations, particularly in harsh chemical environments, by eliminating the presence of acidic protons, particularly in the 2-position, while at the same time increasing the steric bulk.14 In addition, they can enhance the chemical reactivity of the starting material as well as diversify the potential number of ILs by introducing structural perturbations.15 When performing ring substitutions, it is important to consider the overall effect that changing functionalities can have, overall, on the desired chemistry of the heterocycles, for example, in the case of preparing potential ILs, on the ability to quaternize the nitrogen in the 3-position, producing a cationic moiety. A series of energetic ILs containing nitro- and cyanosubstituted imidazolium cations with nonenergetic anions (methyl sulfate, triflate, bis(trifluoromethanesulfonyl)imide)16 have been prepared by Katritzky and co-workers. Stepwise substitution of the imidazole ring in the 2-, 4-, and 5-positions with electron-withdrawing groups such as nitro and cyano decreased the susceptibility of the imidazole to protonation and alkylation with a variety of chemical agents, resulting in a lower likelihood of imidazolium cation formation. These substituent effects appeared to limit salt formation to mononitro- and dicyanosubstituted imidazole starting materials under a wide variety of conditions. Due to the electron-withdrawing nature of substituents such as NO2 and CN, the formation of imidazolium-based IL salts depends strongly on the substituent’s effect on the basicity of the heterocycle precursor. In addition, salt formation is also dependent upon the acidity or methyl cation acidity of the protonating or alkylating agent used in the synthesis. Decreased basicity of the imidazole precursor can be overcome by using a protonating or alkylating agent of suitable strength for the salt-forming reaction to proceed. The energetics behind this synthetic concept for salt formation are outlined in the BornHaber thermodynamic cycle given in Figure 1. The overall enthalpy of reaction (∆Hrxn) for formation of the imidazolium salt is given by the reaction between a substituted imidazole base and a protonating or alkylating agent (RX) in the gas phase to form two ions plus the energy to form the salt in the solid state. The overall reaction enthalpy is given as ∆Hrxn(salt) ) ∆H1 + ∆H2 + ∆H3. ∆H1 is the enthalpy to dissociate the R-X bond heterolytically, i.e., the proton or methyl cation acidity of RX, and is an endothermic step. ∆H2

Figure 1. Born-Haber cycle for the formation of imidazolium-based salts and ionic liquids.

is the affinity of the imidazole for R+, i.e., the proton or methyl cation affinity, and is an exothermic process. ∆H3 is directly related to the lattice energy for salt formation. The enthalpy for formation of the IL from the salt can then be estimated from the enthalpy of fusion of the salt, which from a literature survey of several organic salts and nitrogen-containing heterocycles is approximately 3.5 ( 1.2 kcal mol-1 (see Table SM-14 in Supporting Information).17 Thus, given the required thermodynamic data, it is possible to estimate the thermodynamics of the process to see if a given synthetic strategy is possible. However, such thermodynamic data are, in general, not available, and the experimental synthesis of highly energetic cations in ILs is thus a trial and error process. This paper describes a computational chemistry based method for the assessment of the thermodynamics of energetic salt formation. We have used density functional theory (DFT) and molecular orbital (MO) theory to calculate a variety of electronic properties. The gas-phase proton and methyl cation affinities (addition at the 3-position) of imidazole precursors containing nitro and cyano (strongly electron withdrawing) groups and methyl groups (weakly electron-donating) at the Y position needed for ∆H2 were calculated by using DFT. We performed DFT and subsequently MP2 calculations, the latter extrapolated to the complete basis set (CBS) limit, on a series of protonating and alklyating agents of the type RCl, RBr, RI, (RO)2SO2, RSO3CF3, and RSO3(C6H4)CH3 (R ) H, CH3) to predict reliable proton and methyl cation acidities for ∆H1. We used a simple ionic volume-based method18 that we have previously used in predicting the heats of formation of hydrogen storage19 and highly energetic materials,20 to estimate the lattice energies and enthalpies of the imidazolium-based salts in the solid state. In addition, we have included average phase transition enthalpies to assess the overall condensed-state chemistry and synthetic feasibility. Computational Approach All of the electronic structure calculations were performed using the Gaussian0321 suite of programs on the SGI Altix 350 at the Alabama Supercomputer Center and the NWChem22 suite of programs on the massively parallel 1980 processor HP Linux cluster in the Molecular Science Computer Facility in the William R. Wiley Environmental Molecular Sciences Laboratory at the Pacific Northwest National Laboratory. Proton and Methyl Cation Acidities. For the gas-phase proton acidities of HCl, HBr, HI, (HO)2SO2, HSO3CF3 (TfOH), and HSO3(C6H4)CH3 (TsOH) and the methyl cation acidities of CH3Cl, CH3Br, CH3I, (CH3O)2SO2, CH3SO3CF3 (TfOCH3),

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TABLE 1: MP2/CBS and B3LYP/Aug-cc-pVDZ Proton and Methyl Cation Acidities (∆H1) of RX Compounds in kcal mol-1, with Comparison to Experimental Gas-Phase Values, Where Available, as Well as Gas-Phase Entropies (kcal mol-1 K-1) from B3LYP/Aug-cc-pVDZ Calculations MP2/aug-cc-pVnZ

B3LYP/aug-cc-pVDZ

molecule

∆Eelec (D)

∆Eelec (T)

∆Eelec (Q)

∆Eelec (CBS)

∆ZPE

∆H0

∆H298

∆Eelec

∆ZPE

∆H0

∆H298

S298

expt ∆H298

HCl HBr HI (HO)2SO2 TfOH TsOH CH3Cl CH3Br CH3I (CH3O)2SO2 TfOCH3 TsOCH3

332.0 323.0 313.6 315.8 306.6 323.1 224.2 218.1 211.9 205.3 196.2 214.1

335.3 325.6 316.1 316.7 305.2 321.5 230.6 223.8 217.6 207.6 195.7 213.5

334.9 324.9 315.3 316.5 304.2 320.6 231.1 223.3 216.9 207.5 194.7 212.5

334.5 324.3 314.6 316.4 303.6 320.0 231.2 222.8 216.2 207.4 194.1 212.0

-4.2 -3.7 -3.3 -7.7 -7.4 -7.5 -3.9 -3.5 -3.2 -5.5 -5.3 -5.6

330.3 320.6 311.3 308.7 296.2 312.5 227.3 219.3 213.0 201.9 188.8 206.4

331.3 321.5 312.2 310.1 297.3 313.6 228.6 220.6 214.3 202.8 189.7 207.3

332.3 323.7 315.1 317.2 308.3 326.0 223.9 217.1 210.3 204.6 195.5 214.0

-4.2 -3.7 -3.3 -7.7 -7.4 -7.5 -3.9 -3.5 -3.2 -5.5 -5.3 -5.6

328.1 320.0 311.8 309.5 300.9 318.5 220.0 213.6 207.1 199.1 190.2 208.4

329.0 320.9 312.6 310.9 302.0 319.6 221.4 214.9 208.4 200.0 191.1 209.4

0.045 0.047 0.049 0.074 0.089 0.104 0.056 0.059 0.061 0.095 0.101 0.113

333.4a 323.5b 314.3c 312.5d, 305.4e 227.4f 219.1g 213.3h -

a Reference 32. b Reference 33. c Reference 34. d From ref 31. The experimental values of 306.3 ( 3.135 and 309.6 ( 2.636 are not used here due to larger error bars than the computational results. e Reference 37. f References 32 and 38. g References 33and 38. h References 34 and 38.

and CH3SO3(C6H4)CH3 (TsOCH3), geometries were optimized at the B3LYP/aug-cc-pVDZ level23,24 for all compounds except for the triflate (trifluoromethanesulfonate) and tosylate (ptoluenesulfonate) compounds, which were optimized at both the B3LYP/aug-cc-pVDZ and B3LYP/DZVP2 levels.25 Vibrational frequencies were calculated to ensure that each structure was a minimum on the potential energy surface. The enthalpy correction to the electronic energy obtained at the B3LYP/aug-ccpVDZ level for each structure was used to correct the energies from 0 to 298 K. Starting from the DFT optimized geometries, MP2 calculations were performed with the aug-cc-pVnZ (n ) D, T, Q) basis sets. Pseudopotential basis sets (aug-cc-pV(D,T,Q)-PP) of the same quality were used for bromine and iodine.26 The chlorine, bromine-, iodine-, and sulfate-containing molecules were optimized at each MP2/aug-cc-pVnZ (n ) D, T, Q) level (except CH3Br and CH3I, which were optimized at the MP2/aug-cc-pVDZ level and this geometry was used for single-point calculations with the larger basis sets) starting from the B3LYP/aug-cc-pVDZ geometries. For the larger molecules TfOH, TfOCH3, TsOH, and TsOCH3 and their anions, singlepoint calculations were performed using the B3LYP/DZVP2 optimized geometries. The final MP2 energies were extrapolated to the CBS limit by using a mixed exponential/Gaussian function of the form

E(n) ) ECBS + A exp[-(n - 1)] + B exp[-(n - 1)2]

(1)

with n ) 2 (aug-cc-pVDZ), 3 (aug-cc-pVTZ), and 4 (aug-ccpVQZ).27 Proton and Methyl Cation Affinities. The gas-phase proton and methyl cation affinities of the nitro-, cyano-, and methylsubstituted imidazoles were calculated at the B3LYP level using the DFT-optimized basis sets DZVP2. Vibrational frequencies were calculated for each optimized structure to ensure that the structure was a minimum on the potential energy surface and to enable the prediction of the proton and methyl cation affinities at 0 and 298 K. Lattice Energies. The lattice energies of the substituted imidazolium-based salts were estimated by using a relationship originally developed by Bartlett28 and expanded by Jenkins and co-workers18

[

UL ) 2I

R +β x3 V

]

(2)

which has been shown to be applicable to a wide range of 1:1 salts. I is the ionic strength ()1), V is the molecular volume (in nm3) of the lattice, which is equal to the sum of the individual cation (V+) and anion (V-) volumes, and R and β are empirically derived parameters which take the values of 28.0 and 12.4 kcal mol-1, respectively, for 1:1 salts. The temperature dependence of the lattice enthalpy can be obtained from the relationship18

[(

∆HL ) UL + p

) ( )]

nm nx - 2 + q - 2 RT 2 2

(3)

where p and q are equal to 1 for 1:1 salts and nm and nx are equal to 3 for monatomic ions, 5 for linear polyatomic ions, and 6 for nonlinear polyatomic ions. The individual ion volumes were calculated by using Gaussian03. The volume was taken as that inside the 0.001 au contour of the electron density. The electron density was calculated using B3LYP/DZVP2 for the cations and B3LYP/aug-cc-pVDZ for the anions. With the default parameters, the volume is calculated to an accuracy of about 10%, so a larger number of points was used in the Monte Carlo to obtain the desired level of accuracy. The estimated entropies (in cal K-1 mol-1) of the substituted imidazoles were calculated by using the relationship developed by Glasser and Jenkins29 for organic solids (OS)

S ) 184.99(V) + 13.62

(4)

and the entropies of the corresponding ILs were calculated using the relationship of Glasser30

S ) 297.92(V) + 7.05

(5)

Here, the volumes are the same molecular volume (nm3) as employed in the lattice energy equation and is simply the sum of the volumes of the anion and cation of the salt. As opposed to the lattice energy equation which has a V-1/3 dependence, the lattice entropies increase linearly with molecular volume. Results and Discussion Proton and Methyl Cation Acidities. The series of RX compounds investigated as potential protonating or alkylating agents are listed in Table 1, together with the electronic, zeropoint, and thermal energies and the thermal enthalpy. The latter quantity will hereafter be referred to as the proton or methyl cation acidity (∆H298) at 298 K. In both sets of compounds, the strength of the agent, or its ability to donate a proton or

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TABLE 2: Gas-Phase Proton and Methyl Cation Affinities (-∆H2, kcal mol-1) and Zero-Point Vibrational Energies of Substituted Imidazoles at the B3LYP/DZVP2 Levela CH3+

H+

a

molecule

∆Eelec

∆ZPE

∆H298

∆Eelec

∆ZPE

∆H298

1-methyl-2-nitroimidazole 1-methyl-4-nitroimidazole 1-methyl-5-nitroimidazole 1-methyl-2,4-dinitroimidazole 1-methyl-2,5-dinitroimidazole 1-methyl-4,5-dinitroimidazole 1-methyl-2,4,5-trinitroimidazole 1-methyl-2-cyanoimidazole 1-methyl-4-cyanoimidazole 1-methyl-5-cyanoimidazole 1-methyl-2,4-dicyanoimidazole 1-methyl-2,5-dicyanoimidazole 1-methyl-4,5-dicyanoimidazole 1-methyl-2,4,5-tricyanoimidazole 1-methylimidazole 2-methyl-1H-imidazole 4-methyl-1H-imidazole 5-methyl-1H-imidazole 1,2-dimethylimidazole 1,4-dimethylimidazole 1,5-dimethylimidazole 1,2,4-trimethylimidazole 1,2,5-trimethylimidazole 1,4,5-trimethylimidazole 1,2,4,5-tetramethylimidazole

220.3 220.3 219.5 203.5 204.9 205.6 192.1 223.8 223.6 223.8 210.1 210.5 211.1 199.2 239.2 239.6 238.4 238.8 244.1 243.1 243.3 247.8 248.0 246.8 251.2

-8.3 -8.4 -8.3 -7.9 -8.1 -8.0 -7.6 -8.5 -8.6 -8.5 -8.3 -8.2 -8.3 -8.1 -8.8 -8.7 -8.9 -8.7 -8.8 -8.9 -8.8 -8.9 -8.9 -8.9 -8.9

213.4 213.4 212.6 196.9 198.2 199.1 185.7 216.7 216.4 216.8 203.2 203.6 204.1 192.4 231.8 232.3 231.0 231.5 236.7 235.7 236.0 240.3 240.6 239.4 243.7

116.3 116.7 117.9 97.3 101.5 102.8 86.7 122.3 122.2 121.8 110.1 109.8 110.5 99.9 136.2

-6.3 -6.4 -6.0 -5.8 -5.9 -5.9 -5.6 -6.2 -6.3 -6.1 -5.9 -5.8 -6.0 -5.7 -6.5

111.3 111.7 113.0 92.6 96.8 98.1 82.2 117.3 117.2 116.8 105.3 105.0 105.7 95.2 131.0

139.5 139.4 140.0 142.2 142.9 142.7 144.8

-6.5 -6.7 -6.5 -6.7 -6.6 -6.7 -6.8

134.2 134.0 134.8 136.8 137.5 137.4 139.3

The average gas-phase entropy over all imidazole starting materials (nitro-, cyano-, and methyl-substituted) was 0.09 ( 0.01 kcal mol-1 K-1.

methyl cation in a chemical reaction, increases with decreasing proton or methyl cation acidity. The proton acidities of the acids are comparable at both the MP2 and B3LYP levels of theory, particularly for HCl, HBr, HI, and (HO)2SO2. The calculated value for (HO)2SO2 of Alexeev et al.31 at the CCSD(T)/CBS level is used here in lieu of the experimental proton acidities which have much larger error bars. The average difference between experiment (HCl,32 HBr,33 HI,34 H2SO435,36) and theory is 2.2 kcal mol-1 at the MP2/CBS level and 2.6 kcal mol-1 at the B3LYP/aug-cc-pVDZ level. The largest differences between the two methods for the acidities are for triflic acid (TfOH) and p-toluene sulfonic acid (TsOH). For the former, B3LYP is in better agreement with the available experimental value37 as compared to the MP2 approach, with the differences being 3.4 and 8.1 kcal mol-1, respectively. However, a G3(MP2) calculation for the acidity showed excellent agreement with the MP2/CBS method, yielding an acidity of 297.9 kcal mol-1 at 298 K. This strongly suggests that the experimental value for TfOH is incorrect, although a more comprehensive computational treatment of a broader range of fluoroacids is needed to draw general conclusions (such a study is currently underway in our group). An even larger disparity of 7.1 kcal mol-1 between the MP2 and B3LYP methods is found for TsOH, and due to the result for TfOH, we prefer the MP2/CBS result. Overall, four distinct groups of acidities are evident at the MP2 level, which exhibit the following trend in acidities: TfOH < HI ∼ (HO)2SO2 ∼ TsOH < HBr < HCl. Thus, as expected, triflic acid is the strongest gas-phase acid of the group and should provide the best route for protonating the substituted imidazoles of lowest basicity. In addition, one can compare the MP2/aug-cc-pVDZ values with the MP2/CBS values as the augcc-pVDZ basis set can be used for a wider range of calculations on larger molecules. The aug-cc-pVDZ values for the proton acidities differ from the CBS values by 0.6-2.5 kcal mol-1 (values less than the CBS) for (HO)2SO2, HI, HBr, and HCl

and by ∼ -3.0 kcal mol-1 (values larger than the CBS) for TfOH and TsOH. The differences are larger for the methyl cation acidities with values ranging from 2.1 to 7.0 kcal mol-1 for the halides and the sulfate and by ∼ -2 kcal mol-1 for TfOH and TsOH. Thus, the MP2/aug-cc-pVDZ level provides semiquantitative proton acidities but has more difficulty with the methyl cation acidities. The MP2/CBS level provides a better correlation with experiment for the methyl cation acidities than does the B3LYP level for the subset of alkyl halides for which experimental data are available.32,38 The average difference between experiment and theory for the MP2 and B3LYP levels is 1.2 and 5.0 kcal mol-1, respectively. The acidities of the remaining three methylating agents are comparable at both levels of theory. The MP2/CBS approach predicts an acidity for the triflate compound that is within 1.4 kcal mol-1 of the B3LYP approach. The sulfate and tosylate compounds are also in agreement, with differences of 2.8 and 2.1 kcal mol-1, respectively. As expected, methyl triflate is the strongest methylating agent of the set, with the overall methyl acidities decreasing in the order TfOCH3 < (CH3O)2SO2 < TsOCH3 < CH3I < CH3Br < CH3Cl at the MP2 level. CH3I and TsOCH3 are comparable methylating agents at the B3LYP level. Proton and Methyl Cation Affinities. The set of substituted imidazoles that were studied are listed in Table 2. The first two sets of compounds constitute the nitro- and cyano-substituted compounds, and the last set is the methyl-substituted compounds. In each group, the effect of the ring substituents on the proton and methyl cation affinities of the imidazole was investigated. Mono-, di-, and trisubstitution effects were studied. For the methyl-substituted compounds, the proton affinities of 1-, 2-, 4-, and 5-methylimidazole were also predicted as the availability of experimental data provides a benchmark of the accuracy of the B3LYP approach. The proton affinity is defined as the negative of ∆H298 for the reaction, B + H+ f BH+, where B is imidazole (or any base, for generality). The methyl

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TABLE 3: Experimental39 and Calculated Gas Phase Proton Affinities (kcal mol-1) of Some Substituted and Unsubstituted Imidazoles molecule 1H-imidazole 1-methylimidazole 2-methyl-1H-imidazole 4-methyl-1H-imidazole 1,2-dimethylimidazole 1,4-dimethylimidazole 1,5-dimethylimidazole 1-methyl-5-nitroimidazole a

∆H298 (expt) ∆H298 (theory)a ∆theory-expt 225.3 229.3 230.3 227.7 235.3 233.4 233.7 214.0

226.8 231.8 232.3 231.0 236.7 235.7 236.0 212.6

1.5 2.5 2.0 3.3 1.4 2.3 2.3 -1.4

B3LYP/DGDZVP2.

cation affinity follows in a similar manner, with CH3+ replacing the proton, H+. Table 3 lists experimental proton affinities of imidazole, six methyl-substituted imidazoles, and one nitrosubstituted imidazole which can be compared to the computational values. The computational values are all within 2.5 kcal mol-1 of the experimentally measured quantities, with the exception of 4-methylimidazole which differs by slightly greater than 3 kcal mol-1.39 The calculated values for the methyl substituted imidazoles with no electron-withdrawing groups are larger than the experimental values, whereas the calculated value for 1-methyl-5-nitroimidazole is 1.4 kcal mol-1 below the experimental value. This excellent agreement with experiment shows that the B3LYP/DZVP2 level provides realistic values for the substituent effects on imidazoles for binding either a proton or a methyl cation. The proton affinity is approximately twice as large in magnitude as the analogous methyl cation affinity for the imidazole parent compounds (Table 2). The proton affinity of each nitro-substituted imidazole is lower than the similarly substituted cyano-substituted imidazole (Table 2). This is due to the stronger electron-withdrawing nature of the nitro group, which attracts a larger amount of electron density from the ring system, thus lowering the basicity of the heterocycle, i.e., making it a weaker proton or methyl cation acceptor. The average proton affinity for a monosubstituted nitroimidazole in the 2-, 4-, or 5-position is 213.1 ( 0.5 kcal mol-1, compared to 216.6 ( 0.2 kcal mol-1 for the similarly substituted cyano compounds. The average methyl cation affinities for the monosubstituted nitro and cyano imidazoles are 112.0 ( 0.9 and 117.1 ( 0.2 kcal mol-1, respectively. In both sets of values, the spread in the affinities was lower in the cyano compounds as compared to the nitro compounds. The addition of two nitro or cyano groups to the imidazole ring has a substantial effect on the basicity of the heterocycle. The average proton affinities for the nitro and cyano compounds are 198.1 ( 1.1 and 203.5 ( 0.5 kcal mol-1, respectively, for substitution in the 2,4-, 2,5-, or 4,5-positions. The addition of a second nitro or cyano group thus results in an average lowering of the proton affinities by 15.0 and 13.1 kcal mol-1, respectively. A unique substituent effect is observed in the methyl cation affinities of the nitroimidazoles. Substitution in the 2,4-position results in an enhanced lowering of the methyl cation affinity as compared to the 2,5- and 4,5-substituted compounds. The difference between 2,4- and 2,5-substituted compounds is 4.2 kcal mol-1, whereas the difference between 2,4- and 4,5substituted compounds is 5.5. kcal mol-1, the greatest differentials observed in all of the compounds studied, with an overall average for the three substituents of 95.8 ( 2.9 kcal mol-1. This suggests that substitution patterns in the disubstituted nitro imidazoles may be significant in directing synthetic efforts to make these 1,3-dimethylimidazolium nitro salts. No such effect is observed in the 2,4-, 2,5-, and 4,5-substituted

cyanoimidazoles, with an average methyl cation affinity of 105.3 ( 0.3 kcal mol-1; the small standard deviation indicates little variation based on substitution pattern. Only one structural perturbation is possible for the trisubstituted nitro and cyano compounds. In each case, the proton and methyl cation affinities are lowered substantially as compared to the mono- and disubstituted compounds. The proton affinities of the nitro and cyano compounds are 185.7 and 192.4 kcal mol-1, respectively. This amounts to a lowering of the proton affinity by 27.4 and 24.2 kcal mol-1, respectively, in the nitro and cyano compounds in going from monosubstitution to trisubstitution. In going from di- to trisubstitution, the lowering amounts to 12.4 kcal mol-1 for the nitro compounds and 11.2 kcal mol-1 for the cyano compounds, a smaller decrease than what is observed in the mono- to disubstitution. Significant lowering of the methyl cation affinity is also observed in the trisubstituted case. The methyl cation affinities for the trinitroand tricyanoimidazole are 82.2 and 95.2 kcal mol-1, respectively. The decreases in the monosubstituted/trisubstituted and disubstituted/trisubstituted pairs in the nitro compounds are 29.8 and 13.6 kcal mol-1, respectively, whereas the analogous decreases in the cyano compounds are 21.9 and 10.1 kcal mol-1, respectively. Overall, the addition of nitro groups to the imidazole ring is predicted to have a greater effect on lowering the basicity than analogous addition of cyano groups. Thus it is less likely that one can do additional chemistry, i.e., quaternization, on the nitro imidazoles compared to the cyano compounds upon stepwise addition to the ring architecture due to this basicity effect. Although the addition of methyl groups to the imidazole ring is not likely to result in the generation of energetic materials (which has been suggested for the nitro compounds), they have an opposite effect compared to nitro or cyano substitution as expected. Methyl groups are weak electron donors, so stepwise addition in the 2-, 4-, and 5-positions will add electron density to the ring, thus enhancing its basicity.15 The addition of one methyl group to imidazole (calculated proton affinity of 226.8 kcal mol-1) in the 1-, 2-, 4-, or 5-position results in an increase in the proton affinity of 4.2-5.5 kcal mol-1 depending on the substitution position. Methyl substitution of 1-methylimidazole in the 2-, 4-, and 5-positions gives an average proton affinity of 236.1 ( 0.5 kcal mol-1. The average calculated methyl cation affinity for these compounds is 134.3 ( 0.4 kcal mol-1, slightly higher than the calculated methyl cation affinity of 1-methylimidazole (131.0 kcal mol-1), thus showing only a weak substitution effect on the basicity. The average proton and methyl cation affinities for the disubstituted (2,4-, 2,5-, 4,5-methyl) compounds are 240.1 ( 0.6 and 137.2 ( 0.4 kcal mol-1, respectively, resulting in an average increase from the monosubstituted compounds of 4.0 and 2.9 kcal mol-1. The proton and methyl cation affinities for the trisubstituted compounds (2,4,5-methyl) are 243.7 and 139.3 kcal mol-1, respectively, resulting in increases of 7.6 and 5.0 kcal mol-1 in going from the monosubstituted to the trisubstituted compounds. In going from the disubstituted to the trisubstituted compounds, the proton and methyl cation affinity increases are approximately 3.6 and 2.1 kcal mol-1, respectively. Compared to the nitro and cyano compounds, the changes in proton and methyl cation affinities upon substitution were dramatically lower for the electron-donating methyl-substituted compounds. As noted previously, this is due to the weak electron-donating ability of the methyl substituent as compared to the strong electron-withdrawing abilities of the nitro and cyano groups. As a result, opposing trends are apparent:

Thermodynamics of Energetic Salt Formation

J. Phys. Chem. B, Vol. 109, No. 49, 2005 23201 calculated value (0.205 nm3).41 The calculated volumes should provide a reliable estimation of the relevant lattice energies. The empirical expression is good to within (5 kcal mol-1 based on comparing lattice energies from it with those obtained from experimental data based on a Born-Haber cycle. For example, for NH4CN, KI, and LiF the values are essentially identical within 1 kcal mol-1 as shown by Jenkins et al.18 based on the values reported by Jenkins.42 Table 5 lists the calculated cation volumes as well as the lattice enthalpies (temperature-corrected lattice energies) of the corresponding nitro and cyano salts, sorted by anion type. The V-1/3 dependence of the lattice energy dictates that combinations of the smallest ions will have the largest lattice energies. It should be noted that partitioning of the cell volume into V+ and V- does not make the assumption of spherical ions. In Table 5, for any particular nitro- or cyano-substituted imidazolium cation, the lattice enthalpies of the salt follow anion size and vary as Cl- > Br- > I- > (RO)SO3- > TfO- > TsO-. Within the set of protonated imidazolium salts, the smallest and largest lattice enthalpies belong to 1-methyl-2,4,5-trinitro3H-imidazolium tosylate and 1-methyl-5-cyano-3H-imidazolium chloride, respectively. Likewise, within the methylated salts, the smallest and largest lattice enthalpies belong to 1,3-dimethyl2,4,5-trinitroimidazolium tosylate and the 2- and 4-substituted mononitro and monocyano 1,3-dimethylimidazolium chlorides, respectively. However, due to the V-1/3 dependence on the lattice energy, relatively large changes in the ion volume have little effect on the change in the actual lattice energy. This is evident across the groups of halides for similarly substituted groups of cations. For example, in the 1-methyl-N-nitro-3H-imidazolium halides (n ) 2, 4, 5), the average differences in the lattice enthalpy between chloride-bromide and bromide-iodide are 1.3 and 2.4 kcal mol-1, respectively. In addition, due to the relative

TABLE 4: Theoretical Anion Volumes (nm3) with Comparison to Experimental Crystallographic Values, Where Available anion

vol (expt)

vol (theory)d

ClBrI(OH)SO3(CH3O)SO3TfOTsO-

0.047 ( 0.013a 0.056 ( 0.014a 0.072 ( 0.016a 0.089 ( 0.002a

0.051 0.059 0.075 0.092 0.117 0.121 0.205

0.129 ( 0.007b 0.199c

a Volumes obtained from ref 18a. b Average volume obtained from crystal structures40 of LiCF3SO3, NaCF3SO3, KCF3SO3, R-LiRb2(CF3SO3)3, and (NH4)CF3SO3. c Volume obtained from crystal structure of (NH4)CH3C6H4SO3.41 d 0.001 au contour of the electron density from B3LYP/aug-cc-pVDZ calculations.

increased methyl substitution will have better salt-forming ability whereas increased nitro and cyano substitution will have poorer salt-forming ability due to the deleterious electron-withdrawing effects of the ligands on the ring basicity and the effect of the electron-withdrawing groups is larger than the effect of the electron-donating groups. Lattice Energetics. Use of eqs 3 and 4 for the prediction of the lattice enthalpies and OS and IL entropies requires an estimate of the relevant neutral, cation, and anion volumes. The calculated and experimental (where available) volumes of the anions are given in Table 4. The calculated volumes of the halides, Cl-, Br-, and I-, and monohydrogen sulfate, (OH)SO3-, are in excellent agreement with the experimental averages from crystal structure data.18 The experimental value for the volume of triflate, TfO-, averaged over five crystal structure, is 0.129 ( 0.007 nm3, which differs from the calculated value (0.121 nm3) by only 0.008 nm3.40 The experimental value (0.199 nm3) for the volume of tosylate, TsO-, compares well with the

TABLE 5: Theoretical (B3LYP/DZVP2) Cation Volumes (nm3), Neutral Starting Material Volumes (nm3), and Lattice Enthalpies (-∆H3, kcal mol-1) of Nitro and Cyano Salts lattice enthalpy, by anion type cation (im ) imidazolium)

vol+

vol+Hofe

volneu

volneuHofe

Cl-

Br-

I-

(RO)SO3- f

TfO-

TsO-

1-methyl-2-nitro-3H-im 1-methyl-4-nitro-3H-im 1-methyl-5-nitro-3H-im 1-methyl-2,4-dinitro-3H-im 1-methyl-2,5-dinitro-3H-im 1-methyl-4,5-dinitro-3H-im 1-methyl-2,4,5-trinitro-3H-im 1,3-dimethyl-2-nitroim 1,3-dimethyl-4-nitroim 1,3-dimethyl-4-nitroima 1,3-dimethyl-2,4-dinitroim 1,3-dimethyl-2,4-dinitroimb 1,3-dimethyl-4,5-dinitroim 1,3-dimethyl-2,4,5-trinitroim 1-methyl-2-cyano-3H-im 1-methyl-4-cyano-3H-im 1-methyl-5-cyano-3H-im 1-methyl-2,4-dicyano-3H-im 1-methyl-2,5-dicyano-3H-im 1-methyl-4,5-dicyano-3H-im 1-methyl-2,4,5-tricyano-3H-im 1,3-dimethyl-2-cyanoim 1,3-dimethyl-4-cyanoim 1,3-dimethyl-4-cyanoimc 1,3-dimethyl-2,4-dicyanoim 1,3-dimethyl-2,4-dicyanoimd 1,3-dimethyl-4,5-dicyanoim 1,3-dimethyl-2,4,5-tricyanoim

0.137 0.142 0.140 0.169 0.167 0.171 0.202 0.156 0.160 0.160 0.189 0.189 0.191 0.223 0.133 0.132 0.130 0.154 0.155 0.154 0.180 0.156 0.156 0.156 0.178 0.178 0.180 0.201

0.144 0.144 0.144 0.174 0.174 0.174 0.203 0.168 0.168 0.168 0.198 0.198 0.198 0.227 0.135 0.135 0.135 0.156 0.156 0.156 0.176 0.159 0.159 0.159 0.180 0.180 0.180 0.200

0.144 0.145 0.144 0.178 0.173 0.174 0.203 0.144 0.145 0.144 0.178 0.173 0.174 0.203 0.138 0.136 0.138 0.160 0.159 0.158 0.184 0.138 0.136 0.138 0.160 0.159 0.158 0.184

0.139 0.139 0.139 0.169 0.169 0.169 0.198 0.139 0.139 0.139 0.169 0.169 0.169 0.198 0.130 0.130 0.130 0.151 0.151 0.151 0.171 0.130 0.130 0.130 0.151 0.151 0.151 0.171

122.9 122.0 122.4 117.9 118.2 117.6 113.6 119.8 119.2 119.2 115.2 115.2 115.0 111.3 123.6 123.7 124.1 120.1 119.9 120.1 116.4 119.8 119.8 119.8 116.6 116.6 116.4 113.8

121.5 120.7 121.0 116.8 117.0 116.5 112.7 118.6 118.0 118.0 114.2 114.2 114.0 110.5 122.2 122.3 122.7 118.9 118.7 118.9 115.3 118.6 118.6 118.6 115.6 115.6 115.3 112.8

119.0 118.3 118.6 114.7 115.0 114.5 111.0 116.4 115.8 115.8 112.4 112.4 112.2 108.9 119.6 119.8 120.1 116.6 116.5 116.6 113.4 116.4 116.4 116.4 113.6 113.6 113.4 111.1

117.5 116.9 117.1 113.6 113.8 113.4 110.2 112.3 111.9 111.9 109.1 109.1 108.9 106.2 118.1 118.2 118.5 115.4 115.2 115.4 112.4 112.3 112.3 112.3 110.1 110.1 109.9 108.0

114.0 113.4 113.6 110.6 110.8 110.4 107.6 111.9 111.5 111.5 108.7 108.7 108.6 105.9 114.4 114.5 114.8 112.1 112.0 112.1 109.5 111.9 111.9 111.9 109.7 109.7 109.5 107.7

106.1 105.7 105.9 103.7 103.9 103.6 101.6 104.7 104.4 104.4 102.4 102.4 102.3 100.3 106.4 106.5 106.6 104.8 104.7 104.8 103.0 104.7 104.7 104.7 103.1 103.1 103.0 101.6

a Prepared from 1-methyl-5-nitroimidazole. b Prepared from 1-methyl-2,5-nitroimidazole. c Prepared from 1-methyl-5-cyanoimidazole. Prepared from 1-methyl-2,5-cyanoimidazole. e Calculated following ref 43. f R ) H for protonated salts and R ) CH3 for methylated salts.

23202 J. Phys. Chem. B, Vol. 109, No. 49, 2005

Gutowski et al.

TABLE 6: Theoretical(B3LYP/DZVP2) Cation Volumes (nm3), Neutral Starting Material Volumes (nm3), and Lattice Enthalpies (-∆H3, kcal mol-1) of Methyl Salts lattice enthalpy, by anion type cation (im ) imidazolium)

vol+

vol+Hofd

volneu

volneuHofd

Cl-

Br-

I-

(RO)SO3- e

TfO-

TsO-

1-methyl-3H-im 2-methyl-1H,3H-im 4-methyl-1H,3H-im 4-methyl-1H,3H-ima 1,2-dimethyl-3H-im 1,4-dimethyl-3H-im 1,5-dimethyl-3H-im 1,2,4-trimethyl-3H-im 1,2,5-trimethyl-3H-im 1,4,5-trimethyl-3H-im 1,2,4,5-tetramethyl-3H-im 1,3-dimethylim 1,2,3-trimethylim 1,3,4-trimethylim 1,3,4-trimethylimb 1,2,3,4-tetramethylim 1,2,3,4-tetramethylimc 1,3,4,5-tetramethylim 1,2,3,4,5-pentamethylim

0.103 0.107 0.107 0.107 0.131 0.129 0.129 0.153 0.151 0.153 0.174 0.130 0.154 0.154 0.154 0.176 0.176 0.176 0.197

0.115 0.115 0.115 0.115 0.139 0.139 0.139 0.163 0.163 0.163 0.187 0.139 0.163 0.163 0.163 0.187 0.187 0.187 0.211

0.113 0.114 0.112 0.113 0.137 0.135 0.135 0.159 0.160 0.159 0.180 0.113 0.137 0.135 0.135 0.159 0.160 0.159 0.180

0.110 0.110 0.110 0.110 0.134 0.134 0.134 0.158 0.158 0.158 0.182 0.110 0.134 0.134 0.134 0.158 0.158 0.158 0.182

129.6 128.7 128.7 128.7 123.9 124.3 124.3 120.2 120.6 120.2 117.2 124.1 120.1 120.1 120.1 116.9 116.9 116.9 114.2

127.8 127.0 127.0 127.0 122.5 122.9 122.9 119.0 119.3 119.0 116.1 122.7 118.9 118.9 118.9 115.8 115.8 115.8 113.3

124.6 123.9 123.9 123.9 119.9 120.2 120.2 116.8 117.0 116.8 114.1 120.1 116.6 116.6 116.6 113.9 113.9 113.9 111.5

122.6 121.9 121.9 121.9 118.3 118.6 118.6 115.5 115.7 115.5 113.1 115.2 112.5 112.5 112.5 110.3 110.3 110.3 108.4

118.2 117.7 117.7 117.7 114.6 114.9 114.9 112.2 112.4 112.2 110.1 114.8 112.1 112.1 112.1 109.9 109.9 109.9 108.0

108.9 108.6 108.6 108.6 106.6 106.7 106.7 104.9 105.0 104.9 103.4 106.6 104.8 104.8 104.8 103.3 103.3 103.3 101.9

a Prepared from 5-methyl-1H-imidazole. b Prepared from 1,5-dimethylimidazole. c Prepared from 1,2,5-trimethylimidazole. d Calculated following ref 43. e R ) H for protonated salts and R ) CH3 for methylated salts.

similarity in size between iodide and (HO)SO3-, there is only a 1.5 kcal mol-1 average difference between these salts over the same three cations, despite the differences in the shape of the anions. The calculated ionic volumes of (CH3O)SO3- and TfO- are nearly the same and thus result in 1,3-dimethylsubstituted salts that have identical lattice energies. The difference between the nitro and cyano salts of (HO)SO3- and TfOis more pronounced with an average difference of 3.3 kcal mol-1. The largest anion, TsO-, has an average lattice energy difference of 6.8 kcal mol-1 from the triflate anion for the entire range of nitro and cyano salts and 14.5 kcal mol-1 for the chloride salts. Overall, the lattice enthalpies of the protonated nitro, methylated nitro, protonated cyano, and methylated cyano cover 21.3, 19.5, 21.1, and 18.2 kcal mol-1, respectively, in going from the largest cation/anion combinations to the smallest cation/anion combinations. Table 6 lists the calculated cation volumes as well as the lattice enthalpies (temperature-corrected lattice energies) of the corresponding methyl salts, sorted by anion type. On average, the ion volumes of the mono (2-, 4-, 5-), di (2,4-, 2,5-, 4,5-), and tri (2,4,5-) methyl-substituted protonated imidazolium cations are 0.01, 0.02, and 0.03 nm3, respectively, smaller than the corresponding nitro cations but nearly identical in size to the corresponding cyano cations (differences of only 0.002, 0.002, and 0.006 nm3, respectively). Thus, the lattice enthalpies of the methyl salts differ minimally from the corresponding cyano salts (