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Chem. B 2009, 113, 5690−5693). We can show that for ethyl ammonium nitrate (EAN) C8A7+ is the far most stable aggregate for enthalpic and entropic r...
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2009, 113, 15419–15422 Published on Web 11/02/2009

A Simple Geometrical Explanation for the Occurrence of Specific Large Aggregated Ions in Some Protic Ionic Liquids Ralf Ludwig* Institut fu¨r Chemie, Abteilung Physikalische Chemie, UniVersita¨t Rostock, Dr.-Lorenz-Weg 1, D-18051 Rostock, Germany, and Leibniz-Institut fu¨r Katalyse an der UniVersita¨t Rostock, A.-Einstein-Str. 29a, D-18059 Rostock, Germany ReceiVed: July 28, 2009; ReVised Manuscript ReceiVed: August 26, 2009

Thermochemistry calculations on positively charged aggregates of protic ionic liquids (PILs) support the aggregation pattern observed in electrospray ionization mass spectra (ESI-MS) (Kennedy, D. F.; Drummond, C. J. J. Phys. Chem. B 2009, 113, 5690-5693). We can show that for ethyl ammonium nitrate (EAN) C8A7+ is the far most stable aggregate for enthalpic and entropic reasons as well. The stability can be understood by the formation of a compact hydrogen-bond network. The strength of the H-bond network in C8A7+ makes this aggregate the most stable independent from the length of the cation alkyl chain length and the chosen solvent. Such strongly bound aggregates may justify the classification of PILs as “poor ionic liquids”. Organic salts with melting points below 100 °C are now commonly referred to as ionic liquids (ILs). These liquids represent a relatively new class of nonmolecular materials with unique properties.1-3 The interest in these materials is stimulated by a wide range of potential applications, for example, as solvents for reactions and material processing, as extraction media, or as working fluid for mechanical devices. For many of those applications, the knowledge of the physical properties of the ILs is often an essential necessity. Protic ionic liquids (PILs) are a subset of ionic liquids formed by combination of equimolar amounts of a Brønsted acid and a Brønsted base.4,5 The key property that distinguishes PILs from other ILs is the proton transfer from the acid to the base, leading to the presence of proton-donor and proton-acceptor sites, which can be used to build a hydrogen-bonded network. PILs have a number of unique properties compared to other ILs, just as water is different from normal molecular liquids. Thus, it has been suggested that the hydrogen bonds between ammonium cations and nitrate anions, for example, induce a network structure which in some respects mimics the three-dimensional hydrogen-bonded network of water.6-10 Recently, Kennedy and Drummond observed large aggregated parent ions within some protic ionic liquids (PILs) using electrospray ionization mass spectrometry (ESI-MS).11 They could show that the formation and size of aggregates depends on the nature of the anion and cation. In earlier ESI-MS experiments, the aggregation of aprotic ionic liquids was reported. For [N-butylpyridinium][BF4], Zhao et al. observed small C2A+ (C ) cation, A ) anion) as dominant species; for [C4mim][BF4] and [C4mim][NTf2], Kragl et al. detected also C2A+ as the main aggregate.12,13 In contrast to small aggregates obtained for aprotic ionic liquids, Kennedy and Drummond found larger aggregates for the protic ionic liquids ethylammonium nitrate (EAN), propylammonium nitrate (PAN), and * E-mail: [email protected].

10.1021/jp907204x CCC: $40.75

butylammonium nitrate (BAN), respectively. They observed a similar aggregation pattern for the neat PILs or those dissolved in methanol, iso-propanol, or acetonitrile. In the ESI-MS spectra, they could see a series of singly charged aggregates of the type CnAn-1+, with C8A7+ as the most prominent by close to an order of magnitude. The analysis of the very similar neat PILs PAN and BAN in the positive mode showed identical results. Although the ILs differ in the length of the alkyl chain, the major ion apparent in all ILs was the very stable aggregate C8A7+. Obviously, the hydrogen-bonding network is similar and the increase of the alkyl chain length resulting in increasing dispersion forces plays a minor role. Interestingly, these PILs showed a different aggregation pattern in the negative mode. The negatively charged aggregates do not have a particular stable abundant aggregate analogous to the stable C8A7+ observed in the positive mode. These interesting experimental results encouraged us to understand the aggregation pattern of these PILs in the positive mode. In particular, we wanted to realize why aggregates C8A7+ are the absolutely dominant species independent from the chosen PIL in the neat state or in a solvent. For that purpose, we performed static quantum chemical calculations for larger aggregates of the type CnAn-1+. We considered positive aggregates up to n ) 12, giving C12A11+ as the largest species. For these aggregates, we calculated the structures, energies, and thermodynamic properties including frequency analysis. We present the thermodynamic properties of these positively charged aggregates using pure ab initio methods in combination with standard procedures of statistical thermodynamics.14,15 At first, we calculated positive aggregates CnAn-1+ up to n ) 12 for the PIL EAN. As a result, the EAN structures in the lowest energy state and all vibrational frequencies of each aggregate have been obtained. On the basis of these quantum chemical results, the Gibbs energies have been calculated for temperatures at 200, 300, and 400 K at standard pressures of 105 Pa. The differences in Gibbs energy between a chosen aggregate to that of the most  2009 American Chemical Society

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stable species give equilibrium constants and relative abundances of the aggregates. We determined optimized geometries and harmonic vibrational frequencies for a variety of positively charged EAN aggregates CnAn-1+ at a specific ab initio level, such as the simple RHF/3-21G “split valence double-ζ” model, using standard options of the Gaussian16 program system. For aprotic ionic liquids such as [C1mim][SCN], we could show that aggregate geometries and vibrational frequencies are reproduced reasonably well at the RHF/3-21G level compared to those obtained for smaller aggregates using higher-level theoretical treatments.15,17-19 Here, this assumption is made for the calculation of charged aggregates of protic ionic liquids as well. The starting configurations for calculating the positively charged CnAn-1+ aggregates have been obtained from earlier geometries of neutral clusters of EAN. Those were built in such a way that the ethyl ammonium cations could maximize the number of formed hydrogen bonds. For some aggregate sizes, several minimum structures were found on the potential energy surface. However, they never differed by more than 2 kJ mol-1 in energy per ion. For the thermochemistry calculations, only the aggregates best in energy were considered. It is well-known that the aggregate binding energetics at this level are affected by basis set superposition error (BSSE). Compared to the calculations of imidazolium-based ionic liquids, the BSSE in protic ionic liquids is substantial because of significant hydrogen-bonding contributions which are in the order of the Coulomb interactions.20 Thus, we have corrected the RHF/3-21G energies with the counterpoise (CP) method.21 We want to point out that shortcomings in the basis set will occur in all aggregates and will be mostly compensated by calculating relative properties. The same argument holds for not considering explicitly dispersion forces. Adopting the simple 3-21G methodology allows exploration of a greater range of aggregate species than would otherwise be feasible, and is therefore well suited to the present work. All optimized aggregates were found to have only positive frequencies, demonstrating that they are all true equilibrium species on the RHF/3-21G potential energy surface.16 For the present work, the initial frequency calculation for each aggregate is followed by a thermochemistry analysis using different temperatures and pressures. The equations used for computing thermodynamical data in Gaussian16 are equivalent to those given in standard texts such as “Molecular Thermodynamics” by McQuarrie.14 The analysis uses the standard expressions for an ideal gas in the canonical ensemble (see the Supporting Information). In Figure 1, the binding energies per ion of aggregates CnAn-1+ for EAN are shown. The values ∆E/ion are obtained by the following equation:

∆E/ion ) [E - (n · EC1+ + (n - 1) · EA1-)]/2n - 1

(1) where E is the total energy of the optimized aggregate CnAn-1+. EC1+ and EA1- are the total energies of the isolated optimized ethylammonium cations and nitrate anions, respectively. Subtracting n times the cation energy and (n - 1) times the anion energy from the total energy of the aggregate and dividing the result by (2n - 1) provides the binding energy per ion in a specific aggregate. The binding energies per ion increase with the number of ions within the aggregate (Table 1). For the uncorrected binding energies, this behavior is caused by the basis set superposition error (BSSE) and cooperative effects. The

Figure 1. Binding energies per ion of aggregates CnAn-1+ for EAN. For example, the ∆E/ion for C12A11+ is calculated by subtracting 12 times the single cation energy and 11 times the single anion energy from the total energy of the aggregate. The resulting total binding energy is then divided by the number of ions which is 12 + 11 ) 23 for this aggregate. Additionally, the CP-corrected binding energies (closed symbols) are given.

TABLE 1: Energies (E, au), Counter-Poise-Corrected Energies (ECP, au), and Binding Energies per Ion (∆E/ion, kJ/mol) of Aggregates CnAn-1+ for Ethyl Ammonium Nitrate, Calculated at the RHF/3-21G Hartree-Fock Levela aggregate +

C 2 A1 C3A2+ C4A3+ C5A4+ C6A5+ C7A6+ C8A7+ C9A8+ C10A9+ C11A10+ C12A11+ C1+ A1-

E (au)

ECP (au)

∆E/ion (kJ/mol)

-545.333152 -956.772337 -1368.223307 -1779.653146 -2191.062764 -2602.536576 -3014.010622 -3425.410784 -3836.850685 -4248.286897 -4659.735136 -133.8863964 -277.2876465

-545.291043 -956.673805 -1368.084697 -1779.461541 -2190.811497 -2602.229513 -3013.653430 -3424.983621 -3836.369293 -4247.754120 -4659.156865

-201.82 -230.69 -253.61 -256.42 -251.78 -262.32 -271.08 -263.30 -264.83 -265.96 -268.94

a Additonally, the energies for the single cation and anion are given, respectively.

artificial BSSE is removed by applying the counter-poise correction. Thus, the CP-corrected binding energies clearly show strong cooperative effects with increasing size of the aggregates (see Figure 1). This cooperativity seems to be saturated for aggregate C8A7+ which represents the most stable structure. Larger aggregates are slightly less stable in terms of binding energies per ion. However, the stability of the aggregates cannot be judged solely from the electronic energies, since one must also take into account entropic factors of vibrational origin. Strain-entropy effects are particularly evident in large structures. Thus, larger aggregates can compete on enthalpic grounds but are disfavored for entropic reasons. Therefore, we calculated the corresponding thermal Gibbs energies ∆G/ion for temperatures of 200, 300, and 400 K:

∆G/ion ) [G - (n · GC1+ + (n - 1) · GA1-)]/2n - 1

(2) For each aggregate, the thermal Gibbs energy is defined as G ) H - TS, the thermal enthalpy as H ) E + RT, and the thermal energy as E ) E0 + Etrans + Erot + Evib, with E0 ) ECP elec

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Figure 2. Binding Gibbs energies per ion of aggregates CnAn-1+ for EAN. For example, the ∆G/ion for C12A11+ is calculated by subtracting 12 times the single cation Gibbs energy and 11 times the single anion energy from the total Gibbs energy of the aggregate. The resulting total binding Gibbs energy is then divided by the number of ions which is 12 + 11 ) 23 for this aggregate. The CP correction for the binding energies is included.

+

Figure 3. Relative abundance of the aggregates CnAn-1 for EAN in percent at 300 K. The most stable aggregate C8A7+ is taken as a reference and set to 100%.

+ EZPE. These calculations include the CP-corrected electronic binding energies as well as the zero point energy correction. From Figure 2, it can be seen that the sequence in aggregate stability remains. The dominance of the leading aggregate C8A7+ is more pronounced because of an entropic penalty for the larger aggregates. The entropically favored smaller aggregates cannot compensate for their relatively high enthalpies caused by low cooperativity. Now we calculated the ∆G values of all aggregates with respect to the most stable structure C8A7+ to obtain the equilibrium constant K:

∆G ) RT ln K

(3)

If the most stable aggregate C8A7+ is taken as a reference and set to 100%, the resulting relative abundance of the aggregates CnAn-1+ can be calculated. For 300 K, they are shown in Figure 3. All aggregates show up only in trace amounts up to 10%. Only the aggregate C12A11+ has a higher abundance relative to the most stable structure. There is a clear preference for the aggregate C8A7+ in the positive mode of the ESI-MS experiments as well as in our calulations. Smaller and larger aggregates show up only in trace amounts, at least an order of magnitude lower. That the

Figure 4. Cartoon of a possible stable aggregate C8A7+. The energetically favored cubes are connected by sharing one anion at the corner. In the calculated structure (see Figure 5), one anion and one cation of the lower cube interact with one cation and one anion of the upper cube (as indicated by the arrow) to avoid the 6-fold coordination of the shared anion.

Figure 5. Most stable aggregate C8A7+ for ethyl ammonium nitrate as obtained from ab initio calculations. For visualizing, the skeletal structure connections between the nitrogens of the cations and anions are shown for distances below 3.8 Å. The fully calculated aggregate resembles mainly the artificial structure as given in Figure 4.

calculated smaller aggregates have minor relative abundances than those in the ESI-MS spectra may be related to the kinetics of aggregate formation. However, why is C8A7+ so stable? The answer is obvious from viewing the cartoon of a possible aggregate and the real calculated minimum energy structure, as shown in Figures 4 and 5. For neutral aggregates, a cube structure is favored. In such a configuration, all available donors and acceptors are involved in hydrogen bonding and form a stable H-bond network. The three proton donors of the ethyl ammonium cation point toward three nitrate anions, and all anions have three cationic neighbors as well. This energetically favored configuration can be basically preserved in a positively charged aggregate, as shown in Figure 4. Within the aggregate, two cubes are connected by sharing one anion at the corner. In total, that gives the aggregate C8A7+. This artificial configuration is very close to our calculated structure, as shown in Figure 5. In the energy minimized structure, the nitrogen atoms of the cations and anions are interconnected to visualize the interactions. It can be seen clearly that the upper cube is preserved and resembles that of the cartoon, whereas the lower cube is slightly distorted. Also, this behavior can be simply explained. In the cartoon, the shared anion is coordinated by six cations. Such a coordination is energetically disfavored with the consequence that one anion and one cation of the lower cube

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TABLE 2: Energies (E, au), Counter-Poise-Corrected Energies (ECP, au), and Binding Energies per Ion (∆E/ion, kJ/mol) of Aggregates C8A7+ for Ethyl Ammonium Nitrate (EAN), Propyl Ammonium Nitrate (PAN), and Butyl Ammonium Nitrate (BAN) Calculated at the RHF/3-21G Hartree-Fock Level aggregate

E (au)

ECP (au)

∆E/ion (kJ/mol)

EAN PAN BAN

-3014.010622 -3324.568841 -3635.114977

-3013.653430 -3324.211148 -3634.755252

-271.10 -268.60 -265.59

interact with the next lying cation and anion of the upper cube, as indicated in Figure 4 and shown in Figure 5. The aggregate C8A7+ is the most stable one because the largest number of strong H-bonds can be formed in such a configuration. Consequently, Kennedy and Drummond found C8A7+ to be the dominant species not only for EAN but for PAN and BAN as well. In Table 2, the binding energies per ion for all of these C8A7+ structures are given. Because of the increasing electron pushing effect with longer alkyl chain length, the binding energies per ion slightly decrease in the order EAN, PAN, and BAN, respectively. However, the H-bond network structure remains for all aggregates (see the figure in the Supporting Information). The alkyl chains point toward the gas phase or into the solution and hence have no influence on the H-bond network. That this aggregate is the most stable in the neat PIL or in PILs dissolved in a series of different polar solvents suggests that similar structures already exist in the liquid state. As suggested by Kennedy and Drummond, polydisperse mixtures of aggregated ions can contribute to the relatively poor conductivity exhibited in some PILs. The latter are usually classified as “poor ionic liquids”.11 There is still one question to answer: Why is aggregate C8A7+ found as a dominant species in the ESI-MS spectra measured in the positive mode but no analogue aggregate C7A8- occurs for the negative mode? Whereas nitrate anion NO3- is a flat ion and interactions do not neccessarily take place along the NO bonds, leading to coordination numbers large than 3, this is not possible for the ethyl ammonium cation. Therein, favorable interaction occurs via the NH bonds, excluding larger coordination numbers than 3. Thus, a shared ethyl ammonium cation cannot play a similar role as NO3- in the vertex of two connected cubes. Additionally, there is no room for the alkyl side chain which cannot point toward the gas phase as possible for C8A7+. In conclusion, the present results show that ab initio calculations in combination with statistical thermodynamics are capable of explaining the experimental finding of larger positively charged aggregates CnAn-1+ of protic ionic liquids in ESI-MS experiments. We could show that the absolutely dominant structure C8A7+ of EAN is favored for enthalpic as well as for entropic reasons. The stability of this aggregate can be understood by the formation of a compact hydrogen-bond network in which all proton donors and acceptors of the ethylammonium cation and the nitrate anion are involved in an optimal way. The ideal neutral cube aggregates can be preserved by connecting two cubes via a shared anion. Such a configuration is not possible for the negative analogue C7A8- and is consequently not found in the ESI-MS spectra using the negative mode. The strength of the H-bond network in C8A7+ is responsible for finding this aggregate, being the most stable independent from the alkyl chain length of the neat PILs. The same argument holds for the dissolved PILs. If a critical polarity is not exceeded, the interactions between the solvent molecules

Letters and the solute ions are weaker than those among the ions themselves and the H-bond network remains. These strongly H-bonded aggregates could then explain the classification of PILs as “poor ionic liquids”. In upcoming work, we want to characterize the structure and properties of PIL aggregates in more detail and want to elaborate the differences to aggregates of aprotic ionic liquids. Acknowledgment. This work has been supported by the German Science Foundation (DFG) priority program SPP 1191 with additional support from SFB 652. Supporting Information Available: Theoretical background for the thermochemical calculations, partition functions, and figures of the most stable aggregates C8A7+ for ethyl, propyl, and butyl ammonium nitrate. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Wasserscheid, P.; Welton, T. Ionic Liquids in Synthesis; 2nd ed.; VCH-Wiley: Weinheim, Germany, 2008. (2) Endres, F.; El Abedin, S. Z. Phys. Chem. Chem. Phys. 2006, 8, 2101–2116. (3) Rogers, R. D.; Seddon, K. R. Science 2003, 302, 792–793. (4) Nuthakki, B.; Greaves, T. L.; Krodkiewska, I.; Weerawardena, A.; Burgar, I.; Mulder, R. J.; Drummond, C. J. Aust. J. Chem. 2007, 60, 21– 28. (5) Greaves, T. L.; Weerawardena, A.; Fong, C.; Krodkiewska, I.; Drummond, C. J. J. Phys. Chem. B 2006, 110, 22479–22487. (6) Weinga¨rtner, H.; Knocks, A.; Schrader, W.; Katze, U. J. Phys. Chem. A 2001, 105, 8646–8650. (7) Evans, D. F.; Chen, S.-H.; Schriver, G. W.; Arnett, E. M. J. Am. Chem. Soc. 1981, 103, 481–482. (8) Evans, D. F.; Kaier, E. W.; Benton, W. J. J. Phys. Chem. 1983, 87, 533–535. (9) Evans, D. F.; Yamauchi, A.; Wei, G. J.; Bloomfield, V. A. J. Phys. Chem. 1983, 87, 3537–3541. (10) Fumino, K.; Wulf, A.; Ludwig, R. Angew. Chem., Int. Ed. 2009, 48, 3184–3186. (11) Kennedy, D. F.; Drummond, C. J. J. Phys. Chem. B 2009, 113, 5690–5693. (12) Dyson, P.; Khalaila, I.; Luettgen, S.; McIndoe, J.; Zhao, D. Chem. Commun. 2004, 2204–2205. (13) Dorbritz, S.; Ruth, W.; Kragl, U. AdV. Synth. Catal. 2005, 347, 1273–1279. (14) McQuarrie, D. A. Statistical Mechanics; Harper and Row: New York, 1973. (15) Ludwig, R. Phys. Chem. Chem. Phys. 2008, 10, 4333–4339. (16) 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.; Keitha, 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 C.02; Gaussian, Inc.: Wallingford, CT, 2004. (17) Morrow, T.; Maginn, E. J. J. Phys. Chem. B 2002, 106, 12807– 12813. (18) Shah, J. K.; Maginn, E. J. Fluid Phase Equilib. 2004, 195, 222– 223. (19) Liu, Z.; Haung, S.; Wang, W. J. Phys. Chem. B 2004, 108, 12978– 12989. (20) Fumino, K.; Wulf, A.; Ludwig, R. Phys. Chem. Chem. Phys. 2009, 11, 8790–8794. (21) Boys, S.; Bernardi, F. Mol. Phys. 1970, 19, 553–566.

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