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J. Phys. Chem. C 2007, 111, 10718-10731

Computational Characterization of Energetic Salts Haixiang Gao, Chengfeng Ye, Crystal M. Piekarski, and Jean’ne M. Shreeve* Department of Chemistry, UniVersity of Idaho, Moscow, Idaho 83844-2343 ReceiVed: January 26, 2007; In Final Form: May 9, 2007

Using the experimental (or calculated) values for densities, a combination of theoretical and empirical calculations are powerful tools in predicting heats of formation of energetic salts. The heats of formation of cations and anions and lattice energies were calculated separately based on Born-Haber energy cycles. In this paper, 119 energetic salts were calculated. Heats of formation coupled with densities can be used further for predicting the detonation pressures and velocities and specific impulses of energetic salts. This method provides a straightforward and inexpensive route to screen large numbers of energetic salts

Introduction Energetic materials include explosives and propellants that are useful for a variety of military purposes or industrial applications. While explosives release energy on a microsecond time scale, propellants evolve energy through relatively slow deflagration processes which often take several seconds to achieve complete combustion. These types of materials can be considered to be controllable storage systems for chemical energy. Despite these behavioral differences, these compounds share several chemical similarities. In fact, propellant and explosive mixtures often are comprised of different quantities of the same ingredients.1 Although there is a continuing need to improve energetic materials, in the development of new energetic systems, optimal tradeoffs in energy content, safety, and cost are sought. This is achieved either through formulation, combining known chemical compounds, and/or synthesis, generating new compounds. The costs associated with either of these activities are significant. Therefore, it is desirable to reduce the degree of trial and error in the development of new materials by accurately predicting properties of proposed structures. In this work, we use a combination of ab initio and empirical methods to construct energetic species with desirable properties. Our focus is primarily upon the topics of energy content prediction (commonly termed performance) and the safety characteristics of highly energetic salts. Energetic salts are important systems for the development of high-energy density materials since salts are intrinsically nonvolatile, are typically thermally stable under normal conditions, and are denser than molecular species.2 Designing energetic materials based on combinations of different ions for a specific purpose provides a powerful methodology. The impact on properties of salts as a function of cations and anions and the variation of substituents on those ions are important references for screening and design work.3 In the past, these characteristics were predicted primarily using empirical rules and intuition. The development of molecular modeling techniques now makes it possible to predict many, but not all, relevant material properties via relatively fundamental methods. The standard heat of formation (∆H°f) of a compound is defined as the enthalpy change ∆H° for a reaction (usually hypothetical) whereby it is produced from its elements, in their * To whom correspondence should be addressed. E-mail: jshreeve@ uidaho.edu.

most stable states at a pressure of 1 atm and normally at 298.15 K. Therefore, ∆H°f is a key property of an energetic compound. A relatively small database of these values provides sufficient data for the calculation of numerous heats of chemical reaction, ∆H°r. It is estimated, however, that experimental heats of formation have been determined for less than 0.1% of the more than 10 million known compounds.4 Furthermore, these values are not always reliable; for example, Stewart recently listed 34 compounds for which the experimental heats of formation are questionable.5 Although it is not surprising that a variety of computational techniques have been developed (empirical, semiempirical, and ab initio/density functional) for predicting gas phase heats of formation, empirical methods are usually employed for the prediction of heats of formation for solid or liquid compounds. In this paper, we report the calculation of the heats of formation of some of the new energetic salts synthesized in our laboratory6 using a combination of ab initio and empirical methods. According to Born-Haber energy cycles (Figure 1), heats of formation of salts could be simplified by the formula

∆H°f (ionic salt, 298 K) ) ∆H°f (cation, 298 K) + ∆H°f (anion, 298 K) - ∆HL where ∆HL is the lattice energy of the salt. From a computational perspective, the latter is a difficult quantity to predict accurately. To the best of our knowledge, there is no “first principles” computational/theoretical method currently available for predicting lattice energies. The method which appears to be the most acceptable approach currently available is an empirical model based upon molar volumes developed by Jenkins.7 Several research groups have utilized this model in calculating properties of some new energetic salts.8-10 We describe a computationalchemistry-based method for the assessment of the thermodynamics of energetic salt formation. The objective of the present study is to extend this method to a rather large number of salts having a variety of different cations and anions. Reported are the thermodynamic and detonation properties of 119 energetic salts with different cations and anions calculated by combining an ab initio method and empirical rules. When compared with some literature experimental values, this method gives calculated values which are in good agreement. In addition, we predict detonation pressure, velocity, and specific impulse

10.1021/jp070702b CCC: $37.00 © 2007 American Chemical Society Published on Web 06/23/2007

Computational Characterization of Energetic Salts

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10719 linear polyatomic ions, and 6 for nonlinear polyatomic ions. The equation for lattice potential energy UPOT has the form

UPOT/kJ mol-1 ) γ(Fm/Mm)1/3 + δ

Figure 1. Born-Haber cycle for the formation of energetic salts.

using the CHEETAH 4.0 program11 based on the values we have calculated. Computational Details Computations were performed using the Gaussian 03 (revision D.01) suite of programs.12 As all species considered here are closed shell in nature, the majority of the geometric optimization and frequency analyses for molecules with more than 10 heavy atoms are carried out using B3-LYP functional with 6-31+G** basis set,13 and single energy points were calculated at the MP2(full)/6-311++G** level.14 All of the optimized structures were characterized to be true local energy minima on the potential energy surface without imaginary frequencies. The molecular energies (proton affinities and ionization energies) are calculated at the G215 or G2MP2 level.16 The lattice energy ∆HL (eq 1) is predicted by the formula7

∆HL ) UPOT + [p(nM/2 - 2) + q(nX/2 - 2)]RT where nM and nX depend on the nature of the ions Mp+ and Xq-, respectively, and are equal to 3 for monatomic ions, 5 for

where density is Fm (g cm-3), Mm is the chemical formula mass of the ionic material, g (or Mg), and the coefficients γ/kJ mol-1 cm and δ/kJ mol-1 are values taken from the literature.7 The heats of formation of organic cations and anions are computed using the method of isodesmic reactions.9 The enthalpy of reaction (∆H°r 298) is obtained by combining the MP2(full)/6-311++G** energy difference for the reaction, the scaled zero-point energies, and other thermal factors. Thus, the heats of formation of the organic cations and anions being investigated can be readily obtained. The heats of formation of metal cations are calculated based on ionization energy by the G2 method.15 The lattice energies and the heats of formation of cation and anion are listed in Tables 1 and 2. With values for the heats of formation and densities of energetic salts, the detonation pressures (P) and detonation velocities (D) are calculated based on the traditional ChapmanJouget thermodynamic detonation theory using CHEETAH 4.0.11 Results and Discussion Heats of formation of the simple cations or anions can be calculated at G2 level based on proton affinities (Scheme 1). Heats of formation of metal cations can be calculated at the same level based on electron affinities (Scheme 2). For the more complicated cations or anions, the most efficient computational

TABLE 1: Calculated Values of ∆H°f Compared with Experimental salts

density

∆H°f of cation

∆H°f of anion

lattice energy

calc’d ∆H°f (kJ/mol)

exptl ∆H°f (kJ/mol)

error (kJ/mol)

CaF2 MgF2 CaCl2 LiF NaF KF MgCl2 KNO3 KCl NaNO3 NaCl KClO4 LiCl LiNO3 NH4NO3 NH4F NH4Cl Guanidinium nitrate LiClO4 NH4ClO4 NaClO4 Diguanidine tetrazine nitrate Guanidine nitroformate Hydrazine perchlorate Hydrazine mono-nitrate Ammonium dinitramide Ammonium 2,4,5- trinitroimidazole Triamino-guanidinium nitrate Ammonium 3-5-dinitro 1,2,4 triazolate Triamino-guanidine perchlorate Ammonium 5- nitro-tetrazolate Ammonium azide Hydrazinium azide

3.18 3.15 2.15 2.63 2.56 2.48 2.32 2.10 1.98 2.26 2.17 2.52 2.06 2.38 1.72 1.01 1.52 1.44 2.43 1.95 2.02 1.72 1.8 1.84 1.94 1.81 1.84 1.59 1.63 1.67 1.57 1.35 1.42

1906.6 2305.7 1906.6 674.9 585.0 501.1 2305.7 501.1 501.1 585.0 585.0 501.1 674.9 674.9 626.4 626.4 626.4 566.7 674.9 626.4 585.0 1903.6 566.7 770.0 770.0 626.4 626.4 871.5 626.4 871.5 626.4 626.4 770.0

-258.3 -258.3 -230.3 -258.3 -258.3 -258.3 -230.3 -300.5 -230.3 -300.5 -230.3 -277.8 -230.3 -300.5 -300.5 -258.3 -230.3 -307.9 -277.8 -277.8 -277.8 -307.9 -287.0 -277.8 -307.9 -156.2 -156.7 -307.9 -41.2 -277.8 112.8 197.2 197.2

2700.2 2874.1 2189.5 1032.7 888.4 801.2 2333.9 653.4 699.9 700.1 769.7 629.8 831.7 753.9 659.6 705.1 713.3 559.3 670.9 614.1 613.1 1555.0 513.4 639.0 593.3 593.0 510.5 528.6 524.7 507.7 560.9 644.6 636.6

-1310.4 -1084.9 -743.5 -615.9 -561.5 -558.6 -488.7 -460.2 -428.9 -423.0 -415.1 -406.7 -387.0 -386.6 -341.0 -336.8 -317.1 -300.4 -273.6 -265.7 -305.9 -252.3 -233.9 -146.9 -131.4 -123.0 -41.0 35.1 60.2 86.2 178.2 179.1 330.5

-1228.0a -1124.2a -795.4a -615.9a -576.6a -567.4a -641.4a -494.5a -436.4a -467.8a -411.2a -432.6a -408.8a -483.3a -365.7b -464.0c -314.2d -387.0e -381.2f -295.4f -383.3f -255.2g -197.9h -179.5i -251.9j -150.2k -87.0l -48.1m 3.3n 36.0m 19.7n 112.1o 246.0b

82.4 -39.3 -51.9 0 -15.1 -8.8 -152.7 -34.3 -7.5 -44.8 3.9 -25.9 -21.8 -96.7 -24.7 -127.2 2.9 86.6 -107.6 -29.7 77.4 -2.9 36.0 -32.6 -120.5 -27.2 -46.0 -83.2 -56.9 -50.2 -158.5 -67.0 -84.5

a Reference 18a. b Reference 18b c Reference 18c. d Reference 18d. e Reference 18e. f Reference 18f. g Reference 18 g. h Reference 18h. i Reference 18i. j Reference 18j. k Reference 18k. l Reference 18l. m Reference 18m. n Reference 11a. o Reference 8.

10720 J. Phys. Chem. C, Vol. 111, No. 28, 2007 TABLE 2: Heats of Formation of Energetic Salts

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Computational Characterization of Energetic Salts TABLE 2 (Continued)

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10721

10722 J. Phys. Chem. C, Vol. 111, No. 28, 2007 TABLE 2 (Continued)

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Computational Characterization of Energetic Salts TABLE 2 (Continued)

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10723

10724 J. Phys. Chem. C, Vol. 111, No. 28, 2007 TABLE 2 (Continued)

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Computational Characterization of Energetic Salts TABLE 2 (Continued)

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10725

10726 J. Phys. Chem. C, Vol. 111, No. 28, 2007 TABLE 2 (Continued)

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Computational Characterization of Energetic Salts TABLE 2 (Continued)

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10727

10728 J. Phys. Chem. C, Vol. 111, No. 28, 2007

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TABLE 2 (Continued)

a

Reference 6a. b Reference 6b. c Reference 6c. d Reference 6d. e Reference 6e. f Reference 6f. g Reference 6g. h Reference 6h. i Reference 6i.

Computational Characterization of Energetic Salts

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10729

SCHEME 1: Protonation Reactions

SCHEME 2: Electron Affinities of Metal Cations

procedure for finding accurate heats of formation is based on isodesmic (bond type conserving) reactions.17 We found that if most of the cations and anions were comprised of the 5-membered heterocyclic structures with various functional groups, such as amino, hydrazine or guanidine, it was straightforward to use the structures in Scheme 1 to build isodesmic reactions for more complicated cations and anions (See ESI). To show the reliability of predicted condensed phase heats of formation values of salts, the latter values for 33 salts obtained in the present investigation were compared with experimental data. First, we began by computing the 33 salts for which the experimental heats of formation were available.18 Although these salts (Table 1) represent a wide variety of salt classes, the average absolute deviation from experiment for these calculated heats of formation is -43.5 kJ/mol, with the largest being -158.5 kJ/mol. The calculated values are comparable with the experimentally determined reference data in Table 1. A straight line defined by y ) 0.9231x - 71.529 and having a correlation coefficient (R2) 0.9834 was obtained when the literature heats of formation are plotted along the x axis and the heats of formation calculated using the present method are along the y axis (Figure 2). The solid line indicates excellent agreement between calculated and experimental values.

Figure 2. Calculated thermodynamic values versus experimental data.

The accuracy of the heats of formation of energetic salts obtained from the use of this method is controlled by several factors: (1) the choice of the isodemic reactions used to cancel calculation errors; (2) the level of sophistication (method and basis set) applied to calculate the electronic energy; (3) the uncertainty of the zero-point energy(ZPE) and thermal corrections; (4) the correctness and error tolerance of the heat of formation of the reference compounds; (5) the accuracy of the density of the salts; and (6) the goodness of the estimation of the lattice energy of the salt. We believe that factors 1-4 will commonly lead to an uncertainty of ∼21∼40 kJ/mol. Our calculations show that a 0.1 g/cm3 difference in the density value (5) will lead to a difference of ∼5-30 kJ/mol. The uncertainty in the prediction of the lattice energies of salts usually ranges from 2 to 150 kJ/mol which is obviously the major source of error in calculation of heats of formation of salts. In spite of these uncertainties, the prediction of heats of formation can yield insight into possible materials performance. In Table 2 are tabulated data for 119 salts which we synthesized. These salts are composed of a combination of different energetic cations and anions, which contribute not only to the energy of the salt but also to the density.

10730 J. Phys. Chem. C, Vol. 111, No. 28, 2007

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TABLE 3: Detonation Properties of Selected Salts salts

P, Gpa

νD, m/s

Isp, s

salts

P, Gpa

νD, m/s

Isp, s

45 13 14 42 79 81 80 84 85 2 7 20 16 15 24 29 19 31 33

20 22 16 24 31 26 21 22 25 24 25 23 25 21 18 22 23 25 20

7533 7447 7043 7560 8477 8025 7588 7451 7661 7825 7789 7700 7637 7597 7256 7535 7780 7461 7634

214 214 196 261 263 239 215 216 244 234 257 225 237 221 214 228 217 239 227

32 26 23 28 18 46 38 30 25 11 12 35 88 89 90 102 83 98 55

22 22 19 22 22 25 25 25 22 32 40 22 22 27 22 10 35 11 23

7275 7572 7437 7571 7352 7650 7814 7706 7698 8739 9075 7791 7538 8046 7722 6145 8913 6190 7574

217 222 213 228 217 249 235 246 231 276 275 242 223 247 222 170 263 173 255

The heat of formation of a cation or anion increases as the number of nitrogen atoms increases (5-nitro tetrazolate > 3-nitro triazole > 3,5-dinitro triazolate > 4,5-dinitro imidazolate > 5-amino tetrazolium cation > 3-amino triazolium cation). The addition of functional groups also modifies the heat of formation, usually the azide or amino group increases the heat of formation where, for example, the amino group bonded to nitrogen usually contributes more positively than when bonded to carbon. The methyl, ethyl, and nitro groups usually decrease the heats of formation of a cation or anion, but the nitro group has the advantage of increasing the density and oxygen balance, attributes which are important for energetic materials. Compared with other functional groups, the azide ion has the greatest impact on the heat of formation of the cation. This group is the best choice to increase the heat of formation of high-energy materials although it negatively impacts other properties such as thermal stability. The lattice energy of a salt with mono charged cation and anion usually falls in the range from 400 to 600 kJ/mol, whereas a salt with a doubly charged cation or anion has energies between 1100 and 1600 kJ/mol. The higher lattice energy of the salts with doubly charged cation or anion can be compensated for by the heat of formation of the additional anion or cation, which lowers the impact of lattice energy. The salts described in Table 2 have heats of formation ranging from -388.1 (98) to +1855.8 kJ/mol (72) and specific heats of formation ranging from -1563.0 (98) to +4528.7 J/g (55), and they are candidates for propellants. Among the criteria used in evaluation of potential energetic systems are detonation pressure, P (Gpa), and velocity, VD (m/ s), for explosives and specific impulse, Isp (s), for propellants. The first two refer to the pressure and the rate of propagation of the shock wave front through the material,19 whereas specific impulse is a measure of the thrust of a propellant.19b,20 Each of these quantities depends upon the energy release that accompanies the combustion and decomposition processes that are occurring.19-21 The detonation pressure and velocity are also directly related to the density of the system, for which a high value (ideally, greater than 2.0 g/cm3) is therefore very desirable. Some quite effective techniques for predicting densities are now available.22 Using the calculated heat of formation and the density, the detonation pressure and velocity (based on the traditional Chapman-Jouget thermodynamic detonation theory) and Isp can be obtained by using CHEETAH 4.0 (Table 3).11 For those salts, with the exception of a nitrate with a diazidocontaining cation (11) which exhibits a detonation pressure of

32 Gpa (RDX ) 34) and the analogous perchlorate (12) salt which has a calculated detonation pressure of 40 Gpa (extremely hazardous, unstable material), the nitrate salts are the least meritorious. Overall, perchlorate is the anion of choice for those energetic salts. Perchlorate contributes most positively to the decomposition temperature, density, most often for heat of formation (always when compared with nitrate but rarely with nitroheterocyclic anions). Perchlorate also wins for decomposition pressure, decomposition velocity, and specific impulse. The environmental impact of the perchlorate ion tends to makes it less attractive. Salts 102 and 83 have the lowest and highest densities, respectively. When the values of their P, νD and Isp are compared with those of 98 and 55 which have the lowest and highest specific heats of formation, it is obvious that density plays a more important role in determining the value of the detonation properties. The most positive information gained is that polynitro heterocyclic anions, although not strictly competitive with perchlorate, do appear to be superior to other anions. Of course, they are more environmentally friendly than perchlorates. 4. Conclusions The condensed phase heat of formation of an energetic compound is one of the essential parameters to the explosive user. The present method, apart from being developed as predictive tools, can provide the simplest procedure for estimating condensed phase heats of formation of energetic salts. The method generates reasonably reliable predictions. It is appealing, and the results are very promising because it requires as input only the structural formulas of cations and anions of energetic salts, with the easily available experimental or predicted value of density. The introduced correlation will be very valuable in directing research efforts toward the design of energetic organic molecules. This leads the chemist to rapid and semiquantitative data on which to base new and complex syntheses decisions. Acknowledgment. The authors acknowledge the financial support of the AFOSR, (Grant F49620-03-1-0209), the NSF (Grant CHE0315275), and the ONR (Grant N00014-06-1-1032). Supporting Information Available: Ab initio computational data, geometry coordinates, and isodesmic reactions for cations and anions. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Fried, L. E.; Manaa, M. R.; Pagoria, P. F.; Simpson, R. L. Annu. ReV. Mater. Res. 2001, 31, 291-321. (2) Drake, G.; Hawkins, T.; Brand, A.; Hall, L.; McKay, M.; Vij, A.; Ismail, I. Propellants, Explos., Pyrotech. 2003, 28, 174-180. (3) (a) Singh, R. P.; Verma, R. D.; Meshri, D. T.; Shreeve, J. M. Angew. Chem. 2006, 45, 3584-3601, and references cited therein. (b) Gao, H.; Wang, R.; Twamley, B.; Hiskey, M. A.; Shreeve, J. M. Chem. Comm. 2006, 4007-4009. (4) Afeefy, H. Y.; Liebman, J. F. In Computational Thermochemistry; Irikura, K. K., Frurip, D. J., Eds.; ACS Symposium Series 677; American Chemical Society: Washington, DC, 1998; p 94. (5) Stewart, J. J. P. J. Mol. Model 2004, 10, 6-12. (6) (a) Xue, H.; Gao, Y.; Twamley, B.; Shreeve, J. M. Chem. Mater. 2005, 17, 191-198. (b) Xue, H.; Twamley, B.; Shreeve, J. M. J. Mater. Chem. 2005, 15, 3459-3465. (c) Xue, H.; Twamley, B.; Shreeve, J. M. AdV. Mater. 2005, 17, 2142-2146. (d) Xue, H.; Gao, Y.; Twamley, B.; Shreeve, J. M. Inorg. Chem. 2005, 44, 5068-5072. (e) Xue, H.; Twamley, B.; Shreeve, J. M. Inorg. Chem. 2005, 44, 7009-7013. (f) Jin, C.- M.; Ye, C. F.; Piekarski, C.; Twamley, B.; Shreeve, J. M. Euro. J. Inorg. Chem. 2005, 3760-3767. (g) Ye, C.; Xiao, J-. C.; Twamley, B.; Shreeve, J. M. Chem. Commun. 2005, 2750-2752. (h) Xue, H.; Arritt, S. W.; Twamley, B.; Shreeve, J. M. Inorg. Chem. 2004, 43, 7972-7977. (i) Gao, Y.; Arritt, S. W.; Twamley, B.; Shreeve, J. M. Inorg. Chem. 2005, 44, 1704-1712.

Computational Characterization of Energetic Salts (7) Jenkins, H. D. B.; Tudeal, D.; Glasser, L. Inorg. Chem. 2002, 41, 2364-2367. (8) Galvez-Ruiz, J. C.; Holl, G.; Karaghiosoff, K.; Klapo¨tke, T. M.;. Lohnwitz, K.; Mayer, P.; No¨th, H.; Polborn, K.; Rohbogner, C. J.; Suter, M.; Weigand, J. J. Inorg. Chem. 2005, 44, 4237-4253. (9) Schmidt, M. W.; Gordon, M. S.; Boatz, J. A. J. Phys. Chem. A 2005, 109, 7285-7295. (10) (a) Gao, H.; Ye, C.; Winter, R. W.; Gard, G. L.; Sitzmann, M. E.; Shreeve, J. M. Euro. J. Inorg. Chem. 2006, 3221-3226. (b) Xue, H.; Gao, H.; Twamley, B.; Shreeve, J. M. Euro. J. Inorg. Chem. 2006, 15, 29592965. (c) Gao, Y.; Ye, C.; Twamley, B.; Shreeve, J. M. Chem. Eur. J. 2006, 12, 9010-9018. (11) (a) Fried, L. E.; Glaesemann, K. R.; Howard, W. M.; Souers, P. C. CHEETAH 4.0 User’s Manual, Lawrence Livermore National Laboratory: Livermore, CA, 2004. (b) Lu, J. P. EValuation of the Thermochemical Code -CHEETAH 2.0 for Modelling ExplosiVes Performance, DSTO-TR-1199, DSTO, Edinburgh. 2001. (12) 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.; 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. (13) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989. (14) (a) Pople, J. A.; Binkley, J. R.; Seeger, R. Int. J. Quantum Chem. 1976, S10, 1-19. (b) Aikens, C. M.; Webb, S. P.; Bell, R. L.; Fletcher, D. G.; Schmidt, M. W.; Gordon, M. S. Theor. Chem. Acc. 2003, 110, 233253. (15) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221-7232. (16) Curtiss, L. A.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1993, 98, 1293-1298.

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10731 (17) Hehre, W. J.; Ditchfield, R.; Radom, L.; Pople, J. A. J. Am. Chem. Soc. 1970, 92, 4796-4801. (18) (a) Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynamic Properties of IndiVidual Substances, 4th ed.; CRC Press, Boca Raton, FL, 1994; Vol. 3. (b) Kirpichev, E. P.; Alekseev, A. P.; Rubtsov, Yu. I.; Manelis, G. B. Zh. Fiz. Khim. 1973, 47 (11), 2942. (c) Wagner, H.; Neumann, K. Z. Phys. Chem. (Munich) 1961, 28, 51-70. (d) Matyushin, Yu. N.; Kon’kova, T. S.; Titova, K. V.; Rosolovskii, V. Ya.; Lebedev, Yu. A. IzV. Akad. Nauk SSSR, Ser. Khim. 1985, (4), 787-790. (e) Gilliland, A. A.; Johnson, W. H. J. Res. Natl. Bur. Stand. (U.S.) 1961, 65A, 67-70. (f) Chavez, D. E.; Hiskey, M. A.; Naud, D. L. Propellants, Explos., Pyrotech. 2004, 29, 209-215. (g) Miroshnichenko, E. A.; Lebedev, Yu. A.; Apin, A. Ya. Zh. Fiz. Khim. 1967, 41 (6), 1488-1489. (h) Shidlovskii, A. A.; Semishin, V. I.; Shmagin, L. F. Zh. Prikl. Khim. 1962, 35, 756-759. (i) Sousa-Alonso, A.; Masaguer, J. R.; Coto-Pardo, M. V. Acta Cien. Compost. 1976, 13 (1-2), 61-68. (j) Venkatachalam, S.; Santhosh, G.; Ninan, K. N. Propellants, Explos., Pyrotech. 2004, 29 (3), 178-187. (k) Coburn, M. D. U.S. Patent, 4,028,154, 1977. (l) Matyushin, Yu. N.; Kon’kova, T. S.; Titova, K. V.; Rosolovskii, V. Ya.; Lebedev, Yu. A. IzV. Akad. Nauk SSSR, Ser. Khim. 1982, (3), 498-501. (m) Gardner, P. J.; Head, A. J.; Wu, X. J. Chem. Thermodyn. 1990, 22 (3), 301-305. (19) (a) Iyer, S.; Slagg, N. In Structure and ReactiVity; Liebman, J. F., Greenberg, A., Eds.; VCH Publishers: New York, 1988; Chapter 7. (b) Kohler, J.; Meyer, R. ExplosiVes, 9th ed.; VCH Publishers: New York, 1998. (20) Politzer, P.; Murray, J. X.; Grice, M. E.; Sjoberg, P. In Chemistry of Energetic Materials; Olah, G. A., Squire, D. R., Eds.; Academic Press: New York, 1991; Chapter 4. (21) (a) Kamlet, M. J.; Jacobs, S. J. J. Chem. Phys. 1968, 48, 23-35. (b) Kamlet, M. J.; Ablard, J. E. J. Chem. Phys. 1968, 48, 36-42. (c) Kamlet, M. J.; Dickinson, C. J. Chem. Phys. 1968, 48, 43-50. (22) (a) Gutowski, K. E.; Holbrey, J. D.; Rogers, R. D.; Dixon, D. A. J. Phys. Chem. B 2005, 109, 23196-23208. (b) Walter, D.; Hofmann, M. Acta Crystallogr. Sect. B 2002, B57, 489-493. (c) Ammon, H. L. Struct. Chem. 2001, 12, 205-212. (d) Ammon, H. L.; Mitchell, S. Propellants, Explos., Pyrotech. 1998, 23, 260-278. (e) Holden, J. R.; Du, Z.; Ammon, H. L. J. Comput. Chem. 1993, 14, 422-437. (f) Stine, J. R. Mat. Res. Soc. Symp. Proc. 1993, 296, 3-12. (g) Karfunkel, H. R.; Gdanitz, R. J. J. Comput. Chem. 1992, 13, 1171-1183. (h) Tarver, C. M. J. Chem. Eng. Data 1979, 24, 136-145. (i) Ye, C.; Shreeve, J. M. J. Phys. Chem. B 2007, 111, 1456-1461.