Densities, Heats of Formation, Energetic Properties, and

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Densities, Heats of Formation, Energetic Properties, and Thermodynamics of Formation of Energetic Nitrogen-Rich Salts Containing Substituted Protonated and Methylated Tetrazole Cations: A Computational Study Xiaowen Zhang, Weihua Zhu,* Tao Wei, Chenchen Zhang, and Heming Xiao* Institute for Computation in Molecular and Materials Science and Department of Chemistry, Nanjing UniVersity of Science and Technology, Nanjing 210094, China ReceiVed: June 2, 2010; ReVised Manuscript ReceiVed: June 29, 2010

We have performed density functional theory and volume-based thermodynamics calculations to study the effects of different substituents and energetic anions on the densities, heats of formation, energetic properties, and thermodynamics of formation for a series of energetic nitrogen-rich salts composed of the substituted protonated and methylated tetrazole cations with nitrate, dinitroamide, azide, and perchlorate anions. The volumes of the cations and anions were estimated to get the crystal densities of the salts from electronic structure calculations. The heats of formation (HOFs) of cations, anions, and lattice energies of the salts were calculated separately to obtain the HOFs of the salts based on Born-Haber energy cycles. According to the densities and HOFs, the detonation velocities and detonation pressures of the salts were predicted by the Kamlet-Jacobs equations. Finally, the lattice enthalpies and entropies were used to construct a thermodynamic cycle for salt formation to predict the possibility to synthesize the salts. This procedure provides a straightforward and inexpensive route to screen a large number of potential energetic ionic salts. 1. Introduction The development of new energetic materials is an emerging area of materials chemistry due to a need to replace materials used at present. The general requirements for these potential materials include: (i) high density and energy; (ii) thermal stability/storability; (iii) low handling hazards (e.g., low sensitivity to impact, friction, electrostatic discharge, and low toxicity); and (iv) simple production routes (i.e., three or less synthesis steps) for low cost.1 Energetic ionic salts are considered to be quite ideal for these requirements. They often possess advantages over nonionic materials. First, the ionic salts tend to have very negligible vapor pressure, which essentially eliminates the risk of exposure of personnel to new materials via a major exposure route (inhalation). Second, ionic compounds often have higher densities than atomically similar nonionic molecules. This can generally be attributed to the influence of Coulombic forces to form ordered and dense lattice structures in molecular assemblies. Finally, like inorganic molten salts, these salts are composed solely of ions and have high cohesive energy densities. Therefore, these energetic salts constitute a new class of energetic materials that have received a substantial amount of interest over the past years.2-16 A combination of different potential energetic cations and anions can produce a large number of different ionic salts. Among these energetic ions, the tetrazolium (positively charged tetrazole)17-30 or tetrazolide (negatively charged tetrazole)31-36 ring is an efficient fragment to enhance the performance of energetic materials. First, the heat of formation (HOF) of the tetrazole ring is relatively higher among the azoles. The crystalline HOFs increase from 58.5 to 109 to 237.2 kJ/mol for 1H-imidazole,37 1H-1,2,4-triazole,38 and 1H-tetrazole,39 respectively. Their high positive HOFs are directly attributable to the * To whom correspondence should be addressed. Tel.: +86-25-84315947805. Fax: +86-25-84303919. E-mail: [email protected] (W.Z.); [email protected] (H.X.).

large number of inherently energetic N-N and N-C bonds.17,40,41 Second, the tetrazole generates two molecules of nitrogen per ring upon decomposition. Although the tetrazole ring is (theoretically) energetically similar to an azide group, it is more stable and benign. Third, its structure is uniquely tunable because of its inherent amphoteric behavior. Like the imidazole ring,42 the tetrazole can both accept and donate protons.13 Moreover, careful selection of substituents on any of the positions in the ring and exchange of the counteranion or countercation influence many physical properties such as melting point, boiling point, and viscosity. The parent tetrazole ring can be chemically manipulated to obtain a desired set of energetic properties.43 Much work16,20,21,29,31,44 has concentrated on the synthesis and properties of many tetrazolium-based salts containing different substituents. The energetic salts containing substituted tetrazolium cations, 5,5′-azotetrazolate anions, and bistetrazolates exhibit outstanding HOFs, thermal stabilities, and desirable explosive properties. Among them, the salts of 5,5′-azotetrazolate with protonated nitrogen bases are unique gas-generating agents producing little smoke or residue, which may lead to a variety of applications including gas generators and explosives.5 As for the substituted tetrazolium salts,41 their substituents mainly include amino or methyl groups. For example, Klapo¨tke et al.18 reported that 5-aminotetrazolium nitrate is a powerful and promising explosive with a good oxygen balance and low sensitivity. However, there is still lacking systematical and comprehensive molecular design for energetic salts containing substituted protonated and methylated tetrazole cations. In this work, we performed density functional theory (DFT) and volume-based thermodynamics calculations to screen protonated and methylated tetrazole energetic salts with high energy and good stability. The combination of tetrazolium cations containing different substituents (-CH3, -NO2, -NF2, -CN, -N3, -NH2) with some familiar energetic anions (NO3-,

10.1021/jp1050782  2010 American Chemical Society Published on Web 07/12/2010

Thermodynamics of Formation of Energetic Nitrogen-Rich Salts

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∆Hοf (salt, 298 K) ) ∆Hοf (cation, 298 K) +

SCHEME 1: Born-Haber Cycle for the Formation of Energetic Salts

∆Hοf (anion, 298 K) - ∆HL

(3)

where ∆HL is the lattice energy of the ionic salts, which could be predicted by the formula suggested by Jenkins et al.55 as

∆HL ) UPOT + [p(nM/2 - 2) + q(nX/2 - 2)]RT

(4) N(NO2)2-, N3-, ClO4-)23,45-47 was made to establish the broad relative potential to comprehensively evaluate their performances and thermodynamics of formation. Our focus is primarily upon investigating the important role of different substituents and energetic anions in the design of efficient high-energy salts. The remainder of this Article is organized as follows. A brief description of our computational method is given in section 2. The results and discussion are presented in section 3, followed by a summary of our conclusions in section 4. 2. Computational Method One of the most important physical properties of a solid energetic material is its density. Several approaches48-51 have been developed to accurately predict the crystal density without a prior knowledge of the crystal structure. The methods have demonstrated that the molecular volume alone is sufficient to predict crystal density. For an ionic crystal with formula unit MpXq, its volume is simply the sum of the volumes of the ions contained in the formula unit:52

V ) pVM+ + qVX-

(1)

where M denotes the cation and X denotes the anion. Because the volumes of individual ions are able to be evaluated using the DFT procedure, we used eq 1 to calculate formula unit volumes for ionic crystals. For those compounds that contain hydrogen atoms, a “corrected” molecular volume using a molecular structure optimized at the DFT level can be calculated using:52

V(corrected)Opt ) V(uncorrected)Opt - [0.6763 + 0.9418 × (no. of hydrogen atoms in the ion)] (2) Rice et al.52 reported that the formula unit volumes calculated using the optimized geometries at the B3LYP/6-31G** level and corrected for the number of hydrogen atoms produce average and rms deviations from experimental values of 1.3% and 5.0%, respectively, in much better agreement than the uncorrected values (5.6% and 7.3%, respectively). Therefore, we used the B3LYP/6-31G** method to calculate the molecular volumes for the energetic tetrazolium salts studied here. The volume of each ion was defined as inside a contour of 0.001 electrons/bohr3 density that was evaluated using a Monte Carlo integration. We performed 100 single-point calculations for the optimized structure of each ion to get an average volume. For the salts, the theoretical density was obtained from the molecular weight divided by the average molecular volume. This method has been successfully applied to high-nitrogen compounds.52-54 Based on a Born-Haber energy cycle (Scheme 1), the heat of formation of a salt can be simplified by the formula

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 linear polyatomic ions, and 6 for nonlinear polyatomic ions. The equation for lattice potential energy UPOT (kJ mol-1) has the form:

UPOT ) γ(F/M)1/3 + δ

(5)

where F (g cm-3) is the density, M (g mol-1) is the chemical formula mass of the ionic material, and the coefficients γ (kJ mol-1 cm) and δ (kJ mol-1) are taken from ref 55. The HOFs of the cations were computed using the method of isodesmic reactions.56 The isodesmic reactions used to obtain the HOFs of the tetrazolium cations at 298 K are displayed in Scheme 2. To obtain more accurate HOFs, the geometric optimization of the structures and frequency analyses were carried out at the B3LYP/6-31++G* level, and single-point energies were calculated at the MP2/6-311++G** level. According to the Kamlet-Jacobs equations,57 density (F) affects detonation performance; detonation pressure (P) is dependent on the square of the density, and the detonation velocity (D) is proportional to the density:

j 1/2Q1/2)1/2(1 + 1.30F) D ) 1.01(NM

(6)

j 1/2Q1/2 P ) 1.558F2NM

(7)

where each term in eqs 6 and 7 is defined as follows: D, the detonation velocity (km s-1); P, the detonation pressure (GPa); j , the N, the moles of detonation gases per gram explosive; M -1 average molecular weight of these gases (g mol ); Q, the heat of detonation (J g-1); and F, the loaded density of explosives (g cm-3). For known explosives, their Q and F can be measured experimentally; thus, their D and P can be calculated according to eqs 6 and 7. However, for unknown compounds, their Q and SCHEME 2: Isodesmic Reactions for the Protonated and Methylated Tetrazole Cations

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F cannot be evaluated from experimental measures. Therefore, to estimate their D and P, we first need to calculate their Q and F. For the tetrazolium salts, the theoretical density was suggested to substitute F, and Q was evaluated by the HOF difference between products and explosives according to the principle of exothermic reactions. Based on the F and Q values, the corresponding D and P values can be evaluated. In practice, the D and P values obtained from F can be regarded as their upper limits (maximum values) because F from this method is slightly greater than the loading density of the explosive. To make the formation reaction of a salt be thermodynamically favorable, the free energy change, ∆Grxn, must be less than or equal to zero. The generalized reaction for forming a salt is written as follows:

tetrazole(gas) + RX(gas) f {[tetrazole · R][X]}(salt)

(8) Because two free gas-phase particles in reaction 8 react to form a solid, the entropy change for this process is negative, and this make the term -T∆S be positive, destabilizing contribution from the term. Therefore, the ability for the salt to form will be governed by how negative the enthalpy is. The estimated entropies (J K-1 mol-1) of the substituted tetrazolium salts were calculated by using the relationship developed by Glasser and Jenkins58 for organic solids (OS):

S0298(OS) ) 1.285(M/F) + 57

(9)

Here, F is the same molecular density (g cm-3) as employed in the lattice energy equation above. The calculations were performed with the Gaussian 0359 suite of programs. The optimizations were performed without any symmetry restrictions using the default convergence criteria in the programs. All of the optimized structures were characterized to be true local energy minima on the potential energy surfaces without imaginary frequencies. 3. Results and Discussion 3.1. Density Predictions. High density is desirable for energetic materials because more energy will be packed per unit volume. Here, we investigate the effects of different substituents and anions on the densities of the protonated and methylated tetrazole salts. Formula unit volumes to be used in predicting the crystal densities of ionic crystals were determined using eq 1. The volumes of the cations and anions contained in the tetrazolium salts were calculated using the optimized structures. The frameworks of a series of the protonated (I-VI) and methylated (VII-XII) tetrazole cations are displayed in Figure 1. Table 1 lists the uncorrected and corrected densities of the protonated and methylated tetrazole nitrate salts along with available experimental18,60 and other calculated22,26,61 values. The results show that our computational method to predict the densities of ion compounds is reasonably creditable. When the substituent is -NO2 or -NF2, an increase in the density value of its substituted protonated and methylated tetrazole nitrate salts is large as compared to tetrazolium nitrate (unsubstituted F ) 1.70 g cm-3). This may be attributed to a big π bond formed between the tetrazole ring and substituent, which is favorable to molecular packing in crystal. It is wellknown that π bond interactions not only could help stabilize

Figure 1. Frameworks of protonated (I-VI) and methylated (VII-XII) tetrazole cations.

energetic compounds substantially, but also could increase their density markedly. For the nitrate salts containing the protonated tetrazole cations (I-VI), the substitution of -N3 slightly increases the density value of tetrazolium nitrate, while for the nitrate salts containing the methylated tetrazole cations (VII-XII), the case is quite the contrary. When the H atom of the tetrazole cation is replaced by -CH3, -CN, or -NH2, the density of its nitrate salt is smaller than that of tetrazolium nitrate except for II6 and IV6. Among the nitrate salts containing the cation series I1-I6, the NF2-substituted tetrazolium nitrate has the largest density. The same is true of the salts containing the cation series II, III, IV, V, VI, VII, VIII, IX, X, XI, or XII. This is because incorporating the -NF2 group into the tetrazole cation could enhance the mass of its salts intensively but affect its volume relatively little. This indicates that the -NO2 or -NF2 group is an effective substituent for increasing the densities of the tetrazolium nitrate salts. Figure 2 presents a comparison of the densities of the protonated and methylated tetrazole nitrate salts. The densities of the nitrate salts containing the protonated tetrazole cations



TABLE 1: Information of Volume and Density for the Protonated and Methylated Tetrazole Nitrate Salts cationsa

Vuncorrected (cm3 mol-1)

Vcorrected (cm3 mol-1)

Funcorrected (g cm-3)

Fcorrected (g cm-3)

tetrazolium

80.1

78.0

1.66

1.70

I1 I2 I3 I4 I5 I6 II1 II2 II3 II4 II5 II6 III1 III2 III3 III4 III5 III6 IV1 IV2 IV3 IV4 IV5 IV6 V1 V2 V3 V4 V5 VI1 VI2 VI3 VI4 VI5

Protonated Tetrazole (I-VI) Salts 95.4 92.1 1.54 1.60 100.3 98.8 1.77 1.80 95.5 94.0 1.93 1.96 95.5 94.0 1.65 1.68 101.1 99.5 1.72 1.75 90.9 88.2 1.63 1.68 92.7 89.5 1.59 1.64 98.9 97.3 1.80 1.83 97.0 95.4 1.90 1.93 95.0 93.4 1.66 1.69 101.6 100.0 1.71 1.74 89.3 86.6 1.66 1.71 108.8 104.5 1.48 1.54 121.3 120.3 1.84 1.85 113.2 112.2 2.08 2.09 111.2 110.2 1.65 1.66 124.8 123.8 1.72 1.74 100.0 96.7 1.63 1.69 107.8 103.4 1.49 1.56 120.2 119.2 1.86 1.87 114.0 113.0 2.06 2.08 110.6 109.6 1.65 1.67 123.1 122.1 1.75 1.76 98.9 95.6 1.65 1.70 104.0 100.2 1.56 1.62 109.8 107.7 1.76 1.79 106.1 104.0 1.87 1.91 106.8 104.7 1.62 1.65 111.2 109.1 1.70 1.73 102.2 98.4 1.59 1.65 107.4 105.3 1.80 1.83 106.4 104.3 1.87 1.91 104.7 102.6 1.65 1.69 112.6 110.5 1.68 1.71

VII1 VII2 VII3 VII4 VII5 VII6 VIII1 VIII2 VIII3 VIII4 VIII5 VIII6 IX1 IX2 IX3 IX4 IX5 IX6 X1 X2 X3 X4 X5 X6 XI1 XI2 XI3 XI4 XI5 XII1 XII2 XII3 XII4 XII5

Methylated 109.3 113.6 113.4 110.7 116.6 106.2 107.9 111.7 111.2 109.4 116.8 104.8 121.6 133.6 126.6 123.1 137.4 114.9 122.5 133.5 128.6 126.1 138.2 113.1 118.0 121.7 119.7 120.0 125.8 120.1 122.6 119.4 118.8 126.5

Tetrazole (VII-XII) Salts 104.9 1.47 1.53 110.9 1.69 1.73 110.7 1.75 1.79 108.1 1.55 1.59 113.9 1.61 1.65 102.4 1.52 1.58 103.5 1.49 1.56 109.0 1.72 1.76 108.5 1.78 1.82 106.8 1.57 1.61 114.2 1.61 1.65 101.0 1.55 1.60 116.1 1.44 1.51 131.5 1.77 1.80 124.5 1.97 2.00 121.0 1.60 1.63 135.3 1.67 1.69 110.5 1.54 1.60 117.0 1.43 1.50 131.4 1.77 1.80 126.5 1.94 1.97 124.0 1.56 1.59 136.1 1.66 1.68 108.7 1.57 1.63 113.0 1.49 1.56 118.4 1.70 1.75 116.4 1.78 1.83 116.8 1.56 1.60 122.6 1.61 1.66 115.2 1.47 1.53 119.3 1.69 1.73 116.1 1.78 1.83 115.5 1.57 1.62 123.3 1.60 1.65

Flit. (g cm-3)

1.847b

1.727

c

1.506c

1.50d, 1.55e

1.55f

a Average volume from 100 single-point calculations at the B3LYP/6-31G**. b The experimental data are taken from ref 18. c The calculated datum is taken from ref 26. d The experimental datum is taken from ref 60. e The calculated datum is taken from ref 61. f The calculated datum is taken from ref 22.

(I-VI) are larger than those of the nitrate salts containing the methylated tetrazole cations (VII-XII) with the same substituent

Figure 2. Comparison of the densities of the protonated and methylated tetrazole nitrate salts.

and substitution position. For the protonated tetrazole series I and II, different position of the substituent does not produce an evident effect on the densities of their nitrate salts with the same substituent. A similar situation is also found in the cation series V and VI. The same is true of the methylated tetrazole seires (VII vs VIII and XI vs XII). Also, we note that for the cations with two same substituents III and IV (IX and X), different position of the positive charge does not obviously affect the densities of their nitrate salts. Overall, for the protonated tetrazole series (I-VI), the nitrate salts of the tetrazole cations with two same substituents (III and IV) have higher densities than those with single substituent (I and II) and with two different substituents (V and VI). A similar case is also observed in the nitrate salts containing the methylated tetrazole series (VII-XII). The densities for the salts comprised of the protonated (I-VI) and methylated (VII-XII) tetrazole cations with dinitroamide, azide, and perchlorate anions are listed in Table S1 of the Supporting Information for brevity. When the anion is ClO4-, its corresponding salts have the largest densities among the salts with the same cation. The dinitroamide salts have higher densities than the nitrate ones with the same cation, while the azide salts have the smallest densities. For the perchlorate salts containing the substituted tetrazole cations, the substitution of the -NO2 or -NF2 group increases the density value of tetrazolium perchlorate (unsubstituted F ) 1.89 g cm-3), while the substitution of the -CH3, -CN, -NH2, or -N3 group plays the opposite effect except for the salts containing the cation I5. The same is true of the dinitroamide salts (the density of the dinitroamide salts containing tetrazolium is 1.78 g cm-3). However, for the azide salts, the situation is different. Incorporating the -NO2, -NF2, or -N3 group into the tetrazole cation enhances the density of the azide salts containing tetrazolium (unsubstituted F ) 1.52 g cm-3), whereas for the substituent -CH3, -CN, or -NH2, the case is quite the contrary. This shows that incorporating different anions hardly alters the variation trends of the densities under the influences of different substituents drawn from the substituted tetrazolium nitrates. 3.2. Heats of Formation. The HOF is frequently taken to be indicative of the “energy content” of an energetic compound. Therefore, it is very important to predict the HOF. The calculated HOFs of reference compounds in the isodesmic reactions are listed in Table 2 along with available experimental values. Table 3 presents the HOFs for the protonated and methylated tetrazole cations and their nitrate salts and the lattice energies of their salts. It is seen in Table 3 that our calculated HOFs agree reasonably with other calculated values within small deviation

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TABLE 2: Calculated and Experimental Gas-Phase Heats of Formation (kJ mol-1) for Small Molecules and Ions at 298 K molecules

∆Hf° (calc.)

∆Hf° (expt.)

CH4 NH3 C 2H 6 N 2H 4 CH3NH2 CH3NO2 CH3N3 CH3NF2

-73.6 -47.2a -84.6a 96.2a -22.5a -74.65a 296.5a -115.2a

-74.4 -46.1b -84.8b 95.4b -22.5b -80.8b

a

b

∆Hf° (calc.)

ions

∆Hf° (expt.)

+

H 1,3-H-tetrazolium 1,4-H-tetrazolium NO3N(NO2)2N3ClO4-

1536.2b 1027.5c(1026.8d) 1025.8c(1022.2d) -308c(-307.9f) -128.4c(-123.8e,-162h) 198.1c(197.2f) -278.2c(-277.8f, -278h)

-306.4g 181b -331.1g

a Calculated values at the G2 level. b The data are taken from ref 62. c Protonation reaction: tetrazole + H+ f tetrazolium, NO3- + H+ f HNO3, N(NO2)2- + H+ f HN(NO2)2, N3- + H+ f HN3, ClO4- + H+ f HClO4. d The data are taken from ref 43. e The datum is taken from ref 24. f The datum is taken from ref 44. g The datum is taken from ref 41. h The datum is taken from ref 7.

TABLE 3: Heats of Formation for the Protonated and Methylated Tetrazole Cations and Their Nitrate Salts and Lattice Energies of These Salts cations tetrazolium I1 I2 I3 I4 I5 I6 II1 II2 II3 II4 II5 II6 III1 III2 III3 III4 III5 III6 IV1 IV2 IV3 IV4 IV5 IV6 V1 V2 V3 V4 V5 VI1 VI2 VI3 VI4 VI5

∆Hf° cation (kJ mol-1)

lattice energy (kJ mol-1)

1021.2 572.0 protonated tetrazole (I-VI) salts 968.6 547.4 1171.7 537.4 1113.7 544.5 1392.3 544.5 1480.0 536.3 1087.4 553.9 925.3 551.7 1106.9 539.5 1046.2 542.3 1237.0 545.4 1355.1 535.5 933.2(975.6)a 556.6 (568)b 888.8 529.4 1250.5 510.1 1152.8 519.5 1619.4 522 1831.8 506.3 997.8 (1055.2)c 540.4 892.3 530.8 1244.0 511.3 1157.1 518.5 1622.2 522.7 1839.0 508.1 1010.8 542 999.0 535.3 1175.5 525.1 1122.5 530 1308.7 529.2 1419.3 523.4 900.2(937.2)c 537.9 1086.5 528.3 1017.8 529.6 1291.4 531.9 1400.3 521.6

calcd ∆Hf° (kJ mol-1)

cations

∆Hf° cation (kJ mol-1)

lattice energy (kJ mol-1)

calcd ∆Hf° (kJ mol-1)

141.3 113.3 326.4 261.3 539.9 635.8 225.6 65.7 259.5 196 383.7 511.7 68.7 (87)b 51.5 432.5 325.4 789.5 1017.6 149.5 (252.7)d 53.6 424.8 330.7 791.6 1023.0 160.9 155.7 342.5 284.6 471.7 588.0 54.4 250.3 180.3 451.6 570.9

VII1 VII2 VII3 VII4 VII5 VII6 VIII1 VIII2 VIII3 VIII4 VIII5 VIII6 IX1 IX2 IX3 IX4 IX5 IX6 X1 X2 X3 X4 X5 X6 XI1 XI2 XI3 XI4 XI5 XII1 XII2 XII3 XII4 XII5

methylated tetrazole (VII-XII) salts 931.9 528.8 1129.0 521.1 1063.7 521.4 1346.6 524.7 1435.9 517.4 1046.3 532.2 893.1 530.7 1059.7 523.5 999.6 524.1 1190.3 526.4 1319.8 517.1 898.3 534.1 851.5 (844.8)a 514.9 1210.8 498.4 1107.8 505.6 1565.2 509.3 1796.6 494.6 964.7 521.6 846.0(981.5)e 513.8 1197.3 498.4 1096.1 503.4 1558.4 506 1789.4 493.9 964.0 523.9 962.6 (966.8)a 518.5 (513.3)a 1131.3 512.2 1083.4 514.5 1261.5 514.1 1401.6 507.6 865.2 516 1048.8 511.2 980.3 514.8 1252.5 515.5 1365.7 506.8

95.2 (126.5)b 300 234.4 514 610.6 206.2 54.5 228.3 167.6 356 494.8 56.3 28.7 404.5 294.3 748 994.1 135.2 (174.4)d 24.3 391 284.8 744.5 987.6 132.2 136.2 (129.7)e 311.2 261 439.5 586.1 41.3 229.7 157.6 429.1 551

a The calculated data are taken from ref 44. b The calculated data are taken from ref 60. c The calculated data are taken from ref 24. d The calculated data are taken from ref 26. e The calculated data are taken from ref 41.

except for III6. When the substituent is -NO2, -NF2, -CN, -N3, or -NH2, its substituted protonated and methylated tetrazole nitrate salts have higher HOFs than tetrazolium nitrate (unsubstituted HOF ) 141.3 kJ mol-1) except for II6 and VIII6, while for the substituent -CH3, the case is quite the contrary except for V1. Among the nitrate salts containing the cation series I1-I6, the N3-substituted tetrazolium nitrate has the largest HOF. The same is true of the salts containing the cation series II, III, IV, V, VI, VII, VIII, IX, X, XI, or XII. This may be because nitrogen-nitrogen bonds of energetic compounds usually contribute more to a positive HOF than do nitrogen-carbon bonds.44 These observations indicate that the -N3 or -CN group

plays a very important role in increasing the HOFs of the tetrazolium nitrate salts. This conclusion is consistent with a previous report60 that the HOFs of the substituted triazolium salts enhance intensively as the numbers of -N3 increase. Figure 3 presents a comparison of the HOFs of the protonated and methylated tetrazole nitrate salts. The HOFs of the nitrate salts containing the protonated tetrazole cations (I-VI) are larger than those of the nitrate slats containing the methylated tetrazole cations (VII-XII) with the same substituent and substitution position. For the protonated tetrazole series I and II, different position of the substituent does not produce an evident effect on the HOFs of their nitrate salts with the same substituent. A



Figure 3. Comparison of the HOFs of the protonated and methylated tetrazole nitrate salts.

similar situation is also found in the cation series V and VI. The same is true of the methylated tetrazole seires (VII vs VIII and XI vs XII). Note that for the cations with single substituent I and II (VII and VIII), the nitrate salts of the tetrazolium with a substituent in the N-position of the ring have higher HOFs than those with the same substituent in the C-position. This shows that the substituent bonded to the nitrogen in the tetrazolium ring contributes more positively to the HOFs of its salt than the one bonded to the carbon. For the cations with two same substituents III and IV (IX and X), different position of the positive charge does not obviously affect the HOFs of their nitrate salts. Overall, for the protonated tetrazole series (I-VI), the nitrate salts of the tetrazole cations with two same substituents (III and IV) have higher HOFs than those with single substituent (I and II) and with two different substituents (V and VI). A similar case is also observed in the nitrate salts containing the methylated tetrazole series (VII-XII). The HOFs for the salts comprised of the protonated (I-VI) and methylated (VII-XII) tetrazole cations with dinitroamide, azide, and perchlorate anions are listed in Table S2 of the Supporting Information for brevity. When the anion is N3-, its corresponding salts have the largest HOFs among the salts with the same cation. The dinitroamide salts have higher HOFs than the perchlorate ones with the same cation, while the nitrate salts have the smallest HOFs. For the azide salts containing the substituted tetrazole cations, the substitution of the -NO2, -NF2, -CN, -N3, or -NH2 group increases the HOF value of tetrazolium azide (unsubstituted HOF ) 641.9 kJ mol-1) except for VII6, VIII6, IX6, and X6, while the substitution of the -CH3 group plays the opposite effect except for the salts containing the cation I5. The same is true of the dinitroamide and perchlorate salts (the HOFs of the dinitrazmide and perchlorate salts containing tetrazolium are 356.7 and 192.8 kJ mol-1, respectively). This shows that incorporating different anions does not affect the variation trends of the HOFs under the influences of different substituents drawn from the substituted tetrazolium nitrates. 3.3. Energetic Properties. Detonation velocity and detonation pressure are two important performance parameters for an energetic material. Table 4 shows the predicted heats of detonation (Q), detonation velocities (D), pressures (P), and oxygen balance (OB) for the protonated and methylated tetrazole nitrate salts along with those of commonly used explosives RDX (1,3,5-trnitro-1,3,5-triazinane) and HMX (1,3,5,7-tetranitro1,3,5,7-tetrazocane).

The calculated heats of detonation in Table 4 show that for the protonated tetrazole (I-VI) nitrate salts, the substitution of the group -NF2, -CN, or -N3 increases its value of detonation heat as compared to tetrazolium nitrate (unsubstituted Q ) 1435.3 J g-1), whereas for the substituent -CH3, -NO2, or -NH2, the case is quite the contrary except for I6. However, for the methylated tetrazole (VII-XII) nitrate salts, the situation is different. When the substituent is -NO2, -NF2, -CN, or -N3, its substituted methylated tetrazole nitrate salts have higher heats of detonation than tetrazolium nitrate (unsubstituted Q ) 1435.3 J g-1), while for the substituent -CH3 or -NH2, the case is quite the contrary. This indicates that the -NF2, -CN, or -N3 group is an effective substituent for enhancing the heat of detonation of the substituted tetrazolium nitrates. As is shown in Table 4, our calculated detonation properties of the protonated and methylated tetrazole nitrate salts agree with available experimental22 and other theoretical26,60 values. When the substituent is -NO2, -NF2, or -N3, its substituted protonated and methylated tetrazole nitrate salts have higher D and P values than tetrazolium nitrate (unsubstituted D ) 8.64 km s-1 and P ) 32.07 GPa) except for II2, III2, IV2, VII5, VIII5, XI5, and XII5, while for the substituent -CH3, -CN, or -NH2, the case is quite the contrary. It is observed from Table 4 that the D and P values of I3, II3, III3, IV3, V3, VI3, VIII3, IX3, X3, and XI3 are very high and above or close to 9.0 km s-1 and 40.0 GPa, respectively. This shows that the substitution of the -NO2, -NF2, or -N3 group is favorable for increasing the detonation properties of the substituted tetrazolium nitrate salts. Oxygen balance (OB) is used to indicate the degree to which a compound can be oxidized and to classify energetic materials as either oxygen-deficient or oxygen-rich. OB values near or greater than zero are desirable to reduce toxic fume gases such as carbon monoxide. In general, the higher is the oxygen balance, the greater is the energetic performance. Therefore, oxygen balance is another one of the most important criterion for selecting potential high-energy salts. It is found from Table 4 that when the substituent is -NO2, -NF2, or -N3, the OB values of its substituted protonated tetrazole nitrate salts are close to or greater than zero and superior to those of RDX and HMX. For the methylated tetrazole nitrates, the OB values of their NO2-substituted salts are near zero and higher than those of RDX and HMX. Overall, the higher is the oxygen balance, the larger are the D and P values, and the better is the performance of the tetrazolium nitrate salts. Thus, it can be

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TABLE 4: Predicted Heats of Detonation (Q), Detonation Velocities (D), Pressures (P), and Oxygen Balance (OB) for the Protonated and Methylated Tetrazole Nitrate Saltsa cations

Q (J g-1)

D (km s-1)

tetrazolium

1435.3

8.64

I1 I2 I3 I4 I5 I6 II1 II2 II3 II4 II5 II6 III1 III2 III3 III4 III5 III6 IV1 IV2 IV3 IV4 IV5 IV6 V1 V2 V3 V4 V5 VI1 VI2 VI3 VI4 VI5

Protonated Tetrazole (I-VI) Salts 1327.1 7.84 25.29 1291.3 8.67 33.39 1554.8 9.34 40.63 1777.7 8.64 31.75 1746.1 9.21 36.95 1463.1 8.64 31.70 1249.8 7.88 26.00 1201.5 8.61 33.17 1470.1 9.11 38.31 1541.6 8.37 29.92 1575.4 8.94 34.74 29.89(35.7)b 1209.8 8.34(8.90)b 1153.4 7.29 21.38 1014.9 8.25 30.75 1465.2 10.07 48.99 1831.4 8.33 29.31 1703.1 9.06 35.62 29.78(33.3)c 1250.1 8.36(8.77)c 1156.5 7.34 21.83 1006.7 8.29 31.19 1470.6 10.02 48.38 1834.2 8.37 29.64 1709.1 9.15 36.65 1266.7 8.45 30.68 1300.1 7.93 26.10 1360.6 8.83 34.49 1729.9 9.96 45.59 1560.5 8.34 29.30 1575.5 8.96 34.81 25.45(25.6)d 1150.6 7.79(8.10)d 1246.5 8.78 34.55 1604.7 9.76 43.68 1532.7 8.42 30.19 1553.8 8.85 33.66

-38.1 18.0 0.0 -20.3 0.0 -10.8 -38.1 18.0 0.0 -20.3 0.0 -10.8 -64.6 32.3 3.4 -30.6 3.7 -14.7 -64.6 32.3 3.4 -30.6 3.7 -14.7 -39.5 12.4 -4.0 -23.1 -4.2 -39.5 12.4 -4.0 -23.1 -4.2

VII1 VII2 VII3 VII4 VII5 VII6 VIII1 VIII2 VIII3 VIII4 VIII5 VIII6 IX1 IX2 IX3 IX4 IX5 IX6 X1 X2 X3 X4 X5 X6 XI1 XI2 XI3 XI4 XI5 XII1 XII2 XII3 XII4 XII5 RDX HMX

Methylated 1218.4 1710.3 1705.3 1659.8 1641.2 1374.6 1157.9 1621.0 1624.6 1440.2 1494.0 1153.4 1030.1 1567.5 1869.8 1705.6 1724.1 1162.2 1024.1 1553.8 1860.6 1701.3 1717.4 1158.1 1170.2 1625.3 1640.4 1460.2 1517.7 1041.3 1531.3 1524.2 1446.9 1476.3 1597.39 1633.88

-64.6 -8.3 -24.2 -46.5 -25.5 -39.5 -64.6 -8.3 -24.2 -46.5 -25.5 -39.5 -86.9 10.1 -16.1 -52.8 -17.5 -40.7 -86.9 10.1 -16.1 -52.8 -17.5 -40.7 -63.6 -11.6 -26.3 -47.1 -27.6 -63.6 -11.6 -26.3 -47.1 -27.6 -21.6 -21.6

a

P (GPa) 32.07

Tetrazole (VII-XII) Salts 7.37 21.78 8.98 34.95 9.21 37.50 7.97 26.12 8.50 30.39 7.92 25.67 7.34 21.82 8.97 35.26 9.23 38.09 7.76 24.93 8.29 28.87 7.65 24.17 6.99 19.37 9.03 36.24 10.32 50.24 7.91 26.10 8.78 32.94 25.21(23.4)c 7.82(7.682)c 6.94 18.99 9.02 36.12 10.19 48.51 7.78 24.81 8.74 32.52 7.90 26.00 7.53 22.98 8.98 35.13 9.31 38.83 7.84 25.32 8.41 29.80 20.88(20.2)d 7.23(7.50)d 8.80 33.57 9.16 37.64 7.88 25.76 8.32 29.05 e 34.75[34.70] 8.88[8.75] 9.28[9.10] 39.21[39.00]

OB (%)f -6.0

Average density from 100 single-point calculations at the B3LYP/6-31G**. b The calculated values in parentheses are taken from ref 60. c The calculated values in parentheses are taken from ref 26. d The experimental values in parentheses are taken from ref 22. e The experimental values in square brackets are taken from refs 63-65. f Oxygen balance (%) for CaHbOcNd: 1600 × (c - 2a - b/ 2)/Mw; Mw ) molecular weight of the corresponding compounds.

concluded that the -NO2 or -NF2 group is a good substituent for improving oxygen balance in designing potential high-energy salts. However, it is clear that overmuch oxygen is not favorable for advancing explosive performance of the high-energy salts. The primary reason is that the overmuch oxygen will produce O2 that takes away a great deal of energy during explosion of high-energy salts. Therefore, one had better keep the value of oxygen balance around zero in designing high-energy salts. Figure 4 displays a comparison of the calculated Q, D, and P values for the protonated and methylated tetrazole nitrate salts. Most of the Q, D, and P values of the protonated tetrazole (I-VI) nitrate salts are larger than those of the methylated tetrazole (VII-XII) nitrate salts with the same substituent and substitution position. For the protonated tetrazole series I and II, different position of the substituent does not produce an evident effect on the Q, D, and P values of their nitrate salts with the same substituent. A similar situation is also observed in the cation series V and VI. The same is true of the methylated tetrazole series (VII vs VIII and XI vs XII). Also, we note that for the cations with single substituent I and II (VII and VIII), the nitrate salts of the tetrazolium with a substituent in the N-position of the ring have higher Q, D, and P values than those with the same substituent in the C-position. This shows that the substituent bonded to the nitrogen in the tetrazolium ring is helpful for increasing the energetic properties of its salt than the one bonded to the carbon position. For the cations with two same substituents III and IV (IX and X), different position of the positive charge does not obviously affect the Q, D, and P values of their nitrate salts. Overall, for the protonated tetrazole series (I-VI), the nitrate salts of the tetrazole cations with two same substituents (III and IV) have higher Q, D, and P values than those with single substituent (I and II) and with two different substituents (V and VI). A similar case is also found in the nitrate salts containing the methylated tetrazole series (VII-XII). The D and P values of the salts I2-3, I5-6, II2-3, II5-6, III2-3, III5-6, IV2-3, IV5-6, V2-3, V5, VI2-3, VI5, VII2-3, VII5, VIII2-3, IX2-3, IX5, X2-3, X5, XI2-3, and XII3 are close to or higher than those of RDX. Yet only I3, I5, II3, III3, III5, IV3, IV5, V3, VI3, VII3, VIII3, IX2-3, X2-3, XI3, and XII3 have good detonation performance (D and P) near or over HMX. This indicates that the NF2-substituted tetrazolium nitrate salts have the best energetic properties among the salts. The main reason is that, although the heats of formation of the NF2-substituted tetrazolium nitrate salts are not outstanding among these energetic salts, their high densities compensate this disadvantage. The Q, D, P, and OB values for the salts comprised of the protonated (I-VI) and methylated (VII-XII) tetrazole cations with dinitroamide, azide, and perchlorate anions are listed in Table S3 of the Supporting Information for brevity. As a whole, the salts containing the anion perchlorate have the largest energetic properties among the salts with the same cation. The dinitroamide salts have higher energetic properties than the nitrate ones with the same cation, while the azide salts have the smallest ones. Incorporating different anions hardly affects the variation trends of the energetic properties under the influences of different substituents drawn from the substituted tetrazolium nitrates. 3.4. Thermodynamics of Salt Formation. New energetic compounds not only should have desirable explosive properties, but also should be cheap and easy to synthesize. In this section, we predict the thermodynamics of formation of the substituted protonated and methylated tetrazole salts from typical starting materials. The protonated and methylated tetrazole salts contain-



Figure 4. Comparison of the heats of detonation, detonation velocities, and detonation pressures of the protonated and methylated tetrazole nitrate salts.

SCHEME 3: Synthesis of the Protonated and Methylated Tetrazole Salts

SCHEME 4: Born-Haber Cycle for the Formation of the Protonated and Methylated Tetrazole Salts

ing different substituents on the ring were synthesized through the reactions of neutral substituted tetrazole with hydrogen chloride or chloromethane. Metathesis with AgNO3, AgN(NO2)2, AgN3, or AgClO4 formed substituted tetrazolium nitrate, dinitramide, azide, or perchlorate, respectively (Scheme 3).20,60 The key step is the first one.42 Therefore, if the first step could come true, the corresponding tetrazolium salts can be synthesized. The Born-Haber thermodynamic cycle for the formation of the protonated and methylated tetrazole salts is displayed in Scheme 4. The overall enthalpy of reaction (∆Hrxn) for formation of the substituted tetrazolium salt is given by the enthalpy for the reaction between a substituted tetrazole base and a protonating or methylating agent (RCl) 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 H-Cl or CH3-Cl bond heterolytically. ∆H2 is the affinity of the tetrazole for H+ or CH3+. ∆H3 is directly related to the lattice energy for salt formation. Table 5 lists the thermodynamic data ∆H1, ∆H2, ∆H3, ∆Hrxn, ∆Srxn, and ∆Grxn of the protonated and methylated tetrazole chloride salts. In Table 5, all of the free energies of reaction for the CH3substituted tetrazolium salts are negative. This means that they could be synthesized by the proposed reactions here, which is in agreement with the experimental reports.16,20,60 In addition, the NH2-substituted tetrazolium salts also have negative free energies of reaction except for the salts containing the cations V2-4, VI2-4, XI2-4, or XII2-4. This is consistent with the experimental results.16,18,20 According to our calculated free energies of reaction, other substituted tetrazolium salts should not be easily synthesized. However, considering the uncertainty in the computational methods, Dixon et al.42 assumed a 41.8 kJ mol-1 error bar (including the predicted phase transition approximations) for the free energies of reaction. In other words, if the free energy of reaction is positive and less than 41.8 kJ mol-1, the synthesis of the salt may also be possible within the uncertainty of the computational method. Accordingly, it is inferred that the salts containing the cations I2, I5, II5, VI2-4, VII2-3, VII5, VIII3-5, X5, XI2-4, or XII2-4 may also be synthesized, which is supported by the experimental reports.18,20,60 The possibility for other salts to be synthesized is substantially lowered by our proposed reactions. However, these salts might be possible under alternative experimental methods. It is also seen in Table 5 that all of the enthalpies of reaction for the salts are negative except for III4 and IV3-4, consistent with the weak electron-donating property of the proton or methyl. On the basis of these results, it may be concluded that it will be difficult to synthesize energetic ionic salts with only energetic substituents that are electron withdrawing on the cation. However, combining -CH3 or -NH2 with these energetic substituents is very helpful for producing new energetic salts. Figure 5 exhibits the free energies of reaction (∆Grxn) for formation of the salt containing the protonated and methylated

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TABLE 5: Proton and Methyl Cation Acidities (∆H1) of RCl Compounds, Gas-Phase Proton and Methyl Cation Affinities (-∆H2), Lattice Enthalpies (∆H3), and the Enthalpies of Reaction (∆Hrxn(salt)), Entropies of Reaction (∆Srxn), and Free Energies of Reaction (∆Grxn) for the Formation of the Protonated and Methylated Tetrazole Salts cations I1 I2 I3 I4 I5 I6 II1 II2 II3 II4 II5 II6 III1 III2 III3 III4 III5 III6 IV1 IV2 IV3 IV4 IV5 IV6 V1 V2 V3 V4 V5 VI1 VI2 VI3 VI4 VI5 VII1 VII2 VII3 VII4 VII5 VII6 VIII1 VIII2 VIII3 VIII4 VIII5 VIII6 IX1 IX2 IX3 IX4 IX5 IX6 X1 X2 X3 X4 X5 X6 XI1 XI2 XI3 XI4 XI5 XII1 XII2 XII3 XII4 XII5

∆H1 (kJ mol-1)

∆H2 (kJ mol-1)

∆H3 (kJ mol-1)

∆Hrxn (kJ mol-1)

∆Srxn (J mol-1 K-1)

∆Grxn (kJ mol-1)

1301.9a (1393.6)b 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9 1301.9

Protonated Tetrazole (I-VI) Chloride Salts -884.5 -555.1 -137.6 -821.3 -544.0 -63.3 -810.5 -551.9 -60.5 -785.9 -551.9 -35.8 -853.0 -542.8 -93.8 -874.8 -562.2 -135.1 -887.6 -559.8 -145.5 -782.3 -546.3 -26.7 -815.8 -549.4 -63.3 -796.9 -552.8 -47.7 -850.8 -542.0 -90.8 -907.3 -565.3 -170.6 -911.4 -535.3 -144.7 -804.6 -514.2 -16.9 -778.0 -524.4 -0.5 -742.0 -527.2 32.8 -846.7 -510.1 -54.9 -952.1 -547.3 -197.5 -907.8 -536.8 -142.7 -811.1 -515.6 -24.7 -773.6 -523.4 4.9 -739.2 -528.0 34.8 -839.5 -512.1 -49.7 -939.1 -549.1 -186.3 -907.6 -541.7 -147.4 -815.7 -530.6 -44.3 -836.3 -535.9 -70.2 -820.9 -535.0 -53.9 -893.9 -528.7 -120.6 -926.0 -544.6 -168.7 -856.1 -534.0 -88.2 -864.6 -535.5 -98.1 -842.3 -538.0 -78.3 -900.1 -526.7 -124.9

-342.4 -345.7 -358.2 -329.3 -355.0 -324.7 -331.8 -345.5 -365.3 -329.7 -343.9 -326.4 -348.8 -385.7 -403.8 -350.2 -390.7 -343.2 -355.6 -409.0 -406.0 -352.6 -388.4 -342.7 -358.6 -359.5 -377.6 -353.1 -358.8 -362.1 -368.4 -375.5 -349.4 -368.2

-35.6 39.7 46.3 62.4 12.0 -38.3 -46.6 76.3 45.6 50.5 11.7 -73.3 -40.7 98.1 119.9 137.2 61.5 -95.2 -36.7 97.2 126.0 139.9 66.1 -84.2 -40.5 62.9 42.3 51.3 -13.7 -60.7 21.6 13.8 25.9 -15.2

866.9a (950.5)c 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9 866.9

Methylated Tetrazole (VII-XII) Chloride Salts -490.7 -534.6 -158.4 -433.5 -526.1 -92.7 -430.1 -526.5 -89.6 -401.1 -530.1 -64.3 -466.6 -522.2 -121.9 -485.4 -538.3 -156.8 -489.4 -536.7 -159.2 -399.0 -528.8 -61.0 -432.0 -529.5 -94.6 -413.1 -531.9 -78.2 -455.6 -521.9 -110.6 -511.6 -540.4 -185.2 -518.1 -519.4 -170.7 -413.8 -501.6 -48.5 -392.5 -509.4 -35.0 -365.7 -513.4 -12.2 -451.5 -497.6 -82.2 -554.7 -526.8 -214.6 -523.6 -518.2 -175.0 -427.3 -501.7 -62.1 -404.2 -507.0 -44.3 -372.5 -509.9 -15.5 -458.6 -496.9 -88.6 -555.5 -529.2 -217.9 -513.5 -523.4 -170.0 -429.4 -516.5 -79.1 -444.9 -519.0 -97.0 -437.6 -518.5 -89.3 -481.1 -511.6 -125.8 -530.6 -520.6 -184.3 -463.3 -515.4 -111.8 -471.6 -519.4 -124.1 -450.6 -520.2 -103.9 -504.3 -510.7 -148.2

-382.7 -386.9 -393.5 -368.1 -393.3 -363.2 -370.6 -387.3 -405.3 -369.4 -382.5 -364.7 -390.7 -428.2 -444.9 -393.1 -432.7 -382.3 -389.4 -428.3 -442.3 -389.3 -431.7 -384.6 -397.5 -403.0 -417.9 -388.3 -402.9 -384.4 -402.0 -417.3 -389.5 -409.5

-44.3 22.6 27.7 45.4 -4.7 -48.5 -48.7 54.5 26.2 31.9 3.4 -76.5 -54.2 79.1 97.6 105.0 46.8 -100.7 -58.9 65.6 87.5 100.5 40.1 -103.2 -51.5 41.1 27.6 26.5 -5.7 -69.7 8.0 0.2 12.2 -26.1

a Deprotonation reaction and demethylation reation: HCl f H+ + Cl-, CH3Cl f CH3+ + Cl-. b The experimental data are taken from ref 66. c The experimental data are taken from ref 67.

tetrazole cations. The ∆Grxn values of the protonated tetrazole (I-VI) salts are smaller than those of the methylated tetrazole (VII-XII) ones with the same substituent and substitution position. For the protonated tetrazole series I and II, different position of the substituent does not produce an evident effect

on the ∆Grxn values of their salts with the same substituent. A similar situation is also found in the cation series V and VI. The same is true of the methylated tetrazole seires (VII vs VIII and XI vs XII). For the cations with two same substituents III and IV (IX and X), different position of the positive charge



Figure 5. Comparison of the free energies of reaction (∆Grxn) for the protonated and methylated tetrazole salts.

does not obviously affect the ∆Grxn values of their salts. Overall, for the protonated tetrazole series (I-VI), the salts of the tetrazole cations with two same substituents (III and IV) have higher ∆Grxn values than those with single substituent (I and II) and with two different substituents (V and VI). A similar case is also observed in the salts containing the methylated tetrazole series (VII-XII).

salts. The structure-property relationships provide basic information for the molecular design of novel high-energy salts. Acknowledgment. This work was supported by the NSAF Foundation of National Natural Science Foundation of China and China Academy of Engineering Physics (Grant No. 10876013) and the Specialized Research Fund for the Doctoral Program of Higher Education (200802881043).

4. Conclusions In this work, we have studied the densities, heats of formation, energetic properties, and thermodynamics of formation for a series of energetic nitrogen-rich salts composed of the protonated and methylated tetrazole cations with nitrate, dinitroamide, azide, and perchlorate anions by using the DFT-B3LYP and volume-based thermodynamics methods. The results show that the -NO2 or -NF2 group is an effective substituent for increasing the densities of the substituted tetrazolium salts. The substitution of the -NO2, -NF2, -CN, -N3, or -NH2 group is helpful for increasing the HOFs of the tetrazolium salts. The densities of the protonated tetrazole salts are larger than those of the methylated tetrazole salts with the same substituent and substitution position. The same is true of the HOFs. The calculated energetic properties indicate that the -NO2, -NF2, or -N3 group is an effective structural unit for enhancing the detonation performance for the substituted tetrazolium salts. Most of the detonation properties of the protonated tetrazole salts are better than those of the methylated tetrazole ones with the same substituent and substitution position. The thermodynamics of formation of the protonated and methylated tetrazole salts show that the salts containing the cations I-XII1, I-IV6, VI-X6, I2, I5, II5, VI2-4, VII2-3, VII5, VIII3-5, X5, XI2-4, or XII2-4 may be synthesized easily by the proposed reactions. Energetic ionic salts with only energetic (electron-withdrawing) substituents on the cation are difficult to synthesize. However, combining -CH3 or -NH2 with these energetic substituents is very helpful for producing new energetic salts. According to the detonation performance and thermodynamics of formation, the salts containing the cations I2, I5-6, II5-6, III6, IV6, VI2-3, VII2-3, VII5, VIII3, X5, XI2-3, and XII3 may be considered as the potential candidates of high-energy

Supporting Information Available: Table S1 presents the densities of the salts comprised of the protonated and methylated tetrazole cations with dinitroamide, azide, and perchlorate anions. Table S2 lists the HOFs of the substituted tetrazolium cations, anions, and their salts and the lattice energies of these salts. Table S3 displays the predicted heats of detonation, detonation velocities and pressures, and oxygen balance of the salts comprised of the protonated and methylated tetrazole cations with dinitroamide, azide, and perchlorate anions. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Drake, G.; Hawkins, T.; Brand, A.; Hall, L.; Mckay, M.; Vij, A.; Ismail, I. Propellants, Explos., Pyrotech. 2003, 28, 174. (2) Joo, Y. H.; Twamley, B. Chem.-Eur. J. 2009, 15, 9097. (3) Joo, Y. H.; Shreeve, J. M. Chem.-Eur. J. 2009, 15, 3198. (4) Guo, Y.; Tao, G. H.; Zeng, Z.; Gao, H. X.; Parrish, D. A.; Shreeve, J. M. Chem.-Eur. J. 2010, 16, 3753. (5) Hiskey, M. A.; Goldman, N.; Stine, J. R. J. Energ. Mater. 1998, 16, 119. (6) Hough, W. L.; Smiglak, M.; Rodriguez, H.; Swatloski, R. P.; Spear, S. K.; Daly, D. T.; Pernak, J.; Grisel, J. E.; Carliss, R. D.; Soutullo, M. D.; Davis, J. H.; Rogers, R. D. New J. Chem. 2007, 31, 1429. (7) Gao, Y.; Gao, H.; Piekarski, C.; Shreeve, J. M. Eur. J. Inorg. Chem. 2007, 4965. (8) Valkenburg, M. E. V.; Vaughn, R. L.; Williams, M.; Wilkes, J. S. Thermochim. Acta 2005, 425, 181. (9) Fredlake, C. P.; Crosthwaite, J. M.; Hert, D. G.; Aki, S. N. V. K.; Brennecke, J. F. J. Chem. Eng. Data 2004, 49, 954. (10) Drake, G.; Kaplan, G.; Hall, L.; Hawkins, T.; Larue, J. J. Chem. Crystallogr. 2007, 37, 15. (11) MacFarlane, D. R.; Seddon, K. R. ChemInform 2007, 38, 3. (12) Boatz, J. A.; Voth, G. A.; Gordon, M. S.; Hammes-Schiffer, S. 2009 DoD High Performance Computing Modernization Program Users Group Conference-Design of Energetic Ionic Liquids 2009, 175. (13) Green, M. D.; Long, T. E. J. Macromol. Sci., Polym. ReV. 2008, 49, 291.

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