Molecular Design of Tetrazole- and Tetrazine-Based High-Density

Article pubs.acs.org/jced

Molecular Design of Tetrazole- and Tetrazine-Based High-Density Energy Compounds with Oxygen Balance Equal to Zero Qiong Wu, Weihua Zhu,* and Heming Xiao Institute for Computation in Molecular and Materials Science and Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, China ABSTRACT: The density functional theory method was used to study the geometrical structures, enthalpies of formation (EOFs), energetic properties, and thermal stability of a series of tetrazole- and tetrazine-based derivatives with oxygen balance equal to zero including different substituents and linkages. The results show that the two heterocycles in most of the tetrazole derivatives and all of the tetrazine derivatives are approximately coplanar. Most of the designed compounds have much higher EOFs than HMX, and over half of them have an extremely high EOF above 800 kJ/mol. Seventy-one compounds have better detonation properties than RDX, and 25 compounds have better detonation properties than HMX, indicating that designing the tetrazole- and tetrazine-based derivatives with oxygen balance equal to zero is a very effective way to obtain potential energetic compounds with outstanding detonation properties. Considering the thermal stability and detonation performance, 57 compounds may be considered as potential candidates of high-density energy compounds.

1. INTRODUCTION Energetic nitrogen-rich organic compounds, promising candidates for high-energy density compounds (HEDCs), have attracted considerable attention because of high density, high positive enthalpy of formation (EOF), good detonation performances, and excellent thermal stability.1−11 It is wellknown that most of nitrogen-rich organic compounds are oxygen-deficient. If an explosive has a negative oxygen balance, its combustion will be incomplete and a large amount of toxic gases such as carbon monoxide will be released. This will do harm to the environment and the health of human beings. In addition, generally, the lower the oxygen balance is, the smaller the detonation velocity and pressure are, and the poorer the performance of the explosive is. However, it should be clear that too much oxygen, that is, beyond oxygen content that is needed for oxidating carbon, hydrogen, sulfur, and metal to carbon dioxide, water, sulfur dioxide, and metal oxide, respectively, is also not favorable for advancing the explosive performance of HEDCs. The primary reason is that additional oxygen will produce O2 that takes away a great deal of energy during the explosion. Therefore, one should keep the value of oxygen balance around zero in designing HEDCs. One impressive example is octanitrocubane,12−15 the most powerful high explosives that have been synthesized until now. Its oxygen balance is equal to zero and its predicted density, detonation velocity, and detonation pressure are up to 2.1 g/cm3, 10.1 km/s, and 50.0 GPa, respectively. Therefore, to meet the continuing demand for improved energetic materials, there is a clear need to continue to design and develop new HEDCs with oxygen balance equal to zero.6 In the past several decades, theoretical studies based on quantum chemical treatment have gained acceptance as a very useful research tool to screen the candidates of HEDCs, thereby avoiding expensive and dangerous experimental tests. They can provide understanding in terms of the relationships between molecular structure and property, which in turn can help design better and more efficient laboratory tests. Thus, the optimization © 2013 American Chemical Society

of the candidate compounds with high energy and less sensitivity is the primary step for designing and synthesizing new HEDCs.16 Tetrazole and tetrazine are two azo compounds with high nitrogen contents (80% for tetrazole and 68.3% for tetrazine), making them of interest for the synthesis of highly energetic materials. Much work has concentrated on the synthesis and properties of many tetrazole derivatives17−22 and tetrazine derivatives.6,16,23−26 But it is necessary to further optimize tetrazole-based and tetrazine-based HEDCs. In this work, we reported a systematic study of the geometrical structures, EOFs, energetic properties, and thermal stability of a series of tetrazole (1H-tetrazole and 2H-terazole) and tetrazine (1,2,3,4-tetrazine, 1,2,3,5-tetrazine, 1,2,4,5-tetrazine, 1,2,4,5-tetrazine1,4-dioxide, and 1,2,3,4-tetrazine-1,3-dioxide) derivatives with oxygen balance equal to zero including seven commonly energetic substituents (−NH2, −NO2, −NF2, −N3, −CF3, −CF2NF2, −C(NO2)3) and two linkages (−N(O)N−, −NN−) by using density function theory (DFT). Our main purpose here is to design and select new high-energy density compounds with oxygen balance equal to zero and excellent integrated performances. The remainder of this paper is organized as follows. A brief description of our computational method is given in Computational Methods section followed by the Results and Discussion section, and summary in our Conclusions section.

2. COMPUTATIONAL METHODS The molecular frameworks of a series of tetrazole derivatives (molecular numbering as AI-1-AI-8, AII-1-AII-8, AIII-1-AIII-3, AIV-1-AIV-3, AV-1-AV-2, AVI-1-AVI-3, AVII-1-AVII-3, AVIII-1-AVIII-2, AIX-1-AIX-3, AX-1-AX-3, AXI-1-AXI-2, AXII-1-AXII-3, AXIII-1-AXIII-3, AXIV-1-AXIV-2) and tetrazine Received: April 27, 2013 Accepted: July 31, 2013 Published: August 20, 2013 2748

dx.doi.org/10.1021/je4004367 | J. Chem. Eng. Data 2013, 58, 2748−2762

Journal of Chemical & Engineering Data

Article

The DFT-B3LYP6,11,27,28 method with 6-311G(d,p)11,16,22 basis set was very successfully used to predict the EOF of many organic systems via isodesmic reactions.27−29 Here, we design isodesmic

derivatives (molecular numbering as BI-1-BI-3, BII-1-BII-3, BIII-1-BIII-3, BIV-1-BIV-4, BV-1-BV-8, BVI-1-BVI-2, BVII-1BVII-2, BVIII-1-BVIII-2) are displayed in Figure 1.

Figure 1. continued 2749



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Figure 1. Molecular frameworks of a series of tetrazole and tetrazine derivatives with oxygen balance equal to zero.

As the experimental EOF of CH3N3, CH3CF3, CH3CF2NF2, CH3N2CH3, CH3N(O)CH3, NH2NF2, NH2N3, NH2N2NH2, NH 2 N(O)NNH 2 , NH 2 NH 2 , 1H-tetrazole, 2H-tetrazole, 1,2,3,4-tetrazine, 1,2,3,5-tetrazine, 1,2,4,5-tetrazine, 1,2,3,4tetrazine-1,3-dioxide, and 1,2,4,5-tetrazine-1,4-dioxide are unavailable, additional calculations were carried out for the atomization reaction CaHbOcNd→ aC(g) + bH(g)+ cO(g) + dN(g) by using the G2 theory to get an accurate value of ΔHf. The experimental EOF of reference compounds CH4, NH3, CH3NO2, CH3CH3, CH3NF2, and NH2NO2 are available. Now the most important task was to compute ΔH298. The ΔH298 can be calculated using the following expression:

reactions in which the numbers of all kinds of bonds keep invariable to decrease the calculation errors of EOF. Because the electronic circumstances of reactants and products are very similar in isodesmic reactions, the errors of electronic correction energies can be counteracted, and then the errors of the calculated EOF can be greatly reduced.8,16,21,22 This approach has been demonstrated to predict reliably the EOF of many organic systems.28,29 The isodesmic reactions used to obtain the EOF of the tetrazole and tetrazine derivatives at 298 K are shown in Scheme 1. For the isodesmic reaction, the heat of reaction ΔH298 at 298 K could be calculated from the following equation: ΔH298 = ΔHf,p − ΔHf,R

(1)

ΔH298 = ΔE298 + Δ(PV )

where ΔHf,R and ΔHf,P are the EOF of reactants and products at 298 K, respectively.

= ΔE0 + ΔEZPE + ΔE T + ΔnRT 2750

(2)



Article

Scheme 1. Isodesmic Reactions Used to Obtain the EOF of the Tetrazole and Tetrazine Derivatives at 298 K

where ΔE0 is the change in total energy between the products and the reactants at 0 K; ΔEZPE is the difference between the

zero-point energies (ZPE) of the products and the reactants at 0 K; The ET is the thermal correction from (0 to 298) K for a 2751



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Table 1. Calculated Bond Lengths (nm), Bond Angles (deg), Dihedral Angles (deg) of the Title Compoundsa

compd

N1−N2

N2−N3

N3−N4

AI-1 AI-2 AI-3 AI-4 AI-5 AI-6 AI-7 AI-8 AII-1 AII-2 AII-3 AII-4 AII-5 AII-6 AII-7 AII-8 AIII-1 AIII-2 AIII-3 AIV-1 AIV-2 AIV-3 AV-1 AV-2 AVI-1 AVI-2 AVI-3 AVII-1 AVII-2 AVII-3 AVIII-1 AVIII-2 AIX-1 AIX-2 AIX-3 AX-1 AX-2 AX-3 AXI-1 AXI-2 AXII-1 AXII-2 AXII-3 AXIII-1 AXIII-2 AXIII-3 AXIV-1 AXIV-2

0.1356 0.1350 0.1349 0.1365 0.1355 0.1359 0.1381 0.1383 0.1322 0.1320 0.1324 0.1329 0.1323 0.1326 0.1336 0.1332 0.1346 0.1373 0.1378 0.135 0.1369 0.1387 0.1383 0.1377 0.1363 0.1363 0.1365 0.1377 0.1364 0.1355 0.1356 0.1361 0.1317 0.1332 0.1334 0.1317 0.1333 0.1339 0.1338 0.1337 0.1327 0.1328 0.1328 0.1332 0.1321 0.1315 0.1324 0.1314

0.1280 0.1290 0.1280 0.1275 0.128 0.1277 0.1268 0.1267 0.1351 0.1334 0.1331 0.1331 0.1345 0.1348 0.1357 0.1357 0.1279 0.1273 0.1271 0.1282 0.1279 0.1270 0.1271 0.1274 0.1281 0.1276 0.1277 0.1275 0.1279 0.1285 0.1285 0.1281 0.1335 0.1362 0.1361 0.1337 0.1362 0.136 0.1358 0.1359 0.1354 0.1351 0.135 0.1357 0.1354 0.1346 0.1341 0.1332

0.1370 0.1361 0.1375 0.1368 0.1358 0.1358 0.1365 0.1363 0.1292 0.1309 0.1300 0.1296 0.1291 0.1288 0.1283 0.1284 0.1375 0.136 0.1362 0.1369 0.1353 0.1362 0.1350 0.1361 0.1359 0.1361 0.1363 0.1363 0.1361 0.1352 0.1352 0.1351 0.1296 0.128 0.1281 0.1294 0.1280 0.1280 0.1279 0.1284 0.1289 0.1284 0.1286 0.1288 0.1287 0.1293 0.1296 0.1299

0.1346 0.1356 0.1351 0.135 0.1355 0.1337 0.1334 0.1337 0.1368 0.1369 0.1364 0.1377 0.1374 0.1372 0.1365 0.1363 0.1317 0.1327 0.1321 0.1317 0.1327 0.1318 0.1315 0.1313 0.1327 0.1337 0.134 0.1332 0.1336 0.1343 0.1344 0.1353

N1−N2

N2−N3

N3−N4

N3−C2

BI-1 BI-2 BI-3 BII-1 BII-2 BII-3 BIII-1 BIII-2 BIII-3 BIV-1

0.1320 0.1319 0.1315 0.1340 0.1329 0.1293 0.1324 0.1317 0.1321 0.1361

0.1306 0.1313 0.1354 0.1324 0.1322 0.1312

0.1320 0.1307 0.1301 0.1340 0.1333 0.1288

0.1339

N5−N6

N6−N7

N7−N8

0.1279 0.1278 0.1287 0.1282 0.1284 0.1307 0.131 0.1303 0.1281 0.128 0.1272 0.1275 0.1276 0.1266 0.1267 0.1266 0.1335 0.1347 0.133 0.1337 0.1346 0.1335 0.1328 0.1324 0.1354 0.1346 0.1341 0.1357 0.1361 0.1365 0.1339 0.1352

N1N2N3

N2N3N4

106.3 106.4 106.1 105.6 106.9 106.9 106.6 107.0 115.3 115.5 115.9 115.7 114.4 114.3 113.6 113.6 105.9 106.7 106.6 105.8 106.9 106.0 107.0 106.8 111.8 111.6 111.6 111.7 111.8 111.6 111.6 111.6 115.9 113.7 113.7 116.0 113.8 113.7 113.9 113.7 115.0 114.8 114.7 114.1 114.4 114.9 115.7 116.0

116.6 116.6 111.7 112.4 111.1 111.2 111.7 111.6 104.7 104.9 105.0 105.2 105.4 105.4 105.5 105.6 111.6 111.7 111.8 111.7 111.8 112.6 111.9 111.8 105.9 106.1 106.2 106.5 106.1 106.1 106.2 105.7 104.8 105.4 105.4 104.7 105.4 105.5 105.4 105.5 104.8 104.9 105.0 105.4 105.2 105.1 105.0 104.7

0.1375 0.1364 0.1357 0.1369 0.1361 0.1337 0.1334 0.1337 0.1359 0.1362 0.1385 0.1362 0.137 0.1403 0.1393 0.1399 0.1296 0.1289 0.1307 0.1294 0.1288 0.1303 0.1316 0.1314 0.1289 0.1289 0.129 0.1288 0.1285 0.128 0.1287 0.1286 N2N3N4/ N1N2N3/ N3N4C1/ N1N2C2 N2N3C2 115.7 116.0 117.0 121.4 121.4 117.4 120.3 120.5 120.6 116.1

115.7 117.1 117.8 121.4 121.1 119.3 117.0 117.3 118.6 115.9

C1N1N2 115.7 117.1 117.1 118.6 119.3 122.6 117.0 117.7 117.1 117.5 2752

N5N6N7

N6N7N8

N1N2 N3N4 1.21 1.31 0.54 0.06 0.12 0.47 0.67 1.03 0.03 0.00 0.28 0.02 0.09 0.55 0.12 0.99 0.10 0.21 0.45 1.20 0.11 0.16 0.25 0.20 0.04 0.97 1.20 0.18 0.06 0.49 0.89 0.48 0.01 0.02 0.98 1.85 0.84 0.84 0.52 2.01 0.07 0.06 0.04 2.36 2.40 2.32 1.09 0.58

105.9 111.6 106.4 111.1 106.4 111.2 105.8 111.7 106.0 111.9 105.8 111.4 106.7 111.3 106.6 111.4 111.8 105.9 112.1 105.5 112.9 105.2 112.1 105.9 112.1 106.1 113.6 105.1 113.7 104.5 113.2 105.4 115.9 104.8 115.3 104.9 115.5 105.0 116.0 104.7 115.4 104.9 115.6 104.8 115.3 105.4 115.6 105.3 115.0 104.8 115.0 105.0 115.4 104.9 114.0 105.4 113.9 105.4 113.8 105.4 114.7 105.2 114.1 105.7 N6N7N8/ N5N6N7/ N7N8C3/ N5N6C4 N6N7C4 C3N5N6

N5N6 N7N8

0.10 0.09 0.62 1.19 0.98 1.61 0.01 0.79 0.04 1.19 1.31 0.65 0.50 0.18 0.15 1.86 0.02 0.91 0.00 1.86 1.75 1.43 0.58 0.26 0.07 0.28 0.05 2.56 1.66 1.68 0.29 0.08 N1N2N3N4/ N1N2C2N3/ N1N2N3C2

CRC/NRN/ N4C1C2N8/ N3N2N6N7/ C1N4N8C2

12.9 3.8 14.2 14.36 0.8 14.3 0.3 0.6 85.7 67.9 66.4 2.3 7.9 6.1 0.5 2.7 0.1 1.9 1.1 12.7 12.5 12.1 18.7 10 91.2 90.8 91.2 8.71 8.23 7.54 1.2 2.7 N5N6N7N8/ N5N6C4N7/ N5N6N7C4

CRC

2.45 6.30 4.59 1.00 3.57 22.50 0.92 1.15 0.45 0.02 dx.doi.org/10.1021/je4004367 | J. Chem. Eng. Data 2013, 58, 2748−2762


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Table 1. continued N1−N2 BIV-2 BIV-3 BIV-4 BV-1 BV-2 BV-3 BV-4 BV-5 BV-6 BV-7 BV-8 BVI-1 BVI-2 BVII-1 BVII-2 BVIII-1 BVIII-2 a

0.1325 0.1339 0.1343 0.1353 0.1363 0.1363 0.1354 0.1357 0.1359 0.1355 0.1354 0.1307 0.1307 0.1329 0.1330 0.1316 0.1315

N2−N3

N3−N4

0.1366 0.1356 0.1361 0.1357 0.1356 0.1350 0.1351 0.1350

0.1307 0.1315 0.1325 0.1324

0.1347 0.1344 0.1343 0.1355 0.1350 0.1360 0.1350 0.1350 0.1356 0.1355 0.1355 0.1320 0.1319 0.1326 0.1326

N3−C2

0.1335 0.1334

0.1334 0.1338

N1N2N3/ N1N2C2

N2N3N4/ N3N4C1/ N2N3C2

C1N1N2

118.1 118.4 116.1 116.7 116.2 116.8 116.8 115.9 115.9 116.3 116.2 116.8 116.3 120.9 121.1 120.3 120.4

116.9 118.2 116.4 125.5 125.9 125.6 124.6 124.0 123.8 124.9 124.8 116.9 117.1 120.5 121.6 118.2 117.8

117.9 117.6 119.3 120.7 121.2 121.0 122.8 122.5 122.3 122.7 122.6 117.0 117.0 120.8 119.5 117.9 117.6

N5N6N7/ N5N6C4

116.8 116.4 120.9 121.0 120.3 120.3

N6N7N8/ N7N8C3/ N6N7C4

116.9 117.1 120.5 121.6 118.3 117.9

C3N5N6

N1N2N3N4/ N1N2C2N3/ N1N2N3C2

N5N6N7N8/ N5N6C4N7/ N5N6N7C4

CRC

116.9 116.9 120.8 119.5 117.7 117.7

1.23 0.43 12.56 1.00 1.01 0.01 0.53 14.70 16.10 1.04 5.75 3.87 0.28 0.02 3.04 0.75 1.82

4.79 0.49 0.00 3.05 2.38 2.52

14.7 1.5 2.0 1.0 16.0 4.1

U(bond length) = 0.0001 nm, U(bond angle) = 0.1°, U(dihedral angles) = 0.1°.

For known explosives, their Q and ρ can be measured experimentally; thus their D and P can be calculated according to eqs 5 and 6. However, for some compounds, their Q and ρ cannot be evaluated from experimental measures. Therefore, to estimate their D and P, we first need to calculate their Q and ρ.8,16 The theoretical density was obtained by an improved equation proposed by Politzer et al.,38 in which the interaction index νσ2tot was introduced:

single molecule and ΔET is the difference between the ET of the products and the reactants. The Δ(PV) value in eq 2 is the PV work term and equals ΔnRT for the reactions of ideal gas. For the isodesmic reactions in this work, Δn = 0, so Δ(PV)=0.8,16 Since the condensed phase for most energetic compounds is solid, the calculation of detonation properties requires solidphase EOF (ΔHf,solid). According to Hess’s law of constant heat summation,30 the solid-phase EOF can be obtained from the gas-phase EOF (ΔHf,gas) and heat of sublimation (ΔHsub): ΔHf,solid = ΔHf,gas − ΔHsub

⎞ ⎛ M 2 ρ = α⎜ ⎟ + βν(σtot) + γ V(0.001) ⎝ ⎠

(3)

31−33

Recently, Politzer et al. reported that the heat of sublimation correlates with the molecular surface area and the electrostatic interaction index νσ2tot for energetic compounds. The empirical expression of this approach is as follows: 2 0.5 ΔHsub = aA2 + b(νσtot ) +c

where the M is the molecular mass (g·mol ) and V(0.001) is the volume of the 0.001 electrons·bohr−3 contour of electronic density of the molecule (1.67·10−30 m3·mol). The coefficients α, β, and γ are 0.9183, 0.0028, and 0.0443, respectively. The heat of detonation Q was evaluated by the EOF difference between products and explosives according to the principle of exothermic reactions. The products are supposed to be only CO2, H2O, and N2, so released energy in the decomposition reaction reaches its maximum. On the basis of the ρ and Q values, the corresponding D and P values can be evaluated. The theoretical density of the compounds in this work is slight greater than practical loaded density. Therefore, according to the Kamlet−Jacobs equations, the D and P values can be regarded as their upper limits.16,21,22 The strength of bonding, which could be evaluated by bond dissociation energy, is fundamental to understand chemical processes.39 The energy required for bond homolysis at 298 K and 1 atm corresponds to the enthalpy of reaction A−B(g) → A·(g) + B·(g), which is the bond dissociation enthalpy of the molecule A−B by definition.40 A· and B· are two radicals which are generated from the rupture of the molecule A−B. For many organic molecules, the terms “bond dissociation energy” (BDE) and “bond dissociation enthalpy” usually appear interchangeably in the literature.41 Thus, at 0 K, the homolytic bond dissociation energy can be given in terms of eq 8:

(4)

where A is the surface area of the 0.001 electrons·bohr−3 isosurface of the electronic density of the molecule, ν describes the degree of balance between positive potential and negative potential on the isosurface, and σ2tot is a measure of the variability of the electrostatic potential on the molecular surface. The coefficients a, b, and c have been determined by Rice et al.: a = 1.118·10−3 kJ·mol−1·A−4, b = 6.910 kJ·mol−1, and c = 12.416 kJ·mol−1.34 The descriptors A, ν, and σ2tot were calculated by using the computational procedures proposed by Bulat et al.35 This approach has been demonstrated to predict reliably the heats of sublimation of many energetic compounds.34−36 The detonation velocity and pressure were estimated by the Kamlet−Jacobs equations37 as D = 1.01(NM̅ 1/2 Q1/2)1/2 (1 + 1.30ρ)

(5)

P = 1.558ρ2 NM̅ 1/2 Q1/2

(6)

(7) −1

where each term in eq 5 and eq 6 is defined as follows: D, the detonation velocity (km·s−1); P, the detonation pressure (GPa); N, the moles of detonation gases per gram explosive; M̅ , the average molecular weight of these gases; Q, the heat of detonation (J·g−1); and ρ, the loaded density of explosives (g·cm−3).

BDE0(A − B) = E0(A·) + E0(B·) − E0(A − B)

(8)

where E0(A·) and E0(B·) are the total energies of radicals A· and B· at 0 K, respectively. 2753



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Table 2. Calculated Total Energies (E0), Zero-Point Energies (ZPE), Thermal Corrections (HT), and EOFs of the Reference Compoundsa,b compd

E0/a.u.

ZPE/a.u.

HT/kJ·mol−1

EOFc/kJ·mol−1

EOFd/kJ·mol−1

CH4 CH3NO2 CH3NF2 CH3CH3 CH3CF3 CH3CF2NF2 CH3N(O)CH3 CH3N2CH3 NH3 NH2NO2 NH2NF2 NH2N3 NH2N2NH2 NH2N(O)NNH2 NH2NH2 1H-tetrazole 2H-tetrazole 1,2,3,4-tetrazine 1,2,3,5-tetrazine 1,2,4,5-tetrazine 1,2,3,4-tetrazine-1,3-dioxide 1,2,4,5-tetrazine-1,4-dioxide

−40.5337 −245.0817 −294.2983 −79.8563 −377.6740 −532.1574 −264.5387 −189.3094 −56.5760 −261.1138 −310.3268 −220.1589 −221.3948 −296.5913 −320.2827 −258.3169 −258.3214 −296.3688 −296.4020 −296.3909 −446.7658 −446.7803

0.0446 0.0497 0.0468 0.0744 0.0521 0.0590 0.0897 0.0830 0.0343 0.0394 0.0354 0.0388 0.0630 0.0685 0.0542 0.0468 0.0475 0.0500 0.0512 0.0512 0.0600 0.0601

10.0 14.1 13.8 11.8 15.5 20.9 15.4 16.3 10.0 12.3 13.5 14.2 14.6 16.3 15.5 11.8 11.6 14.2 13.9 13.8 17.8 17.8

−74.6 −80.8 −115.2 −84.0

−76.1 −81.8 −110.6 −85.2 −772.8 −548.3 50.4 141.0 −45.2 −3.7 −25.0 436.0 298.7 250.2 −124.4 333.5 325.7 539.5 450.7 483.8 426.8 398.9

−45.9 −3.9

The scaling factor for ZPE is 0.98 and the scaling for HT is 0.96.46 bU(E0) = 0.0001 a.u., U(ZPE) = 0.0001 a.u., U(HT) = 0.1 kJ·mol−1, U(EOF) = 0.1 kJ·mol−1. cThe experimental values were taken from refs 47and 48. dThe calculated values were calculated at the G2 level. a

1H-tetrazole and 2H-tetrazole are two well conjugated compounds. The conjugation character makes them have stable ring structure since the difference between the N−N single bond and NN double bond is smaller than that of normal N−N single bond and NN double bond. It is seen in Table 1 that all the tetrazole derivatives in the same series have similar bond lengths and bond angles, showing that the substitution of the substituents do not affect the bond lengths and bond angles in the tetrazole ring of parent tetrazoles significantly. However, it is found that the difference between the longest N−N bond length and shortest N−N bond length in the trinitromethylcontaining compounds is larger than that in other compounds in the same series generally. This shows that the conjugation of the rings in the trinitromethyl-containing compounds is destroyed more than that that in other derivatives. This may be because the trinitromethyl has the strongest electronwithdrawing ability among all the substituents and thus it does much more harm to the conjugation of the ring than other groups. The N1N2N3N4 or N5N6N7N8 dihedral angle for all the tetrazole derivatives are smaller than 2.6°, indicating that the planarity of the rings for all the derivatives are good and the substituents have a small effect on the planarity of the tetrazole rings. To investigate whether the two rings in the tetrazole derivatives are coplanar or not, the dihedral angles of CRC, NRC, N4C1C2N8, N3N2N6N7, and C1N4N8C2 are shown in Table 1. It is found that most of these angles are lower than 20°, showing that the two rings in most of the compounds are approximately coplanar except for series AVI and AXII, in which the two rings are nearly vertical. When the dihedral angles of series AVI and AVII are compared, and series AXII and AXIII, respectively, it can be found that the incorporation of the −NN− group may be helpful for forming the bicyclic tetrazole derivatives with two rings in the same plane

The bond dissociation energy with zero-point energy (ZPE) correction can be calculated by eq 9: BDE(A − B)ZPE = BDE0(A − B) + ΔEZPE

(9)

where ΔEZPE is the difference between the ZPEs of the products and the reactants. The calculations were performed at the B3LYP/6-311G(d,p) level with the Gaussian 09 package.42 The structure of a single molecule was drawn by using GaussView code. Then, its input file was made and each molecule was optimized by using the Gaussian program. The molecules were not placed in a cubic cell. The optimizations were performed without any symmetry restrictions. In the geometry optimization, the maximum force was converged less than 0.00045 eV·Å−1, the RMS force less than 0.0003 eV·Å−1, the maximum displacement less than 0.0018 Å, and the RMS displacement less than 0.0012 Å. All of the optimized structures were characterized to be true local energy minima on the potential energy surfaces without imaginary frequencies.16,21,22

3. RESULTS AND DISCUSSION 3.1. Geometrical structure. Table 1 lists some selected bond lengths (N1−N2, N2−N3, N3−N4, N5−N6, N6−N7, N7−N8, N3−C2), bond angles (N1N2N3, N2N3N4, N5N6N7, N6N7N8, N1N2C2, N3N4C1, N2N3C2, C1N1N2, N5N6C4, N7N8C3, N6N7C4, C3N5N6), and dihedral angles (N1N2N3N4, N5N6N7N8, N1N2C2N3, N1N2N3C2, N5N6C4N7, N5N6N7C4, N4C1C2N8, N3N2N6N7, C1N4N8C2, CRC, NRC) of the title compounds. CRC (NRN) are the dihedral angles of two C (N) atoms in the rings which are connected by the two N atoms in the bridged groups (R: −NN− or −NN(O)−). For instance, CRC in AIV-2 stands for the dihedral angle C1NNC2, while NRN in AVII-1 means the dihedral angle N4NNN8. 2754



Article

Table 3. Calculated Total Energies (E0), Zero-Point Energies (ZPE), Thermal Corrections (HT), Molecular Properties, Heats of Sublimation, and EOF of the Title Compoundsa,b E0

ZPE

compd

a.u.

a.u.

AI-1 AI-2 AI-3 AI-4 AI-5 AI-6 AI-7 AI-8 AII-1 AII-2 AII-3 AII-4 AII-5 AII-6 AII-7 AII-8 AIII-1 AIII-2 AIII-3 AIV-1 AIV-2 AIV-3 AV-1 AV-2 AVI-1 AVI-2 AVI-3 AVII-1 AVII-2 AVII-3 AVIII-1 AVIII-2 AIX-1 AIX-2 AIX-3 AX-1 AX-2 AX-3 AXI-1 AXI-2 AXII-1 AXII-2 AXII-3 AXIII-1 AXIII-2 AXIII-3 AXIV-1 AXIV-2 BI-1 BI-2 BI-3 BII-1 BII-2 BII-3 BIII-1 BIII-2 BIII-3 BIV-1

−716.5609 −626.4210 −716.5637 −626.4388 −1248.3570 −1402.8338 −1248.3469 −1402.8234 −716.5728 −626.4330 −716.5743 −626.4516 −1248.3665 −1402.8456 −1248.3536 −1402.8348 −924.4339 −1422.0587 −1331.9177 −1033.8863 −1531.5206 −1441.3673 −1408.3375 −1408.3348 −924.4262 −1422.0339 −1331.9113 −1033.8890 −1531.4912 −1441.3706 −1408.3314 −1408.3234 −924.4501 −1422.0694 −1331.9268 −1033.8994 −1531.5172 −1441.3754 −1408.3410 −1408.3365 −924.4438 −1422.0534 −1331.9322 −1033.8960 −1531.5053 −1441.3844 −1408.3371 −1408.3328 −705.4576 −1203.0667 −1112.9502 −705.4358 −1203.0421 −1112.9101 −705.4721 −1203.0808 −1112.9656 −905.0462

0.0468 0.0507 0.0466 0.0508 0.0846 0.0910 0.0841 0.0910 0.0472 0.0512 0.0470 0.0513 0.0849 0.0915 0.0844 0.0910 0.0759 0.1048 0.1086 0.0847 0.1137 0.1173 0.1378 0.1376 0.0765 0.1046 0.1087 0.0853 0.1129 0.1173 0.1365 0.1366 0.0764 0.1053 0.1091 0.0853 0.1141 0.1180 0.1380 0.1379 0.0773 0.1055 0.1098 0.0856 0.1137 0.1181 0.1368 0.1365 0.0548 0.0833 0.0876 0.0539 0.0823 0.0864 0.0549 0.0834 0.0879 0.0601

ΔHf,gas

HT kJ·mol 26.0 25.5 26.5 25.6 45.4 51.3 45.6 51.1 26.0 25.6 26.4 25.5 45.9 51.6 46.2 51.9 35.5 53.5 53.1 40.6 58.7 58.6 56.1 56.4 35.1 54.4 53.4 40.5 59.2 58.4 57.4 56.4 35.6 54.0 53.6 40.4 58.7 58.4 57.3 57.5 35.0 54.1 53.3 40.0 59.0 58.2 57.9 58.1 27.8 46.3 45.3 28.2 46.6 45.5 28.0 46.3 45.3 33.4

−1

−1

kJ·mol

482.4 869.7 469.9 814.0 −225.6 15.0 −209.6 32.9 455.0 842.7 445.9 784.5 −246.3 −11.7 −223.3 6.7 966.1 913.3 1303.6 1194.1 1116.6 1538.9 1117.4 1124.0 966.9 969.0 1306.7 1244.4 1259.3 1592.7 1164.4 1184.7 930.4 892.3 1287.0 1166.6 1132.1 1524.8 1115.4 1127.1 928.0 925.5 1260.2 1231.8 1229.9 1563.8 1156.3 1166.8 537.1 535.7 858.3 592.4 598.4 960.6 497.8 497.6 816.9 463.7 2755

ΔHsub A

ν

σ2tot

1.46 1.55 1.47 1.53 2.15 2.31 2.14 2.28 1.51 1.58 1.50 1.59 2.25 2.45 2.26 2.46 2.00 2.55 2.64 2.28 2.86 2.94 2.76 2.77 2.00 2.59 2.61 2.31 2.85 2.90 2.79 2.77 2.09 2.73 2.81 2.31 2.95 3.02 2.92 2.91 2.10 2.74 2.83 2.30 2.95 3.03 2.95 2.95 1.65 2.26 2.34 1.61 2.19 2.23 1.65 2.26 2.34 1.79

0.16 0.19 0.19 0.22 0.20 0.19 0.20 0.21 0.20 0.22 0.14 0.22 0.13 0.13 0.10 0.09 0.17 0.14 0.14 0.16 0.17 0.18 0.11 0.19 0.10 0.16 0.20 0.10 0.17 0.18 0.16 0.21 0.20 0.16 0.19 0.14 0.13 0.14 0.08 0.12 0.12 0.08 0.11 0.14 0.10 0.13 0.08 0.10 0.06 0.07 0.10 0.06 0.11 0.17 0.06 0.09 0.11 0.09

8.35 8.87 8.38 8.73 12.25 13.17 12.24 13.04 8.59 9.02 8.57 9.05 12.84 13.98 12.88 14.01 11.39 14.54 15.08 12.99 16.31 16.76 15.74 15.82 11.43 14.79 14.90 13.17 16.27 16.56 15.90 15.81 11.93 15.60 16.03 13.16 16.82 17.26 16.64 16.62 12.00 15.66 16.14 13.14 16.82 17.29 16.84 16.83 9.39 12.89 13.37 9.20 12.47 12.73 9.41 12.90 13.36 10.22

−1

ΔHf,solid

kJ·mol

kJ·mol−1

68.6 78.5 77.7 84.7 91.5 98.7 92.3 96.7 71.2 80.3 67.6 74.1 90.8 100.5 89.9 99.1 95.2 111.3 120.5 104.9 135.5 141.8 135.1 144.2 86.9 116.9 125.8 101.5 133.7 143.5 142.0 146.3 98.7 122.2 131.3 102.0 131.3 140.5 141.1 145.7 92.3 117.1 122.8 104.4 132.4 139.9 140.0 140.9 66.6 89.6 98.1 65.2 91.1 101.4 66.4 92.1 99.6 77.5

413.8 791.2 392.2 729.4 −317.1 −83.7 −301.9 −63.8 383.8 762.4 378.3 710.3 −337.1 −112.2 −313.2 −92.4 870.9 802.0 1183.2 1089.2 981.1 1397.2 982.3 979.8 880.0 852.1 1180.9 1142.9 1125.6 1449.2 1022.5 1038.4 831.7 770.2 1155.7 1064.6 1000.9 1384.3 974.2 981.4 835.7 808.4 1137.4 1127.4 1097.5 1423.9 1016.3 1025.9 470.5 446.1 760.2 527.2 507.3 859.2 431.4 405.5 717.3 386.2



Article

Table 3. continued E0

ZPE

compd

a.u.

a.u.

BIV-2 BIV-3 BIV-4 BV-1 BV-2 BV-3 BV-4 BV-5 BV-6 BV-7 BV-8 BVI-1 BVI-2 BVII-1 BVII-2 BVIII-1 BVIII-2

−814.9325 −1436.8222 −1591.2911 −905.0342 −814.9217 −905.0401 −814.9177 −1436.7995 −1591.2790 −1436.8025 −1591.2813 −1897.4233 −2006.8906 −1897.3826 −2006.8519 −1897.4464 −2006.9167

0.0646 0.0979 0.1041 0.0603 0.0649 0.0603 0.0643 0.0980 0.1045 0.0977 0.1043 0.1485 0.1575 0.1474 0.1557 0.1486 0.1577

ΔHf,gas

HT kJ·mol 32.4 52.4 58.5 33.6 32.6 33.5 32.6 52.6 58.6 52.5 58.6 76.0 81.1 75.6 81.5 76.2 81.2

−1

−1

kJ·mol

779.0 −180.5 81.2 485.8 798.5 470.5 807.6 −130.3 103.9 −139.1 97.5 1140.2 1329.5 1244.3 1427.5 1070.0 1253.2

ΔHsub A

ν

σ2tot

1.85 2.47 2.67 1.78 1.85 1.79 1.85 2.38 2.53 2.40 2.56 3.61 3.89 3.34 3.73 3.74 3.96

0.14 0.09 0.08 0.07 0.15 0.07 0.15 0.08 0.08 0.09 0.08 0.05 0.05 0.06 0.09 0.06 0.08

10.56 14.12 15.22 10.15 10.58 10.20 10.58 13.58 14.46 13.70 14.59 20.60 22.19 19.08 21.27 21.35 22.62

−1

ΔHf,solid

kJ·mol

kJ·mol−1

86.1 105.8 116.4 73.0 83.1 71.5 84.2 97.3 104.4 100.0 107.1 176.8 200.0 157.3 192.7 180.1 202.2

692.9 −286.3 −35.3 412.9 715.4 399.0 723.4 −227.6 −0.5 −239.0 −9.6 963.4 1129.5 1087.0 1234.8 889.8 1051.0

a The scaling factor for ZPE is 0.98 and the scaling for HT is 0.96.46 bU(E0) = 0.0001 a.u., U(ZPE) = 0.0001 a.u., U(HT) = 0.1 kJ·mol−1, U(ΔHf,gas) = 0.1 kJ·mol−1, U(ΔHsub) = 0.1 kJ·mol−1, U(ΔHf,solid) = 0.1 kJ·mol−1, U(A) = 0.01 nm2, U(σ2tot) = 0.01 kJ2·mol−2.

approximately. This may be because the −NN− group can improve the conjugation between the two rings. The effects of the substituent groups and bridged groups on the structure of the tetrazine derivatives are also studied. From the Table 1, it is seen that the difference between different bond lengths and bond angles among BI-1, BII-1, and BIII-1 are smaller than that among other compounds in series BI, BII, and BIII, respectively. This may be because the three compounds have better symmetry and conjugation than others in the same series. The bond lengths and bond angles in eight compounds of series BV are very close each other. The effect of the substituent groups on the bond lengths and bond angles of series BV are smaller than that of series BII. This may be because the two O atoms attached with the ring can improve the conjugation and stability of the 1,2,3,4-tetrazine ring.43 The dihedral angles (N1N2N3N4, N1N2C2N3, and N1N2N3C2) of all the tetrazine derivatives are lower than 6.5° except for BII-3, BIV-4, BV-5, and BV-6, whose dihedral angles are higher than 12°, showing that the rings of the four compounds have worse planarity than other compounds, which may be because they have poorer symmetry than others. From the dihedral angles of CRC, it can be found that the two rings of all the bicyclic tetrazine derivatives are coplanar approximately and the incorporation of the −NN− group is helpful for improving their coplanarity when comparing the CRC angles of BVI-2, BVII-2, and BVIII-3 with those of BV-1, BVII-1, and BVIII-1, respectively. 3.2. Enthalpy of Formation. Table 2 lists the total energies, ZPEs, and thermal corrections for 18 reference compounds in the isodesmic reactions. The experimental EOF of other reference compounds were taken from references 44 and 45. The EOF of CH 3 N 3 , CH 3CF 3 , CH 3 CF 2NF 2 , CH3N2CH3, CH3N(O)CH3, NH2NF2, NH2N3, NH2N2NH2, NH 2 N(O)NNH 2 , NH 2 NH 2 , 1H-tetrazole, 2H-tetrazole, 1,2,3,4-tetrazine, 1,2,3,5-tetrazine, 1,2,4,5-tetrazine, 1,2,3,4tetrazine-1,3-dioxide, and 1,2,4,5-tetrazine-1,4-dioxide were calculated by using the atomization reaction at the G2 level. To validate the reliability of our results, the EOF of CH4, CH3CH3, CH3NO2, CH3NF2, NH3, and NH2NO2 were

calculated at the G2 level from the atomization reactions. Our calculated EOF are very close to their corresponding

Figure 2. A comparison of the solid-phase EOF of the title compounds together with commonly used explosives HMX.

experimental values with the relative errors (calculated by eq 10) of only 2.04 %, 1.38 %, 1.25 %, 3.99 %, 1.53 %, and 5.13 %, respectively. This shows that our calculated EOF at the G2 theory are expected to be reliable. relative error% = 100|X − X 0| /X

(10)

where X is the experimental EOF value and X0 is the calculated EOF value. Table 3 presents the total energies, ZPEs, thermal corrections, molecular properties, and gas-phase and solidphase EOF of the title molecules. It is seen that the molecules with −N3 or −NN− have higher EOF than others in the same series both for the tetrazole and tetrazine derivatives, indicating that the group −N3 or −NN− is an effective group for improving the EOF. It can be also found that the two molecules with different substitution positions but the same 2756



Article

Table 4. Predicted Densities (ρ), Heats of Explosion (Q), Detonation Velocities (D), and Detonation Pressures (P) for the Title Compounds Together with RDX and HMXa,b

a

compd

ρ/g·cm−3

Q/kJ·g−1

P/GPa

D/km·s−1

compd

ρ/g·cm−3

Q/kJ·g−1

P/GPa

D/km·s−1

AI-1 AI-2 AI-3 AI-4 AI-5 AI-6 AI-7 AI-8 AII-1 AII-2 AII-3 AII-4 AII-5 AII-6 AII-7 AII-8 AIII-1 AIII-2 AIII-3 AIV-1 AIV-2 AIV-3 AV-1 AV-2 AVI-1 AVI-2 AVI-3 AVII-1 AVII-2 AVII-3 AVIII-1 AVIII-2 AIX-1 AIX-2 AIX-3 AX-1 AX-2 AX-3 AXI-1

1.99 1.80 2.02 1.85 2.06 2.09 2.07 2.10 1.98 1.80 1.97 1.77 2.03 2.06 2.03 2.05 1.89 1.98 1.88 1.86 1.98 1.87 1.92 1.95 1.86 1.98 1.90 1.84 1.96 1.89 1.93 1.96 1.87 1.96 1.87 1.84 1.93 1.84 1.88

6687.1 7609.3 6557.0 7212.9 4600.4 5325.4 4653.6 5387.8 6506.7 7424.7 6473.2 7090.7 4530.9 5236.3 4614.2 5298.2 7291.2 6774.2 7226.7 7346.8 6745.3 7259.4 6968.9 6961.7 7331.4 6922.4 7219.6 7556.6 7140.5 7405.9 7085.2 7131.3 7119.1 6680.0 7143.0 7250.6 6799.3 7223.4 6945.8

40.5 39.7 41.7 40.7 35.2 38.7 35.5 39.1 39.8 39.3 39.2 37.2 33.8 37.1 34.0 37.1 42.5 41.4 40.7 40.3 41.4 40.6 42.3 43.2 38.7 41.5 41.6 39.9 42.0 41.9 43.1 44.1 38.7 40.0 39.7 39.2 39.7 39.2 40.4

9.3 9.5 9.4 9.5 8.6 9.0 8.6 9.0 9.2 9.4 9.2 9.2 8.4 8.8 8.5 8.8 9.6 9.4 9.5 9.4 9.4 9.5 9.6 9.6 9.3 9.4 9.5 9.4 9.5 9.6 9.7 9.7 9.2 9.3 9.4 9.3 9.3 9.3 9.4

AXI-2 AXII-1 AXII-2 AXII-3 AXIII-1 AXIII-2 AXIII-3 AXIV-1 AXIV-2 BI-1 BI-2 BI-3 BII-1 BII-2 BII-3 BIII-1 BIII-2 BIII-3 BIV-1 BIV-2 BIV-3 BIV-4 BV-1 BV-2 BV-3 BV-4 BV-5 BV-6 BV-7 BV-8 BVI-1 BVI-2 BVII-1 BVII-2 BVIII-1 BVIII-2 RDXa HMXa

1.90 1.85 1.94 1.84 1.85 1.93 1.84 1.86 1.86 1.81 1.96 1.84 1.81 1.98 1.88 1.80 1.97 1.85 2.00 1.86 2.07 2.09 1.98 1.84 1.98 1.85 2.07 2.09 2.07 2.09 1.89 1.88 1.93 1.91 1.90 1.88 1.82 1.91

6966.3 7136.7 6793.0 7086.9 7495.9 7063.5 7334.7 7067.2 7094.9 7336.4 6857.1 7158.9 7666.2 7073.9 7523.1 7109.1 6712.7 7001.1 7038.8 7421.8 5277.7 5901.8 7165.6 7534.0 7099.9 7574.1 5454.8 5997.3 5420.5 5972.6 7255.2 7179.4 7524.3 7395.4 7070.6 6995.2 6686.7 6839.5

40.7 37.8 39.7 38.3 40.5 40.5 39.4 40.0 39.7 36.3 39.8 37.5 37.1 41.1 40.0 35.6 39.5 37.3 41.4 39.4 37.5 40.3 41.2 38.8 40.7 39.1 38.2 40.8 38.1 40.8 40.6 40.0 42.9 41.7 38.9 38.3 34.0 39.0

9.4 9.2 9.3 9.2 9.5 9.4 9.4 9.4 9.4 9.0 9.2 9.1 9.1 9.4 9.4 9.0 9.2 9.1 9.4 9.3 8.8 9.1 9.4 9.3 9.3 9.3 8.9 9.2 8.9 9.2 9.4 9.4 9.6 9.5 9.2 9.2 8.7 9.1

The experimental values were taken from ref 49. bU(ρ) = 0.01 g·cm−3, U(Q) = 0.1 kJ·g−1, U(P) = 0.1 GPa, U(D) = 0.1 km·s−1.

3.3. Energetic Properties. Table 4 lists the calculated ρ, Q, D, P, and oxygen balance (OB) values of the title molecules along with two famous explosives 1,3,5-trinitro-1,3,5-triazinane (RDX) and HMX. Figure 3a displays the densities and heats of detonation of the 75 designed compounds along with HMX. It is found that the molecules with the combination of −NF2, −CF3, −CF2NF2 with −C(NO2)3, or the combination of −NO2 with −NF2 have higher densities than those with the combination of other substituents, while the molecules with −N3 possess relatively lower densities. The molecules with the combination of −NH2 with −C(NO2)3 also have very high densities, which may be partly caused by the formation of hydrogen bonds in crystal. The molecules with the same substituents and ring but different bridged groups or substitution positions have similar densities, indicating that the bridged groups and substitution positions have a small effect on their densities. Overall, among 48 tetrazole-based compounds studied here, 24 compounds have

substituent or bridged groups and ring have very similar EOF values such as AI-1 and AII-1, AIII-1 and AIX-1, BV-1 and BV3, showing that the substitution positions produce little effect on the EOF. Figure 2 presents a comparison of the solid-phase EOF of the title molecules along with HMX (1,3,5,7-tetranitro-1,3,5,7tetrazocane).44 It is seen that most of the designed molecules possess a very high solid-phase EOF. For example, among the 48 tetrazole derivatives, 40 molecules have a much higher solidphase EOF than HMX and 31 molecules possess a solid-phase EOF over 800 kJ·mol−1. Though the solid-phase EOF of the tetrazine detivatives are lower than those of the tetrazole derivatives, there also are 22 molecules with a much higher solid-phase EOF than HMX and 7 molecules with a solid-phase EOF above 800 kJ·mol−1. AVII-3 has the highest solid-phase EOF value (1449.2 kJ·mol−1) among all the 75 designed molecules. 2757



Article

Figure 3. A comparison of the calculated ρ and Q values of the title compounds together with commonly used explosives HMX.

Figure 4. A comparison of the calculated D and P values of the title compounds together with that of commonly used explosives RDX and HMX.

higher ρ than HMX (1.91 g·cm−3), and the others have higher ρ than RDX (1.82 g·cm−3) except for AI-2, AII-2, and AII-4. There are nine compounds whose densities are over 2.00 g·cm−3. For the 27 tetrazine-based compounds studied here, 13 compounds have higher ρ than HMX (1.91 g·cm−3), and the other have higher ρ than RDX (1.82 g·cm−3) except for BI-1, BII-1, and BIII-1. There are six compounds whose densities are above 2.00 g·cm−3. AI-8 has the highest ρ value (2.10 g·cm−3) among all the 75 title compounds. Overall, most of the designed molecules have high densities. It can be seen from Figure 3b that most of the title compounds have very high Q values except for the molecules containing −CF3 or −CF2NF2, indicating that the combination of −NO2 with −NF2, −N3, or itself, and the combination of −C(NO2)3 with −NF2, −N3, −NH2, or itself are helpful for increasing their heats of explosion, while the substitution of −CF3 or −CF2NF2 reduces their Q values. It is also found that the bridged groups and substitution positions have a small effect on their heats of explosion. In a word, there are 51 compounds (31 tetrazole derivatives and 20 tetrazine derivatives) possessed higher Q than HMX. This is mainly because these compounds have oxygen balance equal to zero. BII-1 has the highest Q value (7662.4 kJ·g−1) among all the title compounds. Figure 4 presents a comparison of the calculated D and P values of the title molecules together with RDX and HMX. It is surprising that almost all of the designed molecules (71

molecules: 44 tetrazole derivatives, and all of the 27 tetrazine derivatives) possess higher D and P than RDX except for AI-5, AI-7, AII-5, and AII-7. The deepest impression is that 51 compounds (35 tetrazole derivatives and 16 tetrazine derivatives) own higher D and P than HMX, which is one of the most commonly used energetic ingredients in various high performance explosives and propellant formulations. This shows that the combination of −NF2 with −NO2, −C(NO2)3, or itself, the combination of −NO2 with −N3 or itself, or the combination of −C(NO2)3 with −NH2 or −N3 in a tetrazole or tetrazine molecule with oxygen balance equal to zero is a very effective way to design a explosive with higher D and P than HMX, while the molecules with the combination of −C(NO2)3 with CF3 or −CF2NF2 have comparable D and P with RDX. If the 71 compounds could be synthesized, they will have good performances. Thus, further investigations are still needed. In addition, AVIII-2 has the highest D (9.7 km·s−1) and P (44.0 GPa) values among all of the 75 designed molecules. In addition, it is found that the compounds in series AI have higher D and P than corresponding ones in series BI, while BV1and BV-2 (BV-5 and BV-6) have very similar D and P with BV-3 and BV-4 (BV-7 and BV-8), respectively, showing that the effects of substitution positions on D and P are incorporated with those of the molecular structures. In all, it can be inferred that most of the designed compounds have outstanding 2758



Article

Table 5. Bond Dissociation Energies (BDE/kJ·mol−1) of the Relatively Weak Bonds of the Title Compoundsa compd

ring−NF2

ring−NO2

AI-1 AI-2 AI-3 AI-4 AI-5 AI-6 AI-7 AI-8 AII-1 AII-2 AII-3 AII-4 AII-5 AII-6 AII-7 AII-8 AIII-1 AIII-2 AIII-3 AIV-1 AIV-2 AIV-3 AV-1 AV-2 AVI-1 AVI-2 AVI-3 AVII-1 AVII-2 AVII-3 AVIII-1 AVIII-2 AIX-1 AIX-2 AIX-3 AX-1 AX-2 AX-3 AXI-1 AXI-2 AXII-1 AXII-2 AXII-3 AXIII-1 AXIII-2 AXIII-3 AXIV-1 AXIV-2 BI-1 BI-2 BI-3 BII-1 BII-2 BII-3 BIII-1 BIII-2 BIII-3 BIV-1 BIV-2 BIV-3 BIV-4

100.9

227.1 246.5 106.6 71.8

206.0

ring−N3

C(NO2)2−NO2

ring-bridge

ring−NH2

279.0

255.8 260.8 133.4 104.0

343.2

722.5 193.2

231.3

151.9

232.7 198.3 715.6 198.5 717.3

200.1

238.6

173.9

242.4

155.1 370.6 105.7 105.5 114.5 114.9

123.2 146.1 191.1

115.6 116.5

62.6 115.6 128.9

112.7 116.1 106.3 113.9

242.6 263.4 355.9

96.1 98.5

225.4 263.2 360.3

102.3 100.6 103.7 100.8

136.1 163.4 204.1

114.8 113.7

94.9 102.5 145.3

111.3 109.7 108.4 113.9

251.7 276.8 372.5

104.9 104.9

248.6 279.6 379.1

N−F/N−N2 204.2 724.1

148.8

105.3 102.3 113.9 105.2 107.4

CF2−NF2

102.4 102.4 103.2 103.5

497.1 504.9 521.3 250.5 288.4 251.3 309.2 275.7 179.4 167.8 139.2 142.3 107.8 83.0 97.6 92.2 529.1 537.5 535.6 334.2 253.3 256.3 244.5 235.2 144.1 216.4 191.1 132.1 93.0 82.3 92.1 91.7

707.5 197.0 721.5 234.4 245.1 191.7 727.7 194.7 721.1 492.2 465.5 200.0 707.5 197.5 702.6 323.2 311.6 199.1 711.6 195.4 714.3 487.2 481.3

218.8 249.3 357.1

106.8 105.8

206.8 398.2

276.5

101.9 70.5

197.8 387.5

349.5

106.7 110.2

212.5 379.2 171.0 375.6

184.0 208.5 206.3 238.5 223.3

193.1 206.1

338.2 89.2 67.4 2759

127.7

237.3



Article

Table 5. continued

a

compd

ring−NF2

ring−NO2

BV-1 BV-2 BV-3 BV-4 BV-5 BV-6 BV-7 BV-8 BVI-1 BVI-2 BVII-1 BVII-2 BVIII-1 BVIII-2

211.6

227.4 234.9 197.2 202.2

259.1

ring−N3

C(NO2)2−NO2

ring-bridge

ring−NH2

CF2−NF2

N−F/N−N2 199.7 374.5 175.5 377.2

329.2 352.3 74.1 80.5 108.2 107.1 105.7 104.4 117.3 112.5 107.0 106.9

150.2

239.1

129.5

232.9

440.5 244.7 378.9 223.7 405.9 222.0

U (BDE) = 0.1 kJ·mol−1.

Overall, considering the thermal stability (80 kJ·mol−1)50 and detonation performance, 57 molecules (AI-1 to AI-3, AI-5 to AI-8, AII-1 to AII-4, AII-6, AII-8, AIII-1 to AIII-3, AIV-2 to AIV-3, AV-1 to AV-2, AVI-1, AVII-1 to AVII-2, AIX-1 to AIX-3, AX-2 to AX-3, AXI-1 to AXI-2, AXII-1 to AXII-3, AXIII-1, BI-1 to BI-3, BII-1 to BII-3, BIII1 to BIII-3, BIV-1 to BIV-2, BV-1 to BV-4, BV-7 to BV-8, BVI-1 to BVI-2, BVII-1 to BVII-2, and BVIII-1 to BVIII-2) may be considered as the potential candidates of HEDCs.

detonation properties. This may be caused by their high heats of detonation and densities. It should be notable that 25 compounds (AI-2, AI-4, AII-2, AIII-1, AIII-3, AIV-1, AIV-3, AVI-3, AVII-1, AVII-3, AIX-3, AX-1, AX-3, AXI-1, AXI-2, AXIII-1, AXIII-2, AXIV-1, AXIV-2, BII-3, BIV-2, BV-4, AVI-1, AVI-2, and AVII-2) have lower densities but higher D and P than HMX. This is mainly because these 25 molecules possess very high heats of detonation, indicating that the heat of detonation plays a more important role in improving the detonation properties than does the density sometimes.32 Our observations indicate that designing the tetrazole and tetrazine derivatives with oxygen balance equal to zero is a very effective way to obtain potential energetic compounds with outstanding detonation properties. 3.4. Thermal Stability. The bond dissociation energy (BDE) can provide very useful information for understanding the stability of energetic materials. Generally, the smaller is the energy for breaking a bond, the weaker the bond is, and the easier the bond becomes a trigger bond; that is to say, the corresponding compound is more unstable Therefore, the calculated BDE could be used to measure the relative order of thermal stability for energetic compounds. However, it is important to note that the BDEs are simply one piece of evidence for molecular stability, but not the conclusive one. The sensitivity of explosives involves many complex factors. The structure of an explosive is the intrinsic factor in determining its sensitivity. Recently, Politzer et al.45 reported that the available free space per molecule in the unit cell for the explosives can be used as a parameter to estimate their relative sensitivities. Table 5 lists the BDE values of several relatively weak bonds of the title molecules. It is seen that most of the molecules have the BDEs of around 100 kJ·mol−1, which are over the energy barrier (80 kJ·mol−1) for HEDCs suggested by Chung et al.,50 showing that some molecules are sensitive to some degree. This may be because the molecules contain at least one strong electron-withdrawing group such as −C(NO2)3, −NF2, and −NO2 or have some sensitive groups like −N3, −NN−, and −N(O)N− or have a long nitrogen chain such as the chain with 7 N atoms or 10 N atoms, which may damage their stabilities to a certain extent. It is also seen that the BDE value of the NO2−C(NO2)2 bond is lower than that of other bonds for most of the molecules, suggesting that the NO2−C(NO2)2 bond cleavage is a possible thermal decomposition path for these compounds.

4. CONCLUSIONS In this work, we reported a systematic study of the geometrical structures, EOF, energetic properties, and thermal stability of a series of tetrazole- and tetrazine-based derivatives with oxygen balance equal to zero by using the DFT-B3LYP method. The results show that the two rings in most of the tetrazole derivatives and all of the tetrazine derivatives are approximately coplanar. Most of the designed compounds have much higher EOF than HMX and over half of them have extremely high EOF over 800 kJ·mol−1. Among all the 75 designed molecules, 71 compounds have higher D and P than RDX and 25 compounds have higher D and P than HMX, indicating that designing the tetrazole- and tetrazine-based derivatives with oxygen balance equal to zero is a very effective way to obtain potential energetic compounds with outstanding detonation properties. Considering the thermal stability and detonation performance, 57 compounds may be considered as the potential candidates of HEDCs.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 86-25-84315947-805. Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 21273115) and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. Notes

The authors declare no competing financial interest.

■

REFERENCES

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Molecular Design of Tetrazole- and Tetrazine-Based High-Density

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