Abstract
Forty nitramines by incorporating −C=O, −NH2, −N3, −NF2, −NHNO2, −NHNH2, −NO2, −ONO2, −C(NO2)3, and −CH(NO2)2 groups based on a 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX) framework were designed. Their electronic structures, heats of formation (HOFs), detonation properties, thermal stabilities, electrostatic potential, and thermodynamic properties were systematically investigated by density functional theory. The comprehensive relationships between the structures and performance of different substituents were studied. Results indicate that −C(NO2)3 has the greatest effect on improvement of HOFs among the whole substituted groups. Thermodynamic parameters, such as standard molar heat capacity (Cp,mθ), standard molar entropy (Sm), and standard molar enthalpy (Hmθ), of all designed compounds increase with the increasing number of energetic groups, and the volumes of energetic groups have a great influence on standard molar enthalpy. Except for −NH2(R1), −NHNH2(R5), and B3, all of the designed compounds have higher detonation velocities and pressures than HMX. Among them, E7 exhibits an extraordinarily high detonation performance (D = 10.89 km s–1, P = 57.3 GPa), E1 exhibits a relatively poor detonation performance (D = 8.93 km s–1, P = 35.5 GPa), and −NF2 and −C(NO2)3 are the best ones in increasing the density by more or less 12%.
1. Introduction
In recent years, to meet the continuous improvement of energetic materials,1−4 researchers are committed to designing and developing novel high-energy-density compounds (HEDCs). 1,3,5,7-Tetranitro-1,3,5,7-tetraazacyclooctane (HMX) and hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) have been widely used as powerful solid explosives and propellants in both civil and military fields. HMX exhibits a good balance between the sensitivity and explosive performances, with high energetic performances (density 1.91 g cm–3, detonation velocity 9.10 km s–1, and detonation pressure 39.0 GPa),5 which is very close to the criteria of the high-energy-density materials (HEDMs) (density >1.9 g cm–3, detonation velocity >9.0 km s–1, detonation pressure >40.0 GPa).6 Therefore, the framework of HMX can be considered as a good parent structure for the development of novel HEDCs.
The study found that incorporating more nitro groups via C or N functionalization based on the HMX framework is a popular and effective strategy to acquire better energetic performances.7 Moreover, increasing the number of nitro groups and replacing the CH group with a nitrogen atom to introduce more N–N bonds into the cyclic nitramines can lead to an increase in mass density and heat of formation (HOF), thus improving the detonation performance.8 Many new cyclic nitramines have been successfully developed as candidates for HEDCs.9 For example, Pan et al.7 computationally designed four bicyclic nitramines and three cage nitramines by introducing −N(NO2)–CH2–N(NO2)–, −N(NO2)–, and O– linkages in the framework of HMX. Jeong10 theoretically investigated NNO2-substituted RDX and HMX derivatives as HEDMs and found that RDX–(NNO2)1 and HMX–(NNO2)1 exhibit excellent detonation performances (detonation velocities, 9.529 and 9.575 km s–1; detonation pressure, 40.818 and 41.570 GPa). Obviously, designing cyclic nitramine-based HEDMs has not been fully developed.
It is obvious that there are four methylene groups in the structure of HMX, which can be occupied by the carbonyl group, nitro group, amino group, and so on. The designed 40 compounds are shown in Scheme 1, and their electronic structures, thermal stabilities, sensitivities, and detonation performance were investigated. For simplicity, we only presented the isodesmic reactions of HMX derivatives in Scheme 2. This theoretical study will provide useful information for synthesizing new molecules similar to HMX and understanding the relationship between energetic groups attached to the aliphatic ring and detonation performance.
Scheme 1. Designed Energetic Molecules Based on the HMX Ring.
Scheme 2. Isodesmic Reactions of HMX Derivatives.
2. Results and Discussion
2.1. Electronic Structures and Energy Gap
To study the chemical stability of these designed compounds, the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) energy gaps are calculated, which provides information on how easily electrons are excited and allows the qualitative comparison of chemical reaction vulnerabilities by electron transfer.11 The frontier molecular orbital energies and their gaps (ΔEHOMO–LUMO) for designed compounds are displayed in Table 1. From Table 1, it is found that the HOMO energy levels increased when −NH2, −N3, −NHNO2, −NHNH2, and −C(NO2)3 groups were introduced compared to the solo HMX ring (HOMO: −8.53 eV, LUMO: −2.69 eV, HOMO–LUMO gap: 5.84 eV). However, the number of carbonyl, −N3, −NF2, −CH(NO2)2, −C(NO2)3, −NO2, and −ONO2 groups had a marginal effect on HOMO energy levels (A1, B2, B3, B6, B7, B8, and B9). The order of HOMO energy levels on energetic groups is as follows: −NHNH2 > −C(NO2)3 > −NH2 > −N3 > −NHNO2 > −NF2 > −ONO2 > −NO2 > −C=O > −CH(NO2)2 (A1, B1–B9). However, the relationship between LUMO energy levels and energetic groups can be written as a different trend: −NHNH2 > −NH2 > −N3 > −NF2 > −NHNO2 > −ONO2 > −NO2 > −C=O > −CH(NO2)2 > −C(NO2)3 (A1, B1–B9).
Table 1. Calculated HOMO and LUMO Energies (eV) and Energy Gaps (ΔELUMO–HOMO) of Designed Compounds.
| compd. | A1 | A2 | A3 | A4 | B1 | B2 | B3 | B4 | B5 | B6 |
|---|---|---|---|---|---|---|---|---|---|---|
| HOMO | –8.76 | –8.89 | –9.39 | –9.69 | –8.18 | –8.26 | –8.61 | –8.50 | –7.52 | –8.77 |
| LUMO | –3.39 | –3.72 | –3.92 | –4.08 | –2.69 | –2.83 | –2.85 | –2.88 | –2.47 | –3.71 |
| ΔEHOMO–LUMO | 5.37 | 5.17 | 5.47 | 5.61 | 5.49 | 5.43 | 5.76 | 5.62 | 5.05 | 5.06 |
| compd. | B7 | B8 | B9 | C1 | C2 | C3 | C4 | C5 | C6 | C7 |
|---|---|---|---|---|---|---|---|---|---|---|
| HOMO | –8.13 | –8.75 | –8.65 | –7.85 | –8.23 | –8.68 | –8.96 | –7.48 | –9.17 | –8.15 |
| LUMO | –3.81 | –3.18 | –3.05 | –2.67 | –2.92 | –3.01 | –2.98 | –2.45 | –3.85 | –4.14 |
| ΔEHOMO–LUMO | 4.32 | 5.57 | 5.60 | 5.18 | 5.31 | 5.67 | 5.98 | 5.03 | 5.32 | 4.01 |
| compd. | C8 | C9 | D1 | D2 | D3 | D4 | D5 | D6 | D7 | D8 |
|---|---|---|---|---|---|---|---|---|---|---|
| HOMO | –9.03 | –8.91 | –7.95 | –8.27 | –8.94 | –9.11 | –7.24 | –9.38 | –8.15 | –9.23 |
| LUMO | –3.53 | –3.27 | –2.70 | –2.99 | –3.20 | –3.23 | –2.22 | –4.11 | –4.31 | –3.73 |
| EHOMO–LUMO | 5.50 | 5.64 | 5.25 | 5.28 | 5.74 | 5.88 | 5.02 | 5.27 | 3.84 | 5.50 |
| compd. | D9 | E1 | E2 | E3 | E4 | E5 | E6 | E7 | E8 | E9 |
|---|---|---|---|---|---|---|---|---|---|---|
| HOMO | –9.02 | –7.78 | –8.29 | –9.07 | –8.90 | –6.02 | –9.54 | –8.23 | –9.44 | –9.11 |
| LUMO | –3.34 | –2.66 | –3.09 | –3.45 | –3.40 | –2.20 | –4.36 | –4.09 | –3.99 | –3.43 |
| EHOMO–LUMO | 5.68 | 5.12 | 5.20 | 5.62 | 5.50 | 3.82 | 5.18 | 4.14 | 5.45 | 5.68 |
Figure 1 displays the variation trends of ΔELUMO–HOMO of series B among designed compounds. Obviously, all of the title compounds have relatively large energy gaps from 3.82 to 5.98 eV, which shows that these molecules exhibit good stabilities in the chemical process. However, their energy gaps are smaller than those of HMX (5.84 eV), except for B5 (5.98 eV) and C5 (5.88 eV). Among them, B5 has the largest energy gap (5.98 eV), whereas D6 has the smallest energy gap (3.82 eV). Therefore, all of these compounds are less chemically stable than HMX. In addition, compound B5 may be less active than other compounds in chemical processes, while compound D6 may exhibit a little higher reactivity and lower stability. As can be seen from Figure 1, the HOMO of B4, B6, B7, B8, and B9 is mainly distributed on designed substituted groups; this suggests that the −NHNO2, CH(NO2)2, −C(NO2)3, −NO2, and −ONO2 groups affect the distribution of HOMO, and −N3, −NHNH2, and −C(NO2)3 make contributions to the LUMO.
Figure 1.
Variation trends of ΔELUMO–HOMO of the designed compounds.
2.2. Heat of Formation
Heat of formation (HOF) is usually taken as the indicator of the “energy content” of an HEDM. Therefore, it is significant to predict HOF accurately. Accurate HOFs are usually predicted by either atomization reactions (mainly for small molecules) or isodesmic reactions (mainly for complex compounds). Table 2 lists calculated total energies (E0), zero-point energies (ZPEs), and thermal corrections (HT) for the reference compounds in the isodesmic reactions.
Table 2. Calculated Total Energies (E0), Zero-Point Energies (ZPEs), Thermal Corrections (HT), and Heats of Formation (HOFs) of the Reference Compounds.
| compd. | E0 (au)a | ZPEb(kJ·mol–1) | HTb (kJ·mol–1) | ΔHf, gas (kJ·mol–1) |
|---|---|---|---|---|
| CH4 | –40.501859 | 115.8 | 10.1 | –74.6c |
| CH2O | –114.499886 | 68.8 | 10.1 | –115.9c |
| CH3N3 | –204.086152 | 130.3 | 14.3 | 293.412 |
| CH3NF2 | –294.226205 | 121.4 | 13.7 | –98.013 |
| CH3CH(NO2)2 | –95.845347 | 210.0 | 23.0 | –105.113 |
| CH3C(NO2)3 | –300.349171 | 213.7 | 29.4 | –73.913 |
| CH3NH2 | –151.164950 | 165.7 | 11.5 | –23.0c |
| CH3NHNO2 | –488.823136 | 174.6 | 16.1 | –73.214 |
| CH3NHNH2 | –693.310709 | 211.3 | 13.5 | 94.5c |
| CH3NO2 | –245.010975 | 128.9 | 11.7 | –81.0c |
| CH3ONO2 | –320.196991 | 140.8 | 15.6 | –122.0c |
| HMX | –1196.595457 | 497.1 | 48.1 | 272.615 |
Calculated at the DFT-D3/M06-2X/def2-TZVPP level.
Calculated at the B3LYP/6-311G(d,p) level, and the scaling factor is 0.9888 for ZPE and 1.0062 for HT.
Obtained from http://webbook.nist.gov.
Table 3 presents the total energies, ZPEs, thermal corrections, ΔHf,gas, A, v, σtot2, ΔHsub, and ΔHf,solid of HMX-based energetic derivatives. It is seen that most of the compounds except A4 have positive ΔHf,gas range from 24.6 (A3) to 2254.1 kJ mol–1 (E7). In particular, the designed compounds have much larger ΔHf,gas values than the parent compound HMX except for series A, B3, C3, and B9–E9. This shows that −C(NO2)3 has the greatest effect on improvement of HOFs among the whole substituted groups while the −C=O group makes less contribution. Moreover, gas-phase heats of formation of monosubstituted HMX derivatives of −C(NO2)3 (B7) and −N3 (B2) have more than tripled compared with HMX. Interestingly, with the increase of the number of −C(NO2)3 and −N3 groups, the values of ΔHf,gas and ΔHf,solid also increase. This suggests that when designing compounds, we can look for high-energy compounds in E series derivatives with −C(NO2)3 and −N3 substitution sites. In addition, introducing the −NH2, −NHNH2, and −NO2 substituents could also increase the HOF value. However, series A and B9–E9 shows different trends from the abovementioned ones, which may decrease the values of ΔHf,gas and ΔHf,solid. These high positive HOFs make a great contribution to increasing detonation properties such as detonation velocities and detonation pressures.
Table 3. Calculated Molecular Properties and Heats of Formation of the Designed Compounds.
| compd. | E0 (au)a | ZPE (kJ mol–1)b | HT (kJ mol–1)b | ΔHf,gas (kJ mol–1) | A (Å2) | ν | σtot2 (kcal mol–1)2 | ΔHsub (kJ mol–1) | ΔHf,solid (kJ mol–1) |
|---|---|---|---|---|---|---|---|---|---|
| A1 | –1270.612882 | 445.2 | 50.1 | 178.1 | 248.1 | 0.1495 | 199.5 | 118.9 | 59.3 |
| A2 | –1344.620564 | 391.3 | 52.8 | 107.1 | 251.9 | 0.1034 | 176.5 | 112.8 | –5.7 |
| A3 | –1418.632902 | 338.7 | 55.0 | 24.6 | 260.5 | 0.0690 | 219.4 | 115.1 | –90.5 |
| A4 | –1492.632399 | 285.3 | 57.3 | –24.9 | 258.9 | 0.0831 | 138.9 | 110.8 | –135.7 |
| B1 | –1251.945635 | 541.4 | 51.6 | 303.8 | 252.7 | 0.1655 | 197.1 | 123.2 | 180.6 |
| B2 | –1360.175995 | 503.8 | 54.7 | 644.1 | 269.9 | 0.1171 | 240.1 | 130.4 | 513.7 |
| B3 | –1450.309513 | 493.3 | 56.1 | 269.4 | 263.4 | 0.1287 | 233.8 | 127.8 | 141.6 |
| B4 | –1456.428256 | 547.1 | 57.2 | 305.1 | 275.7 | 0.1094 | 261.4 | 134.2 | 170.9 |
| B5 | –1307.266537 | 586.4 | 54.2 | 417.7 | 262.2 | 0.1861 | 203.8 | 131.7 | 286.0 |
| B6 | –1644.897138 | 583.1 | 64.0 | 285.5 | 296.9 | 0.0877 | 245.3 | 142.9 | 142.6 |
| B7 | –1849.210686 | 572.8 | 72.1 | 760.0 | 322.2 | 0.1020 | 237.5 | 162.3 | 597.6 |
| B8 | –1401.091649 | 501.9 | 54.3 | 295.8 | 263.0 | 0.0876 | 268.8 | 123.2 | 172.6 |
| B9 | –1476.282814 | 512.2 | 57.2 | 236.7 | 276.3 | 0.1071 | 228.0 | 131.8 | 104.8 |
| C1 | –1307.304273 | 586.0 | 53.7 | 310.7 | 257.7 | 0.1845 | 176.3 | 126.0 | 184.7 |
| C2 | –1523.747246 | 509.6 | 61.8 | 1038.8 | 297.3 | 0.1117 | 235.6 | 146.6 | 892.2 |
| C3 | –1704.021064 | 489.7 | 63.5 | 271.5 | 278.4 | 0.1682 | 170.4 | 136.0 | 135.5 |
| C4 | –1716.267930 | 597.0 | 66.5 | 318.8 | 309.2 | 0.0911 | 219.5 | 150.1 | 168.7 |
| C5 | –1417.940917 | 676.6 | 60.1 | 553.7 | 284.3 | 0.2131 | 177.2 | 145.1 | 408.6 |
| C6 | –2093.193930 | 667.5 | 80.9 | 309.6 | 341.4 | 0.0667 | 285.4 | 172.8 | 136.8 |
| C7 | –2501.816730 | 646.5 | 97.7 | 1270.1 | 403.0 | 0.0971 | 188.8 | 223.4 | 1046.7 |
| C8 | –1605.570777 | 505.8 | 61.1 | 362.6 | 281.9 | 0.0631 | 340.1 | 133.2 | 229.4 |
| C9 | –1755.968677 | 526.7 | 66.5 | 203.2 | 304.2 | 0.0858 | 242.0 | 147.2 | 56.0 |
| D1 | –1362.653342 | 630.8 | 57.4 | 344.4 | 269.5 | 0.1805 | 177.5 | 132.6 | 211.9 |
| D2 | –1687.327455 | 515.6 | 68.7 | 1409.8 | 324.1 | 0.0944 | 232.7 | 162.2 | 1247.6 |
| D3 | –1957.730403 | 485.4 | 71.1 | 278.8 | 302.3 | 0.1206 | 119.9 | 140.7 | 138.1 |
| D4 | –1976.105350 | 646.8 | 76.0 | 338.5 | 342.5 | 0.0726 | 228.4 | 171.6 | 166.9 |
| D5 | –1528.621211 | 765.9 | 66.5 | 674.0 | 305.1 | 0.2317 | 177.9 | 160.8 | 513.3 |
| D6 | –2541.489545 | 752.5 | 97.6 | 337.3 | 394.9 | 0.0557 | 229.1 | 211.3 | 126.0 |
| D7 | –3154.433404 | 722.3 | 121.1 | 1752.2 | 458.6 | 0.0720 | 169.6 | 293.6 | 1458.7 |
| D8 | –1810.061465 | 509.9 | 67.5 | 398.7 | 300.1 | 0.0433 | 369.7 | 140.6 | 258.1 |
| D9 | –2035.642618 | 540.1 | 76.5 | 200.9 | 340.5 | 0.0704 | 196.0 | 167.6 | 33.3 |
| E1 | –1418.011055 | 675.4 | 60.0 | 354.4 | 276.5 | 0.1862 | 162.6 | 135.8 | 218.6 |
| E2 | –1850.898426 | 521.4 | 76.0 | 1805.4 | 353.0 | 0.0953 | 205.5 | 182.1 | 1623.2 |
| E3 | –2211.412140 | 480.4 | 77.7 | 356.8 | 312.4 | 0.0625 | 148.6 | 142.5 | 214.3 |
| E4 | –2235.930879 | 695.1 | 85.6 | 387.9 | 370.8 | 0.0813 | 262.2 | 197.9 | 190.0 |
| E5 | –1639.272900 | 852.8 | 73.6 | 867.6 | 321.6 | 0.2419 | 200.2 | 176.0 | 691.6 |
| E6 | –2989.779373 | 838.6 | 113.9 | 380.8 | 420.6 | 0.0685 | 179.1 | 234.2 | 146.6 |
| E7 | –3807.042565 | 796.3 | 146.2 | 2254.1 | 517.8 | 0.0825 | 112.3 | 357.1 | 1897.0 |
| E8 | –2014.537070 | 513.3 | 74.6 | 474.6 | 320.4 | 0.0301 | 387.6 | 150.7 | 324.0 |
| E9 | –2315.316157 | 553.5 | 86.7 | 199.6 | 372.1 | 0.0672 | 165.5 | 190.1 | 9.5 |
Calculated at the DFT-D3/M06-2X/def2-TZVPP level.
Calculated at the DFT-D3/B3LYP/6-311G(d,p) level.
2.3. Detonation Property
Detonation velocity (D) and detonation pressure (P) are two important performance parameters for energetic materials. The calculated ρ, Q, D, P, and oxygen balance (OB) of the title compounds are presented in Table 4. As can be seen, the calculated detonation parameters of HMX are consistent with the experimental values, suggesting that the calculation methods are reliable. Generally, the higher the oxygen balance, the larger the detonation velocity and pressure. However, too much oxygen is not favorable for improving the explosive performance of energetic compounds because the additional oxygen will produce O2 that takes away a great deal of energy during the explosion of energetic materials. Thus, the ideal oxygen balance is equal to zero. As shown in Table 4, the OB values (ranging from −30.8 to 29.6%) of the −NHNO2 (R4) and −CH(NO2)2 (R6) substituents as well as A2 are nearly zero, exhibiting a better oxygen balance compared to that of HMX (−21.6%), making it combust completely and thus avoid releasing some toxic gases such as carbon monoxide in its decomposition.
Table 4. Predicted Densities (ρ), Heats of Detonation (Q), Detonation Velocities (D), Detonation Pressures (P), and Oxygen Balance (OB) for the Title Compounds.
| compd. | Q (kJ g–1) | D (km s–1) | P (GPa) | ρ (g cm–3) | OB (%) |
|---|---|---|---|---|---|
| A1 | 6.72 | 9.26 | 39.2 | 1.89 | –10.3 |
| A2 | 6.68 | 9.43 | 41.2 | 1.94 | 0 |
| A3 | 6.61 | 9.49 | 42.4 | 1.99 | 9.5 |
| A4 | 6.63 | 9.63 | 44.5 | 2.06 | 18.2 |
| B1 | 6.69 | 9.04 | 36.4 | 1.81 | –23.1 |
| B2 | 7.05 | 9.25 | 38.5 | 1.85 | –16.6 |
| B3 | 5.76 | 9.09 | 38.9 | 1.94 | –16.1 |
| B4 | 6.89 | 9.45 | 40.8 | 1.89 | –9.0 |
| B5 | 6.80 | 9.08 | 36.6 | 1.81 | –24.5 |
| B6 | 7.06 | 9.51 | 41.6 | 1.91 | –8.0 |
| B7 | 8.24 | 10.08 | 47.3 | 1.95 | 1.8 |
| B8 | 7.10 | 9.53 | 41.6 | 1.90 | –7.0 |
| B9 | 7.16 | 9.62 | 42.6 | 1.91 | –2.2 |
| C1 | 6.47 | 9.01 | 36.3 | 1.82 | –24.5 |
| C2 | 7.27 | 9.41 | 40.2 | 1.87 | –12.7 |
| C3 | 4.97 | 9.28 | 41.2 | 2.06 | –12.1 |
| C4 | 6.87 | 9.71 | 43.8 | 1.94 | 0 |
| C5 | 6.73 | 9.05 | 36.2 | 1.79 | –27.0 |
| C6 | 7.21 | 9.84 | 45.5 | 1.99 | 0 |
| C7 | 8.99 | 10.49 | 52.2 | 2.03 | 13.5 |
| C8 | 7.40 | 9.88 | 45.6 | 1.97 | 4.1 |
| C9 | 7.40 | 9.96 | 46.6 | 1.99 | 11.5 |
| D1 | 6.35 | 8.97 | 35.8 | 1.81 | –25.8 |
| D2 | 7.39 | 9.53 | 41.4 | 1.89 | –9.5 |
| D3 | 4.38 | 9.39 | 42.4 | 2.14 | –8.9 |
| D4 | 6.87 | 9.84 | 45.4 | 1.98 | 6.7 |
| D5 | 6.64 | 9.03 | 35.9 | 1.78 | –29.0 |
| D6 | 7.32 | 9.97 | 47.1 | 2.02 | 5.3 |
| D7 | 9.39 | 10.73 | 55.3 | 2.09 | 20.5 |
| D8 | 7.57 | 10.12 | 48.6 | 2.03 | 13.0 |
| D9 | 7.63 | 10.18 | 49.4 | 2.04 | 21.7 |
| E1 | 6.17 | 8.93 | 35.5 | 1.81 | –26.9 |
| E2 | 7.54 | 9.63 | 42.5 | 1.90 | –7.0 |
| E3 | 4.04 | 9.59 | 44.7 | 2.23 | –6.5 |
| E4 | 6.93 | 10.00 | 47.4 | 2.02 | 11.9 |
| E5 | 6.73 | 9.05 | 35.9 | 1.77 | –30.8 |
| E6 | 7.41 | 10.14 | 49.4 | 2.07 | 9.0 |
| E7 | 9.68 | 10.89 | 57.3 | 2.13 | 25.1 |
| E8 | 7.80 | 10.32 | 51.2 | 2.07 | 20.2 |
| E9 | 7.82 | 10.37 | 51.8 | 2.08 | 29.6 |
| HMX | 6.85a/6.84b | 9.06a/9.10b | 36.65a/39.0b | 1.82a/1.91b | –21.6a/–21.6b |
Calculated data.
Experimental data from ref (5).
Figure 2 displays the variation trends of Q, ρ, D, and P of the designed compounds. As can be seen from Figure 2a, introducing −N3, −CH(NO2)2, −C(NO2)3, −NO2, and −ONO2 groups is conducive to improving the detonation heat, which can be seen in series B, C, and D. However, the unique substituent groups −NH2 (R1) and −NF2 (R3) decrease the detonation heat. However, the detonation heat of the substituent group −NHNO2 (R4) is nearly the same as that of HMX (6.84 kJ g–1), and the detonation heat of −C=O (A1–A4) is much the same as that of RDX (6.65 kJ g–1), indicating that more nitrogen content and nitro groups are beneficial to increase the detonation heat.
Figure 2.
(a)–(d) Variation trends of Q, ρ, D, and P of the designed compounds.
As shown in Figure 2b, the density increased by 17% as the number of the −NF2 substituent increased to four (B3–E3). Among all substituted energetic groups, −NF2 and −C(NO2)3 are proven to be the best ones in increasing the density by more or less 12%. The carbonyl group shows similar effects to the nitramine group. The general influence order of different energetic groups on values of ρ can be written as follows: −C(NO2)3 ≈ −NF2 > −NO2 ≈ −ONO2 ≈ −CH(NO2)2 > −NHNO2 ≈ −C=O > −N3 > −NH2 > −NHNH2.
As shown in Figure 2c,d, the influence of different energetic groups on values of D and P was approximately the same throughout the series. Except for −NH2 (R1), −NHNH2 (R5), and B3, all of the title compounds present extraordinarily high detonation properties(D > 9.20 km s–1 and P > 39.3 GPa), superior to those of HMX (9.10 km s–1 and 39.0 GPa) and RDX (8.75 km s–1 and 34.0 GPa). The general influence order of different energetic groups on values of D can be written as follows: −C(NO2)3 > −ONO2 > −NO2 > −CH(NO2)2 > −NHNO2 > −N3 ≈ −C=O > −NF2 > −NHNH2 > −NH2 (series B), and the order for values of P is as follows: −C(NO2)3 > −ONO2 > −NO2 = −CH(NO2)2 > −NHNO2> −C=O > −NF2 > −N3 > −NHNH2 > −NH2 (series B). It can be concluded that −C(NO2)3 is the most effective group in improving D and P values (E7, D = 10.89 km s–1, P = 57.3 GPa). In conclusion, except for −NH2(R1), −NHNH2(R5), and B3, all of the designed compounds have higher detonation velocities and pressures than HMX.
2.4. Thermal Stability
Thermal stability is a more important indicator than detonation performance. It is of practical significance to determine whether the compounds are kinetically stable enough to be of practical interest. Therefore, the study of the pyrolysis mechanism is important for understanding the decomposition process of energetic materials, which could be evaluated by bond dissociation energy (BDE).16 Previous studies17,18 on nitro compounds such as nitroaromatic and nitramine molecules have shown that the BDE is positively correlated with their sensitivity. Generally, the larger the BDE, the more thermally stable the molecule.
The bond order, as a quantitative description of chemical bonds, has been widely used for understanding the molecular electronic structure and predicting the molecular reactivity and stability, which has a good correlation with the bond dissociation energy. Thus, several relatively weak bonds as the breaking bond have been selected based on the bond overlap population Laplacian bond order (LBO)19 to calculate BDE. However, previous studies20−22 have shown that the N–NO2 bond usually acts as the trigger bond during the decomposition process of energetic materials. Therefore, the BDE of the potential N–NO2 trigger bond of every molecule was also calculated. Table 5 lists the relatively weak bonds for the title compounds.
Table 5. Bond Dissociation Energies (BDEs, kJ mol–1) for the Weakest Bonds.
| C–NO2 |
N–NO2 |
N–F |
N–NH2 |
O–NO2 |
||||||
|---|---|---|---|---|---|---|---|---|---|---|
| compd. | rupture bonds | BDE | rupture bonds | BDE | rupture bonds | BDE | rupture bonds | BDE | rupture bonds | BDE |
| HMX | 2(N)–4(N) | 259.8 | ||||||||
| A1 | 7(N)–11(N) | 179.9 | ||||||||
| A2 | 7(N)–11(N) | 176.3 | ||||||||
| A3 | 7(N)–11(N) | 171.5 | ||||||||
| A4 | 8(N)–11(N) | 176.1 | ||||||||
| B1 | 18(N)–25(N) | 212.3 | ||||||||
| B2 | 7(N)–13(N) | 173.3 | ||||||||
| B3 | 18(N)–25(N) | 211.6 | 28(N)–30(F) | 267.9 | ||||||
| B4 | 2(N)–4(N) | 163.2 | ||||||||
| B5 | 18(N)–25(N) | 219.3 | 28(N)–30(N) | 289.3 | ||||||
| B6 | 28(C)–30(N) | 176.9 | 10(N)–14(N) | 165.6 | ||||||
| B7 | 7(N)–13(N) | 182.4 | ||||||||
| B8 | 6(C)–28(N) | 189.4 | 10(N)–14(N) | 187.1 | ||||||
| B9 | 10(N)–14(N) | 179.4 | 28(O)–29(N) | 163.5 | ||||||
| C1 | 9(N)–13(N) | 196.6 | ||||||||
| C2 | 10(N)–15(N) | 147.5 | ||||||||
| C3 | 10(N)–14(N) | 178.5 | 30(N)–32(F) | 264.3 | ||||||
| C4 | 2(N)–4(N) | 159.1 | ||||||||
| C5 | 17(N)–24(N) | 222.9 | ||||||||
| C6 | 27(C)–29(N) | 176.7 | 9(N)–13(N) | 154.8 | ||||||
| C7 | 7(N)–12(N) | 157.1 | ||||||||
| C8 | 6(C)–27(N) | 179.3 | 9(N)–13(N) | 187.5 | ||||||
| C9 | 9(N)–13(N) | 183.9 | 31(O)–32(N) | 158.5 | ||||||
| D1 | 9(N)–13(N) | 180.7 | ||||||||
| D2 | 10(N)–14(N) | 148.8 | ||||||||
| D3 | 10(N)–14(N) | 176.1 | 32(N)–34(F) | 262.6 | ||||||
| D4 | 2(N)–4(N) | 156.9 | ||||||||
| D5 | 17(N)–23(N) | 219.4 | ||||||||
| D6 | 26(C)–28(N) | 180.8 | 17(N)–23(N) | 185.5 | ||||||
| D7 | 7(N)–11(N) | 154.2 | ||||||||
| D8 | 6(C)–26(N) | 175.4 | 7(N)–11(N) | 144.9 | ||||||
| D9 | 7(N)–11(N) | 147.4 | 30(O)–31(N) | 157.0 | ||||||
| E1 | 9(N)–13(N) | 181.4 | ||||||||
| E2 | 7(N)–11(N) | 148.7 | ||||||||
| E3 | 17(N)–22(N) | 186.5 | 28(N)–29(F) | 257.1 | ||||||
| E4 | 17(N)–22(N) | 141.4 | ||||||||
| E5 | 7(N)–11(N) | 184.4 | 40(N)–42(N) | 269.9 | ||||||
| E6 | 9(N)–13(N) | 125.8 | ||||||||
| E7 | 9(N)–13(N) | 158.6 | ||||||||
| E8 | 9(N)–13(N) | 145.1 | ||||||||
| E9 | 9(N)–13(N) | 147.4 | 37(O)–38(N) | 156.1 | ||||||
As shown in Table 5, obviously, the N–NO2 bonds of the designed compounds have lower BDE values than other bonds in the molecule except for B9, C9, and D6, proving that N–NO2 is the weakest one and the rupture of the N–NO2 bond is likely the initial step in thermal decomposition for these compounds. The C–N bond of D6 has a lower BDE value (180.8 kJ mol–1) than the N–N bond (185.5 kJ mol–1), and O–N bonds of B9 and C9 have lower BDE values (163.5 and 158.5 kJ mol–1, respectively) than those of N–N bonds (179.4 and 183.9 kJ mol–1, respectively).
It is seen that the BDEs of all of the compounds are over the barrier 83.60 kJ mol–1 that a stable HEDM should exceed suggested by Chung et al.,23 which means that all of the designed compounds have suitable thermal stability.
2.5. Electrostatic Potential
ESP is a measurable and fundamentally significant physical property of compounds as it provides information about the distribution of charge density and molecular reactivity.24 For a typical organic molecule, the regions of positive electrostatic potential are more extensive in area than the negative ones, but the latter tend to be stronger. However, in the case of energetic molecules, due to the introduction of electron-attracting components, such as −C(NO2)3, −NH2, and −NF2, the positive potential is strengthened and the negative is weakened; as a result, the former may become considerably dominant.
The maximum and minimum surface ESPs of the designed compounds (series B) are displayed in Figure 3. In this section, the electrostatic potential (ESP) of three cocrystal molecules is calculated with the help of Multiwfn at 0.001 e·bohr–3 electron density and the 0.25 bohr lattice point spacing surface. Figure 3 shows that the positive ESPs (red areas) are mainly distributed on the parent skeleton, while the negative ESPs (blue areas) are concentrated on the edges of the molecules, especially on the nitrogen and oxygen atoms of nitro groups, mainly due to their higher electronegativities. The positive areas of compounds B1–B9 were calculated as 133 Å2 (ratio 52%), 138 Å2 (ratio 51%), 141 Å2 (ratio 53%), 141 Å2 (ratio 51%), 136 Å2 (ratio 52%), 148 Å2 (ratio 50%), 167 Å2 (ratio 52%), 127 Å2 (ratio 48%), and 141 Å2 (ratio 51%), respectively. It is noted that the positive regions are not only larger but also stronger in magnitude than the negative ones except for B8, which is consistent with Murray’s research.25 A previous study26 indicated that the more sensitive molecules have regions of high electron deficiency over covalent bonds within the inner skeleton of the molecular structure, which manifests in the positive electrostatic potential in a surface area bar graph is too extensive. Clearly, the positive electrostatic potentials of B1, B3, and B5 are more extensive, which might result in relatively high impact sensitivity.
Figure 3.
Electrostatic potential of representative designed molecules.
2.6. Thermodynamic Properties
As the main contents of thermodynamic parameters, standard molar heat capacity (Cp,mθ), standard molar entropy (Sm), and standard molar enthalpy (Hmθ) can provide useful information in the state equation, macroscopic properties, and chemical reactions of energetic materials.27 The variation trends of Cp,m, Smθ, and Hm of the designed compounds at different temperatures (from 200 to 600 K) were investigated. The related equation for these parameters at different temperatures can be written in the following form
 |
where a, b, and c are constant and summarized in Table 6. At a certain temperature, with a monosubstituted energetic group attached to the HMX ring, it is found that the maximum values of Hmθ appear on groups −CH(NO2)2 and −C(NO2)3 (B6, B7), and the minimum values arise at groups −NH2, −N3, and −NO2 (B1, B2, and B8), which indicates that the volume of energetic groups has a great effect on standard molar enthalpy. This phenomenon may be caused by the strong space steric effects of energetic groups. Besides, Cp,m, Smθ, and Hm of all designed compounds increased with the increasing number of energetic groups.
Table 6. Calculated Smθ, Cp,m, and Hmθ of the Designed Compounds.
|
Hmθ |
Smθ |
Cp,mθ |
||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| compd. | a | b | c × 10–4 | a | b | c × 10–4 | a | b | c × 10–4 | R2 |
| A1 | –6.97 | 0.10 | 2.93 | 284.53 | 1.13 | –3.46 | 30.26 | 0.99 | –5.06 | 0.9999 |
| A2 | –8.82 | 0.12 | 2.78 | 292.10 | 1.21 | –4.14 | 44.91 | 0.99 | –5.35 | 0.9999 |
| A3 | –10.63 | 0.14 | 2.66 | 291.95 | 1.28 | –4.72 | 53.39 | 1.00 | –5.90 | 0.9999 |
| A4 | –12.77 | 0.16 | 2.51 | 292.92 | 1.35 | –5.38 | 66.5 | 1.01 | –6.27 | 0.9999 |
| B1 | –6.74 | 0.10 | 3.23 | 279.25 | 1.17 | –3.29 | 26.04 | 1.05 | –5.04 | 0.9999 |
| C1 | –8.84 | 0.11 | 3.46 | 254.21 | 1.25 | –3.51 | 20.41 | 1.16 | –5.90 | 0.9999 |
| D1 | –10.24 | 0.12 | 3.64 | 256.47 | 1.35 | –3.91 | 24.71 | 1.24 | –6.40 | 0.9999 |
| E1 | –12.22 | 0.13 | 3.85 | 239.66 | 1.44 | –4.19 | 21.63 | 1.35 | –7.20 | 0.9999 |
| B2 | –8.31 | 0.11 | 3.24 | 279.10 | 1.25 | –3.81 | 34.85 | 1.09 | –5.46 | 0.9999 |
| C2 | –10.89 | 0.14 | 3.43 | 289.19 | 1.43 | –4.72 | 47.53 | 1.20 | –6.38 | 0.9999 |
| D2 | –13.69 | 0.17 | 3.63 | 292.14 | 1.61 | –5.62 | 59.86 | 1.31 | –7.32 | 0.9999 |
| E2 | –16.19 | 0.19 | 3.81 | 304.93 | 1.8 | –6.55 | 74.41 | 1.42 | –8.17 | 0.9999 |
| B3 | –8.16 | 0.12 | 3.26 | 290.02 | 1.27 | –3.93 | 36.12 | 1.10 | –5.62 | 0.9999 |
| C3 | –11.20 | 0.14 | 3.51 | 291.96 | 1.47 | –4.86 | 44.33 | 1.26 | –6.93 | 0.9999 |
| D3 | –13.91 | 0.17 | 3.76 | 303.59 | 1.66 | –5.76 | 51.29 | 1.41 | –8.27 | 0.9999 |
| E3 | –17.67 | 0.20 | 4.03 | 289.58 | 1.86 | –6.63 | 54.03 | 1.60 | –9.85 | 0.9999 |
| B4 | –8.36 | 0.11 | 3.50 | 283.58 | 1.30 | –3.82 | 29.34 | 1.17 | –5.90 | 0.9999 |
| C4 | –10.54 | 0.14 | 3.97 | 295.94 | 1.53 | –4.63 | 35.13 | 1.37 | –7.17 | 0.9999 |
| D4 | –12.87 | 0.17 | 4.42 | 306.88 | 1.76 | –5.51 | 44.17 | 1.55 | –8.33 | 0.9999 |
| E4 | –15.87 | 0.19 | 4.86 | 311.25 | 1.99 | –6.49 | 54.56 | 1.74 | –9.59 | 0.9999 |
| B5 | –7.61 | 0.10 | 3.44 | 277.12 | 1.24 | –3.46 | 24.94 | 1.13 | –5.48 | 0.9999 |
| C5 | –9.49 | 0.12 | 3.86 | 267.96 | 1.39 | –3.90 | 26.04 | 1.28 | –6.33 | 0.9999 |
| D5 | –11.28 | 0.13 | 4.25 | 265.00 | 1.55 | –4.44 | 31.87 | 1.41 | –7.02 | 0.9999 |
| E5 | –13.48 | 0.15 | 4.60 | 257.67 | 1.73 | –5.13 | 44.28 | 1.53 | –7.57 | 0.9999 |
| B6 | –9.62 | 0.13 | 3.83 | 292.01 | 1.46 | –4.41 | 39.74 | 1.28 | –6.39 | 0.9999 |
| C6 | –13.84 | 0.18 | 4.59 | 314.05 | 1.87 | –6.02 | 61.49 | 1.57 | –8.15 | 0.9999 |
| D6 | –17.77 | 0.22 | 5.37 | 330.33 | 2.27 | –7.58 | 81.11 | 1.87 | –9.94 | 0.9999 |
| E6 | –22.31 | 0.27 | 6.12 | 332.91 | 2.67 | –9.18 | 103.17 | 2.16 | –11.70 | 0.9999 |
| B7 | –14.3 | 0.17 | 4.06 | 291.48 | 1.70 | –5.60 | 45.99 | 1.48 | –8.32 | 0.9999 |
| C7 | –23.00 | 0.25 | 5.02 | 315.49 | 2.34 | –8.50 | 79.01 | 1.96 | –11.90 | 0.9999 |
| D7 | –32.16 | 0.33 | 6.04 | 308.15 | 2.97 | –11.10 | 98.88 | 2.47 | –15.80 | 0.9999 |
| E7 | –41.15 | 0.42 | 7.01 | 313.09 | 3.62 | –14.00 | 130.25 | 2.96 | –19.30 | 0.9999 |
| B8 | –8.16 | 0.11 | 3.27 | 274.87 | 1.24 | –3.72 | 32.66 | 1.09 | –5.44 | 0.9999 |
| C8 | –10.57 | 0.14 | 3.48 | 280.70 | 1.42 | –4.55 | 44.27 | 1.20 | –6.30 | 0.9999 |
| D8 | –13.33 | 0.16 | 3.71 | 275.68 | 1.59 | –5.35 | 53.98 | 1.32 | –7.22 | 0.9999 |
| E8 | –15.68 | 0.18 | 3.92 | 283.42 | 1.77 | –6.22 | 68.32 | 1.42 | –7.98 | 0.9999 |
| B9 | –8.36 | 0.11 | 3.39 | 289.99 | 1.30 | –3.94 | 34.06 | 1.14 | –5.81 | 0.9999 |
| C9 | –11.37 | 0.14 | 3.73 | 304.51 | 1.53 | –4.98 | 44.56 | 1.32 | –7.16 | 0.9999 |
| D9 | –13.94 | 0.18 | 4.06 | 322.08 | 1.77 | –6.09 | 60.56 | 1.48 | –8.28 | 0.9999 |
| E9 | –16.62 | 0.21 | 4.37 | 340.42 | 2.02 | –7.22 | 77.00 | 1.63 | –9.42 | 0.9999 |
Figure 4 shows Cp,mθ, Sm, and Hmθ of compounds B1 and B7. Interestingly, the related thermodynamic parameters rise gradually with the increase of the temperature. The only difference is that the growth rates of Cp,m and Smθ decrease significantly with the increasing temperature, while the growth rate of Hm shows an opposite effect. The conclusion can be drawn that the thermodynamic parameters are mainly affected by transformations and rotations of chemical bonds at lower temperatures, while the vibrational movement is the key factor at higher temperatures.
Figure 4.
Relationships between the thermodynamic equations and temperature for B1 and B7.
3. Conclusions
In this work, a series of energetic derivatives were designed and investigated based on the framework of 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX) by the density functional theory method at the DFT-D3-B3LYP/6-311G(d,p) level. The following conclusions can be drawn:
-
(1)
The –NHNO2, CH(NO2)2, −C(NO2)3, −NO2, and −ONO2 substituents affect the distribution of HOMO, and −N3, −NHNH2, and −C(NO2)3 make contributions to the LUMO.
-
(2)
Introducing the −NH2, −NHNH2, and −NO2 substituents can increase the HOF value. −C(NO2)3 has the greatest effect on improvement of HOFs among the whole substituted groups, while the −C=O group makes less contribution.
-
(3)
The −N3, −CH(NO2)2, −C(NO2)3, −NO2, −ONO2 substituents are conducive to improving the detonation heat, whereas −NH2 and −NF2 decrease the detonation heat. However, the detonation heat of the substituent group −NHNO2 is nearly the same as that of HMX (6.84 kJ g–1), and the detonation heat of–C=O is much the same as that of RDX (6.65 kJ g–1).
-
(4)
The −NF2 and −C(NO2)3 substituents are the best ones in increasing the density by more or less 12%. The carbonyl group shows similar effects to the nitramine group.
-
(5)
–C(NO2)3 is the most effective group in improving D and P values (E7, D = 10.89 km s–1, P = 57.3 GPa). Except for −NH2(R1), −NHNH2(R5), and B3, all of the designed compounds have higher detonation velocities and pressures than HMX.
-
(6)
The volume of energetic groups has a great effect on standard molar enthalpy because of the strong space steric effects of energetic groups. Besides, Cp,mθ, Sm, and Hmθ of all designed compounds increased with the increasing number of energetic groups. Furthermore, the thermodynamic parameters are mainly affected by transformations and rotations of chemical bonds at lower temperatures, while the vibrational movement is the key factor at higher temperatures.
4. Computational Details
All quantum mechanical calculations in this work were implemented in Gaussian 16.28 Molecular structures of the designed compounds were optimized at the B3LYP-D3/6-311G(d,p) level.29−31 Previous studies have shown that the basis set 6-311G(d,p) is able to figure out the accurate energy, molecular structure, and vibrational frequency that are very close to their experimental results.32−34 Then, the M06-2X-D3 method was selected to calculate the molecular single-point energy of explosives with the def2-TZVPP basis group. The stable structure was judged by the “no imaginary frequency” criterion. Moreover, the stable structures were obtained when all optimized structures corresponded to the local energy minimum points on the respective potential energy surface. The gas-phase HOFs were calculated by isodesmic reactions. Furthermore, the heat of sublimation (ΔHsub), the solid-phase HOFs (ΔHf,solid), and the crystal density (ρ) were calculated. Besides, detonation velocity and detonation pressure (P) were employed to evaluate the detonation performance. Moreover, the bond dissociation energy (BDE) is a fundamental indicator to understanding chemical processes.35
Acknowledgments
This study was supported by the National Natural Science Foundation of China (Grant No. 11702129). The authors are grateful to the High Performance Computing Center of Nanjing Tech University for supporting the computational resources.
Supporting Information Available
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c04237.
Formula for calculating gas-phase HOFs, the heat of sublimation (ΔHsub), the solid-phase HOFs (ΔHf,solid), and the crystal density (ρ); details on calculating the detonation velocity, detonation pressure, and the bond dissociation energy (BDE) (PDF)
Author Contributions
This manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript.
The authors declare no competing financial interest.
Supplementary Material
References
- Thottempudi V.; Gao H. X.; Shreeve J. M. Trinitromethyl-substituted 5-Nitro- or 3-Azo-1,2,4triazoles: synthesis, characterization, and energetic properties. J. Am. Chem. Soc. 2011, 133, 6464–6471. 10.1021/ja2013455. [DOI] [PubMed] [Google Scholar]
- Wu Q.; Tan L. H.; Hang Z. S.; Wang J. Y.; Zhang Z. W.; Zhu W. H. A new design strategy on cage insensitive high explosives: symmetrically replacing carbon atoms by nitrogen atoms followed by the introduction of N-oxides. RSC Adv. 2015, 5, 93607–93614. 10.1039/C5RA19062B. [DOI] [Google Scholar]
- Wu Q.; Zhu W. H.; Xiao H. M. A new design strategy for high-energy low-sensitivity explosives: combining oxygen balance equal to zero, a combination of nitro and amino groups, and N-oxide in one molecule of 1-amino-5-nitrotetrazole-3N-oxide. J. Mater. Chem. A 2014, 2, 13006–13015. 10.1039/C4TA01879F. [DOI] [Google Scholar]
- Sikder A. K.; Sikder N. A review of advanced high performance, insensitive and thermally stable energetic materials emerging for military and space applications. J. Hazard. Mater. 2004, 112, 1–15. 10.1016/j.jhazmat.2004.04.003. [DOI] [PubMed] [Google Scholar]
- Politzer P.; Murray J. S. Some perspectives on estimating detonation properties of C, H, N, O compounds. Cent. Eur. J. Energ. Mater. 2011, 8, 209–220. [Google Scholar]
- Xu X. J.; Xiao H. M.; Ju X. H.; Gong X. D.; Zhu W. H. Computational studies on polynitrohexaazaadmantanes as potential high energy density materials. J. Phys. Chem. A 2006, 110, 5929–5933. 10.1021/jp0575557. [DOI] [PubMed] [Google Scholar]
- Pan Y.; Zhu W. Theoretical design on a series of novel bicyclic and cage nitramines as high energy density compounds. J. Phys. Chem. A 2017, 121, 9163–9171. 10.1021/acs.jpca.7b10462. [DOI] [PubMed] [Google Scholar]
- Jaidann M.; Roy S.; Abou-Rachid H.; Lussier L. S. A DFT theoretical study of heats of formation and detonation properties of nitrogen-rich explosives. J. Hazard. Mater. 2010, 176, 165–173. 10.1016/j.jhazmat.2009.10.132. [DOI] [PubMed] [Google Scholar]
- Wang F.; Wang G.; Du H.; Zhang J.; Gong X. Theoretical studies on the heats of formation, detonation properties, and pyrolysis mechanisms of energetic cyclic nitramines. J. Phys. Chem. A 2011, 115, 13858–13864. 10.1021/jp2047536. [DOI] [PubMed] [Google Scholar]
- Jeong K. New theoretically predicted RDX and β-HMX-based high-energy-density molecules. Int. J. Quantum Chem. 2018, 118, e25528 10.1002/qua.25528. [DOI] [Google Scholar]
- Lin H.; Zhu Q.; Huang C.; Yang D. D.; Lou N.; Zhu S. G.; Li H. Z. Dinitromethyl, fluorodinitromethyl derivatives of RDX and HMX as high energy density materials: a computational study. Struct. Chem. 2019, 30, 2401–2408. 10.1007/s11224-019-01366-1. [DOI] [Google Scholar]
- Gutowski K. E.; Rogers R. D.; Dixon D. A. Accurate thermochemical properties for energetic materials applications. II. Heats of formation of imidazolium-, 1,2,4-triazolium-, and tetrazolium-based energetic salts from isodesmic and lattice energy calculations. J. Phys. Chem. B 2007, 111, 4788–4800. 10.1021/jp066420d. [DOI] [PubMed] [Google Scholar]
- Miroshnichenko E. A.; Kon’kova T. S.; Matyushin Y. N. Thermochemistry of primary nitramines. Dokl. Phys. Chem. 2003, 392, 253–255. 10.1023/A:1026182227885. [DOI] [Google Scholar]
- Zhai D.; Wang J.; Hao L.; Ma C.; Ma P.; Pan Y.; Jiang J. Molecular design and properties of bridged energetic pyridines derivatives. RSC Adv. 2019, 9, 37747–37758. 10.1039/C9RA07087G. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Lyman J. L.; Liau Y. C.; Brand H. V. Thermochemical functions for gas-phase, 1, 3, 5, 7-tetranitro-1, 3, 5, 7-tetraazacyclooctane (HMX), its condensed phases, and its larger reaction products. Combust. Flame 2002, 130, 185–203. 10.1016/S0010-2180(02)00364-4. [DOI] [Google Scholar]
- Henry D. J.; Parkinson C. J.; Mayer P. M.; Radom L. Bond dissociation energies and radical stabilization energies associated with substituted methyl radicals. J. Phys. Chem. A 2001, 105, 6750–6756. 10.1021/jp010442c. [DOI] [Google Scholar]
- Rice B. M.; Sahu S.; Owens F. J. Density functional calculations of bond dissociation energies for NO2 scission in some nitroaromatic molecules. J. Mol. Struct.: THEOCHEM 2002, 583, 69–72. 10.1016/S0166-1280(01)00782-5. [DOI] [Google Scholar]
- Harris N. J.; Lammertsma K. Ab initio density functional computations of conformations and bond dissociation energies for hexahydro-1, 3, 5-trinitro-1, 3, 5-triazine. J. Am. Chem. Soc. 1997, 119, 6583–6589. 10.1021/ja970392i. [DOI] [Google Scholar]
- Lu T.; Chen F. Bond order analysis based on the Laplacian of electron density in fuzzy overlap space. J. Phys. Chem. A 2013, 117, 3100–3108. 10.1021/jp4010345. [DOI] [PubMed] [Google Scholar]
- Wang G.; Gong X.; Liu Y.; Xiao H. A theoretical investigation on the structures, densities, detonation properties, and pyrolysis mechanism of the nitro derivatives of phenols. Int. J. Quantum Chem. 2010, 110, 1691–1701. 10.1002/qua.22306. [DOI] [PubMed] [Google Scholar]
- Qiu L.; Xiao H.; Gong X.; Ju X.; Zhu W. Theoretical studies on the structures, thermodynamic properties, detonation properties, and pyrolysis mechanisms of spiro nitramines. J. Phys. Chem. A 2006, 110, 3797–3807. 10.1021/jp054169g. [DOI] [PubMed] [Google Scholar]
- Zhang J. Y.; Du H. C.; Wang F.; Gong X. D.; Huang Y. S. DFT studies on a high energy density cage compound 4-trinitroethyl-2, 6, 8, 10, 12-pentanitrohezaazaisowurtzitane. J. Phys. Chem. A 2011, 115, 6617–6621. 10.1021/jp1118822. [DOI] [PubMed] [Google Scholar]
- Chung G.; Schmidt M. W.; Gordon M. S. An ab initio study of potential energy surfaces for N8 isomers. J. Phys. Chem. A 2000, 104, 5647–5650. 10.1021/jp0004361. [DOI] [Google Scholar]
- Xie Z.; Hu S.; Cao X. Theoretical insight into the influence of molecular ratio on the binding energy and mechanical property of HMX/2-picoline-N-oxide cocrystal, cooperativity effect and surface electrostatic potential. Mol. Phys. 2016, 114, 2164–2176. 10.1080/00268976.2016.1190038. [DOI] [Google Scholar]
- Peter J. S. M. P. L. Effects of strongly electron-attracting components on molecular surface electrostatic potentials: application to predicting impact sensitivities of energetic molecules. Mol. Phys. 1998, 93, 187–194. 10.1080/002689798169203. [DOI] [Google Scholar]
- Rice B. M.; Hare J. J. A quantum mechanical investigation of the relation between impact sensitivity and the charge distribution in energetic molecules. J. Phys. Chem. A 2002, 106, 1770–1783. 10.1021/jp012602q. [DOI] [Google Scholar]
- Zhang J.; Xiao H. Computational studies on the infrared vibrational spectra, thermodynamic properties, detonation properties, and pyrolysis mechanism of octanitrocubane. J. Chem. Phys. 2002, 116, 10674–10683. 10.1063/1.1479136. [DOI] [Google Scholar]
- Frisch M. J.; Trucks G. W.; Schlegel H. B.; Scuseria G. E.; Robb M. A.; Cheeseman J. R.; Scalmani G.; Barone V.; Petersson G. A.; Nakatsuji H.. et al. Gaussian 16; Gaussian, Inc.: Wallingford CT, 2016.
- Pan Y.; Li J. S.; Cheng B. B.; Zhu W. H.; Xiao H. M. Computational studies on the heats of formation, energetic properties, and thermal stability of energetic nitrogen-rich furazano[3,4-b]pyrazine-based derivatives. Comput. Theor. Chem. 2012, 992, 110–119. 10.1016/j.comptc.2012.05.013. [DOI] [Google Scholar]
- Fan X. W.; Ju X. H. Theoretical studies on four-membered ring compounds with NF2, ONO2, N3, and NO2 groups. J. Comput. Chem. 2008, 29, 505–513. 10.1002/jcc.20809. [DOI] [PubMed] [Google Scholar]
- Wei T.; Zhu W. H.; Zhang X. W.; Li Y. F.; Xiao H. M. Molecular design of 1,2,4,5-tetrazine based high-energy density materials. J. Phys. Chem. A 2009, 113, 9404–9412. 10.1021/jp902295v. [DOI] [PubMed] [Google Scholar]
- Fan X. W.; Ju X. H.; Xiao H. M.; Qiu L. Theoretical studies on heats of formation, group interactions, and bond dissociation energies in neopentyl difluoroamino compounds. J. Mol. Struct.: THEOCHEM 2006, 801, 55–62. 10.1016/j.theochem.2006.08.057. [DOI] [Google Scholar]
- Wei T.; Zhu W.; Zhang J.; Xiao H. DFT study on energetic tetrazolo-[1, 5-b]-1, 2, 4, 5-tetrazine and 1, 2, 4-triazolo-[4, 3-b]-1, 2, 4, 5-tetrazine derivatives. J. Hazard. Mater. 2010, 179, 581–590. 10.1016/j.jhazmat.2010.03.043. [DOI] [PubMed] [Google Scholar]
- Fan X. W.; Ju X. H.; Xiao H. M. Density functional theory study of piperidine and diazocine compounds. J. Hazard. Mater. 2008, 156, 342–347. 10.1016/j.jhazmat.2007.12.024. [DOI] [PubMed] [Google Scholar]
- Politzer P.; Murray J. S. Relationships between dissociation energies and electrostatic potentials of C-NO2 bonds: applications to impact sensitivities. J. Mol. Struct. 1996, 376, 419–424. 10.1016/0022-2860(95)09066-5. [DOI] [Google Scholar]
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