English

• 1. INTRODUCTION

  High-energy-density materials (HEDM) are applied extensively in industry and military, so the development of new high-energy-density materials is an important aspect in materials science^[1-5]. In general, good high-energy-density materials have some special chemical and physical characters including good oxygen balance, good thermal stability, high-energy-density, and low sensitivity^[6-8]. Nowadays, high-energy-density materials with low sensitivity to compact and friction are focus of research to scientists. However, high-energy-density is usually contradictory with low sensitivity and the balance between them is difficult to achieve.

  In 1888 and 1998, famous 1, 3, 5-triamino-2, 4, 6-trinitrobenzen (TATB) and 1, 1-diamino-2, 2-dinitroethylene (FOX-7) were synthesized^{[9, 10]}, respectively. Recently, the calculations about the aminonitrocyclopropanes have shown their heats of formation close to zero and the densities close to 2 g∙cm^-3, which is regarded as a typical feature of the next-generation explosive^[11]. The low heat of formation indicates good insensitivity, and the high density is usually accompanied with an excellent detonation characters. More instances can also be found elsewhere^{[12, 13]}. Therefore, the planar structure is not always necessary and introducing both the amino and nitro groups into a molecule may be an effective way to achieve the balance between the detonation characters and the molecular sensitivity.

  Inspired by the former works, the piperidine was chosen as the parent body and nitro and amino groups were introduced into it to design new high-energy-density derivatives. The regulation between stabilities and sensitivities can be achieved through adjusting the positions of nitro groups and amino groups. Thermal stabilities and detonation characters are calculated systematically and our work will be helpful for further exploration of the title molecules.

  2. COMPUTATIONAL METHODS

  All of the optimizations are carried out at the B3PW91/6-311+G(d, p) level by using the G03 software package on a computer cluster^[14]. Frequency analyses are performed at the same level, and the stationary points on the potential energy surface are confirmed. All optimized structures are listed in Fig. 1 and labeled as α, β₁, β₂, β₃, γ, and δ.

  Figure 1

  

  Figure 1.  Optimized geometries of nitro- and amino-substituted piperidine molecules at the B3PW91/6–311+G(d, p) level

  DownLoad: Full-Size Img PowerPoint

  The heats of formation are calculated based on the isodesmic reaction as follows^[15]:

  $ \begin{array}{l} {{\rm{C}}_4}{{\rm{H}}_{10 - 2n}}{({\rm{N}}{{\rm{H}}_2})_n}{({\rm{N}}{{\rm{O}}_2})_n} + 2n{\rm{C}}{{\rm{H}}_4} \to {{\rm{C}}_4}{{\rm{H}}_{10}} + \\ n{\rm{C}}{{\rm{H}}_3}{\rm{N}}{{\rm{H}}_2} + n{\rm{C}}{{\rm{H}}_3}{\rm{N}}{{\rm{O}}_2}(n = 1 \sim 5) \end{array} $

  (1)

  The reaction enthalpy can be obtained from the following formula:

  $ {\Delta _r}{H_{{\text{298K}}}} = \sum {\Delta _f}{H_{{\text{298K}}}}(P) - \sum {\Delta _f}{H_{{\text{298K}}}}(R) $

  (2)

  in which ${\Delta _f}{H_{{\text{298K}}}}(R)$ and ${\Delta _f}{H_{{\text{298K}}}}(P)$ are the heats of formation of reagent and product, respectively. ΔH₂₉₈ can be calculated with the following formula:

  $ {\Delta _r}{H_{{\text{298K}}}} = \Delta {E_0} + \Delta ZPE + \Delta {H_{\text{T}}} + \Delta nRT $

  (3)

  Since the heats of formation can be obtained from NIST WebBook for reference molecules, the heats of formation can be estimated for the title molecules.

  The detonation velocities and detonation pressures are calculated by using the Kamlet-Jacobs equation as follows^[16]:

  $ D = (1.011 + 1.312\rho ){(N{\overline M ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}{Q^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}})^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}} $

  (4)

  $ P = 1.558{\rho ^2}N{\overline M ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}{Q^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}} $

  (5)

  The bond dissociation energies are estimated through homolytic reactions:

  $ A - B \to A \bullet + B \bullet $

  (6)

  $ BD{E_{{\text{(A - B)}}}} = \left[ {{E_{\text{A}}} + {E_{\text{B}}}} \right] - {E_{{\text{(A - B)}}}} $

  (7)

  The zero point energy corrections are also considered as below:

  $ BD{E_{({\rm{A}}-{\rm{B}})}}_{{\rm{ZPE}}} = {\rm{ }}[{E_{{\rm{A}} \bullet }} + {E_{{\rm{B}} \bullet }}]-{E_{\left( {{\rm{A}} - {\rm{B}}} \right)}} + \Delta ZPE$

  (8)

  The characteristic heights are calculated from the equation^[17]:

  $ {H_{50}} = 0.1926 + 98.64Q_{_{NO2}}^2 - 0.03405O{B_{100}} $

  (9)

  in which Q_NO2 is the net charge on nitro group and $ O{B_{100}} $ is the oxygen balance value. Q_NO2 in equation 9 can be deduced by equation 10 as follows:

  $ {Q_{{\text{NO2}}}} = {Q_{\text{N}}} + {Q_{{\text{O1}}}} + {Q_{{\text{O2}}}} $

  (10)

  Q_N, Q_O1, and Q_O2 are the net charges on N, O₁ and O₂ atoms, respectively. OB₁₀₀ can be calculated by using Eq. (11):

  $ O{B_{100}} = 100(2{N_{\rm{O}}}{\rm{ - }}{N_{\rm{H}}}{\rm{ - }}2{N_{\rm{C}}}{\rm{ - }}2{N_{{\rm{COO}}}})/M $

  (11)

  N_O, N_H, N_C, and N_COO represent the number of -O, -H, -C, and -COO, respectively. M is a molecular weight.

  3. RESULTS AND DISCUSSION

  3.1 Heats of formation

  Heat of formation is an important index of thermal chemistry for high-energy-density molecule. It is related to the detonation characters and can be used to predict the energy-content for target molecule. So the heats of formation of the title molecules are calculated and listed in Table 1 accompanied with the reference data.

  Table 1

  

  Table 1.  Total Energies (E₀, a.u.), Zero Point Energies (ZPE, a.u.), Thermal Correction Energies (H_T, a.u.) and Heats of Formation (HOF, kJ/mol) Calculated at the B3PW91/6-311+G(d, p) Level

  DownLoad: CSV

  Compound	ZPE	E	H	HT	HOF
  α	0.16726	−527.58733	−527.57720	0.17738	−9.60
  β1	0.18609	−787.41406	−787.39980	0.20035	−50.41
  β2	0.18610	−787.41221	−787.39798	0.20033	−45.63
  β3	0.18655	−787.39957	−787.38586	0.20026	−13.80
  γ	0.20495	−1047.2224	−1047.2045	0.22282	−44.31
  δ	0.22469	−1307.0294	−1307.0083	0.24575	−35.83

  From Table 1, it is found that all molecules have negative heats of formation, but the values are close to zero. Although positive heats of formation have been found for many high energy density compounds, it must be mentioned that the negative heats of formation are not contradictory to the high energy density. For example, famous insensitive explosive 3-nitro-l, 2, 4-triazol-5-one (NTO) and 2, 2-dinitro-ethene-1, 1-diamine (DADE) have the heats of formation of −33.4^[18], −30.9^[10] and −32.0 kJ/mol^[19], respectively. Therefore, our results are reasonable and the outstanding stability is evaluated for the title molecules.

  The linear regression is performed between the heats of formation and the substituent number. However, no evident linear equation was confirmed for the low R² value and the groups additivity rule is confirmed not responsible for the title molecules. In general, the heats of formation rise with the introduction of nitro groups, but the situation is different here. In order to find out the reason, the molecular structures were checked carefully. It is found that more hydrogen bonds are formed when more nitro groups are introduced because of the twisted structure, which causes the instability from the introduction of nitro groups to be counteracted.

  In summary, the derivatives designed by us showed unusual stability for their negative heats of formation, especially as high energy density compounds. This also suggests the excellent insensitivity can be expected for title molecules.

  3.2 Bond dissociation energies and impact sensitivity

  The kinetic stability is important to estimate the potential application as high-energy-density material and the bond dissociation energies have been proved to be good parameter for this purpose^[20]. Therefore, the dissociation energies of the title molecules were calculated and listed in Table 2.

  Table 2

  

  Table 2.  Bond Dissociation Energy (BDE, kJ/mol), Zero Point Energy (ZPE, a.u.), Electronic Energy (E, a.u.) and the Bond Orders Calculated at the B3PW91/6–311+G(d, p) Level

  DownLoad: CSV

  Compound	ZPE	E	BDE	Bond order
  α	0.16725	−527.587	230.29	0.7143
  β1	0.18609	−787.414	234.80	0.6531
  β2	0.18609	−787.412	231.10	0.6763
  β3	0.18655	−787.4	207.01	0.7288
  γ	0.20495	−1047.22	227.99	0.6749
  δ	0.22468	−1307.03	197.22	0.7274
  RDX				145.62
  HMX				160.41

  In Table 2, all of the bond dissociation energies are quite large, even the least bond dissociation energy (197.22 kJ/mol) of δ is larger than 145.62 kJ/mol of RDX and 160.41 kJ/mol of HMX. This indicates excellent kinetic stability of the title molecules. All of the trigger bonds are C−N, which is consistent with the fact that C−N is the weakest bond compared to others. All of the bond orders are close to 1.0, and the single bond nature of C−N is confirmed. Furthermore, the correlation between the bond order and bond dissociation energy is performed, but no relationship is confirmed. For example, the bond dissociation energy (231.10 kJ/mol) of β₂ is less than that (234.80 kJ/mol) of β₁, but the bond order (0.6763) of β₂ is greater than that (0.6531) of β₁. In consideration of the undetectability of bond order in experiment, the bond dissociation energy is a more reliable parameter to predict the kinetic stability.

  In addition, the largest bond association energy is 230.29 kJ/mol of α, as well as the least is 197.22 kJ/mol of δ. The deviation is about 30 kJ/mol, which shows the bond dissociation energy is not affected by the introduction of nitro groups. The situation is different for the title molecules compared to other available data for which more energetic molecules have less stability.

  3.3 Detonation performance

  Detonation velocity and detonation pressure are two important parameters for high-energy-density molecules. Kamlet-Jacobs equation has been proved reliable to predict these two parameters so they were calculated in this paper by using the Kamlet-Jacobs equation and the final data are listed in Table 2. For comparison purpose, the corresponding data of RDX and HMX are also shown.

  From Table 2, the molecular densities are located from 1.8092 g/cm³ of δ to 1.3983 g/cm³ of α, and all density values of the derivatives are improved markedly compared to the parent molecule. It is also concluded that the detonation pressure and detonation velocity increased with the introduction of nitro groups. The linear regression was performed and the correlation equation is y = 1.1824x − 6.397 with the R² value of 0.9607 for the detonation velocity and y = 0.1589x − 1.3237 with the R² to be 0.988 for the detonation pressure. Obviously, the groups additivity rule is compatible for the detonation parameters of the title molecules. On considering the low heats of formation, the detonation characters are affected chiefly by the elemental composition rather than the heats of formation. Compared to HMX and RDX, δ shows better detonation velocity and detonation pressure. However, the explosive heat of δ is about 300 kJ/mol less than that of RDX, which indicates better insensitivity of δ than that of RDX, so the H₅₀ values are calculated further.

  Table 3

  

  Table 3.  Molecular Density (ρ, g/cm³), Detonation Heats (Q, kJ/g), Detonation Velocity (D, km/s), Detonation Pressure (P, GPa) and Character Height (H₅₀, cm) Calculated at the B3PW91/6-311+G(d, p) Level

  DownLoad: CSV

  Compound	Q	ρ	D	P	H50
  α	996.45	1.3983	6.05	13.80	52
  β1	1115.28	1.5687	7.17	20.96	50
  β2	1120.81	1.5704	7.19	21.06	46
  β3	1157.71	1.5937	7.32	22.05	56
  γ	1222.64	1.7035	7.99	27.39	42
  δ	1292.24	1.8092	8.58	32.79	34
  RDX	1591.03	1.78(1.82)	8.87(8.75)	34.67(34.00)	26
  HMX	1633.90	1.88(1.91)	9.28(9.10)	39.19(39.00)	29

  Usually, drop hammer experiments were used to test impact sensitivities. In theory, equation 9 can be used for calculation. Based on our calculations, all derivatives of piperidine have H₅₀ values from 34 cm of δ to 56 cm of β₃. These values are all larger than 26 cm of RDX and 29 cm of HMX, and excellent insensitivity characters are indicated for the title molecules. On the consideration of both compact sensitivity and detonation characters, δ has better characters than RDX and can be regarded as the potential high energy density compounds.

  4. CONCLUSION

  Based on our calculations, the negative heats of formation are obtained for the derivatives of piperidine, and the introduction of nitro- and amino-groups reduced molecular heats of formation accompanied with the molecular density increased. Among six designed molecules, δ has the largest detonation velocity and detonation pressure with the largest molecular density. In addition, large dissociation energies are confirmed, indicating the excellent thermal stability for all derivatives. Furthermore, all derivatives designed have better H₅₀ values with RDX and HMX, which indicated their lower compact sensitivity. Overall consideration about the thermal stability and the detonation characters shows the molecule δ is screened out as a high-energy-density molecule for its better insensitivity and comparable detonation characters to RDX and HMX.

  
  
• 1. [1]

     Murray, J. S.; Concha, M.; Seminario, J. M.; Politzer, P. Computational study of relative bond strengths and stabilities of a series of amine and nitro derivatives of triprismane and some azatriprismanes. J. Phys. Chem. 1991, 95, 1601−1605. doi: 10.1021/j100157a018

  2. [2]

     Li, B.; Li, L.; Chen, S. Thermal stability and detonation character of nitro-substituted derivatives of imidazole. J. Mol. Model. 2019, 25, 298−304. doi: 10.1007/s00894-019-4190-5

  3. [3]

     Li, B.; Zhou, M.; Peng, J.; Li, L.; Guo, Y. Theoretical calculations about nitro-substituted pyridine as high-energy-density compounds (HEDCs). J. Mol. Model. 2019, 25, 23−28. doi: 10.1007/s00894-018-3904-4

  4. [4]

     Li, B. T.; Li, L. L.; Li, X. Computational study about the derivatives of pyrrole as high-energy-density compounds. Mol. Simul. 2019, 45, 1459−1464. doi: 10.1080/08927022.2019.1655561

  5. [5]

     Liu, T.; Jia, J.; Li, B.; Gao, K. Theoretical exploration on structural stabilities and detonation properties of nitrimino substituted derivatives of cyclopropane. Chin. J. Struct. Chem. 2019, 38, 688−694.

  6. [6]

     Tsyshevsky, R.; Pagoria, P.; Zhang, M.; Racoveanu, A.; DeHope, A.; Parrish, D.; Kuklja, M. M. Searching for low-sensitivity cast-melt high-energy-density materials: synthesis, characterization, and decomposition kinetics of 3, 4-bis(4-nitro-1, 2, 5-oxadiazol-3-yl)-1, 2, 5-oxadiazole-2-oxide. J. Phys. Chem. C 2015, 119, 3509−3521. doi: 10.1021/jp5118008

  7. [7]

     Agrawal, J. P. Recent trends in high-energy materials. Prog. Energy Combust. Sci. 1998, 24, 1−30. doi: 10.1016/S0360-1285(97)00015-4

  8. [8]

     Fischer, D.; Klapötke, T. M.; Stierstorfer, J. 1, 5-di(nitramino) tetrazole: high sensitivity and superior explosive performance. Angew. Chem. Int. Ed. 2015, 54, 10299−10302. doi: 10.1002/anie.201502919

  9. [9]

     Boddu, V. M.; Viswanath, D. S.; Ghosh, T. K.; Damavarapu, R. 2, 4, 6-triamino-1, 3, 5-trinitrobenzene (TATB) and TATB-based formulations — a review. J. Hazard. Mater. 2010, 181, 1−8. doi: 10.1016/j.jhazmat.2010.04.120

  10. [10]

      Evers, J.; Klapötke, T. M.; Mayer, P.; Oehlinger, G.; Welch, J. α- and β-FOX-7, polymorphs of a high energy density material, studied by X-ray single crystal and powder investigations in the temperature range from 200 to 423 k. Inorg. Chem. 2006, 45, 4996−5007. doi: 10.1021/ic052150m

  11. [11]

      Halstead, J. M.; Whittaker, J. N.; Ball, D. W. Aminonitrocyclopropanes as possible high-energy materials. Quantum chemical calculations. Propellants, Explos., Pyrotech. 2012, 37, 498−501. doi: 10.1002/prep.201100102

  12. [12]

      Dorohoi, D. O.; Airinei, A.; Dimitriu, M. Intermolecular interactions in solutions of some amino-nitro-benzene derivatives, studied by spectral means. Spectrochim. Acta, Part A 2009, 73, 257−262. doi: 10.1016/j.saa.2009.02.011

  13. [13]

      Kofman, T. 5-Amino-3-nitro-1, 2, 4-triazole and its derivatives. Russ. J. Org. Chem. 2002, 38, 1231−1243. doi: 10.1023/A:1021641709157

  14. [14]

      Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision B. 01. Gaussian, Inc., Pittsburgh PA 2003.

  15. [15]

      Ponomarev, D.; Takhistov, V. What are isodesmic reactions? J. Chem. Educ. 1997, 74, 201−207. doi: 10.1021/ed074p201

  16. [16]

      Kamlet, M. J.; Jacobs, S. J. Chemistry of detonations. I. A simple method for calculating detonation properties of C–H–N–O explosives. J. Chem. Phys. 1968, 48, 23−35. doi: 10.1063/1.1667908

  17. [17]

      Kamlet, M. J.; Adolph, H. G. The relationship of impact sensitivity with structure of organic high explosives. Ⅱ. Polynitroaromatic explosives. Propell. Explos. Pyrot. 1979, 4, 30−34. doi: 10.1002/prep.19790040204

  18. [18]

      Finch, A.; Gardner, P.; Head, A.; Majdi, H. The enthalpies of formation of 1, 2, 4-triazol-5-one and 3-nitro-1, 2, 4-triazol-5-one. J. Chem. Thermodyn. 1991, 23, 1169−1173. doi: 10.1016/S0021-9614(05)80150-8

  19. [19]

      Lenchitz, C.; Velicky, R.; Silvestr, G.; Schlosbe, L. P. Thermodynamic properties of several nitrotoluenes. J. Chem. Thermodyn. 1971, 3, 689−712. doi: 10.1016/S0021-9614(71)80090-3

  20. [20]

      Harper, L. K.; Shoaf, A. L.; Bayse, C. A. Predicting trigger bonds in explosive materials through wiberg bond index analysis. ChemPhysChem. 2015, 16, 3886−3892. doi: 10.1002/cphc.201500773

• 

  Figure 1  Optimized geometries of nitro- and amino-substituted piperidine molecules at the B3PW91/6–311+G(d, p) level

  下载: 全尺寸图片 幻灯片

  Table 1.  Total Energies (E₀, a.u.), Zero Point Energies (ZPE, a.u.), Thermal Correction Energies (H_T, a.u.) and Heats of Formation (HOF, kJ/mol) Calculated at the B3PW91/6-311+G(d, p) Level

  Compound	ZPE	E	H	HT	HOF
  α	0.16726	−527.58733	−527.57720	0.17738	−9.60
  β1	0.18609	−787.41406	−787.39980	0.20035	−50.41
  β2	0.18610	−787.41221	−787.39798	0.20033	−45.63
  β3	0.18655	−787.39957	−787.38586	0.20026	−13.80
  γ	0.20495	−1047.2224	−1047.2045	0.22282	−44.31
  δ	0.22469	−1307.0294	−1307.0083	0.24575	−35.83

  下载: 导出CSV

  Table 2.  Bond Dissociation Energy (BDE, kJ/mol), Zero Point Energy (ZPE, a.u.), Electronic Energy (E, a.u.) and the Bond Orders Calculated at the B3PW91/6–311+G(d, p) Level

  Compound	ZPE	E	BDE	Bond order
  α	0.16725	−527.587	230.29	0.7143
  β1	0.18609	−787.414	234.80	0.6531
  β2	0.18609	−787.412	231.10	0.6763
  β3	0.18655	−787.4	207.01	0.7288
  γ	0.20495	−1047.22	227.99	0.6749
  δ	0.22468	−1307.03	197.22	0.7274
  RDX				145.62
  HMX				160.41

  下载: 导出CSV

  Table 3.  Molecular Density (ρ, g/cm³), Detonation Heats (Q, kJ/g), Detonation Velocity (D, km/s), Detonation Pressure (P, GPa) and Character Height (H₅₀, cm) Calculated at the B3PW91/6-311+G(d, p) Level

  Compound	Q	ρ	D	P	H50
  α	996.45	1.3983	6.05	13.80	52
  β1	1115.28	1.5687	7.17	20.96	50
  β2	1120.81	1.5704	7.19	21.06	46
  β3	1157.71	1.5937	7.32	22.05	56
  γ	1222.64	1.7035	7.99	27.39	42
  δ	1292.24	1.8092	8.58	32.79	34
  RDX	1591.03	1.78(1.82)	8.87(8.75)	34.67(34.00)	26
  HMX	1633.90	1.88(1.91)	9.28(9.10)	39.19(39.00)	29

  下载: 导出CSV
•