火炸药学报    2018, Vol. 41 Issue (3): 236-242   DOI: 10.14077/j.issn.1007-7812.2018.03.004 0

### Citation

WANG Ke, LIU Ning, WU Zong-kai, FU Xiao-long, LI Huan, SHU Yuan-jie, LI Jun-qiang, PANG Wei-qiang. Theoretical Investigation on Structure and Performance of Furazano-[3, 4-d]-pyridazine-based Fused-ring Compounds[J]. Chinese Journal of Explosives & Propellants, 2018, 41(3): 236-242. DOI: 10.14077/j.issn.1007-7812.2018.03.004

### Foundation

National Natural Science(No.51373159);Funds for International Cooperation and Exchange(No.51511130036)

### Biography

WANG Ke(1991-), male, research field:theoritical design of energetic materials.E-mail:zhuazhangmangxiewk@163.com

### Corresponding author

PANG Wei-qiang(1979-), male, Dr., research field:design and simulation of propellants.E-mail:7697111103@qq.com

### Article History

Revised date: 2017-07-02
Theoretical Investigation on Structure and Performance of Furazano-[3, 4-d]-pyridazine-based Fused-ring Compounds
WANG Ke1, LIU Ning1, WU Zong-kai1, FU Xiao-long1, LI Huan1, SHU Yuan-jie1, LI Jun-qiang1, PANG Wei-qiang1
Xi'an Modern Chemistry Research Institute, Xi'an 710065, China
Abstract: Three series of novel furazano-[3, 4-d]-pyridazine-based fused-ring compounds were designed, and their structures and performance were studied by density functional theory (DFT) at B3LYP/6-311g(d, p) level. Detonation performance was estimated by Kamlet-Jacobs equations. The results show that the compounds of A and B series exhibit good coplanarity and their dihedral angles vary within ±5°, but the coplanarity of C series was particularly damaged because of electron-withdrawing effect of more functional groups. Otherwise, all designed nitro-containing compounds possess high densities (1.896-2.153 g/cm3), detonation velocities (8.55-9.98 km/s) and detonation pressures (33.70-48.90 GPa) compared with RDX and HMX. As the number of nitro-containing groups increases, the densities, detonation performance and specific impulse (Isp) and impact sensitivities gradually increase (the trend of detonation performance is contrary for N3-substituted compounds), but the heats of formation (HOFs), bond dissociation energies (BDEs), band gaps (ΔE), and electric spark sensitivities (EES) gradually decrease (the trend of HOFs and EES is contrary for N3-substituted compounds). Otherwise, these functional groups decrease molecular stabilities in the order of -ONO2 > -C(NO2)3 > -CF(NO2)2 > -NO2 > -N3. Four kinds of NO2-replaced(A1, B1 and C1) and CF(NO2)2-substituted (A3) fused-ring compounds have the potential to become high-energy density materials (HEDMs).
Key words: furazano-[3, 4-d]-pyridazine     density functional theory     detonation performance     coplanarity
Introduction

It has been a huge challenge for energetic materials to achieve a fine balance between good detonation performance and safety, and novel insensitive or low sensitive high-energy density materials (HEDM) have become developing targets of energetic materials[1-2]. Because the high heats of formation (HOF), good thermal stabilities, large densities and high amount of active oxygen, furazan-and furoxan-based derivatives have become excellently powerful skeletons for designing and synthesizing novel HEDMs in recent years[3-4]. For example, 4, 4′-oxybis(3-nitro-1, 2, 5- oxadiazole) (FOF-1, ρ=1.907 g/cm3, D= 8 930 m/s), 4, 4′-oxybis(3-(fluorodinitromethyl)-1, 2, 5-oxadiazole) (FOF-13, ρ=1.92 g/cm3, D=8 497 m/s) and 3, 4-bis (3-nitrofurazano- 4-yl)furoxan (DNTF, ρ=1.86 g/cm3, D=8 930 m/s)[5-6]. However, their applications are restricted by the conflict between energy and safety, and it is urgent to search new insensitive or low sensitive high-energy density furazan or furoxan derivatives. Recently, furazan-or furoxan-based fused-ring compounds have aroused a great interest from explosive researchers because of their high density, good detonation performance and safety. Liu et al.[7] reported the synthesis of 4, 8-di(nitratomethyl)difurazano[3, 4-b:3′, 4′-e] pyrazine (DNDP), which shows high density (2.00 g/cm3), good detonation performance (9 070 m/s, 43 GPa) and thermal stability (decomposition temperature, 250.5 ℃). And DNDP has the potential to be high-energy explosive. Benzotrifuroxan (BTF) exhibits high energy, good detonation-initiation performances, and it is an ideal non-hydrogen explosive. Meanwhile, its safety, thermal stability and detonation performance are close to those of HMX[8]. However, there are few reports about furazano-[3, 4-d]-pyridazine- based fused-ring compounds.

Our previous work[9] found that furazano- [3, 4-d]-pyridazine derivatives exhibited high densities, good thermal stabilities, and good energetic properties because of their unique conjugated structure and high nitrogen content, which indicates furazano-[3, 4-d]-pyridazine ring is an useful fragment to design novel energetic compounds. Therefore, furazano- [3, 4-d]-pyridazine-based fused-ring compounds may have the potential to be HEDMs.

In this study, three furazano-[3, 4-d]- pyridazine-based fused-ring compounds were designed and first reported, and five high-energy functional groups were introduced to improve the energetic properties. And their heats of formation (HOFs), molecular stability, and energetic properties were systematically studied by density functional theory (DFT) method. Meanwhile, based on the computational HOFs and densities, their detonation velocities and detonation pressures were evaluated. It is hoped that our results can help better understand the molecular design principles of novel HEDMs and provide available information.

1 Computational methods

The frameworks of furazano-[3, 4-d]-pyridazine-based fused-ring compounds are shown in Fig. 1.Structure optimizations of the title compounds were performed at B3LYP/6-311g (d, p) level[9] in Gaussian 09 quantum chemical package[10]. Moreover, previous studies had proved that this method and basis set were reliable to predict the structure and performance of energetic materials[11]. All optimized structures were characterized to be truly relative energy minima of the potential surface by frequency calculation (no imaginary frequencies were found). Meanwhile, isodesmic reactions (Fig. 2) were designed to predict the gas phase heats of formation (HOF). Based on Monte Carlo integration, volume of every compound was estimated by performing 100 single-point energy calculations, which is the volume to be defined as inside a contour of 0.001 electrons/bohr3 density.

 Figure 1 The frameworks of furazano-[3, 4-d]-pyridazine-based fused-ring compounds
 Figure 2 The isodesmic reaction scheme

Otherwise, the natural bond orbital (NBO) of the designed compounds was analyzed and the bond dissociation energies (BDE) of the weakest bond were predicted. Detonation performance was estimated by widely used empirical Kamlet-Jacobs equations[12]. Energy Calculation Star (ECS)[13] was used to calculate the specific impulse of the title compounds. The electric spark sensitivities were evaluated by Eq.1 put forward by Keshavarz et al[14] :

 ${E_{{\rm{ES}}}}\left( {\rm{J}} \right) = 4.60 - 0.733a + 0.724d + 9.16{r_{b/d}} - 5.14{C_{{\rm{R, OR}}}}$ (1)

where a, b and d is the number of carbon, hydrogen and oxygen atoms in CaHbNcOd, respectively, rb/d is the ratio of hydrogen to oxygen atoms and CR, OR is the number of certain groups such as alkyl (R) or alkoxy (OR) groups attached to an aromatic ring.

2 Results and discussion 2.1 Molecular geometries

The bond lengths and dihedral angels of the designed compounds are presented in Tables 1 and 2.

Table 1 Selected bond lengths of the optimized structure of the designed compounds from calculations at B3LYP/6-311G(d, p) level
Table 2 Selected dihedral angles of the optimized structure of the designed compounds from calculations at B3LYP/6-311G(d, p) level

It is easily seen that all bond lengths of the designed compounds are almost shorter than corresponding single bonds but longer than double bonds, respectively, which indicates these parent structures conjugate. For A series, all functional groups linking with triazole ring have few effects on the length of C(6)=C(7) and C(11)=C(12) (except —N3) double bonds or C(7) —N(8) and C(12)—N(13) singles bond, which is similar to B series. However, for B or C series, because more functional groups are introduced into imidazole ring, all bonds linking with functional groups are particularly stretched compared with those in the parent compound B and C (except C(7) —N(8) and N(12) —C(13) single bonds), which indicates introduced functional groups impair the conjunction of the parent ring. Otherwise, for A and B series, these functional groups have few effects on the coplanarity of the designed compounds, whose dihedral angles vary within ±5°. However, for C series, these functional groups sharply damage their coplanarity, especially dihedral angles formed by imidazole ring and pyridazine ring.

2.2 Density and energetic properties

Density is one of the most important physical properties for all energetic materials to evaluate detonation velocity and detonation pressure. The densities, detonation performances and impulse specifics of the title compounds are presented in Table 3. It can be seen that the derivatives exhibit higher densities (1.747-2.153 g/cm3) compared with the parent compounds (1.610-1.706 g/cm3), and the densities of nitro-containing groups substituted compounds (1.896-2.153 g/cm3, except A5) all surpass that of HMX (1.91 g/cm3). Five functional groups increase the densities of the designed compounds in the order:-C(NO2)3>—CF(NO2)2>—ONO2>—NO2 >-N3 (except A1 and A5). Therein, C2 possesses the highest density. From A series to C series, it can been seen that their densities improve as with the number of functional groups increasing. Otherwise, B2, B3, C2 and C3 may be not stable because of the strong steric hindrance effect of—C(NO2)3 and—CF(NO2)2 resulting from introducing two groups to every imidazole ring.

Table 3 Predicted density and detonation performance of designed compounds along with the RDX and HMX

Detonation performances are computed by widely used Kamlet-Jacobs equations. It can be seen from Table 3 that the derivatives possess good detonation velocities of 7.73 to 9.98 km/s and detonation pressures of 26.22 to 48.90 GPa. The effect of-N3 enhancing detonation performance is poor. However, when-NO2 is introduced, A1, B1 and C1 exhibit similar detonation performance (8.55-8.62 km/s, 33.70-34.52 GPa) compared with RDX (8.75 km/s, 34.70 GPa). While-C(NO2)3, -CF(NO2)2 or-ONO2 are introduced, their corresponding compounds exhibit excellent detonation performance (except A3 and A5) and surpass that of HMX (9.10 km/s, 39.00 GPa). Five functional groups increase the detonation performance of the designed compounds in the order:-C(NO2)3>-CF(NO2)2>-ONO2>-NO2>-N3. Otherwise, when their number increase, the corresponding compounds exhibit better detonation performance.

The calculated Isp of these compounds are also listed in Table 3. As the number of functional groups increase, the Isp values gradually increase from A series to C series. The Isp values (230.5-260.5 s) of all derivatives (except-NO2 and N3-substituted compounds) approximate that of HMX (266 s) because of possessing more high-energy functional groups.

2.3 Molecular stability

The molecular frontier orbital energy and energy gap of the designed compounds are presented in Table 4. The bond gap (ΔE=|ε(HOMO)- ε(LUMO)|) is an important index to estimate the molecular stability, especially for the compounds with similar frameworks[18]. The smaller energy gap is, the less molecular stability of the compound, which is because the electron easily transits from HOMO to LUMO. On the contrary, a large ΔE indicates good stability and low sensitivity. It is easy seen that the ΔE values of three series decrease in the order: A series>B series>C series, owning to the latter having more energetic functional groups. A1 owns the highest ΔE value and may be the most stable derivative.

Table 4 The frontier orbital energy, bond dissociation energy (BDE) and Wiberg Bond Order (BO) of the designed compounds

The stability of the high energetic explosives was emphasized in practical applications. The computational BDEs of the trigger bond can be seen as a quantitative parameter for molecular stability. In addition, the Wiberg bond order values also reflect the strength of trigger bond. A large Wiberg bond order indicates that the bond is hard to rupture and thus the molecule is stable. The C—NO2 and O—NO2 bond is the weakest bond in the designed compounds. B and C series possess lower BDE values because of more functional groups introduced to imidazole ring. A series exhibits the best stability. And these functional groups decrease the BDEs in the order:—ONO2>—C(NO2)3>—CF(NO2)2>—NO2>—N3. Meanwhile, A1, B1 and C1 (220.572-249.423 kJ/mol) exhibit higher BDEs than those of RDX (149.654 kJ/mol) and HMX (154.905 kJ/mol), and A1 possesses the highest BDE value. Finally, A1, B1 and C1 may be potential HEDMs.

2.4 Sensitivity

The nitro net charge (—QNO2) is related to impact sensitivity and the —QNO2 values can be regarded as a parameter to predict the impact sensitivity of nitro-containing compounds [19]. The —QNO2 can be evaluated by the sum of charge on the oxygen (—QO1 and —QO2) and nitrogen (—QN) atoms in nitro group via Eq.2.

 ${Q_{{\rm{NO2}}}} = {Q_{{\rm{O1}}}} + {Q_{{\rm{O2}}}} + {Q_{\rm{N}}}$ (2)

The lower —QNO2, the larger impact sensitivity. As listed in Table 5, all derivatives (except A5 and N3-substituted compounds) show lower —QNO2 values than RDX and HMX, which indicates they possess higher impact sensitivities. And the derivatives exhibit higher impact sensitivities as with the number of nitro groups increasing in every series. Meanwhile, A series may exhibit the smallest impact sensitivities, because A series possess less nitro group.

Table 5 The nitro net charge (—QNO2), oxygen balance and electric spark sensitivity (EES) of the designed

The electric spark sensitivity (EES) of energetic compounds can be regarded as a parameter to electrostatic discharge, which is determined by subjecting the explosive to a high-voltage discharge from a capacitor. Except N3-substituted compounds, EES values of the rest derivative (3.82-13.90 J) are superior to that of HMX (2.69 J), which indicates all nitro-containing compounds exhibit lower electric spark sensitivity compared with HMX, and -N3-compounds show the highest electric spark sensitivity. Finally, based on the computational BDEs (the main condition), H50, EES, and ΔE values, A1, B1 and C1 may meet the HEDMs′ requirement of molecular stability.

2.5 Heats of formation

The total energy (E0), zero point energy (ZPE), thermal correction to enthalpy (HT) and heats of formation (ΔHf) of the designed compounds are listed in Table 6. The results show that all compounds exhibit high positive HOFs. For nitro-containning compounds, their HOFs values decrease in the order of A series > B series > C series, which may result from triazole ring substituted by imidazole ring owning the lower HOFs and more introducing functional groups. Namely, as the number of nitro-containing groups increases, the HOFs of corresponding compounds particularly decrease from A series to C series. When-CF(NO2)2 is introduced, the HOFs of the corresponding compounds particularly decrease compared with the parent compounds. On the contrary, when-N3 is introduced, the HOFs of the corresponding compounds gradually increase.

Table 6 Total energy (E0), zero point energy (ZPE), thermal correction to enthalpy (HT) and heats of formation (ΔHf(g)) of the designed compounds
3 Conclusion

Based on DFT calculations, the relationship between structure and performance of three furazano-[3, 4-d]- pyridazine-based fused-ring compounds was studied, the main results are presented as follows.

(1) All designed derivatives exhibit high densities, high positive HOFs and good detonation performance. Their densities and detonation performance (except N3-substituted compounds) increase as with the number of functional groups increasing. However, the trend of HOFs is contrary. Otherwise, the effect of—N3 improving detonation performance is ordinary. But the detonation performances of all nitro-containing derivatives (except A1 and A5) are superior those of RDX and HMX, and their specific impulses approximate the latter (except NO2-substituted compounds).

(2) The calculated densities, ΔE, BDEs and—QNO2 show that the molecular stabilities of designed compounds gradually decrease as with the number of functional groups increasing for three series. The functional groups increase impact sensitivities in the order:—C(NO2)3>—CF(NO2)2>—NO2>—ONO2. The functional groups increase electric spark sensitivities in the order:—N3>—NO2>—CF(NO2)2>—ONO2>—C(NO2)3. Based on above properties, these groups decrease molecular stabilities in the order:—ONO2>—C(NO2)3>—CF(NO2)2>—NO2>—N3.

(3) Consequently, comprehensively considering these performances, A1, A3, B1 and even C3 may have the potential to be HEDMs. And these results provide theoretical support for designing novel fused-ring compounds.

References
 [1] SHU Yuan-jie, HUO Ji-chuan. Theory of Explosives[M]. Beijing: Chemical Industry Press, 2011. [2] WANG Xi-jie, XU Kang-zhen, et al. The insensitive energetic material trifurazano-oxacycloheptatriene (TFO):synthesis and detonation properties[J]. Propellants, Explosives, Pyrotechnics, 2015, 40(1): 9–12. DOI:10.1002/prep.v40.1 [3] SHU Yuan-jie, WANG Bo-zhou. Chemistry of Furoxan:Structure and Synthesis[M]. Chengdu: Times Press, 2013. [4] Frem D. Theoretical studies on energetic properties of s-triazine substituted aminofurazan and aminofuroxan derivatives-high performance energetic material systems[J]. Combustion, Explosion, and Shock Waves, 2014, 50(4): 441–446. DOI:10.1134/S0010508214040121 [5] WANG Bo-zhou, LI Hui, LI Ya-nan, et al. Review on energetic compounds based on furoxanyl ether[J]. Chinese Journal of Energetic Materials, 2012, 20(4): 385–390. [6] HU Huan-xing, QIN Guang-ming, ZHANG Zhi-zhang, et al. 3, 4-Dinitro-furazanfuroxan explosive: CN, 0210. 7[P]: 2002. [7] LIU Ning, LIAN Peng, et al. Synthesis, Characterization and performance of difurazanopyrazine derivatives[J]. Chinese Journal of Energetic Materials, 2014, 22(4): 473–477. [8] ZHOU Yan-shui, WANG Xi-jie, et al. Crystal structure of benzotrifuroxan[J]. Chinese Journal of Explosives & Propellants (Huozhayao Xuebao), 2012, 35(4): 26–29. [9] WANG Ke, SHU Yuan-jie, LIU Ning, et al. Theoretical studies on structure andperformance of[1, 2, 5] -oxadiazolo-[3, 4-d]-pyridazine-based derivatives[J]. Journal of Physical Organic Chemistry, 2017, 30(1): e3591. DOI:10.1002/poc.v30.1 [10] Frisch M J, Trucks G W, Schlegel H B, et al., Gaussian 09[M]. Revision B. 01. Wallingford: Gaussian, Inc., 2009. [11] SHAO Yu-lin, ZHU Wei-hua, XIAO He-ming. Structure-property relationships of energetic nitrogen-rich salts composed of triaminoguanidinium or ammonium cation and tetrazole-based anions[J]. Journal of Molecular Graphics and Modelling, 2013, 40: 54–63. DOI:10.1016/j.jmgm.2012.12.003 [12] Keshavarz M H. Prediction method for specific impulse used as performance quantity for explosives[J]. Propellants, Explosives, Pyrotechnics, 2008, 33: 360–364. DOI:10.1002/prep.v33:5 [13] LI Meng, ZHAO Feng-qi, et al. Comparison of three kinds of energy calculation programs in formulation design of solid propellants[J]. Chinese Journal of Explosives & Propellants (Huozhayao Xuebao), 2013, 36(3): 73–77. [14] Keshavarz M H. Prediction method for specific impulse used as performance quantity for explosives[J]. Propellants, Explosives, Pyrotechnics, 2008, 33: 360–364. DOI:10.1002/prep.v33:5 [15] LIN He, CHEN Peng-wan, ZHU Shun-guan, et al. Theoretical studies on the thermodynamic properties, density, detonation properties, and pyrolysis mechanisms of trinitromethyl-substituted aminotetrazoole compounds[J]. Journal of Molecular Modeling, 2013, 19(6): 2413–2422. DOI:10.1007/s00894-013-1783-2 [16] Keshavarz M H, Pouretedal H R. Predicting the detonation velocity of CHNO explosives by a simple method[J]. Propellants, Explosives, Pyrotechnics, 2005, 30(2): 105–108. DOI:10.1002/(ISSN)1521-4087 [17] Kuo K K, Acharya R. Applications of Turbulent and Multi-Phase Combustion[M]. [S. l. ]: Wiley, 2012: 52. [18] Fan X W, Ju X H, Xiao H M, et al. Theoretical studies on heats of formation, group interaction, and bond dissociation energies in neopentyldifluoroamino compounds[J]. Journal of Molecular Structure(THEOCHEM), 2006, 801(1/3): 55–62. [19] MA Cong-ming, HUO Ke-hui, LIU Zu-liang, et al. Quantum chemistry study on the structures and detonation properties for nitro derivatives of pyrido-dicycloureas[J]. Chinese Journal of Explosives & Propellants (Huozhayao Xuebao), 2015, 38(6): 32–38.