J Mol Model (2014) 20:2155 DOI 10.1007/s00894-014-2155-2
ORIGINAL PAPER
Theoretical investigation on the structure and performance of N, N′-azobis-polynitrodiazoles Mei Jing & Huarong Li & Jun Wang & Yuanjie Shu & Xiaoyu Zhang & Qing Ma & Yigang Huang
Received: 29 November 2013 / Accepted: 22 January 2014 / Published online: 16 March 2014 # Springer-Verlag Berlin Heidelberg 2014
Abstract Six novel high energy density compounds of N, N′azobis-polynitrodiazoles were designed. Their optimized geometric and electronic structures, band gaps, and heats of formation were explored at B3LYP/aug-cc-pVDZ level of density functional theory (DFT). Detonation properties were predicted by Kamlet-Jacobs equations. Results show that the designed compounds have high densities (1.80 to 1.84 g· cm−3) and excellent detonation performance (D 8.51 to 9.02 km·s−1, P 32.16 to 36.58 GPa). In addition, the bond dissociation energies of C-NO2 bonds were found to range from 223.59 to 240.46 kJ·mol−1. All of them appear to be potential explosives compared with the well known ones, 1,3,5-trinitro-1,3,5-triazine (RDX, 8.75 km·s−1, 34.70 GPa) and octahydro- 1,3,5,7-tetranitro-1,3,5,7-tetraazocane (HMX, 8.96 km · s−1, 35.96 GPa), especially R3 (8.98 km · s−1, 36.19 GPa) and R6 (9.02 km·s−1, 36.58 GPa). Finally, the position and number of nitro groups in the N, N′-azobispolynitrodiazoles determine the heat of formation, stability, sensitivity, density, and detonation performance of these compounds.
Keywords Bond dissociation energy . Density . Detonation performance . N, N′-azobis-polynitrodiazoles . Sensitivity
M. Jing : H. Li : J. Wang (*) : Y. Shu (*) : X. Zhang : Q. Ma : Y. Huang Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang 621900, China e-mail: [email protected] e-mail: [email protected] M. Jing Department of Materials Science and Engineering, Southwest University of Science and Technology, Mianyang 621010, China
Introduction In order to meet the developing requirements of modern weapons and avoid the unintentional catastrophic explosions, searching for novel energetic compounds with better security and performance becomes urgent and imperative [1]. Due to the high heat of formation (HOF), good thermal stability, low sensitivity, and excellent detonation performance, nitroimidazoles and nitropyrazoles have drawn renewed attention from explosive researchers currently [2–6]. Cho [7] studied the molecular structure of 4(5)-nitroimidazole and 4,5dinitroimidazole (4,5-DNI). Yin [8] investigated the relationship between structures and properties of a series of nitroimidazole compounds. Recently, Ravi [9–11] researched the geometric, thermodynamic and detonation properties of amino- and methyl- substituted trinitrodiazoles and aminonitroimidazoles. All of these studies suggested that nitrodiazoles are good potential energetic materials. However, most of the experimental and theoretical studies were focused on monocyclic nitrodiazoles, very few on N, N′-azobispolynitrodiazoles till now. It is generally considered that introducing−N=N−onto nitrodiazole rings can improve the performance of nitrodiazoles in three aspects [12]: First, it could increase the HOFs and densities. Second, it gives an environmentally friendly gas of nitrogen without consuming oxygen during decomposition. Moreover, −N=N−bond contributes to the delocalization of π-electrons over the nitrodiazoles ring and makes the structure more stable. Therefore, it is necessary to predict HOFs, densities, stabilities, sensitivities, and detonation properties of N, N′-azobispolynitrodiazoles before trying to synthesize them. It is known that detonation property and security are of great importance for explosives [13]. Detonation performance is usually valued by detonation velocity (D) and detonation pressure (P), and the security can be generally measured by the so-called sensitivity. In fact, sensitivity is quite
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complicated which relates to impact sensitivity, shock sensitivity, and electric spark sensitivity. Zhang [14, 15] developed a method to assess impact sensitivities by calculating the Mulliken net charges of the nitro groups. Politzer [16, 17] put forward that the bond dissociation energies (BDEs) of trigger bonds and molecular electrostatic potential (MESP) were related to the impact sensitivities. Zhou [18] used nucleus-independent chemical shift to evaluate the security of hazardous materials. Zeman [19] related the impact and electric spark sensitivities to detonation properties, thermal decompositions, and 13C, 15 N NMR chemical shifts of poly nitro compounds. Wang [20, 21] provided an appropriate relationship between electric spark sensitivity, detonation pressure, and detonation velocity for nitramines and nitroarenes. Consequently, it is appropriate to analyze stability and sensitivity based on the above aspects. In this paper, we designed six N, N′ -azobispolynitrodiazole compounds based on the systematic structures and property relationships of nitrodiazoles, and investigated their molecular and explosive properties at B3LYP/augcc-pVDZ level by DFT method, as well as the reference compounds 2,4-dinitroimidazole (2,4-DNI), 3,4dinitropyrazole (3,4-DNP), and 4,5-DNI using the same method, which were used to prove the results to be reliable.
Methods and computational details Geometry optimization of the title compounds were performed at B3LYP/aug-cc-pVDZ level in the Gaussian 09 quantum chemical package [22]. In addition, Ravi [9–11] has proved that this basis set and method was suitable to investigate nitrodiazoles. All the optimized structures were positively identified to be true relative energy minima of the potential surfaces by frequency calculations (no imaginary frequencies were found). Based on the optimized geometries, the other relative properties, such as HOFs, BDEs, and MESP of these compounds, were calculated and discussed below. Detonation properties were evaluated by the widely used empirical Kamlet-Jacobs equations [23]: 1=2 D ¼ 1:01 N M 1=2 Q1=2 ð1 þ 1:3 ρÞ
ð1Þ
P ¼ 1:558 N M 1=2 Q1=2 ρ2
ð2Þ
where D is the detonation velocity (km·s−1), P is the detonation pressure (GPa), ρ is the density of the explosive (g·cm−3), N is the amount (mol−1) of gaseous detonation products per gram of explosive, M is the average molecular weight of the gaseous products, and Q is the chemical energy of the
detonation (cal·g−1), which can be derived from the heats of formation (HOFs) of the products and reactants. In this paper, we use atomization approach (based on the results of quantum calculations) to estimate the gas phase heats of formation (ΔHf (g, 298 K) [24, 25]). Zhou [24] has also successfully and efficiently obtained the HOFs of highnitrogen energetic substituted s-tetrazine compounds using atomization approach, the detailed calculation procedure is as follows (Scheme 1): Namely, the gas-phase heat of formation of M at 298 K can be written as Eq. 3: ΔH f ðg; 298 KÞ ¼ ΔH f ðM; 0KÞ þ Σ ni ðH Xi ð0KÞ−H Xi ð298KÞÞ atom
þ ðH M ð298KÞ−H M ð0KÞÞ
ð3Þ where ni stands for the number of atoms of Xi in M, HXi (0 K) stands for the HOF of Xi at 0 K, which can be found from ref. [26], and ΔHf (M, 0 K) can be derived from HXi (0 K). (HM(298 K)-HM(0 K)) and (HXi(0 K)-HXi(298 K)) represent the enthalpy correction of the molecular (M) and atom (Xi) between 0 K and 298 K, respectively, and they can be performed by Gaussian 09 package. Finally, the ΔHf (g, 298 K) values can be calculated using our own computer code. However, it has been reported that gas-phase HOFs are usually deficient in estimating the detonation performance of energetic materials [27]. Consequently, the solid state HOFs of the designed compounds were needed to determine detonation properties. They can be calculated via Eqs. (4) and (5) developed by Politzer et al. [28–30]: ΔH f ðsolid; 298 KÞ ¼ ΔH f ðgas; 298 KÞ−ΔH sub ð298 KÞ
ð4Þ
0:5 ΔH sub 298 K; kcal⋅mol−1 ¼ αðAS Þ2 þ β v σ2tot þγ
ð5Þ
where ΔHsub is the sublimation enthalpy, α, β and γ are adopted from ref. [29]. As is the molecular surface, v is a measure of balance between positive and negative potential on the molecular surface, and σ2tot represents the variability of electrostatic potential.
Scheme 1 The atomization scheme
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The densities of these compounds can be calculated using the following equation, as put up by Politzer et al. [31]: crystal density ðρÞ ¼ α0
M mol Vm
þ β0 vσ2tot þ γ 0
BDEðR−XÞ ¼ EðRÞ þ EðXÞ−EðR−XÞ
ð7Þ
ð6Þ
where M mol is the molecular mass (g·mol−1) and Vm is the volume (Å3 ·mol−1) defined as the space inside a counter of electron density of 0.001 e/Bohr3. α', β' and γ' are taken from ref. [31]. The bond dissociation energy is considered as a quite convincing criterion for the molecular stablity [32], which means the difference between the energy of a molecule and those of the radicals produced when a bond of this molecule is broken. It is significant to understand the pyrolysis mechanism of the compounds [33–35]. Also, the energy required for homolytic bond cleavage at 298 K and 1 atm is important to the enthalpy of reaction [32, 36, 37]. The
logH 50 ¼
BDE of the trigger bond was calculated by the following Eqs:
where E is the total energy. R–X is the designed molecule. R and X are the radicals produced when the trigger bond is broken. The BDE with zero point energy correction (BDEZPE) is: BDEZPE ðR−XÞ ¼ BDEðR−XÞ þ ΔZEP
where ΔZPE is the zero point energy correction. Impact sensitivity can be expressed by the height (H50) that a standard weight falling upon the explosive gives 50 % probability of initiating explosion. Here, a simple and appropriate way [38] was adopted to estimate H50 of the designed compounds, and it can be written as follows:
46:2923 a þ 35:6305 b−7:7005c þ 7:9425 d þ 44:4167nð−CNC−Þ þ 102:2749 nð−CNNC−Þ M
where a, b, c, and d present the number of carbon atoms, hydrogen atoms, nitrogen atoms and oxygen atoms, respectively. n(–CNC–) and n(–CNNC–) are the number of –CNC– and – CNNC– moieties in the aromatic ring. M means the average molecular weight.
Results and discussion Optimized structures First of all, we have optimized the structures of the title compounds at the DFT-B3LYP/aug-cc-pVDZ level and the molecular frameworks are presented in Fig. 1. Research works [39, 40] have shown that explosives with a greater number of directly linked nitrogen atoms will have better energetic properties. Therefore, we have designed six stable N, N′-azobispolynitrodiazole structures, in which R1∼R3 contain four nitrogen atoms linked directly to structure and R4∼R6 contain six nitrogen atoms linked directly to structure. From Table 1, the lowest frequencies varying from 10.21 to 59.87 cm−1 are for the dihedral angles of nitro groups [41]. The geometries, bond lengths, bond angles, and total energies vary with the position and number of the nitro groups in the N, N′-azobispolynitrodiazoles.
ð8Þ
ð9Þ
The selected dihedral angles and bond lengths of N−N= N−N are presented in Table 2. The dihedral angles range from 0 to 5° except R4 (9.90 °). We take N−N=N−N as a plane and find that the coplanarity of R4 is worst with the two pyrazole rings deviating from the plane obviously (this phenomenon can also be observed from Fig. 2). R2 is a well symmetrical and coplanar molecule with two imidazole rings and two nitro groups (C4−NO2 and C4′−NO2) in one plane. The bond lengths of N(1)−N(6) vary from 1.366 to 1.391 Å, and N(6)=N(6′) vary from 1.243 to 1.246 Å, which are shorter than that of N−N (1.429 Å) but longer than that of N=N (1.025 Å) compared with te-trazene (N4 −H4H2N−N= N−NH2), respectively [32, 42, 43]. It indicates that the structure of N, N′-azobis- polynitrodiazole and te-trazene is different in essence. Due to the electron-withdrawing effect of diazole rings to the−N−N=N−N−structure, the−N=N−has stronger capability, thus, these molecules are more stable compared to te-trazene structure.
Electrostatic potentials and frontier molecular orbital energies MESP is the potential energy of a proton at a particular location near a molecule. The MESPs that calculated by
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Fig. 1 Illustration with the atomic numbering of title compounds, with trigger linkages (C−NO2) encircled in red; the list of values besides each structure shows the trigger length (in Å), nitro group charge (in e) and midpoint electrostatic potential. (All the molecules are symmetric, so we selected half of the molecule for our research)
Materials Studio 6.0 package [44] based on the optimized geometry are depicted in Fig. 2. The calculated partial charges represented as spheres exhibit how the molecule would interact with approaching protons or positive charges [45]. As is shown in Fig. 2, the strongly positive MESP surface (colored in blue) is prominent in the center of the molecule, while the negative MESP surface (colored in red) primarily caused by electron-withdrawing group (−NO2) is in the surrounding of the molecule. Politzer and Murray et al. [17, 46–49] considered that, in terms of energetic materials, the positive regions are larger as well as stronger in magnitude than the negative ones. Consequently, the designed molecules can be employed as promising energetic compounds. The molecular frontier orbital energies and their gap energies are presented in Table 1. The band gap (ΔE=|ε(HOMO)–ε(LUMO)|) is an important parameter to evaluate the molecular stability, especially for the compounds with similar frameworks
[50, 51]. A small ΔE can lead to enhanced reactivity and poor stability with respect to chemical and photochemical processes [52, 53]. For example, it causes the electron transition from HOMO to LUMO easily, thus leading the molecule to become less stable. On the contrary, a large ΔE implies high stability and low sensitivity. The ΔE of R5 (397.42 kJ·mol−1) is the largest and R3 (377.13 kJ·mol−1) is the smallest, indicating that the former is more stable than the latter. Compounds R1 and R2, R4 and R5, and R3 and R6 have similar band gaps, implying that the position and number of nitro groups make a slight difference on band gaps of the title compounds. Usually, the higher the total energy of the molecule, the less stable the compound. According to the total energies (Table 1), the most unstable compounds are R3 (-4693498.44 kJ · mol−1) and R6 (4693432.36 kJ·mol−1) among the six compounds. For these molecules, the highly delocalized conjugated π-system strengthens bonds in the N, N′-azobis-polynitrodiazoles, leading
Table 1 Lowest frequency (ωL), total energy (E0), zero-point energy (ZPE), thermal correction to enthalpy (HT) and frontier orbital energy of
designed molecules and some reference compounds, as computed at the B3LYP/aug-cc-pVDZ level
Comp
ωL/ (cm−1)
E0/ (kJ·mol−1)
ZPE/ (kJ·mol−1)
HT/ (kJ·mol−1)
LUMO/ (kJ·mol−1)
HOMO/ (kJ·mol−1)
ΔE/ (kJ·mol−1)
R1 R2 R3 R4
11.48 11.51 10.76 12.86
−3619652.85 −3619648.32 −4693498.44 −3619555.15
365.03 366.40 374.31 364.03
419.62 421.23 444.01 419.02
−470.49 −460.99 −521.79 −444.42
−856.02 −848.61 −898.92 −841.84
385.53 387.63 377.13 395.40
R5 R6 2,4-DNI 4,5-DNI 3,4-DNP
15.51 10.21 59.87 23.73 10.43
−3619584.40 −4693432.36 −1667812.84 −1667789.79 −1667739.26
364.63 374.32 199.85 199.63 199.67
419.04 444.60 224.73 225.06 225.32x
−467.94 −511.68 −362.84 −357.12 −314.95
−863.34 −891.65 −825.14 −798.83 −824.67
397.42 379.96 462.30 441.71 509.71
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Table 2 Selected bond lengths and dihedral angles of the optimized geometry for the titled compounds from B3LYP/aug-cc-pVDZ calculations Bonds lengths /( Å) N(1)−N(6) N(6)=N(6′) Dihedral angles /(°) N(1)−N(6)=N(6′)−N(1′)
R1
R2
1.371 1.244
1.368 1.246
177.00
179.99
R3
R4
1.380 1.243
1.391 1.244
9.90
the molecules to become stabilized. The difference in stabilities is mainly attributed to the trigger bond lengths, BDEs and slight discrepancies in total energies, which in turn are caused by the position or number of nitro groups.
Impact sensitivity H50 is a complicated matter of an energetic compound because it contains metastable state of undergoing very rapid and high exothermic reactions [54]. Table 3 shows that the H50 values of R1, R2, R4, and R5 are higher compared with R3 and R6. The results shows that the more nitro groups the molecule has, the lower H50, that is to say, the less insensitive the compound. Moreover, it is evident that R4, R5, and R6 have higher H50 than that of R1, R2, and R3, which is probably attributed to the stability of pyrazole rings. Mulliken atomic charge analysis of nitro groups is also used to estimate the impact sensitivities of the title compounds. Normally, for the majority of nitro explosives, R– NO2 (R=N, C or O) bonds are the weakest bonds and their breaking is usually the initial step in the decomposition or detonation. The nitro group charge (−QNO2) is calculated by the sum of net Mulliken atomic charges on the nitrogen and
R5
176.21
R6
1.380 1.245
1.366 1.244
176.59
178.88
te-trazene[40] 1.429 1.025 —
oxygen atoms of the nitro group: −QNO2 ¼ QN þ QOð1Þ þ QOð2Þ
ð10Þ
2ðQC þ QN Þ RðC−NÞ
ð11Þ
V mid ¼
where Vmid is the midpoint electrostatic potential, R(C-N) is the length of trigger bond, QC, QN and QO(1) and QO (2) are the Mulliken charges on carbon, nitrogen and oxygen atoms, respectively. The computed Wiberg bond order values, −QNO2 values, trigger lengths, and Vmid of the molecules are summarized in Table 3. The higher negative charge the nitro group possesses, the weaker the electron-withdrawing ability, then the greater stability the overall of the compound and thus the lower the impact sensitivity. Wiberg bond order values also reflect the strength of trigger bond, a large Wiberg bond order indicates the bond is hard to rupture and thus the molecule is stable. The calculated Vmid values vary from 0.66 to 2.72, are superior to those of 2,4,6-trinitrotoluene (TNT) (0.25), 1,3,5-triamino-2,4,6trinitrobenzene (TATB) (0.42), 2,6-diamino-3,5-dinitropyrazine1-oxide (LLM-105) (0.26), and 3-nitro-1,2,4-triazol-5-one (NTO) (0.26) [41]. The calculated−QNO2 values vary from 0.48 to 0.64 e, according to that predicted by Zhang [14, 15], these−QNO2 values are found to be higher than those of
16.00
8.00 0.00
R1
R2
R3
-8.00 -16.00 R4
R5
R6
Fig. 2 3D molecular electrostatic potential maps of title molecules. (Red and blue stand for negative and positive electrostatic regions, respectively, with colors representing values between −16.00 kJ·mol−1 and 16.00 kJ·mol−1)
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Comp
bond
Length/
Vmid
(Å)
Wiberg bond order
−QNO2
H50/
BDE/ −1
(e)
(kJ·mol )
(cm)
R1
C(2)−NO2
1.443
0.956
1.842
0.510
245.37
31.7
R2
C(4)−NO2 C(4)−NO2 C(5)−NO2
1.462 1.454
0.909 0.927
1.477 1.369
0.507 0.536
235.39 261.97
31.7
1.466 1.467
0. 893 0.901
2.381 1.440
0.550 0.490
235.82 229.05
11.5
1.460
0.918
1.245
0.517
238.82
R3
C(2)−NO2 C(4)−NO2 C(5)−NO2
R4
C(3)−NO2
1.466 1.471
0.897 0.879
2.628 1.336
0.546 0.641
223.59 235.98
38.0
R5
C(4)−NO2 C(3)−NO2
1.441 1.462
0.962 0.917
2.412 0.673
0.574 0.523
261.52 261.93
38.0
R6
C(5)−NO2 C(3)−NO2
1.455 1.474
0.930 0.874
0.660 1.266
0.478 0.606
240.46 232.96
13.3
C(4)−NO2 C(5)−NO2
1.442
0.960
2.716
0.552
242.91
1.470
0.881
1.396
0.609
230.87
2,4,6,8,10,12-hexanitro- 2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) (0.08 e), HMX (0.11 e), and RDX (0.13e), suggesting that these compounds are more insensitive.
Bond dissociation energies The calculated BDE of the trigger bond can be used as a quantitative index for molecular stability [12]. It should be emphasized that this criterion only applies to molecules whose weakest bond is the R−NO2 bond [32, 38]. In general, if BDE> 80 kJ·mol−1, then the compound could be considered as a practical energetic material; otherwise, if BDE>120 kJ·mol−1, then it could be considered as excellent energetic material which meets the stability requirements of HEDMs [12]. The calculated BDEs (Table 3) of R1∼R6 vary from 223.59 to 240.46 kJ· mol−1. Compared with that of TNT (251.16 kJ·mol−1), RDX (160.09 kJ·mol−1), and TATB (305.79 kJ·mol−1), all of the designed compounds possess high BDEs and are content with the stability requirements of HEDMs. Furthermore, by contrast the BDEs of R3 and R6 with R1∼R4, it is observed that the number of nitro groups have strong influence on the BDEs (e.g., BDE decreases with the increasing number of nitro groups). It can be deduced that R3 and R6 are susceptible to pyrolysis. Based on the BDE, H50 and ΔE values, we achieve Fig. 3, from where we come to reach a conclusion that the stability of the title compounds increases as follows: R3
ORIGINAL PAPER
Theoretical investigation on the structure and performance of N, N′-azobis-polynitrodiazoles Mei Jing & Huarong Li & Jun Wang & Yuanjie Shu & Xiaoyu Zhang & Qing Ma & Yigang Huang
Received: 29 November 2013 / Accepted: 22 January 2014 / Published online: 16 March 2014 # Springer-Verlag Berlin Heidelberg 2014
Abstract Six novel high energy density compounds of N, N′azobis-polynitrodiazoles were designed. Their optimized geometric and electronic structures, band gaps, and heats of formation were explored at B3LYP/aug-cc-pVDZ level of density functional theory (DFT). Detonation properties were predicted by Kamlet-Jacobs equations. Results show that the designed compounds have high densities (1.80 to 1.84 g· cm−3) and excellent detonation performance (D 8.51 to 9.02 km·s−1, P 32.16 to 36.58 GPa). In addition, the bond dissociation energies of C-NO2 bonds were found to range from 223.59 to 240.46 kJ·mol−1. All of them appear to be potential explosives compared with the well known ones, 1,3,5-trinitro-1,3,5-triazine (RDX, 8.75 km·s−1, 34.70 GPa) and octahydro- 1,3,5,7-tetranitro-1,3,5,7-tetraazocane (HMX, 8.96 km · s−1, 35.96 GPa), especially R3 (8.98 km · s−1, 36.19 GPa) and R6 (9.02 km·s−1, 36.58 GPa). Finally, the position and number of nitro groups in the N, N′-azobispolynitrodiazoles determine the heat of formation, stability, sensitivity, density, and detonation performance of these compounds.
Keywords Bond dissociation energy . Density . Detonation performance . N, N′-azobis-polynitrodiazoles . Sensitivity
M. Jing : H. Li : J. Wang (*) : Y. Shu (*) : X. Zhang : Q. Ma : Y. Huang Institute of Chemical Materials, China Academy of Engineering Physics, Mianyang 621900, China e-mail: [email protected] e-mail: [email protected] M. Jing Department of Materials Science and Engineering, Southwest University of Science and Technology, Mianyang 621010, China
Introduction In order to meet the developing requirements of modern weapons and avoid the unintentional catastrophic explosions, searching for novel energetic compounds with better security and performance becomes urgent and imperative [1]. Due to the high heat of formation (HOF), good thermal stability, low sensitivity, and excellent detonation performance, nitroimidazoles and nitropyrazoles have drawn renewed attention from explosive researchers currently [2–6]. Cho [7] studied the molecular structure of 4(5)-nitroimidazole and 4,5dinitroimidazole (4,5-DNI). Yin [8] investigated the relationship between structures and properties of a series of nitroimidazole compounds. Recently, Ravi [9–11] researched the geometric, thermodynamic and detonation properties of amino- and methyl- substituted trinitrodiazoles and aminonitroimidazoles. All of these studies suggested that nitrodiazoles are good potential energetic materials. However, most of the experimental and theoretical studies were focused on monocyclic nitrodiazoles, very few on N, N′-azobispolynitrodiazoles till now. It is generally considered that introducing−N=N−onto nitrodiazole rings can improve the performance of nitrodiazoles in three aspects [12]: First, it could increase the HOFs and densities. Second, it gives an environmentally friendly gas of nitrogen without consuming oxygen during decomposition. Moreover, −N=N−bond contributes to the delocalization of π-electrons over the nitrodiazoles ring and makes the structure more stable. Therefore, it is necessary to predict HOFs, densities, stabilities, sensitivities, and detonation properties of N, N′-azobispolynitrodiazoles before trying to synthesize them. It is known that detonation property and security are of great importance for explosives [13]. Detonation performance is usually valued by detonation velocity (D) and detonation pressure (P), and the security can be generally measured by the so-called sensitivity. In fact, sensitivity is quite
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complicated which relates to impact sensitivity, shock sensitivity, and electric spark sensitivity. Zhang [14, 15] developed a method to assess impact sensitivities by calculating the Mulliken net charges of the nitro groups. Politzer [16, 17] put forward that the bond dissociation energies (BDEs) of trigger bonds and molecular electrostatic potential (MESP) were related to the impact sensitivities. Zhou [18] used nucleus-independent chemical shift to evaluate the security of hazardous materials. Zeman [19] related the impact and electric spark sensitivities to detonation properties, thermal decompositions, and 13C, 15 N NMR chemical shifts of poly nitro compounds. Wang [20, 21] provided an appropriate relationship between electric spark sensitivity, detonation pressure, and detonation velocity for nitramines and nitroarenes. Consequently, it is appropriate to analyze stability and sensitivity based on the above aspects. In this paper, we designed six N, N′ -azobispolynitrodiazole compounds based on the systematic structures and property relationships of nitrodiazoles, and investigated their molecular and explosive properties at B3LYP/augcc-pVDZ level by DFT method, as well as the reference compounds 2,4-dinitroimidazole (2,4-DNI), 3,4dinitropyrazole (3,4-DNP), and 4,5-DNI using the same method, which were used to prove the results to be reliable.
Methods and computational details Geometry optimization of the title compounds were performed at B3LYP/aug-cc-pVDZ level in the Gaussian 09 quantum chemical package [22]. In addition, Ravi [9–11] has proved that this basis set and method was suitable to investigate nitrodiazoles. All the optimized structures were positively identified to be true relative energy minima of the potential surfaces by frequency calculations (no imaginary frequencies were found). Based on the optimized geometries, the other relative properties, such as HOFs, BDEs, and MESP of these compounds, were calculated and discussed below. Detonation properties were evaluated by the widely used empirical Kamlet-Jacobs equations [23]: 1=2 D ¼ 1:01 N M 1=2 Q1=2 ð1 þ 1:3 ρÞ
ð1Þ
P ¼ 1:558 N M 1=2 Q1=2 ρ2
ð2Þ
where D is the detonation velocity (km·s−1), P is the detonation pressure (GPa), ρ is the density of the explosive (g·cm−3), N is the amount (mol−1) of gaseous detonation products per gram of explosive, M is the average molecular weight of the gaseous products, and Q is the chemical energy of the
detonation (cal·g−1), which can be derived from the heats of formation (HOFs) of the products and reactants. In this paper, we use atomization approach (based on the results of quantum calculations) to estimate the gas phase heats of formation (ΔHf (g, 298 K) [24, 25]). Zhou [24] has also successfully and efficiently obtained the HOFs of highnitrogen energetic substituted s-tetrazine compounds using atomization approach, the detailed calculation procedure is as follows (Scheme 1): Namely, the gas-phase heat of formation of M at 298 K can be written as Eq. 3: ΔH f ðg; 298 KÞ ¼ ΔH f ðM; 0KÞ þ Σ ni ðH Xi ð0KÞ−H Xi ð298KÞÞ atom
þ ðH M ð298KÞ−H M ð0KÞÞ
ð3Þ where ni stands for the number of atoms of Xi in M, HXi (0 K) stands for the HOF of Xi at 0 K, which can be found from ref. [26], and ΔHf (M, 0 K) can be derived from HXi (0 K). (HM(298 K)-HM(0 K)) and (HXi(0 K)-HXi(298 K)) represent the enthalpy correction of the molecular (M) and atom (Xi) between 0 K and 298 K, respectively, and they can be performed by Gaussian 09 package. Finally, the ΔHf (g, 298 K) values can be calculated using our own computer code. However, it has been reported that gas-phase HOFs are usually deficient in estimating the detonation performance of energetic materials [27]. Consequently, the solid state HOFs of the designed compounds were needed to determine detonation properties. They can be calculated via Eqs. (4) and (5) developed by Politzer et al. [28–30]: ΔH f ðsolid; 298 KÞ ¼ ΔH f ðgas; 298 KÞ−ΔH sub ð298 KÞ
ð4Þ
0:5 ΔH sub 298 K; kcal⋅mol−1 ¼ αðAS Þ2 þ β v σ2tot þγ
ð5Þ
where ΔHsub is the sublimation enthalpy, α, β and γ are adopted from ref. [29]. As is the molecular surface, v is a measure of balance between positive and negative potential on the molecular surface, and σ2tot represents the variability of electrostatic potential.
Scheme 1 The atomization scheme
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The densities of these compounds can be calculated using the following equation, as put up by Politzer et al. [31]: crystal density ðρÞ ¼ α0
M mol Vm
þ β0 vσ2tot þ γ 0
BDEðR−XÞ ¼ EðRÞ þ EðXÞ−EðR−XÞ
ð7Þ
ð6Þ
where M mol is the molecular mass (g·mol−1) and Vm is the volume (Å3 ·mol−1) defined as the space inside a counter of electron density of 0.001 e/Bohr3. α', β' and γ' are taken from ref. [31]. The bond dissociation energy is considered as a quite convincing criterion for the molecular stablity [32], which means the difference between the energy of a molecule and those of the radicals produced when a bond of this molecule is broken. It is significant to understand the pyrolysis mechanism of the compounds [33–35]. Also, the energy required for homolytic bond cleavage at 298 K and 1 atm is important to the enthalpy of reaction [32, 36, 37]. The
logH 50 ¼
BDE of the trigger bond was calculated by the following Eqs:
where E is the total energy. R–X is the designed molecule. R and X are the radicals produced when the trigger bond is broken. The BDE with zero point energy correction (BDEZPE) is: BDEZPE ðR−XÞ ¼ BDEðR−XÞ þ ΔZEP
where ΔZPE is the zero point energy correction. Impact sensitivity can be expressed by the height (H50) that a standard weight falling upon the explosive gives 50 % probability of initiating explosion. Here, a simple and appropriate way [38] was adopted to estimate H50 of the designed compounds, and it can be written as follows:
46:2923 a þ 35:6305 b−7:7005c þ 7:9425 d þ 44:4167nð−CNC−Þ þ 102:2749 nð−CNNC−Þ M
where a, b, c, and d present the number of carbon atoms, hydrogen atoms, nitrogen atoms and oxygen atoms, respectively. n(–CNC–) and n(–CNNC–) are the number of –CNC– and – CNNC– moieties in the aromatic ring. M means the average molecular weight.
Results and discussion Optimized structures First of all, we have optimized the structures of the title compounds at the DFT-B3LYP/aug-cc-pVDZ level and the molecular frameworks are presented in Fig. 1. Research works [39, 40] have shown that explosives with a greater number of directly linked nitrogen atoms will have better energetic properties. Therefore, we have designed six stable N, N′-azobispolynitrodiazole structures, in which R1∼R3 contain four nitrogen atoms linked directly to structure and R4∼R6 contain six nitrogen atoms linked directly to structure. From Table 1, the lowest frequencies varying from 10.21 to 59.87 cm−1 are for the dihedral angles of nitro groups [41]. The geometries, bond lengths, bond angles, and total energies vary with the position and number of the nitro groups in the N, N′-azobispolynitrodiazoles.
ð8Þ
ð9Þ
The selected dihedral angles and bond lengths of N−N= N−N are presented in Table 2. The dihedral angles range from 0 to 5° except R4 (9.90 °). We take N−N=N−N as a plane and find that the coplanarity of R4 is worst with the two pyrazole rings deviating from the plane obviously (this phenomenon can also be observed from Fig. 2). R2 is a well symmetrical and coplanar molecule with two imidazole rings and two nitro groups (C4−NO2 and C4′−NO2) in one plane. The bond lengths of N(1)−N(6) vary from 1.366 to 1.391 Å, and N(6)=N(6′) vary from 1.243 to 1.246 Å, which are shorter than that of N−N (1.429 Å) but longer than that of N=N (1.025 Å) compared with te-trazene (N4 −H4H2N−N= N−NH2), respectively [32, 42, 43]. It indicates that the structure of N, N′-azobis- polynitrodiazole and te-trazene is different in essence. Due to the electron-withdrawing effect of diazole rings to the−N−N=N−N−structure, the−N=N−has stronger capability, thus, these molecules are more stable compared to te-trazene structure.
Electrostatic potentials and frontier molecular orbital energies MESP is the potential energy of a proton at a particular location near a molecule. The MESPs that calculated by
2155, Page 4 of 9
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Fig. 1 Illustration with the atomic numbering of title compounds, with trigger linkages (C−NO2) encircled in red; the list of values besides each structure shows the trigger length (in Å), nitro group charge (in e) and midpoint electrostatic potential. (All the molecules are symmetric, so we selected half of the molecule for our research)
Materials Studio 6.0 package [44] based on the optimized geometry are depicted in Fig. 2. The calculated partial charges represented as spheres exhibit how the molecule would interact with approaching protons or positive charges [45]. As is shown in Fig. 2, the strongly positive MESP surface (colored in blue) is prominent in the center of the molecule, while the negative MESP surface (colored in red) primarily caused by electron-withdrawing group (−NO2) is in the surrounding of the molecule. Politzer and Murray et al. [17, 46–49] considered that, in terms of energetic materials, the positive regions are larger as well as stronger in magnitude than the negative ones. Consequently, the designed molecules can be employed as promising energetic compounds. The molecular frontier orbital energies and their gap energies are presented in Table 1. The band gap (ΔE=|ε(HOMO)–ε(LUMO)|) is an important parameter to evaluate the molecular stability, especially for the compounds with similar frameworks
[50, 51]. A small ΔE can lead to enhanced reactivity and poor stability with respect to chemical and photochemical processes [52, 53]. For example, it causes the electron transition from HOMO to LUMO easily, thus leading the molecule to become less stable. On the contrary, a large ΔE implies high stability and low sensitivity. The ΔE of R5 (397.42 kJ·mol−1) is the largest and R3 (377.13 kJ·mol−1) is the smallest, indicating that the former is more stable than the latter. Compounds R1 and R2, R4 and R5, and R3 and R6 have similar band gaps, implying that the position and number of nitro groups make a slight difference on band gaps of the title compounds. Usually, the higher the total energy of the molecule, the less stable the compound. According to the total energies (Table 1), the most unstable compounds are R3 (-4693498.44 kJ · mol−1) and R6 (4693432.36 kJ·mol−1) among the six compounds. For these molecules, the highly delocalized conjugated π-system strengthens bonds in the N, N′-azobis-polynitrodiazoles, leading
Table 1 Lowest frequency (ωL), total energy (E0), zero-point energy (ZPE), thermal correction to enthalpy (HT) and frontier orbital energy of
designed molecules and some reference compounds, as computed at the B3LYP/aug-cc-pVDZ level
Comp
ωL/ (cm−1)
E0/ (kJ·mol−1)
ZPE/ (kJ·mol−1)
HT/ (kJ·mol−1)
LUMO/ (kJ·mol−1)
HOMO/ (kJ·mol−1)
ΔE/ (kJ·mol−1)
R1 R2 R3 R4
11.48 11.51 10.76 12.86
−3619652.85 −3619648.32 −4693498.44 −3619555.15
365.03 366.40 374.31 364.03
419.62 421.23 444.01 419.02
−470.49 −460.99 −521.79 −444.42
−856.02 −848.61 −898.92 −841.84
385.53 387.63 377.13 395.40
R5 R6 2,4-DNI 4,5-DNI 3,4-DNP
15.51 10.21 59.87 23.73 10.43
−3619584.40 −4693432.36 −1667812.84 −1667789.79 −1667739.26
364.63 374.32 199.85 199.63 199.67
419.04 444.60 224.73 225.06 225.32x
−467.94 −511.68 −362.84 −357.12 −314.95
−863.34 −891.65 −825.14 −798.83 −824.67
397.42 379.96 462.30 441.71 509.71
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Table 2 Selected bond lengths and dihedral angles of the optimized geometry for the titled compounds from B3LYP/aug-cc-pVDZ calculations Bonds lengths /( Å) N(1)−N(6) N(6)=N(6′) Dihedral angles /(°) N(1)−N(6)=N(6′)−N(1′)
R1
R2
1.371 1.244
1.368 1.246
177.00
179.99
R3
R4
1.380 1.243
1.391 1.244
9.90
the molecules to become stabilized. The difference in stabilities is mainly attributed to the trigger bond lengths, BDEs and slight discrepancies in total energies, which in turn are caused by the position or number of nitro groups.
Impact sensitivity H50 is a complicated matter of an energetic compound because it contains metastable state of undergoing very rapid and high exothermic reactions [54]. Table 3 shows that the H50 values of R1, R2, R4, and R5 are higher compared with R3 and R6. The results shows that the more nitro groups the molecule has, the lower H50, that is to say, the less insensitive the compound. Moreover, it is evident that R4, R5, and R6 have higher H50 than that of R1, R2, and R3, which is probably attributed to the stability of pyrazole rings. Mulliken atomic charge analysis of nitro groups is also used to estimate the impact sensitivities of the title compounds. Normally, for the majority of nitro explosives, R– NO2 (R=N, C or O) bonds are the weakest bonds and their breaking is usually the initial step in the decomposition or detonation. The nitro group charge (−QNO2) is calculated by the sum of net Mulliken atomic charges on the nitrogen and
R5
176.21
R6
1.380 1.245
1.366 1.244
176.59
178.88
te-trazene[40] 1.429 1.025 —
oxygen atoms of the nitro group: −QNO2 ¼ QN þ QOð1Þ þ QOð2Þ
ð10Þ
2ðQC þ QN Þ RðC−NÞ
ð11Þ
V mid ¼
where Vmid is the midpoint electrostatic potential, R(C-N) is the length of trigger bond, QC, QN and QO(1) and QO (2) are the Mulliken charges on carbon, nitrogen and oxygen atoms, respectively. The computed Wiberg bond order values, −QNO2 values, trigger lengths, and Vmid of the molecules are summarized in Table 3. The higher negative charge the nitro group possesses, the weaker the electron-withdrawing ability, then the greater stability the overall of the compound and thus the lower the impact sensitivity. Wiberg bond order values also reflect the strength of trigger bond, a large Wiberg bond order indicates the bond is hard to rupture and thus the molecule is stable. The calculated Vmid values vary from 0.66 to 2.72, are superior to those of 2,4,6-trinitrotoluene (TNT) (0.25), 1,3,5-triamino-2,4,6trinitrobenzene (TATB) (0.42), 2,6-diamino-3,5-dinitropyrazine1-oxide (LLM-105) (0.26), and 3-nitro-1,2,4-triazol-5-one (NTO) (0.26) [41]. The calculated−QNO2 values vary from 0.48 to 0.64 e, according to that predicted by Zhang [14, 15], these−QNO2 values are found to be higher than those of
16.00
8.00 0.00
R1
R2
R3
-8.00 -16.00 R4
R5
R6
Fig. 2 3D molecular electrostatic potential maps of title molecules. (Red and blue stand for negative and positive electrostatic regions, respectively, with colors representing values between −16.00 kJ·mol−1 and 16.00 kJ·mol−1)
2155, Page 6 of 9
Comp
bond
Length/
Vmid
(Å)
Wiberg bond order
−QNO2
H50/
BDE/ −1
(e)
(kJ·mol )
(cm)
R1
C(2)−NO2
1.443
0.956
1.842
0.510
245.37
31.7
R2
C(4)−NO2 C(4)−NO2 C(5)−NO2
1.462 1.454
0.909 0.927
1.477 1.369
0.507 0.536
235.39 261.97
31.7
1.466 1.467
0. 893 0.901
2.381 1.440
0.550 0.490
235.82 229.05
11.5
1.460
0.918
1.245
0.517
238.82
R3
C(2)−NO2 C(4)−NO2 C(5)−NO2
R4
C(3)−NO2
1.466 1.471
0.897 0.879
2.628 1.336
0.546 0.641
223.59 235.98
38.0
R5
C(4)−NO2 C(3)−NO2
1.441 1.462
0.962 0.917
2.412 0.673
0.574 0.523
261.52 261.93
38.0
R6
C(5)−NO2 C(3)−NO2
1.455 1.474
0.930 0.874
0.660 1.266
0.478 0.606
240.46 232.96
13.3
C(4)−NO2 C(5)−NO2
1.442
0.960
2.716
0.552
242.91
1.470
0.881
1.396
0.609
230.87
2,4,6,8,10,12-hexanitro- 2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) (0.08 e), HMX (0.11 e), and RDX (0.13e), suggesting that these compounds are more insensitive.
Bond dissociation energies The calculated BDE of the trigger bond can be used as a quantitative index for molecular stability [12]. It should be emphasized that this criterion only applies to molecules whose weakest bond is the R−NO2 bond [32, 38]. In general, if BDE> 80 kJ·mol−1, then the compound could be considered as a practical energetic material; otherwise, if BDE>120 kJ·mol−1, then it could be considered as excellent energetic material which meets the stability requirements of HEDMs [12]. The calculated BDEs (Table 3) of R1∼R6 vary from 223.59 to 240.46 kJ· mol−1. Compared with that of TNT (251.16 kJ·mol−1), RDX (160.09 kJ·mol−1), and TATB (305.79 kJ·mol−1), all of the designed compounds possess high BDEs and are content with the stability requirements of HEDMs. Furthermore, by contrast the BDEs of R3 and R6 with R1∼R4, it is observed that the number of nitro groups have strong influence on the BDEs (e.g., BDE decreases with the increasing number of nitro groups). It can be deduced that R3 and R6 are susceptible to pyrolysis. Based on the BDE, H50 and ΔE values, we achieve Fig. 3, from where we come to reach a conclusion that the stability of the title compounds increases as follows: R3
