J Comput Aided Mol Des DOI 10.1007/s10822-015-9837-4
A simple, fast and convenient new method for predicting the stability of nitro compounds Xueli Zhang • Xuedong Gong
Received: 22 December 2014 / Accepted: 13 February 2015 Ó Springer International Publishing Switzerland 2015
Abstract A new method has been proposed to understand and predict the stability of nitro compounds. This method uses the maximum electron densities at the critical points of two N–O bonds of nitro groups (qmax), and it is more simple and faster than the existing methods and applicable to bigger systems. The correlations between the qmax and total energy (E), bond lengths (RCNO2 , RNNO2 and RONO2 ), bond dissociation energy (BDE), and impact sensitivity (h50) reveal that the molecular stability, which can be reflected by E, R, BDE and h50, generally decreases with the increasing qmax. The compound with the larger qmax is less stable. For the nitrating reaction, the smaller qmax of the product generally implies the easier and faster reaction and the higher occurrence ratio of the product. Therefore, qmax can be applied to predict the stability of nitro compounds and the easiness of the nitrating reaction. Keywords Nitro compounds Electron density Bond critical point Stability
Introduction Various kinds of energetic materials are widely consumed in military and industry applications [1]. The most commonly used are 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX), 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX), Electronic supplementary material The online version of this article (doi:10.1007/s10822-015-9837-4) contains supplementary material, which is available to authorized users. X. Zhang X. Gong (&) Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China e-mail: [email protected]
2,4,6-trinitrotoluene (TNT), nitroglycerin (NG), and nitrocellulose (NC) [2–8]. Some new energetic materials, such as hexaazahexanitroisowurtzitane (CL-20), 2,6-diamino3,5-dinitropyrazine-1-oxide (LLM-105), 1,1-diamino-2,2dinitroethylene (FOX-7), 1,3,3-trinitroazetidine (TNAZ), and octanitrocubane (ONC) have also shown their applications in the armed and civilian applications [1, 8–17]. No matter whether these energetic materials are classical or new, they all have nitro groups in their molecular structures. Therefore, the nitro group is the common part of most explosives in use, and is usually introduced into the designed explosives by researchers [18–24]. Nitro group is the root for explosion of these explosives. It provides oxygens to oxidize carbon and hydrogen atoms etc. to rapidly release a large amount of heats on explosion. Hence, the properties especially the stability of the nitro group are important in evaluating the stability, synthesis feasibility and practicability of nitro compounds. While the nitro groups in different compounds are different, which naturally results in different stabilities of explosives, so a simple while effective way to predict the stability will be very helpful for the developments of nitro compounds. In fact, researchers have ever stopped finding ways to assess the stability of nitro compounds, and some methods have been applied to the researches of nitro explosives. Depluech and Cherville [25, 26] showed that electronic structures of molecules could affect the thermal stabilities and other properties of nitro compounds. Bates [27] proposed that the stabilities of tetrazole derivatives were lower when the electron attracting abilities of the introduced substituents were stronger. Kamlet and Adolph [28] concluded that the higher oxygen balance should lead to the higher sensitivity of nitro compounds. According to the works of Politzer et al. [29] and Zhang [17, 31], electrostatic potential of molecule and the charges on nitro group
123
J Comput Aided Mol Des
should also be tightly related with the stability of nitro compounds. Corresponding methods have been developed and applied to various groups of compounds. These methods, though have their applications, have some shortcomings. For example, the method using electrostatic potential is time consuming; the method of Bates can be applied to tetrazole derivatives only; the approach using the charges on nitro groups or bond lengths is sensitive to the theoretical levels. In this paper, a new approach has been proposed to understand and predict the stability of nitro compounds. The method tightly relates the stability of nitro compounds to the maximum value of the total electron densities (qmax) at the critical points of two N–O bonds of the nitro groups. We named this method MEDBCP (maximum electron density at the bond critical point) for simple and clear narration. Compared to the existing methods, MEDBCP is timesaving, wider applicable and little sensitive to theoretical level, namely, it is a simpler, faster and more convenient method for evaluating the stability of nitro compounds.
Proposing of MEDBCP Analyzing the qmaxs obtained at the same level of density functional theory (DFT) such as B3LYP/6-31G* in Table 1, we find that qmax increases gradually from CH3 NO2 to CH2(NO2)2, CH(NO2)3 and C(NO2)4 (0.990170, 0.997738, 1.011890, 1.015845 a.u.) and approaches to that of NO2 molecule (1.024828 a.u.). This implies that the nitro group in the less stable compounds may be more similar to the NO2 molecule and their qmaxs are more comparable. Therefore, qmax can be used as an indicator of
the similarity between the nitro group of compounds and the isolated NO2 molecule. There is no doubt about the fact that when the nitro group of a nitro compound is more similar to the isolated NO2 molecule, the connection between the nitro group and the skeleton of the compound is weaker, that is, the X–NO2 (X=C, N or O) bond is more easy to break to initiate pyrolysis or explosion of the nitro compound. So we speculate that qmax should be tightly related with the stability of nitro compounds. To confirm this conjecture, we estimated the correlations between qmax and various indexes that reflect the stability of nitro compounds, such as total energy (E) of isomer, bond length (R), bond dissociation energy (BDE) and impact sensitivity (h50) which have been used to assess the nitro group charge method [17]. The relationships between qmax and various indexes show that qmax is a convenient indicator of stability of nitro compounds belonging to the same group, though, as was commonly found for other indicators used in previous methods [32], it can not be directly applied to compounds belonging to different groups. In addition, calculation of qmax is faster and easier than, for example, electrostatic potential used in other methods [25, 26, 29, 30], and applications of MEDBCP are not limited only to the tetrazole compounds or N–NO2 and C–NO2 compounds [27, 30], i.e., it has a wider applicability. A further comparison of the data in Table 1 shows that qmaxs obtained at different levels with the atom in molecule theory are very close to each other and not sensitive to the calculation levels (the relative deviations of qmaxs obtained at various levels to the B3LYP/6-31G* results are \0.5 %), which means a relatively low theoretical level is acceptable, so this method can be applied to large molecules. In this work, B3LYP/6-31G* has been employed in the following sections.
Table 1 qmaxs (a.u.) at BCPs (orange dots) of CH3NO2, CH2(NO2)2, CH(NO2)3, C(NO2)4 and NO2 and the relative deviations of qmaxs at various levels of DFT to that obtained at the B3LYP/6-31G* level
CH3NO2
CH2(NO2)2
CH(NO2)3
C(NO2)4
NO2
B3LYP/6-31G*
0.99017, 0
0.997738, 0
1.011890, 0
1.015845, 0
1.024828, 0
B3LYP/6-311G** (%)
0.994333, 0.4
1.002290, 0.5
1.012967, 0.1
1.021061, 0.5
1.027266, 0.2
B3LYP/6-311 ??G** (%)
0.992988, 0.3
1.000686, 0.3
1.011047, -0.1
1.018705, 0.3
1.027851, 0.3
B3LYP/Aug-cc-pvdz (%)
0.994333, 0.4
1.002290, 0.5
1.012967, 0.1
1.021061, 0.5
1.028586, 0.4
M062X/6-31G* (%)
0.989500, -0.1
0.997186, -0.1
1.007385, -0.4
1.015044, -0.1
1.028312, 0.3
123
J Comput Aided Mol Des Table 2 Predicted qmaxs (a.u.) and Es (a.u.) of the isomers of nitro compounds
NH2
NH2
NH2 NO2
Nitrophenylamine
NO2
ρmax E
0.962242 -492.10952
0.981420 -492.10498
NO2
0.973430 -492.10871 NO2
NO2
NO2 NO2
Dinitrobenzene
NO2
ρmax E
0.991100 -641.22949
0.986548 -641.24625
Trinitrobenzene
NO2
NO2
NO2 O2N
NO2
O2N NO2
ρmax E
NO2
0.986728 -641.24601
1.007996 -845.70996
0.995150 -845.72079
O2N
NO2
0.990579 -845.73670 NO2
NO2
NO2 N
Nitrotetrazole
N
N N
ρmax E
1.039774 -462.69667 NH2
N
NH
N
N
0.996670 -462.72130 NH2
N HN
N N
0.995232 -462.73513 NH2
Nitroaminopropane O2N
ρmax E
0.986649 -378.99402
Computational details The geometries of compounds were optimized at the B3LYP/6-31G* level of DFT using the Gaussian program package [33]. The optimized structures were confirmed to be local minima without imaginary frequencies. The electron density at the bond critical point (q) derived from QTAIM (quantum theory of atom in molecule) [34] was analyzed using the Multiwfn [35], a freely available and easily operated program, with the input files (.wfn) generated from geometry optimizations. qmax is obtained by comparing the q of nitro groups in a compound: qi;t ¼ qi;1 þ qi;2 ði ¼ 1; 2; . . .nÞ
qmax ¼ Max q1;t ; q2;t ; . . .qn;t
NO2
ð1Þ ð2Þ
where n stands for the number of nitro groups of a compound. qi,1 and qi,2 represent the qs of two N–O bonds of the ith nitro group and the qi,t is the sum of them.
0.987370 -378.98692
NO2
0.989816 -378.98143
Bond dissociation energy, which is fundamental to understand the pyrolysis mechanism and the thermal stability [36–39] of the bond and the nitro compound, was calculated at the B3LYP/6-31G* level using the following equation: BDE ¼ ER1 þ ER2 ER1R2
ð3Þ
where ER1-R2, ER1 and ER2 stand for the zero-point-corrected total energies of the parent molecule and the radicals produced by bond breaking, respectively. Results and discussion The stability of a nitro compound is usually measured by using the total energy of isomers, bond length, bond dissociation energy, impact sensitivity, and so on [17, 40–43]. Therefore, correlations between qmax and these indexes were estimated to evaluate the efficiency of the MEDBCP. Due to a large number of nitro compounds and the limited space, only the relationships between qmaxs and various
123
J Comput Aided Mol Des NO2 (2) 0.962347 (3) 0.982483 (4) 0.981118 (2,3) 0.985798 (2,4) 0.984507 (2,5) 0.985950
(1.449) (1.474) (1.470) (1.493) (1.487) (1.491)
1 2
6
3
NO2
(2,6) 0.942220 (1.429) (2,3,4) 0.955356 (1.438) (2,3,5) 0.963145 (1.453) (2,3,6) 0.945190 (1.432 ) (2,4,6) 0.934474 (1.419 ) (2,4,5) 0.954211 (1.437 )
5 4
7 6
8
1
5
4
(2) (3) (4) (5) (6) (7)
2 3
0.953026 0.978581 0.976929 0.976844 0.977765 0.978504
(1.442) (1.480) (1.477) (1.479) (1.479) (1.479)
(II)
O2N
(1) 0.968004 (1.458) (3) 0.969390 (1.459) (4) 0.985743 (1.478) (1,4) 0.965360 (1.457) (1,3) 0.955271 (1.440)
NO2 (3,4) 0.978285 (3,5) 0.970204 2 (3,4,5) 0.962232 (1,3,4) 0.955782 3 (1,3,5) 0.936217
1 6 5 4
(1.461) (1.445) (1.446) (1.441) (1.424)
(2) NO2 (3) (4) 1 (5) 2 (6) 3 (7)
7
6 5
8
4
(1.465) (1.454) (1.436)
6 O2N
NO2
1 2
5 4
8
3
7 NO2
9
10
1
6
5
4
8 7
9
10
6
1
5
2 NO2 3
4
2 3
(2) (3) (4) (5) (6) (7) (8) (9)
0.947461 0.976754 0.966987 0.975271 0.975742 0.975757 0.974028 0.975406
(1.437) (1.477) (1.458) (1.472) (1.472) (1.472) (1.471) (1.472)
(IV)
(I)
(3) 0.983364 (4) 0.977965 (5) 0.978755 (6) 0.978587 (7) 0.978674 (8) 0.978779 (9) 0.978192 (10) 0.978214
(1.489) (1.470) (1.471) (1.469) (1.471) (1.471)
(III)
NO2 (2) 0.983388 (2,4) 0.966458 (2,4,6) 0.940119
0.984465 0.979689 0.980017 0.979835 0.980464 0.980020
(1.487) (1.468) (1.469) (1.468) (1.468) (1.468) (1.468) (1.468)
8 7
9
10
1
6
5
4
2 3
(1) 0.979161 (2) 0.978541 (3) 0.973649 (10) 0.969435
(1.472) (1.472) (1.467 ) (1.460 )
NO2 (VI)
(V) NO2 4
3 O2N
N
6 5
N
O2N
NO2 2 3
3
2 3
(3) 1.000544 (3,6) 0.999555
6 5
N
O2N
2
NO2
N
6
O2N (3) 1.003078 (3,5) 1.002389
5
N
2
(1.520) (1.518)
6
4
3 2
O
NO2
5
N
NO2
6
NO2
4
3
(1.518 ) (1.517)
5
N
O2N O2N
N
2
(3) 0.988344 (1.478) (3,5) 0.975397 (1.465)
N
N 3
O N
6
O2N (4) 0.982826
(1.442)
1
2
1
2
O2N
4
(2) 0.979931 (4) 0.971783 (4,2) 0.961105 (2,6) 0.964348 (4,2,6) 0.940469
(1.456) (1.456) (1.441) (1.443) (1.423 )
(2) 0.995542 (2,4) 0.960658 (2,6) 0.969633 (2,4,6) 0.945325
(1.503) (1.441) (1.445) (1.425)
(1) 0.983349 (2E) 0.981391 (2Z) 0.978800
(1.490) (1.461) (1.456)
(1) 0.993601 (1,2) 0.970922
(1.500) (1.455)
(2) 0.980034 (2,2) 0.961681
(1.456) (1.434)
4
O2N
N
(1.491) (1.478)
NO2 5
O (VIII)
(VII)
(3) 0.991072 (3,5) 0.977993
H N1 N 5
(N1) 0.985749 (1.445) (5) 0.971404 (1.426) (N1,5)0.970412 (1.425)
NO2 O2N
O2N
1
2
O2N
˚ ) for compounds with –NH2 at different positions (1st column) Fig. 1 Predicted qmaxs (2nd column in a.u.) and bond lengths (3rd column in A
123
J Comput Aided Mol Des NO2 (4) 0.935027 (1.386) (N1) 0.969747 (1.427) (N1,4)0.951086 (1.404 ) HN N 1 (IX) 4
O2N
5
3
HN NO2
(Non) 0.985253 (1.386)
NO2 NH
(Non) 0.986315
NO2
2 4
(X)
(1.385)
(Non) 1.017310 (1.470)
H N NO2
(Non) 1.023110 (1.411 )
O NO2
NO2
O2N
1
3
(Non) 0.990636
(1.390)
(Non) 1.024218 (1.411 )
O NO2
O2N
NO2 H N NO2
O2N O2N
(Non) 1.026542 (1.417 )
O (Non) 0.990253 (1.389) NO2
NO2
(Non) 1.052717 (1.501 )
HO O (XII)
(XI)
O2N
NO2 1.001354
N
NO2 N
3 N
2
O2N
N O
1 N NO2
RDX 1.006685 (1.441) (1) 1.004565 (1.435) (1,2) 1.002895 (1.432) (1,2,3) 0.993153 (1.399)
H2N
0.975115 N O
NO2 4
N
N
1
3
N N
2
NO2
HMX 0.998788 (1) 0.996436 (1,2) 0.995230 (1,2,3) 0.996888 (1,2,3,4) 0.995280
(1.414) (1.411) (1.403) (1.415) (1.403)
O2N
XIII
(1.467)
O
NO2
N
O2N
(1.477) (1.412) (1.451) (1.436) (1.436)
(Non) 0.985649 (1.387)
H N NO2
N
(1) 0.980939 (2) 0.947558 (3) 0.975312 (4Z) 0.964182 (4E) 0.964359
NO2
(1.422)
O
O2N 4
N O
3 2
N
1
O
(1) 0.985940 (2) 0.985285 (3) 0.983090 (4) 0.984091 (3,4) 0.982864 (2,3,4) 0.983098
(1.443) (1.440) (1.438) (1.439) (1.438) (1.439)
XIV
Fig. 1 continued
parameters of the classical and commonly used nitro compounds were presented. Correlations between qmax and total energies of isomers Nitro benzene derivatives, such as TNT, 1,3,5-triamino2,4,6-trinitrobenzene (TATB), trinitrobenzene (TNB) etc. are widely used as highly energetic materials. Here, qmaxs
and Es of the isomers of nitrophenylamine, dinitrobenzene, trinitrobenzene, nitrotetrazole and nitroaminopropane were evaluated. Table 2 shows the computational results. Obviously, for the isomers of nitro compounds, the larger qmax corresponds to the higher total energy, i.e., the more unstable conformation. Therefore, qmax can be used as the criterion for evaluating the relative stabilities of the isomers of nitro compounds.
123
J Comput Aided Mol Des Fig. 2 Correlations between qmax and bond length
123
J Comput Aided Mol Des Fig. 2 continued
Correlations between qmax and bond length For the insensitive explosives TATB, FOX-7, 2,6-diamino3,5-dinitropyrazine (ANPZ) and 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) [17], breaking of the C– NO2 bond is the initial step of pyrolysis [31, 44–46]. So the strength of the C–NO2 bond is the crucial factor determining the stability of these nitro compounds. Inspecting these insensitive explosives shows that they are all conjugated structures with the amino group, which is helpful for improving stability, melt point, and crystal density [31, 47, 48]. So a large number of molecules whose structures are analogous to these insensitive explosives with 1–3 nitro groups and 1–3 amino groups at different
positions were designed. The positions of the amino groups, qmaxs and the lengths of the C–NO2 bonds (RCNO2 s), N–NO2 bonds (RNNO2 s) or O–NO2 bonds (RONO2 s) of 120 molecules are shown in Fig. 1. The correlations between qmax and RCNO2 , RNNO2 or RONO2 were investigated. Twelve linear equations were obtained for twelve groups of compounds and are shown in Fig. 2 and Table 3. The correlation coefficients of the fitted equations are 0.942–0.999, which reveals that qmax and the bond lengths of C–NO2, N–NO2 and O–NO2 are linearly dependent. The larger qmax corresponds to the longer bond which can be reflected by the positive coefficients of qmaxs in Table 3. What’s more, qmax should be more sensitive to the change
123
J Comput Aided Mol Des Table 3 Linear correlation equations and correlation coefficients (Rcs) between qmaxs and bond lengths (N is the number of molecules used in fitting)
Group
N
Equation
Rc
Representative
I
25
RCNO2 = 0.3666 ? 1.1263qmax
0.942
TNB, DATB, TATB
II
6
RCNO2 = 0.03842 ? 1.4732qmax
0.999
III
6
RCNO2 = -2.6281 ? 4.1819qmax
0.994
IV
8
RCNO2 = 0.2060 ? 1.2981qmax
0.991
V
8
RCNO2 = -2.2992 ? 3.8504qmax
0.991
VI
4
RCNO2 = 0.2681 ? 1.2302qmax
0.989
VII
6
RCNO2 = -0.6638 ? 2.1776qmax
0.974
VIII
11
RCNO2 = 0.06865 ? 1.4306qmax
0.947
IX
7
RCNO2 = 0.2980 ? 1.1630qmax
0.998
DNF, ANTZ
X
12
RCNO2 = -0.3984 ? 1.9039qmax
0.944
FOX-7
XI
6
RNNO2 = -1.2868 ? 2.7081qmax
0.990
XII
4
RONO2 = -1.7620 ? 3.0989qmax
0.999
XIII
9
RNNO2 = 0.5587 ? 0.3106qmax
0.976
XIV
8
RCNO2 = -0.3056 ? 1.7733qmax
0.997
in the stability of nitro compounds than bond length. For example, the RCNO2 s of 5-amino-nitronaphthalene, 6-amino-nitronaphthalene and 7-amino-nitronaphthalene in group II (in Fig. 1) are the same, while the corresponding qmaxs are 0.976844, 0.977765 and 0.978504 a.u., respectively. According to these conclusions, the larger qmax agrees with the longer X–NO2 bond in which the –NO2 should be more similar to the isolated NO2 molecule. Therefore, the higher degree of similarity between –NO2 and the NO2 molecule can be indicated by the larger qmax. MEDBCP should be a sensitive and effective way to evaluate molecular stability. For the compounds belonging to other groups which are not studied in this paper, their qmaxs may also be correlated to the bond lengths that determine the molecular stability. Correlations between qmax and BDE BDE is the energy required for breaking a bond, which is a basic parameter reflecting the thermal stability [36–39]. C– NO2, N–NO2 O–NO2, Ph–NO2 (–NO2 attached to the benzene ring) bonds widely exist in explosives, and BDEs of these bonds are important parameters for evaluating the stability of nitro explosives. qmaxs and BDEs of 30 compounds containing these bonds were calculated, and results are tabulated in Table 4. Based on these data, linear equations between BDEs and qmaxs were fitted: BDEðCNO2 Þ ¼ 4132:42 3955:30qmax R ¼ 0:963 BDEðNNO2 Þ ¼ 2958:20 2801:97qmax R ¼ 0:999 BDEðONO2 Þ ¼ 4619:98 4363:87qmax R ¼ 0:992 BDEðPhNO2 Þ ¼ 2220:19 19911:27qmax R ¼ 0:918 The correlation coefficients of these equations are larger than 0.918, so the linear relationships between BDEs and
123
ANPZ, LLM-105
RDX, HMX
qmaxs are acceptable. The negative coefficients of qmax suggest that the larger qmax corresponds to the smaller BDE and the weaker bond, i.e., the lower thermal stability and the higher degree of the similarity between –NO2 and the NO2 molecule. Therefore, qmax should be an alternative parameter that can be used to assess the thermal stability of nitro compounds. Correlation between qmax and h50 Impact sensitivity is an important parameter reflecting the stability of explosive and is influenced by many factors, such as molecular structure, crystal structure, chemical and physical properties, surface and interface properties of explosive components, and test conditions [49]. Impact sensitivity is usually reported as h50. qmaxs of 33 nitro compounds (structures are shown Figure S1) whose h50s are available were calculated, and results are listed in Table 5. The relationship between qmax and h50 is shown in Fig. 3. Seen from this figure, h50 generally decreases with the increasing qmax. So the compound with the larger qmax is more vulnerable to external stimulus and has the higher impact sensitivity, and its –NO2 is more similar to the isolated NO2 molecule. In addition, h50 of the molecule with qmax above 1.0 a.u. is generally lower than 50 cm, or vice versa. What can not be ignored is that the correlation coefficient of the fitted equation is not good, so it has not been presented here. As was mentioned above, impact sensitivity can be affected by many factors, while qmax is simply obtained from the N–O bonds of the nitro groups of compounds. So MEDBCP can be used to predict the impact sensitivity of nitro explosives only qualitatively or semiquantitatively.
J Comput Aided Mol Des Table 4 Predicted BDE (kJ/mol) and qmax (a.u.) of nitro compounds
Bond
C-NO2
N-NO2 O-NO2
Compound CH3NO2 C2H5NO2 C3H7NO2 C4H9NO2 C5H11NO2 C6H13NO2 C3H7C(NO2)3 C3H7CH(NO2)2 C4H9C(NO2)3 Cyclo-C6H11NO2 C(NO2)4 CH2(NO2)2 C2H5NHNO2 C3H7NHNO2 C(NO2)3C2H4NHNO2 CH3O-NO2 C2H5ONO2 O2N
NH2
NO2
ρmax 0.990174 0.987426 0.986667 0.98654 0.986398 0.986323 1.008205 0.999691 1.007454 0.989015 1.015831 0.997734 0.985649 0.985253 0.990253 1.026542 1.02311
BDE 229.15 226.94 230.70 230.17 230.68 230.66 135.12 163.41 135.39 225.84 129.72 167.60 192.56 192.84 178.32 151.32 147.28
0.983390
278.20
Compound C2(NO2)6 CH3CH(NO2)2 C2H5NO2 C2H5C(NO2)3 Cyclo-C3H5NO2 C2H5CH(NO2)2 CH3C(NO2)3 CH(NO2)3
ρmax 1.020653 0.99993 0.987426 1.008192 0.98838 0.999806 1.007593 1.00814
BDE 114.98 161.85 226.94 137.07 248.81 164.80 144.34 152.17
CH3N(NO2)2 CH3NHNO2 CH(NO2)2C2H4NHNO2 C3H7ONO2 HOONO2
1.017013 0.986315 0.990636 1.024218 1.052717
103.68 189.45 176.47 148.58 24.85
0.966460
292.40
0.955780
308.80
0.985800
254.90
NH2
0.985950
255.60
NH2
0.963150
301.80
0.954210
320.00
NO2
0.968000
288.80
NO2
0.955270
310.30
O2N
NH2
NO2 NH2
NO2
NO2
NO2 H2N O2N
NH2
NH2
O2N
0.940119
310.00
NO2 NH2
NO2
0.962230 H2N
308.50
NH2
O2N H2N
NH2
NH2
NH2 O2N H2N
NO2
NO2
0.936220
NH2
365.80
NH2
NH2
NO2
NO2
NH2
Ph-NO2
NO2
0.984510
260.60 H2N
NH2 NO2 NH2
NO2
0.955360
319.60
NH2
H2N
NH2
H2N
NH2 NO2
NO2
NH2
0.934470
393.10
H2N NO2 NH2 NH2
NH2
O2N
NO2
0.969390
294.40
O2N
0.965360
291.90
O2 N
NH2 NH2 O2N
NO2
NH2
NH2
NH2
123
J Comput Aided Mol Des Table 5 Impact sensitivity (h50) and qmax
h50s are from Ref. [54] unless indicated
No.
Chemical name
qmax (a.u.)
h50 (cm)
1
1,4-Dinitroimidazole
1.018386
55
2
2,4-Dinitroimidazole
0.986654
105
3
2,4,6,8,10,12-Hexanitrohexaazaisowurtzitane (e-polymorph)
1.011370
21 [50]
4
N,N-Dinitro-1,2-ethanediamine
0.986327
34 [51]
5
1,1-Diamino-2,2-dinitro-ethylene
0.961719
126 [52]
6
1,3,5,7-Tetranitro-1,3,5,7-tetraazacyclooctane
0.998788
32 [50]
7
2,24,4,6,6-Hexanitrostilbene
0.990053
54 [51]
8
2-Methoxy-1,3,5-trinitrobenzene
0.989108
192
9
Nitroguanidine
0.942069
[320 [53]
10
3-Nitro-1,2,4-triazole-5-one
0.985297
291 [51]
11
Hexahydro-1,3,5-trinitro-1,3,5-striazine
1.006685
24
12
Hexanitrobenzene
1.006100
11
13
Pentanitrobenzene
1.009100
11
14
1,2,3,5-Tetranitrobenzene
1.010590
28
15 16
1,3,5-Trinitrobenzene 2,4,6-Trinitroaniline
0.990590 0.983370
71 141
17
1,3-Diamino-2,4,6-trinitrobenzene
0.966460
320
18
1,3,5-Triamino-2,4,6-trinitrobenzene
0.940590
490
19
3,3-Diamino-2,24,4,6,6-hexanitrobiphenyl
0.980790
67
20
4,6-Dinitrobenzofuroxan
0.987550
76
21
7-Amino-4,6-dinitrobenzofuroxan
0.980590
100
22
7-Amino-4,5,6-trinitrobenzofuroxan
1.011930
56
23
8-Amino-7-nitrobenzobisfuroxan
0.981330
56
24
Pentanitrotoluene
1.003800
18
25
2,3,4,5-Tetranitrotoluene
1.005140
15
26
2,3,4,6-Tetranitrotoluene
1.005570
19
27
2,3,5,6-Tetranitrotoluene
1.002330
25
28
2,4,6-Trinitrotoluene
0.988940
98
29
2,3,4-Trinitrotoluene
1.003780
56
30
3,4,5-Trinitrotoluene
1.006900
107
31 32
2-Amino-3,4,5,6-tetranitrotoluene 3-Amino-2,4,5,6-tetranitrotoluene
1.006630 0.967710
36 37
33
4-Amino-2,3,5,6-tetranitrotoluene
1.002280
47
Relationships between qmax and nitrating reaction
Fig. 3 Correlation between qmax and h50
123
Most of nitro compounds are prepared by nitrating reactions [55, 56]. We find that some characteristics of nitrating reactions may also be predicted by qmax, such as difficulty, product, and relative reaction rate. qmaxs of the reactants and products in five nitrating processes (Fig. 4) were calculated. For the process 1, the reaction temperatures get higher and the nitrification abilities of the added acids get stronger from reactions 1a to 1c, in other words, the nitrating reactions from 1a to 1c are more and more difficult to take place. The increases in qmaxs of the products correspond to the increasingly harsh
J Comput Aided Mol Des
NO2
(1)
mixed acid
concentrated H2SO4
55-60 oC
fuming HNO3 90 oC (1b)
(1a)
concentrated H2SO4
[0.986649]
NO2 mixed acid
+
30 oC
45 oC
O2N
(2b)
(2a)
NO2 CH3
CH3 [0.979479]
[ 0.979479]
OH
dilute HNO3
[0.988953]
NO2
NO2
OH (3)
[ 0.990410]
CH3
mixed acid
NO2
NO2
NO2
CH3
fuming HNO3 100-110oC O2N (1c)
NO2
[0.982237]
(2)
NO2
NO2
NO2 concentrated HNO3
+
20 oC (3a) [0.981094]
O2N
(3b)
OH
NO2 OH
[0.977201]
[0.990207]
NO2 1
1
2
2
NO2
(4) (4a)
(4b) [0.978221]
[0.980931]
10
10
NO2
1
1 (5a)
(5b)
3
3
[0.980301]
[0.978733]
(5)
NO2
2
2
NO2 10
10 1
1 2
(5c)
2
3
(5d)
3
NO2
[0.979528]
6
(6)
7
N
(7)
6 N
7
5
4
8
N
5
4
8
1
[0.978552]
3 2
3 N
2 3 4 5
[0.990182] [0.981564] [0.983695] [0.979239]
6 [0.981548] 7 [0.982963] 8 [0.985628]
1 3 4 5
[0.988875] [0.987763] [0.979491] [0.979442]
6 [0.983678] 7 [0.981704] 8 [0.981626]
Fig. 4 Nitrating processes and qmaxs (in brackets) of products. The number in the processes 6 and 7 represents the nitro-substitution position
reaction conditions of 1a–1c. The similar situations happen to 2 and 3. In comparison with the reaction temperature of 1a, those of 2a and 3a are lower. And the qmaxs of the products of 2a and 3a are smaller than that of the product of 1a. So we can conclude that the nitrating reaction whose product possesses
larger qmax is more difficult to take place. According to the previous study [17], the nitrating velocities of 1a, 4a and 4b increase in the order of 1a \ 4b \ 4a, and qmaxs of the products of these reactions have the totally contrary order. Therefore, the smaller qmax of the product may correspond to
123
J Comput Aided Mol Des
the higher nitrating velocity. For the processes 4 and 5, qmaxs of the products have the orders of 1-nitronaphthalene \ 5-nitronaphthalene and 10-nitrophenanthrene \ 1-nitrophenanthrene \ 3-nitrophenanthrene \ 2-nitrophenanthrene, respectively. These orders are completely opposite to the orders of their occurrence ratios in nitrating reactions [17]. Previous investigations show that 5-nitroquinoline and 5-nitroisoquinoline are the main mononitro-derivatives of quinoline and isoquinoline. qmaxs shown in the processes 6 and 7 reveal that 5-nitroquinoline and 5-nitroisoquinoline have the smallest qmaxs in comparison with that of their isomers. Therefore, the smaller qmax of the nitrating product is consistent with the higher occurrence ratio, which may be employed to predict the most possible product of the nitrating reaction.
Conclusions The correlations between qmax and E, R and BDE were evaluated for nitro compounds, and that between qmax and h50 was roughly estimated because h50 is influenced by many factors. The larger qmax generally corresponds to the higher E, bigger R, smaller BDE and lower h50 which indicate the higher degree of similarity between –NO2 and the isolated NO2 molecule. Therefore, qmax should be an index reflecting the degree of similarity between –NO2 and the isolated NO2 molecule, and can be used to measure the stability of nitro compounds. In addition, the larger qmax of nitrating product is consistent with the lower occurrence of the product, and the more difficulty and the lower speed of the reaction. In a word, qmax can be used to understand and evaluate the stability of nitro compounds. MEDBCP can be used to evaluate the stability of compounds more easily and faster. In comparison with the existing methods, it has the following advantages: (1) (2)
Calculation of qmax is simple, only geometry optimization has to be done. The requirement for theoretical level is not high for estimating qmax and results are less sensitive to the quality of basis set than, for example, geometrical parameters. The B3LYP/6-31G* level is enough for geometry optimization and calculation of qmax. This helps to save computer resources and makes MEDBCP can be applied to large molecules.
References 1. Singh RP, Verma RD, Meshri DT, Shreeve JM (2006) Angew Chem Int Edit 45(22):3584–3601 2. Cook MA (1958) The science of high explosives, vol 139. RE Krieger Pub Co, Malabar
123
3. Urbanski T (1964) Chemistry and technology of explosives, vol 6. Pergamon Press, Oxford 4. Agrawal JP (1998) Prog Energ Combust 24(1):1–30 5. Singh G, Kapoor IPS, Mannan SM, Kaur J (2000) J Hazard Mater 79(1):1–18 6. Fried LE, Manaa MR, Pagoria PF, Simpson RL (2001) Ann Rev Mater Res 31(1):291–321 7. Shlyapochnikov V, Tafipolsky M, Tokmakov I, Baskir E, Anikin O, Strelenko YA, Luk’yanov O, Tartakovsky V (2001) J Mol Struct 559(1):147–166 8. Pagoria PF, Lee GS, Mitchell AR, Schmidt RD (2002) Thermochim Acta 384(1):187–204 9. An C, Li H, Geng X, Li J, Wang J (2013) Propellants Explos Pyrotech 38(2):172–175 10. Zhang J, Wu P, Yang Z, Gao B, Zhang J, Wang P, Nie F, Liao L (2014) Propellants Explos Pyrotech 39(5):653–657 11. Bolton O, Simke LR, Pagoria PF, Matzger AJ (2012) Cryst Growth Des 12(9):4311–4314 12. Bayat Y, Zeynali V (2011) J Energy Mater 29(4):281–291 13. Mandal AK, Thanigaivelan U, Pandey RK, Asthana S, Khomane RB, Kulkarni BD (2012) Org Process Res Dev 16(11):1711–1716 14. Vo TT, Zhang J, Parrish DA, Twamley B, Shreeve JM (2013) J Am Chem Soc 135(32):11787–11790 15. Behrens R Jr, Bulusu S (2013) Defence Sci J 46(5):361–369 16. Ma H, Feng X, Zhu T, Miao C, Ma Y, Feng M (2012) Chem Propellants Polym Mater 10(4):20–24 17. Zhang C (2009) J Hazard Mater 161(1):21–28 18. Zhang XL, Gong XD (2014) J Mol Model 20(8):1–11 19. Thottempudi V, Gao H, Shreeve JM (2011) J Am Chem Soc 133(16):6464–6471 20. Ghule VD (2012) J Phys Chem A 116(37):9391–9397 21. Wang G, Gong X, Liu Y, Du H, Xu X, Xiao H (2010) J Hazard Mater 177(1):703–710 22. Wang G, Gong X, Liu Y, Xiao H (2009) Spectrochim Acta A 74(2):569–574 23. Ravi P, Gore G, Venkatesan V, Tewari SP, Sikder A (2010) J Hazard Mater 183(1):859–865 24. Xu XJ, Xiao HM, Gong XD, Ju XH, Chen ZX (2005) J Phys Chem A 109(49):11268–11274 25. Delpuech A, Cherville J (1978) Propellants Explos 3(6):169–175 26. Delpuech A, Cherville J (1979) Propellants Explos 4(6):121–128 27. Bates LR (1986) Paper presented at the Proceedings 13th Symposium on Explosives and Pyrotechnics 28. Kamlet MJ, Adolph HG (1979) Propellants Explos Pyrotech 4:30–34 29. Chemistry Computational (1999) Reviews of Current Trends. World Scientific, River Edge 30. Murray JS, Concha MC, Politzer P (2009) Mol Phys 107(1):89–97 31. Zhang C (2006) Chem Phys 324(2):547–555 32. Zhang C, Shu Y, Huang Y, Zhao X, Dong H (2005) J Phys Chem B 109(18):8978–8982 33. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, 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 JE, Hratchian HP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng
J Comput Aided Mol Des
34. 35. 36.
37. 38. 39. 40. 41. 42. 43. 44.
CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2004) Gaussian 03, Revision CO2. Gaussian Gaussian Inc, Wallingford Bader RF (1991) Chem Rev 91(5):893–928 Lu T, Chen F (2012) J Comput Chem 33(5):580–592 Benson SW (1976) Thermochemical kinetics: methods for the estimation of thermochemical data and rate parameters. Wiley, New York Yao XQ, Hou XJ, Wu GS, Xu YY, Xiang HW, Jiao H, Li YW (2002) J Phys Chem A 106(31):7184–7189 Shao J, Cheng X, Yang X (2005) J Mol Struct Theochem 755(1):127–130 Fan XW, Ju XH, Xia QY, Xiao HM (2008) J Hazard Mater 151(1):255–260 Zhang XL, Liu Y, Wang F, Gong XD (2014) Chem Asian J 9(1):229–236 Liu H, Du H, Wang G, Gong X (2012) Struct Chem 23(2):479–486 Wang GX, Gong XD, Liu Y, Du HC, Xu XJ, Xiao HM (2011) J Comput Chem 32(5):943–952 Liu Y, Wang L, Wang G, Du H, Gong X (2012) J Mol Model 18(4):1561–1572 Politzer P, Alper HE (1999) Detonation initiation and sensitivity in energetic compounds: some computational treatments, vol 4. World Scientific, Singapore
45. Ju X-H, Xiao H-M, Xia Q-Y (2003) J Chem Phys 119(19):10247–10255 46. Zhang C, Shu Y, Zhao X, Dong H, Wang X (2005) J Mol Struct Theochem 728(1):129–134 47. Liu H, Wang F, Wang GX, Gong XD (2012) J Mol Model 18(10):4639–4647 48. Liu H, Wang F, Wang GX, Gong XD (2012) J Comput Chem 33(22):1790–1796 49. Armstrong R, Coffey C, DeVost V, Elban W (1990) J Appl Phys 68(3):979–984 50. Simpson R, Urtiew P, Ornellas D, Moody G, Scribner K, Hoffman D (1997) Propellants Explos Pyrotech 22(5):249–255 51. Storm CB, Stine JR, Kramer JF (1990) Paper presented at the chemistry and physics of energetic materials, Dordrecht, The Netherlands ¨ stmark H, Langlet A, Bergman H, Wingborg N, Wellmar U, 52. O Bemm U (1998) Paper presented at the 11th Detonation (International) Symposium, Snowmass 53. Hall TN, Holden JR (1988) Technical Report NSWC MP-88-116. Naval Surface Warfare Center, Dahlgren 54. Rice BM, Hare JJ (2002) J Phys Chem A 106(9):1770–1783 55. Akhavan J (2011) The chemistry of explosives, 3rd edn. The Royal Society of Chemistry, London 56. Urbanski T (1964) Chemistry and technology of explosives, vol 1. Pergamon Press, New York
123
A simple, fast and convenient new method for predicting the stability of nitro compounds Xueli Zhang • Xuedong Gong
Received: 22 December 2014 / Accepted: 13 February 2015 Ó Springer International Publishing Switzerland 2015
Abstract A new method has been proposed to understand and predict the stability of nitro compounds. This method uses the maximum electron densities at the critical points of two N–O bonds of nitro groups (qmax), and it is more simple and faster than the existing methods and applicable to bigger systems. The correlations between the qmax and total energy (E), bond lengths (RCNO2 , RNNO2 and RONO2 ), bond dissociation energy (BDE), and impact sensitivity (h50) reveal that the molecular stability, which can be reflected by E, R, BDE and h50, generally decreases with the increasing qmax. The compound with the larger qmax is less stable. For the nitrating reaction, the smaller qmax of the product generally implies the easier and faster reaction and the higher occurrence ratio of the product. Therefore, qmax can be applied to predict the stability of nitro compounds and the easiness of the nitrating reaction. Keywords Nitro compounds Electron density Bond critical point Stability
Introduction Various kinds of energetic materials are widely consumed in military and industry applications [1]. The most commonly used are 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX), 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX), Electronic supplementary material The online version of this article (doi:10.1007/s10822-015-9837-4) contains supplementary material, which is available to authorized users. X. Zhang X. Gong (&) Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China e-mail: [email protected]
2,4,6-trinitrotoluene (TNT), nitroglycerin (NG), and nitrocellulose (NC) [2–8]. Some new energetic materials, such as hexaazahexanitroisowurtzitane (CL-20), 2,6-diamino3,5-dinitropyrazine-1-oxide (LLM-105), 1,1-diamino-2,2dinitroethylene (FOX-7), 1,3,3-trinitroazetidine (TNAZ), and octanitrocubane (ONC) have also shown their applications in the armed and civilian applications [1, 8–17]. No matter whether these energetic materials are classical or new, they all have nitro groups in their molecular structures. Therefore, the nitro group is the common part of most explosives in use, and is usually introduced into the designed explosives by researchers [18–24]. Nitro group is the root for explosion of these explosives. It provides oxygens to oxidize carbon and hydrogen atoms etc. to rapidly release a large amount of heats on explosion. Hence, the properties especially the stability of the nitro group are important in evaluating the stability, synthesis feasibility and practicability of nitro compounds. While the nitro groups in different compounds are different, which naturally results in different stabilities of explosives, so a simple while effective way to predict the stability will be very helpful for the developments of nitro compounds. In fact, researchers have ever stopped finding ways to assess the stability of nitro compounds, and some methods have been applied to the researches of nitro explosives. Depluech and Cherville [25, 26] showed that electronic structures of molecules could affect the thermal stabilities and other properties of nitro compounds. Bates [27] proposed that the stabilities of tetrazole derivatives were lower when the electron attracting abilities of the introduced substituents were stronger. Kamlet and Adolph [28] concluded that the higher oxygen balance should lead to the higher sensitivity of nitro compounds. According to the works of Politzer et al. [29] and Zhang [17, 31], electrostatic potential of molecule and the charges on nitro group
123
J Comput Aided Mol Des
should also be tightly related with the stability of nitro compounds. Corresponding methods have been developed and applied to various groups of compounds. These methods, though have their applications, have some shortcomings. For example, the method using electrostatic potential is time consuming; the method of Bates can be applied to tetrazole derivatives only; the approach using the charges on nitro groups or bond lengths is sensitive to the theoretical levels. In this paper, a new approach has been proposed to understand and predict the stability of nitro compounds. The method tightly relates the stability of nitro compounds to the maximum value of the total electron densities (qmax) at the critical points of two N–O bonds of the nitro groups. We named this method MEDBCP (maximum electron density at the bond critical point) for simple and clear narration. Compared to the existing methods, MEDBCP is timesaving, wider applicable and little sensitive to theoretical level, namely, it is a simpler, faster and more convenient method for evaluating the stability of nitro compounds.
Proposing of MEDBCP Analyzing the qmaxs obtained at the same level of density functional theory (DFT) such as B3LYP/6-31G* in Table 1, we find that qmax increases gradually from CH3 NO2 to CH2(NO2)2, CH(NO2)3 and C(NO2)4 (0.990170, 0.997738, 1.011890, 1.015845 a.u.) and approaches to that of NO2 molecule (1.024828 a.u.). This implies that the nitro group in the less stable compounds may be more similar to the NO2 molecule and their qmaxs are more comparable. Therefore, qmax can be used as an indicator of
the similarity between the nitro group of compounds and the isolated NO2 molecule. There is no doubt about the fact that when the nitro group of a nitro compound is more similar to the isolated NO2 molecule, the connection between the nitro group and the skeleton of the compound is weaker, that is, the X–NO2 (X=C, N or O) bond is more easy to break to initiate pyrolysis or explosion of the nitro compound. So we speculate that qmax should be tightly related with the stability of nitro compounds. To confirm this conjecture, we estimated the correlations between qmax and various indexes that reflect the stability of nitro compounds, such as total energy (E) of isomer, bond length (R), bond dissociation energy (BDE) and impact sensitivity (h50) which have been used to assess the nitro group charge method [17]. The relationships between qmax and various indexes show that qmax is a convenient indicator of stability of nitro compounds belonging to the same group, though, as was commonly found for other indicators used in previous methods [32], it can not be directly applied to compounds belonging to different groups. In addition, calculation of qmax is faster and easier than, for example, electrostatic potential used in other methods [25, 26, 29, 30], and applications of MEDBCP are not limited only to the tetrazole compounds or N–NO2 and C–NO2 compounds [27, 30], i.e., it has a wider applicability. A further comparison of the data in Table 1 shows that qmaxs obtained at different levels with the atom in molecule theory are very close to each other and not sensitive to the calculation levels (the relative deviations of qmaxs obtained at various levels to the B3LYP/6-31G* results are \0.5 %), which means a relatively low theoretical level is acceptable, so this method can be applied to large molecules. In this work, B3LYP/6-31G* has been employed in the following sections.
Table 1 qmaxs (a.u.) at BCPs (orange dots) of CH3NO2, CH2(NO2)2, CH(NO2)3, C(NO2)4 and NO2 and the relative deviations of qmaxs at various levels of DFT to that obtained at the B3LYP/6-31G* level
CH3NO2
CH2(NO2)2
CH(NO2)3
C(NO2)4
NO2
B3LYP/6-31G*
0.99017, 0
0.997738, 0
1.011890, 0
1.015845, 0
1.024828, 0
B3LYP/6-311G** (%)
0.994333, 0.4
1.002290, 0.5
1.012967, 0.1
1.021061, 0.5
1.027266, 0.2
B3LYP/6-311 ??G** (%)
0.992988, 0.3
1.000686, 0.3
1.011047, -0.1
1.018705, 0.3
1.027851, 0.3
B3LYP/Aug-cc-pvdz (%)
0.994333, 0.4
1.002290, 0.5
1.012967, 0.1
1.021061, 0.5
1.028586, 0.4
M062X/6-31G* (%)
0.989500, -0.1
0.997186, -0.1
1.007385, -0.4
1.015044, -0.1
1.028312, 0.3
123
J Comput Aided Mol Des Table 2 Predicted qmaxs (a.u.) and Es (a.u.) of the isomers of nitro compounds
NH2
NH2
NH2 NO2
Nitrophenylamine
NO2
ρmax E
0.962242 -492.10952
0.981420 -492.10498
NO2
0.973430 -492.10871 NO2
NO2
NO2 NO2
Dinitrobenzene
NO2
ρmax E
0.991100 -641.22949
0.986548 -641.24625
Trinitrobenzene
NO2
NO2
NO2 O2N
NO2
O2N NO2
ρmax E
NO2
0.986728 -641.24601
1.007996 -845.70996
0.995150 -845.72079
O2N
NO2
0.990579 -845.73670 NO2
NO2
NO2 N
Nitrotetrazole
N
N N
ρmax E
1.039774 -462.69667 NH2
N
NH
N
N
0.996670 -462.72130 NH2
N HN
N N
0.995232 -462.73513 NH2
Nitroaminopropane O2N
ρmax E
0.986649 -378.99402
Computational details The geometries of compounds were optimized at the B3LYP/6-31G* level of DFT using the Gaussian program package [33]. The optimized structures were confirmed to be local minima without imaginary frequencies. The electron density at the bond critical point (q) derived from QTAIM (quantum theory of atom in molecule) [34] was analyzed using the Multiwfn [35], a freely available and easily operated program, with the input files (.wfn) generated from geometry optimizations. qmax is obtained by comparing the q of nitro groups in a compound: qi;t ¼ qi;1 þ qi;2 ði ¼ 1; 2; . . .nÞ
qmax ¼ Max q1;t ; q2;t ; . . .qn;t
NO2
ð1Þ ð2Þ
where n stands for the number of nitro groups of a compound. qi,1 and qi,2 represent the qs of two N–O bonds of the ith nitro group and the qi,t is the sum of them.
0.987370 -378.98692
NO2
0.989816 -378.98143
Bond dissociation energy, which is fundamental to understand the pyrolysis mechanism and the thermal stability [36–39] of the bond and the nitro compound, was calculated at the B3LYP/6-31G* level using the following equation: BDE ¼ ER1 þ ER2 ER1R2
ð3Þ
where ER1-R2, ER1 and ER2 stand for the zero-point-corrected total energies of the parent molecule and the radicals produced by bond breaking, respectively. Results and discussion The stability of a nitro compound is usually measured by using the total energy of isomers, bond length, bond dissociation energy, impact sensitivity, and so on [17, 40–43]. Therefore, correlations between qmax and these indexes were estimated to evaluate the efficiency of the MEDBCP. Due to a large number of nitro compounds and the limited space, only the relationships between qmaxs and various
123
J Comput Aided Mol Des NO2 (2) 0.962347 (3) 0.982483 (4) 0.981118 (2,3) 0.985798 (2,4) 0.984507 (2,5) 0.985950
(1.449) (1.474) (1.470) (1.493) (1.487) (1.491)
1 2
6
3
NO2
(2,6) 0.942220 (1.429) (2,3,4) 0.955356 (1.438) (2,3,5) 0.963145 (1.453) (2,3,6) 0.945190 (1.432 ) (2,4,6) 0.934474 (1.419 ) (2,4,5) 0.954211 (1.437 )
5 4
7 6
8
1
5
4
(2) (3) (4) (5) (6) (7)
2 3
0.953026 0.978581 0.976929 0.976844 0.977765 0.978504
(1.442) (1.480) (1.477) (1.479) (1.479) (1.479)
(II)
O2N
(1) 0.968004 (1.458) (3) 0.969390 (1.459) (4) 0.985743 (1.478) (1,4) 0.965360 (1.457) (1,3) 0.955271 (1.440)
NO2 (3,4) 0.978285 (3,5) 0.970204 2 (3,4,5) 0.962232 (1,3,4) 0.955782 3 (1,3,5) 0.936217
1 6 5 4
(1.461) (1.445) (1.446) (1.441) (1.424)
(2) NO2 (3) (4) 1 (5) 2 (6) 3 (7)
7
6 5
8
4
(1.465) (1.454) (1.436)
6 O2N
NO2
1 2
5 4
8
3
7 NO2
9
10
1
6
5
4
8 7
9
10
6
1
5
2 NO2 3
4
2 3
(2) (3) (4) (5) (6) (7) (8) (9)
0.947461 0.976754 0.966987 0.975271 0.975742 0.975757 0.974028 0.975406
(1.437) (1.477) (1.458) (1.472) (1.472) (1.472) (1.471) (1.472)
(IV)
(I)
(3) 0.983364 (4) 0.977965 (5) 0.978755 (6) 0.978587 (7) 0.978674 (8) 0.978779 (9) 0.978192 (10) 0.978214
(1.489) (1.470) (1.471) (1.469) (1.471) (1.471)
(III)
NO2 (2) 0.983388 (2,4) 0.966458 (2,4,6) 0.940119
0.984465 0.979689 0.980017 0.979835 0.980464 0.980020
(1.487) (1.468) (1.469) (1.468) (1.468) (1.468) (1.468) (1.468)
8 7
9
10
1
6
5
4
2 3
(1) 0.979161 (2) 0.978541 (3) 0.973649 (10) 0.969435
(1.472) (1.472) (1.467 ) (1.460 )
NO2 (VI)
(V) NO2 4
3 O2N
N
6 5
N
O2N
NO2 2 3
3
2 3
(3) 1.000544 (3,6) 0.999555
6 5
N
O2N
2
NO2
N
6
O2N (3) 1.003078 (3,5) 1.002389
5
N
2
(1.520) (1.518)
6
4
3 2
O
NO2
5
N
NO2
6
NO2
4
3
(1.518 ) (1.517)
5
N
O2N O2N
N
2
(3) 0.988344 (1.478) (3,5) 0.975397 (1.465)
N
N 3
O N
6
O2N (4) 0.982826
(1.442)
1
2
1
2
O2N
4
(2) 0.979931 (4) 0.971783 (4,2) 0.961105 (2,6) 0.964348 (4,2,6) 0.940469
(1.456) (1.456) (1.441) (1.443) (1.423 )
(2) 0.995542 (2,4) 0.960658 (2,6) 0.969633 (2,4,6) 0.945325
(1.503) (1.441) (1.445) (1.425)
(1) 0.983349 (2E) 0.981391 (2Z) 0.978800
(1.490) (1.461) (1.456)
(1) 0.993601 (1,2) 0.970922
(1.500) (1.455)
(2) 0.980034 (2,2) 0.961681
(1.456) (1.434)
4
O2N
N
(1.491) (1.478)
NO2 5
O (VIII)
(VII)
(3) 0.991072 (3,5) 0.977993
H N1 N 5
(N1) 0.985749 (1.445) (5) 0.971404 (1.426) (N1,5)0.970412 (1.425)
NO2 O2N
O2N
1
2
O2N
˚ ) for compounds with –NH2 at different positions (1st column) Fig. 1 Predicted qmaxs (2nd column in a.u.) and bond lengths (3rd column in A
123
J Comput Aided Mol Des NO2 (4) 0.935027 (1.386) (N1) 0.969747 (1.427) (N1,4)0.951086 (1.404 ) HN N 1 (IX) 4
O2N
5
3
HN NO2
(Non) 0.985253 (1.386)
NO2 NH
(Non) 0.986315
NO2
2 4
(X)
(1.385)
(Non) 1.017310 (1.470)
H N NO2
(Non) 1.023110 (1.411 )
O NO2
NO2
O2N
1
3
(Non) 0.990636
(1.390)
(Non) 1.024218 (1.411 )
O NO2
O2N
NO2 H N NO2
O2N O2N
(Non) 1.026542 (1.417 )
O (Non) 0.990253 (1.389) NO2
NO2
(Non) 1.052717 (1.501 )
HO O (XII)
(XI)
O2N
NO2 1.001354
N
NO2 N
3 N
2
O2N
N O
1 N NO2
RDX 1.006685 (1.441) (1) 1.004565 (1.435) (1,2) 1.002895 (1.432) (1,2,3) 0.993153 (1.399)
H2N
0.975115 N O
NO2 4
N
N
1
3
N N
2
NO2
HMX 0.998788 (1) 0.996436 (1,2) 0.995230 (1,2,3) 0.996888 (1,2,3,4) 0.995280
(1.414) (1.411) (1.403) (1.415) (1.403)
O2N
XIII
(1.467)
O
NO2
N
O2N
(1.477) (1.412) (1.451) (1.436) (1.436)
(Non) 0.985649 (1.387)
H N NO2
N
(1) 0.980939 (2) 0.947558 (3) 0.975312 (4Z) 0.964182 (4E) 0.964359
NO2
(1.422)
O
O2N 4
N O
3 2
N
1
O
(1) 0.985940 (2) 0.985285 (3) 0.983090 (4) 0.984091 (3,4) 0.982864 (2,3,4) 0.983098
(1.443) (1.440) (1.438) (1.439) (1.438) (1.439)
XIV
Fig. 1 continued
parameters of the classical and commonly used nitro compounds were presented. Correlations between qmax and total energies of isomers Nitro benzene derivatives, such as TNT, 1,3,5-triamino2,4,6-trinitrobenzene (TATB), trinitrobenzene (TNB) etc. are widely used as highly energetic materials. Here, qmaxs
and Es of the isomers of nitrophenylamine, dinitrobenzene, trinitrobenzene, nitrotetrazole and nitroaminopropane were evaluated. Table 2 shows the computational results. Obviously, for the isomers of nitro compounds, the larger qmax corresponds to the higher total energy, i.e., the more unstable conformation. Therefore, qmax can be used as the criterion for evaluating the relative stabilities of the isomers of nitro compounds.
123
J Comput Aided Mol Des Fig. 2 Correlations between qmax and bond length
123
J Comput Aided Mol Des Fig. 2 continued
Correlations between qmax and bond length For the insensitive explosives TATB, FOX-7, 2,6-diamino3,5-dinitropyrazine (ANPZ) and 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) [17], breaking of the C– NO2 bond is the initial step of pyrolysis [31, 44–46]. So the strength of the C–NO2 bond is the crucial factor determining the stability of these nitro compounds. Inspecting these insensitive explosives shows that they are all conjugated structures with the amino group, which is helpful for improving stability, melt point, and crystal density [31, 47, 48]. So a large number of molecules whose structures are analogous to these insensitive explosives with 1–3 nitro groups and 1–3 amino groups at different
positions were designed. The positions of the amino groups, qmaxs and the lengths of the C–NO2 bonds (RCNO2 s), N–NO2 bonds (RNNO2 s) or O–NO2 bonds (RONO2 s) of 120 molecules are shown in Fig. 1. The correlations between qmax and RCNO2 , RNNO2 or RONO2 were investigated. Twelve linear equations were obtained for twelve groups of compounds and are shown in Fig. 2 and Table 3. The correlation coefficients of the fitted equations are 0.942–0.999, which reveals that qmax and the bond lengths of C–NO2, N–NO2 and O–NO2 are linearly dependent. The larger qmax corresponds to the longer bond which can be reflected by the positive coefficients of qmaxs in Table 3. What’s more, qmax should be more sensitive to the change
123
J Comput Aided Mol Des Table 3 Linear correlation equations and correlation coefficients (Rcs) between qmaxs and bond lengths (N is the number of molecules used in fitting)
Group
N
Equation
Rc
Representative
I
25
RCNO2 = 0.3666 ? 1.1263qmax
0.942
TNB, DATB, TATB
II
6
RCNO2 = 0.03842 ? 1.4732qmax
0.999
III
6
RCNO2 = -2.6281 ? 4.1819qmax
0.994
IV
8
RCNO2 = 0.2060 ? 1.2981qmax
0.991
V
8
RCNO2 = -2.2992 ? 3.8504qmax
0.991
VI
4
RCNO2 = 0.2681 ? 1.2302qmax
0.989
VII
6
RCNO2 = -0.6638 ? 2.1776qmax
0.974
VIII
11
RCNO2 = 0.06865 ? 1.4306qmax
0.947
IX
7
RCNO2 = 0.2980 ? 1.1630qmax
0.998
DNF, ANTZ
X
12
RCNO2 = -0.3984 ? 1.9039qmax
0.944
FOX-7
XI
6
RNNO2 = -1.2868 ? 2.7081qmax
0.990
XII
4
RONO2 = -1.7620 ? 3.0989qmax
0.999
XIII
9
RNNO2 = 0.5587 ? 0.3106qmax
0.976
XIV
8
RCNO2 = -0.3056 ? 1.7733qmax
0.997
in the stability of nitro compounds than bond length. For example, the RCNO2 s of 5-amino-nitronaphthalene, 6-amino-nitronaphthalene and 7-amino-nitronaphthalene in group II (in Fig. 1) are the same, while the corresponding qmaxs are 0.976844, 0.977765 and 0.978504 a.u., respectively. According to these conclusions, the larger qmax agrees with the longer X–NO2 bond in which the –NO2 should be more similar to the isolated NO2 molecule. Therefore, the higher degree of similarity between –NO2 and the NO2 molecule can be indicated by the larger qmax. MEDBCP should be a sensitive and effective way to evaluate molecular stability. For the compounds belonging to other groups which are not studied in this paper, their qmaxs may also be correlated to the bond lengths that determine the molecular stability. Correlations between qmax and BDE BDE is the energy required for breaking a bond, which is a basic parameter reflecting the thermal stability [36–39]. C– NO2, N–NO2 O–NO2, Ph–NO2 (–NO2 attached to the benzene ring) bonds widely exist in explosives, and BDEs of these bonds are important parameters for evaluating the stability of nitro explosives. qmaxs and BDEs of 30 compounds containing these bonds were calculated, and results are tabulated in Table 4. Based on these data, linear equations between BDEs and qmaxs were fitted: BDEðCNO2 Þ ¼ 4132:42 3955:30qmax R ¼ 0:963 BDEðNNO2 Þ ¼ 2958:20 2801:97qmax R ¼ 0:999 BDEðONO2 Þ ¼ 4619:98 4363:87qmax R ¼ 0:992 BDEðPhNO2 Þ ¼ 2220:19 19911:27qmax R ¼ 0:918 The correlation coefficients of these equations are larger than 0.918, so the linear relationships between BDEs and
123
ANPZ, LLM-105
RDX, HMX
qmaxs are acceptable. The negative coefficients of qmax suggest that the larger qmax corresponds to the smaller BDE and the weaker bond, i.e., the lower thermal stability and the higher degree of the similarity between –NO2 and the NO2 molecule. Therefore, qmax should be an alternative parameter that can be used to assess the thermal stability of nitro compounds. Correlation between qmax and h50 Impact sensitivity is an important parameter reflecting the stability of explosive and is influenced by many factors, such as molecular structure, crystal structure, chemical and physical properties, surface and interface properties of explosive components, and test conditions [49]. Impact sensitivity is usually reported as h50. qmaxs of 33 nitro compounds (structures are shown Figure S1) whose h50s are available were calculated, and results are listed in Table 5. The relationship between qmax and h50 is shown in Fig. 3. Seen from this figure, h50 generally decreases with the increasing qmax. So the compound with the larger qmax is more vulnerable to external stimulus and has the higher impact sensitivity, and its –NO2 is more similar to the isolated NO2 molecule. In addition, h50 of the molecule with qmax above 1.0 a.u. is generally lower than 50 cm, or vice versa. What can not be ignored is that the correlation coefficient of the fitted equation is not good, so it has not been presented here. As was mentioned above, impact sensitivity can be affected by many factors, while qmax is simply obtained from the N–O bonds of the nitro groups of compounds. So MEDBCP can be used to predict the impact sensitivity of nitro explosives only qualitatively or semiquantitatively.
J Comput Aided Mol Des Table 4 Predicted BDE (kJ/mol) and qmax (a.u.) of nitro compounds
Bond
C-NO2
N-NO2 O-NO2
Compound CH3NO2 C2H5NO2 C3H7NO2 C4H9NO2 C5H11NO2 C6H13NO2 C3H7C(NO2)3 C3H7CH(NO2)2 C4H9C(NO2)3 Cyclo-C6H11NO2 C(NO2)4 CH2(NO2)2 C2H5NHNO2 C3H7NHNO2 C(NO2)3C2H4NHNO2 CH3O-NO2 C2H5ONO2 O2N
NH2
NO2
ρmax 0.990174 0.987426 0.986667 0.98654 0.986398 0.986323 1.008205 0.999691 1.007454 0.989015 1.015831 0.997734 0.985649 0.985253 0.990253 1.026542 1.02311
BDE 229.15 226.94 230.70 230.17 230.68 230.66 135.12 163.41 135.39 225.84 129.72 167.60 192.56 192.84 178.32 151.32 147.28
0.983390
278.20
Compound C2(NO2)6 CH3CH(NO2)2 C2H5NO2 C2H5C(NO2)3 Cyclo-C3H5NO2 C2H5CH(NO2)2 CH3C(NO2)3 CH(NO2)3
ρmax 1.020653 0.99993 0.987426 1.008192 0.98838 0.999806 1.007593 1.00814
BDE 114.98 161.85 226.94 137.07 248.81 164.80 144.34 152.17
CH3N(NO2)2 CH3NHNO2 CH(NO2)2C2H4NHNO2 C3H7ONO2 HOONO2
1.017013 0.986315 0.990636 1.024218 1.052717
103.68 189.45 176.47 148.58 24.85
0.966460
292.40
0.955780
308.80
0.985800
254.90
NH2
0.985950
255.60
NH2
0.963150
301.80
0.954210
320.00
NO2
0.968000
288.80
NO2
0.955270
310.30
O2N
NH2
NO2 NH2
NO2
NO2
NO2 H2N O2N
NH2
NH2
O2N
0.940119
310.00
NO2 NH2
NO2
0.962230 H2N
308.50
NH2
O2N H2N
NH2
NH2
NH2 O2N H2N
NO2
NO2
0.936220
NH2
365.80
NH2
NH2
NO2
NO2
NH2
Ph-NO2
NO2
0.984510
260.60 H2N
NH2 NO2 NH2
NO2
0.955360
319.60
NH2
H2N
NH2
H2N
NH2 NO2
NO2
NH2
0.934470
393.10
H2N NO2 NH2 NH2
NH2
O2N
NO2
0.969390
294.40
O2N
0.965360
291.90
O2 N
NH2 NH2 O2N
NO2
NH2
NH2
NH2
123
J Comput Aided Mol Des Table 5 Impact sensitivity (h50) and qmax
h50s are from Ref. [54] unless indicated
No.
Chemical name
qmax (a.u.)
h50 (cm)
1
1,4-Dinitroimidazole
1.018386
55
2
2,4-Dinitroimidazole
0.986654
105
3
2,4,6,8,10,12-Hexanitrohexaazaisowurtzitane (e-polymorph)
1.011370
21 [50]
4
N,N-Dinitro-1,2-ethanediamine
0.986327
34 [51]
5
1,1-Diamino-2,2-dinitro-ethylene
0.961719
126 [52]
6
1,3,5,7-Tetranitro-1,3,5,7-tetraazacyclooctane
0.998788
32 [50]
7
2,24,4,6,6-Hexanitrostilbene
0.990053
54 [51]
8
2-Methoxy-1,3,5-trinitrobenzene
0.989108
192
9
Nitroguanidine
0.942069
[320 [53]
10
3-Nitro-1,2,4-triazole-5-one
0.985297
291 [51]
11
Hexahydro-1,3,5-trinitro-1,3,5-striazine
1.006685
24
12
Hexanitrobenzene
1.006100
11
13
Pentanitrobenzene
1.009100
11
14
1,2,3,5-Tetranitrobenzene
1.010590
28
15 16
1,3,5-Trinitrobenzene 2,4,6-Trinitroaniline
0.990590 0.983370
71 141
17
1,3-Diamino-2,4,6-trinitrobenzene
0.966460
320
18
1,3,5-Triamino-2,4,6-trinitrobenzene
0.940590
490
19
3,3-Diamino-2,24,4,6,6-hexanitrobiphenyl
0.980790
67
20
4,6-Dinitrobenzofuroxan
0.987550
76
21
7-Amino-4,6-dinitrobenzofuroxan
0.980590
100
22
7-Amino-4,5,6-trinitrobenzofuroxan
1.011930
56
23
8-Amino-7-nitrobenzobisfuroxan
0.981330
56
24
Pentanitrotoluene
1.003800
18
25
2,3,4,5-Tetranitrotoluene
1.005140
15
26
2,3,4,6-Tetranitrotoluene
1.005570
19
27
2,3,5,6-Tetranitrotoluene
1.002330
25
28
2,4,6-Trinitrotoluene
0.988940
98
29
2,3,4-Trinitrotoluene
1.003780
56
30
3,4,5-Trinitrotoluene
1.006900
107
31 32
2-Amino-3,4,5,6-tetranitrotoluene 3-Amino-2,4,5,6-tetranitrotoluene
1.006630 0.967710
36 37
33
4-Amino-2,3,5,6-tetranitrotoluene
1.002280
47
Relationships between qmax and nitrating reaction
Fig. 3 Correlation between qmax and h50
123
Most of nitro compounds are prepared by nitrating reactions [55, 56]. We find that some characteristics of nitrating reactions may also be predicted by qmax, such as difficulty, product, and relative reaction rate. qmaxs of the reactants and products in five nitrating processes (Fig. 4) were calculated. For the process 1, the reaction temperatures get higher and the nitrification abilities of the added acids get stronger from reactions 1a to 1c, in other words, the nitrating reactions from 1a to 1c are more and more difficult to take place. The increases in qmaxs of the products correspond to the increasingly harsh
J Comput Aided Mol Des
NO2
(1)
mixed acid
concentrated H2SO4
55-60 oC
fuming HNO3 90 oC (1b)
(1a)
concentrated H2SO4
[0.986649]
NO2 mixed acid
+
30 oC
45 oC
O2N
(2b)
(2a)
NO2 CH3
CH3 [0.979479]
[ 0.979479]
OH
dilute HNO3
[0.988953]
NO2
NO2
OH (3)
[ 0.990410]
CH3
mixed acid
NO2
NO2
NO2
CH3
fuming HNO3 100-110oC O2N (1c)
NO2
[0.982237]
(2)
NO2
NO2
NO2 concentrated HNO3
+
20 oC (3a) [0.981094]
O2N
(3b)
OH
NO2 OH
[0.977201]
[0.990207]
NO2 1
1
2
2
NO2
(4) (4a)
(4b) [0.978221]
[0.980931]
10
10
NO2
1
1 (5a)
(5b)
3
3
[0.980301]
[0.978733]
(5)
NO2
2
2
NO2 10
10 1
1 2
(5c)
2
3
(5d)
3
NO2
[0.979528]
6
(6)
7
N
(7)
6 N
7
5
4
8
N
5
4
8
1
[0.978552]
3 2
3 N
2 3 4 5
[0.990182] [0.981564] [0.983695] [0.979239]
6 [0.981548] 7 [0.982963] 8 [0.985628]
1 3 4 5
[0.988875] [0.987763] [0.979491] [0.979442]
6 [0.983678] 7 [0.981704] 8 [0.981626]
Fig. 4 Nitrating processes and qmaxs (in brackets) of products. The number in the processes 6 and 7 represents the nitro-substitution position
reaction conditions of 1a–1c. The similar situations happen to 2 and 3. In comparison with the reaction temperature of 1a, those of 2a and 3a are lower. And the qmaxs of the products of 2a and 3a are smaller than that of the product of 1a. So we can conclude that the nitrating reaction whose product possesses
larger qmax is more difficult to take place. According to the previous study [17], the nitrating velocities of 1a, 4a and 4b increase in the order of 1a \ 4b \ 4a, and qmaxs of the products of these reactions have the totally contrary order. Therefore, the smaller qmax of the product may correspond to
123
J Comput Aided Mol Des
the higher nitrating velocity. For the processes 4 and 5, qmaxs of the products have the orders of 1-nitronaphthalene \ 5-nitronaphthalene and 10-nitrophenanthrene \ 1-nitrophenanthrene \ 3-nitrophenanthrene \ 2-nitrophenanthrene, respectively. These orders are completely opposite to the orders of their occurrence ratios in nitrating reactions [17]. Previous investigations show that 5-nitroquinoline and 5-nitroisoquinoline are the main mononitro-derivatives of quinoline and isoquinoline. qmaxs shown in the processes 6 and 7 reveal that 5-nitroquinoline and 5-nitroisoquinoline have the smallest qmaxs in comparison with that of their isomers. Therefore, the smaller qmax of the nitrating product is consistent with the higher occurrence ratio, which may be employed to predict the most possible product of the nitrating reaction.
Conclusions The correlations between qmax and E, R and BDE were evaluated for nitro compounds, and that between qmax and h50 was roughly estimated because h50 is influenced by many factors. The larger qmax generally corresponds to the higher E, bigger R, smaller BDE and lower h50 which indicate the higher degree of similarity between –NO2 and the isolated NO2 molecule. Therefore, qmax should be an index reflecting the degree of similarity between –NO2 and the isolated NO2 molecule, and can be used to measure the stability of nitro compounds. In addition, the larger qmax of nitrating product is consistent with the lower occurrence of the product, and the more difficulty and the lower speed of the reaction. In a word, qmax can be used to understand and evaluate the stability of nitro compounds. MEDBCP can be used to evaluate the stability of compounds more easily and faster. In comparison with the existing methods, it has the following advantages: (1) (2)
Calculation of qmax is simple, only geometry optimization has to be done. The requirement for theoretical level is not high for estimating qmax and results are less sensitive to the quality of basis set than, for example, geometrical parameters. The B3LYP/6-31G* level is enough for geometry optimization and calculation of qmax. This helps to save computer resources and makes MEDBCP can be applied to large molecules.
References 1. Singh RP, Verma RD, Meshri DT, Shreeve JM (2006) Angew Chem Int Edit 45(22):3584–3601 2. Cook MA (1958) The science of high explosives, vol 139. RE Krieger Pub Co, Malabar
123
3. Urbanski T (1964) Chemistry and technology of explosives, vol 6. Pergamon Press, Oxford 4. Agrawal JP (1998) Prog Energ Combust 24(1):1–30 5. Singh G, Kapoor IPS, Mannan SM, Kaur J (2000) J Hazard Mater 79(1):1–18 6. Fried LE, Manaa MR, Pagoria PF, Simpson RL (2001) Ann Rev Mater Res 31(1):291–321 7. Shlyapochnikov V, Tafipolsky M, Tokmakov I, Baskir E, Anikin O, Strelenko YA, Luk’yanov O, Tartakovsky V (2001) J Mol Struct 559(1):147–166 8. Pagoria PF, Lee GS, Mitchell AR, Schmidt RD (2002) Thermochim Acta 384(1):187–204 9. An C, Li H, Geng X, Li J, Wang J (2013) Propellants Explos Pyrotech 38(2):172–175 10. Zhang J, Wu P, Yang Z, Gao B, Zhang J, Wang P, Nie F, Liao L (2014) Propellants Explos Pyrotech 39(5):653–657 11. Bolton O, Simke LR, Pagoria PF, Matzger AJ (2012) Cryst Growth Des 12(9):4311–4314 12. Bayat Y, Zeynali V (2011) J Energy Mater 29(4):281–291 13. Mandal AK, Thanigaivelan U, Pandey RK, Asthana S, Khomane RB, Kulkarni BD (2012) Org Process Res Dev 16(11):1711–1716 14. Vo TT, Zhang J, Parrish DA, Twamley B, Shreeve JM (2013) J Am Chem Soc 135(32):11787–11790 15. Behrens R Jr, Bulusu S (2013) Defence Sci J 46(5):361–369 16. Ma H, Feng X, Zhu T, Miao C, Ma Y, Feng M (2012) Chem Propellants Polym Mater 10(4):20–24 17. Zhang C (2009) J Hazard Mater 161(1):21–28 18. Zhang XL, Gong XD (2014) J Mol Model 20(8):1–11 19. Thottempudi V, Gao H, Shreeve JM (2011) J Am Chem Soc 133(16):6464–6471 20. Ghule VD (2012) J Phys Chem A 116(37):9391–9397 21. Wang G, Gong X, Liu Y, Du H, Xu X, Xiao H (2010) J Hazard Mater 177(1):703–710 22. Wang G, Gong X, Liu Y, Xiao H (2009) Spectrochim Acta A 74(2):569–574 23. Ravi P, Gore G, Venkatesan V, Tewari SP, Sikder A (2010) J Hazard Mater 183(1):859–865 24. Xu XJ, Xiao HM, Gong XD, Ju XH, Chen ZX (2005) J Phys Chem A 109(49):11268–11274 25. Delpuech A, Cherville J (1978) Propellants Explos 3(6):169–175 26. Delpuech A, Cherville J (1979) Propellants Explos 4(6):121–128 27. Bates LR (1986) Paper presented at the Proceedings 13th Symposium on Explosives and Pyrotechnics 28. Kamlet MJ, Adolph HG (1979) Propellants Explos Pyrotech 4:30–34 29. Chemistry Computational (1999) Reviews of Current Trends. World Scientific, River Edge 30. Murray JS, Concha MC, Politzer P (2009) Mol Phys 107(1):89–97 31. Zhang C (2006) Chem Phys 324(2):547–555 32. Zhang C, Shu Y, Huang Y, Zhao X, Dong H (2005) J Phys Chem B 109(18):8978–8982 33. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, 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 JE, Hratchian HP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng
J Comput Aided Mol Des
34. 35. 36.
37. 38. 39. 40. 41. 42. 43. 44.
CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2004) Gaussian 03, Revision CO2. Gaussian Gaussian Inc, Wallingford Bader RF (1991) Chem Rev 91(5):893–928 Lu T, Chen F (2012) J Comput Chem 33(5):580–592 Benson SW (1976) Thermochemical kinetics: methods for the estimation of thermochemical data and rate parameters. Wiley, New York Yao XQ, Hou XJ, Wu GS, Xu YY, Xiang HW, Jiao H, Li YW (2002) J Phys Chem A 106(31):7184–7189 Shao J, Cheng X, Yang X (2005) J Mol Struct Theochem 755(1):127–130 Fan XW, Ju XH, Xia QY, Xiao HM (2008) J Hazard Mater 151(1):255–260 Zhang XL, Liu Y, Wang F, Gong XD (2014) Chem Asian J 9(1):229–236 Liu H, Du H, Wang G, Gong X (2012) Struct Chem 23(2):479–486 Wang GX, Gong XD, Liu Y, Du HC, Xu XJ, Xiao HM (2011) J Comput Chem 32(5):943–952 Liu Y, Wang L, Wang G, Du H, Gong X (2012) J Mol Model 18(4):1561–1572 Politzer P, Alper HE (1999) Detonation initiation and sensitivity in energetic compounds: some computational treatments, vol 4. World Scientific, Singapore
45. Ju X-H, Xiao H-M, Xia Q-Y (2003) J Chem Phys 119(19):10247–10255 46. Zhang C, Shu Y, Zhao X, Dong H, Wang X (2005) J Mol Struct Theochem 728(1):129–134 47. Liu H, Wang F, Wang GX, Gong XD (2012) J Mol Model 18(10):4639–4647 48. Liu H, Wang F, Wang GX, Gong XD (2012) J Comput Chem 33(22):1790–1796 49. Armstrong R, Coffey C, DeVost V, Elban W (1990) J Appl Phys 68(3):979–984 50. Simpson R, Urtiew P, Ornellas D, Moody G, Scribner K, Hoffman D (1997) Propellants Explos Pyrotech 22(5):249–255 51. Storm CB, Stine JR, Kramer JF (1990) Paper presented at the chemistry and physics of energetic materials, Dordrecht, The Netherlands ¨ stmark H, Langlet A, Bergman H, Wingborg N, Wellmar U, 52. O Bemm U (1998) Paper presented at the 11th Detonation (International) Symposium, Snowmass 53. Hall TN, Holden JR (1988) Technical Report NSWC MP-88-116. Naval Surface Warfare Center, Dahlgren 54. Rice BM, Hare JJ (2002) J Phys Chem A 106(9):1770–1783 55. Akhavan J (2011) The chemistry of explosives, 3rd edn. The Royal Society of Chemistry, London 56. Urbanski T (1964) Chemistry and technology of explosives, vol 1. Pergamon Press, New York
123
