Substituent Effects on the Properties Related to Detonation

ARTICLE pubs.acs.org/JPCA

Substituent Effects on the Properties Related to Detonation Performance and Sensitivity for 2,20 ,4,40 ,6,60-Hexanitroazobenzene Derivatives Yan Liu, Xuedong Gong,* Lianjun Wang, Guixiang Wang, and Heming Xiao School of Chemical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, People’s Republic of China

bS Supporting Information ABSTRACT: To look for superior and safe high energy density compounds (HEDCs), 2,20 ,4,40 ,6,60 -hexanitroazobenzene (HNAB) and its -NO2, -NH2, -CN, -NC, ONO2, -N3, or -NF2 derivatives were studied at the B3LYP/6-31G* level of density functional theory (DFT). The isodesmic reactions were applied to calculate the heats of formation (HOFs) for these compounds. The theoretical molecular density (F), detonation energy (Ed), detonation pressure (P), and detonation velocity (D), estimated using the Kamlet-Jacobs equations, showed that the detonation properties of these compounds were excellent. The effects of substituent groups on HOF, F, Ed, P, and D were studied. The order of contribution of the substituent groups to P and D was -NF2 > ONO2 > -NO2 > -N3 > -NH2. Sensitivity was evaluated using the nitro group charges, frontier orbital energies, and bond dissociation enthalpies (BDEs). The trigger bonds in the pyrolysis process for all these HNAB derivatives may be Ring-NO2, Ring-NdN, Ring-NF2, or O-NO2 varying with the attachment of different substituents. BDEs of trigger bonds except those of ONO2 derivatives are relatively large, which means these compounds suffice the stability request of explosives. Taking both detonation properties and sensitivities into consideration, some -NF2 and -NO2 derivatives may be potential candidates for HEDCs.

1. INTRODUCTION High energy density compounds (HEDCs) have been used widely for both military and civilian applications. To meet the requirements of future military and space applications, researchers have always been trying to develop HEDCs more excellent than the existing ones.1-4 For HEDCs, besides high detonation performance, sensitivity is a prerequisite requirement. They should be safe, stable, and reliable enough to detonate under specific conditions. So good thermal stability and low impact and shock sensitivities are of equal importance to detonation performance, but these requirements are somewhat reciprocally exclusive. The explosives with better explosive performance usually exhibit higher impact sensitivity;5 thus the foremost objective is to find the molecule having better detonation performance and safety than those currently used. Nitro compounds, as an important class of HEDCs, have attracted continuous attention due to their ability to endure the high temperature and low pressure encountered in space environments.6,7 Also, incorporation of amino groups to a benzene ring having nitro groups is the simplest approach to enhance the thermal stability of explosives. For example, 2,4,6triamino-1,3,5-trinitrobenzene (TATB) is the current industry standard and is used extensively in military applications and in nuclear weapons.8,9 Because of its high heat-resistant and insensitive property, it is the only insensitive explosive authorized by the U.S. Department of Energy,10 while it is a pity that its explosive performance is not excellent. To improve the explosive r 2011 American Chemical Society

performance, incorporating some energy-rich functional groups into benzene ring is an effective and widely used means. These functional groups may impart explosive properties to the compound, accordingly raising its detonation performance. Moreover, introduction of conjugation in explosive molecules can also improve detonation performance and increase thermal stability. For example, the azo bridge (-NdN-) not only desensitizes explosives but also dramatically increases the heats of formation and explosive properties.11 There exists an azo bridge in some important explosives such as 3,30 -azo-bis(6-amino-1,2,4,5-tetrazine) (DAAT) and 2,20 ,4,40 ,6,60 -hexanitroazobenzene (HNAB).12 The detonation pressure (P) and detonation velocity (D) are the most important factors in evaluating the performance of energetic materials. P is directly proportional to the squared density (F), and D is dependent on the density according to the empirical equation proposed by Kamlet and Jacobs,13 so the density of the explosive is a critical parameter. A high heat of formation (HOF) is also required for effective energetic materials, which reflects the energy content of the charge depending on performance metrics.14 The sensitivity of explosives indicates the stability to various external stimuli such as heat, impact, shock, and electric spark.15 Prediction of the sensitivity, which can be approached from Received: January 17, 2011 Revised: January 24, 2011 Published: February 11, 2011 1754

dx.doi.org/10.1021/jp200512j | J. Phys. Chem. A 2011, 115, 1754–1762

The Journal of Physical Chemistry A

Figure 1. Molecular frameworks of HNAB derivatives.

molecular structure, is a very important step for developing new energetic materials. Previous investigations have shown that the rupture of the weakest bond of the energetic material compound is the first step in detonation initiation; therefore, the properties of these bonds such as electrostatic potential, bond lengths, bond strength, and the nitro group charges (QNO2) are related to the sensitivity.16,17 The strength of the weakest bond is most widely used to index the relative sensitivity at present, and it can be evaluated by the bond dissociation enthalpy (BDE).18 Rice et al. concluded that there is a rough correlation between the logarithm of the impact sensitivity values and BDEs of the weakest bond in some nitroaromatic molecules.19 Yet experimental values of BDE may not be easily accessible because the thermochemistry of short-lived species is not amenable to the traditional calorimetric techniques, whereas computational chemistry can be a more convenient and reliable method. With the rapid development of computer technology and theoretical chemistry, computer-aided molecular design (CAMD) has been an effective means in the design of new excellent materials, including HEDC of course, especially for those with danger, which may optimize the expensive, time-consuming, and often hazardous synthesis, testing, and fielding of a new material.15 Molecular modeling methods to quantitatively predict explosive performance, such as the heat of formation, density, detonation velocity, detonation pressure, and sensitivity, have been adopted to select the most promising substances for laboratory synthesis and further consideration.20-26 In this Article, our primary interest here is to look for potential HEDC in a series of HNAB derivatives by incorporating energyrich functional groups such as nitro (-NO2), amino (-NH2), cyan (-CN), isocyan (-NC), nitrate (-ONO2), azido (-N3), or difluoroamino (-NF2) groups in the place of hydrogen atom (see Figure 1 for the structural diagrams of these compounds, substituents for I-VII are I-NO2, II-NH2, III-CN, IV-NC, V-ONO2, VI-N3, and VII-NF2, respectively). The density function theory (DFT) has been used to study the heats of formation, electronic structure, density, energetic properties, and thermal stability of these HNAB derivatives; accordingly, the important role of substituents in the design of efficient HEDCs was investigated.

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theory at the B3LYP level with the 6-31G* basis set in the Gaussian 03 program package.27 Vibrational frequency analyses were performed at the same level. The optimized structures were confirmed to be local minima without imaginary frequencies. According to the previous study,28 a scaling factor of 0.96 was used uniformly to approximately correct the systematic overestimation to the vibrational frequencies in the B3LYP/6-31G* calculations. The isodesmic reactions were applied to calculate the HOFs of the title compounds at 298.15 K. The details of the computation procedure are given in previous studies.29-31 The theoretical molecular density (F) of each title compound was calculated from the molar weight (M) divided by the average molar volume (V), which was gained from the arithmetic average value of 100 single-point molar volumes, defined as the volume of 0.001 electrons Bohr-3 electron density envelope and computed by Monte Carlo integration implemented in the G03 program on the basis of the optimized geometrical structure.22,23,32,33 For each title compound, explosive reaction is designed in terms of the maximal exothermal principle; that is, all the N atoms turn into N2, the O atoms react with the H atoms to give H2O at first, and then form CO2 with the C atom. If the number of O atoms is more than what is needed to oxidize H and C atoms, redundant O atoms will convert into O2. If the content of O is not enough to satisfy full oxidation of the H and C atoms, the remain H atoms will convert into H2, and C atoms will exist as solid-state C. Also, halogen atoms (X) form hydrogen halide with hydrogen atoms. Detonation energy can be deduced from the explosion reaction, and then the empirical Kamlet-Jacobs (K-J) equations can be used to estimate the detonation velocity D and detonation pressure P of the explosives with CHNOX elements:13 0:5

D ¼ 1:01ðNM Ed 0:5 Þ0:5 ð1 þ 1:30FÞ 0:5

P ¼ 1:558F2 NM Ed 0:5 where F is the density of the explosive (g cm-3), N is the moles of gas produced by per gram of explosive, and M is the mean molecular weight of the gaseous detonation products. For the CaHbOcNdFe explosives studied here, 2a þ b/2 > c g b/2, N, M, and Ed are calculated according to the following formulas: N ¼ ðb þ 2c þ 2d þ 3eÞ=4Mw M ¼ ð56d þ 88c þ 88e - 8bÞ=ðb þ 2c þ 2d þ 3eÞ Ed 10-3 ¼ ½28:9b þ 94:05ðc=2 - b=4Þ þ 59:5e þ 0:239HOF=Mw where a, b, c, d, and e stand for the number of C, H, O, N, and F atoms in the compound, respectively; MW is the molecular weight of the title compounds (g mol-1). The gas-phase BDE for a bond R1-R2 is defined as the enthalpy change of the bond homolysis reaction at 298 K in a vacuum, which can be calculated from the sum of enthalpies (H298) of the products (radicals) minus that of reactant (parent molecule). R 1 -R 2 ðgÞ f R 1 3 ðgÞ þ R 2 3 ðgÞ

2. COMPUTATIONAL METHODS The geometries of HNAB derivatives were fully optimized without any symmetry restriction using the density functional

BDEðR 1 -R 2 Þ ¼ H298 ðR 1 3 Þ þ H298 ðR 2 3 Þ - H298 ðR 1 -R 2 Þ 1755

dx.doi.org/10.1021/jp200512j |J. Phys. Chem. A 2011, 115, 1754–1762


Figure 2. The calculated HOFs versus the number of substituents (n) of the title compounds.

where R1-R2 denotes the neutral molecules, and R1 3 and R2 3 stand for the corresponding product radicals after the bond dissociation; BDE(R1-R2) is the bond dissociation enthalpy of the bond R1-R2; and H298(R1-R2), H298(R1 3 ), and H298(R2 3 ) are the enthalpies of the parent compound and the corresponding radicals, respectively. The enthalpy for each species was calculated using the following equation: H298 ¼ Ee þ ZPE þ Htrans þ Hrot þ Hvib þ RT where Ee is electronic energy; ZPE is the zero-point energy; Htrans, Hrot, and Hvib are the standard thermal correction terms calculated using the equilibrium statistical mechanics with harmonic oscillator and rigid rotor approximations; and RT (PV work term) is the conversion factor from energy to enthalpy. Because the experimental values of HNAB derivatives are not available, three classical explosives, TATB, 1,3,5,7-tetranitro1,3,5,7-tetraazacyclooctane (HMX), and hexahydro-1,3,5-trinitro-1,3,5-s-triazine (RDX), were calculated applying the same methods to validate the feasibility of the computational methods and to compare the results.

3. RESULTS AND DISCUSSION 3.1. Detonation Performance. Heat of formation reflects the energy content of a compound. High positive HOF is usually required for an effective energetic material. Previous studies indicated that the calculated values of HOF by applying the isodesmic reactions agree well with experiments when appropriate reference compounds have been chosen.21-25,31,34-37 In this study, conjugated bonds have been kept unbroken as much as possible, which has proven to be a reliable means of reducing errors of HOF. To show the tendencies more intuitionisticly, the plots of the calculated HOF versus the number of substituents (n) are presented in Figure 2, in which the isomers with two substituents in the same benzene ring have been adopted. Evidently, all the derivatives of HNAB have quite large positive HOF, which is favorable for high energy density materials. It can also be seen from Figure 2 that different substituent groups exert diverse influences on HOF. -N3, -NC, -CN, and -NO2 groups increase the HOF. If one more -N3, -NC, -CN, or -NO2 group is introduced, the contribution of them to HOF is in the order of -N3 > -NC > -CN > -NO2, and the magnitudes, on

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average, are 512.88, 256.95, 185.95, and 52.10 kJ mol-1, respectively. Difluoroamino (-NF2) group has little effect on HOF, whereas one more amino (-NH2) or nitrate (-ONO2) group leads to the decrease of HOF by 36.05 and 40.69 kJ mol-1. It is obvious that the plots all show good linear relationships with correlation coefficients (R) larger than 0.99 except difluoroamino derivatives, which indicates good group additivity of HOF for various HNAB derivatives. Furthermore, for the isomers with the same kind and number of substituting groups, the values of HOF are slightly different, indicating that HOF is a little influenced by the position of the substituting groups. The HOFs of isomers with substituting groups (-NO2, -NC, -CN, and -NF2) in two rings are slightly higher than those in the same ring. Taking nitro derivatives, for example, the HOF of I-2 (461.03 kJ mol-1) is higher than that of I-3 (446.85 kJ mol-1). This is because there are six adjacent nitro groups in I-2, while only five in I-3, which leads to larger repulsion energies in I-2, thus the higher HOF. As for the isomers with -NH2, -ONO2, and -N3, the cases are on the contrary. The effect of hydrogen bonds in II-2 is larger than that in II-3, so the HOF of II-2 (265.74 kJ mol-1) is lower than that of II-3 (271.74 kJ mol-1). Table 1 presents the correlation equations obtained for isomers with substituents in the same benzene ring or in different rings. It is evident that the slopes of the linear correlation equations are the same. This indicates that good group additivity has nothing to do with the position of the substituents. The density estimation techniques are crucial due to the great contribution of density to D and P. Among them, the “group or volume additivity” method, in which the molar volume is obtained by summing up the volume of composition atoms or functional groups, is the simplest, earliest, and most widely used method for the density prediction. However, it has the deficiency that it cannot readily account for the molecular conformation, isomerization, and crystal packing efficiency. Because HEDCs are usually in agglomerate solids, their densities are closer to crystal densities, which can be obtained from the crystal packing patterns in various space groups based on the molecular mechanics (MM) method. However, this procedure cannot be applied routinely in modeling explosives because it requires extensive computational works and resources. In addition, many HEDCs may exist in several polymorphic forms; it is quite difficult to find the exact crystal packing patterns and the corresponding crystal densities from simulation. Hence, the method based on quantum chemistry calculation is employed here as mentioned in the Computational Methods. Previous studies have proved that this method is reliable and simple as compared to the experimental value. To further validate this method, the crystal density of HNAB has been calculated using various methods for comparison.38 The crystal density of HNAB was predicted by the rigorous molecular packing calculations using the polymorph module in Materials Studio39 under space groups of P21, P21/c, P-1, P212121, C2/c, Pbca, Pna21, Pbcn, Cc, and C2. The unit cell was optimized with the Dreiding and Universal force fields. Table 2 lists the volume (V), density (F), unit cell total energy (ET), van der Waals energy (EvdW), and unit cell lattice parameters of molecular packings for HNAB in 10 space groups under Dreiding and Universal force fields, respectively. Obviously, the densities predicted under the Dreiding force field are a little larger than the experimental crystal density (1.80 g cm-3),12 whereas those under the Dreiding force field are a bit smaller than 1.80 g cm-3. All densities obtained are close to the experimental crystal density, especially under the Dreiding force field. The densities under the Dreiding force field are very close 1756



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Table 1. Comparisons of the Linear Correlation Equations Applying Different Isomers with Substituents in the Same Benzene Ring or in Different Rings substituent

substituents in the same benzene ring

substituents in different rings

-N3

HOF = 340.30 þ 512.88n

HOF = 339.66 þ 512.88n

-NC -CN

HOF = 343.42 þ 256.95n HOF = 341.65 þ 185.95n

HOF = 344.70 þ 256.95n HOF = 342.09 þ 185.95n HOF = 349.29 þ 52.10n

-NO2

HOF = 346.44 þ 52.10n

-NF2

HOF = 345.48 þ 5.06n

HOF = 350.00 þ 5.06n

-NH2

HOF = 343.33 - 36.05n

HOF = 342.47 - 36.05n

-ONO2

HOF = 349.38 - 40.69n

HOF = 345.16 - 40.69n

Table 2. Volume, Density, Unit Cell Total Energy, van der Waals Energy, and Unit Cell Lattice Parameters of Molecular Packings for HNAB force field Dreiding

Universal

space group P21

V (Å3)

F (g cm-3)

ET (kJ mol-1)

EvdW (kJ mol-1)

a (Å)

b (Å)

c (Å)

R (deg)

β (deg)

γ (deg)

809.93

1.85

40.52

2.81

7.59

7.26

14.94

90.0

79.4

90.0

P21/c P-1

1603.26 816.15

1.87 1.84

39.92 40.49

1.44 1.41

14.58 17.50

7.42 8.07

16.87 6.92

90.0 112.0

61.5 93.7

90.0 112.0

P212121

1636.10

1.84

41.33

2.63

29.96

7.47

7.31

90.0

90.0

90.0

C2/c

3266.53

1.84

40.97

1.49

6.97

14.81

32.74

90.0

105.0

90.0

Pbca

3280.21

1.83

41.80

5.28

14.39

6.97

32.69

90.0

90.0

90.0

Pna21

1615.98

1.86

40.44

2.26

14.85

14.94

7.28

90.0

90.0

90.0

Pbcn

3351.69

1.79

42.14

4.34

32.00

15.41

6.80

90.0

90.0

90.0

Cc

1652.13

1.82

41.53

2.41

6.88

15.10

16.37

90.0

103.9

90.0

C2 P21

1651.08 858.38

1.82 1.75

41.10 30.33

2.34 1.08

16.26 9.09

15.37 16.17

15.87 6.79

90.0 90.0

24.6 120.7

90.0 90.0

P21/c

1732.48

1.73

30.76

3.36

14.81

17.47

14.51

90.0

152.5

90.0

861.65

1.74

30.92

0.62

13.87

8.44

11.86

136.7

85.8

110.0

P212121

1716.94

1.75

30.25

3.06

14.94

6.82

16.85

90.0

90.0

90.0

C2/c

3507.84

1.71

31.56

2.66

22.28

15.90

16.36

90.0

142.8

90.0

Pbca

3473.13

1.73

30.67

3.50

34.20

14.90

6.82

90.0

90.0

90.0

Pna21

1760.11

1.71

31.25

3.10

16.09

6.80

16.09

90.0

90.0

90.0

Pbcn Cc

3542.94 1733.91

1.70 1.73

31.78 30.78

3.53 3.30

32.06 6.96

16.17 17.47

6.83 14.53

90.0 90.0

90.0 100.8

90.0 90.0

C2

1736.90

1.73

31.45

0.71

16.46

15.90

19.00

90.0

159.6

90.0

P-1

to the theoretical molecular density (F = 1.84 g cm-3) (see Table 3). Moreover, the calculated molecular density of HNAB (1.84 g cm-3), TATB (1.86 g cm-3), RDX (1.80 g cm-3), and HMX (1.84 g cm-3) are in good agreement with the available experimental values (1.80, 1.854, 1.82, 1.91 g cm-3),12,40,41 respectively. This indicates that the method of calculating theoretical molecular density (F) based on quantum chemistry is acceptable. The calculated molecular density and detonation properties, including Ed, D, and P of the title compounds and TATB, RDX, HMX, are listed in Table 3. It can be seen that the calculated D and P values of TATB, RDX, and HMX all agree well with the available experimental values. This shows that the detonation properties predicted according to the K-J equation for the title compounds will be reliable. Figure 3 has been made to show the variation tendencies of F, Ed, D, and P with the number of the substituent more clearly. As is evident from Table 3 and Figure 3, these substituent groups indeed have influences on the values of F, Ed, D, and P. Most substituent groups increase F, D, and P as compared to HNAB except for -CN and -NC, and only -NH2 causes the decrease of Ed. The variation trends of D and P with n are the same for each substituent, and that of F differs from D and P in the interlacing of four -NH2 and four -N3 substituent derivatives. While the

influences of substituents on the tendency of Ed are not similar to those of F, D, and P, for example, introduction of -N3 promotes Ed most. The reason is that D and P mainly depend on F, whereas Ed relies on HOF. Because of this, only the plots of Ed show a good linear relationship in Figure 3, which indicates a good group additivity of Ed for various HNAB derivatives. The correlation equations of Ed and n for different substituents are as follows: Ed ¼ 1506:56 þ 49:00n R ¼ 0:9959 ðfor -NO2 derivativesÞ Ed ¼ 1466:40 - 47:04n R ¼ 0:9992 ðfor -NH2 derivativesÞ Ed ¼ 1473:65 þ 4:76n R ¼ 0:9809 ðfor - CN derivativesÞ Ed ¼ 1485:26 þ 33:10n R ¼ 0:9989 ðfor - NC derivativesÞ Ed ¼ 1506:14 þ 45:56n R ¼ 0:9942 ðfor -ONO2 derivativesÞ 1757



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Table 3. Predicted Densities and Detonation Properties of the Title Compounds F

Ed

D

P

I-1

1.88

1550.14

8.33

31.59

I-2

1.94

1611.46

8.72

35.25

I-3

1.94

1605.20

8.71

hI-4 I-5

1.97

1655.94

1.99

1698.63

comp.

F

Ed

D

P

V-1

1.93

1546.28

8.53

33.62

V-2

1.93

1602.49

8.77

35.49

35.18

V-3

1.96

1611.27

8.88

36.76

8.98

37.69

V-4

2.01

1648.62

9.22

40.20

9.19

39.69

V-5

2.01

1682.78

9.37

41.53

-NO2

comp. -ONO2

-N3

-NH2 II-1 II-2

1.85 1.88

1421.66 1369.52

8.00 8.05

28.88 29.50

VI-1 VI-2

1.87 1.87

1587.75 1684.82

8.31 8.51

31.37 32.91

II-3

1.86

1372.50

7.99

28.85

VI-3

1.88

1686.26

8.54

33.14

II-4

1.86

1324.00

8.00

29.00

VI-4

1.88

1769.20

8.70

34.44

II-5

1.94

1280.05

8.22

31.34

VI-5

1.90

1845.25

8.94

36.59

-CN

-NF2

III-1

1.85

1479.47

7.93

28.40

VII-1

1.93

1557.79

8.52

33.50

III-2

1.89

1482.47

7.97

29.03

VII-2

2.03

1626.38

9.09

39.20

III-3 III-4

1.84 1.83

1481.41 1488.26

7.82 7.73

27.49 26.80

VII-3 VII-4

2.02 2.10

1616.64 1675.48

9.04 9.50

38.73 43.65

III-5

1.85

1493.06

7.72

26.83

VII-5

2.13

1718.40

9.80

46.90

IV-1

1.85

1516.75

7.98

28.73

IV-2

1.87

1552.87

8.00

29.05

HNAB

1.84

(1.80)12

1479.31

7.97

(7.65)41

28.56

IV-3

1.85

1549.82

7.93

28.34

TATB

1.86

(1.854)40

1124.31

7.79

(7.93)40

27.21

(29.1)40

IV-4

1.83

1586.57

7.84

27.57

RDX

1.80

(1.82)41

1598.52

8.87

(8.75)41

34.98

(34.0)41

1.84

41

9.29

41

38.78

(39.0)41

-NC

IV-5

1.80

1615.86

7.71

26.38

HMX

(1.91)

1754.24

(9.10)

Figure 3. Correlations between F, Ed, D, P, and the number of various substituents for HNAB derivatives. 1758


The Journal of Physical Chemistry A Ed ¼ 1508:26 þ 58:54n R ¼ 0:9982 ðfor -N3 derivativesÞ Ed ¼ 1506:91 þ 54:07n R ¼ 0:9974 ðfor -NF2 derivativesÞ As compared to Table 1, it can be seen that the effect of substituent on Ed is different from that on HOF, although Ed is calculated from HOF. The order of the contribution of various substituent groups to Ed is -N3 > -NF2 > -NO2 > -ONO2 > NC > -CN > -NH2, while that to HOF is -N3 > -NC > -CN > -NO2 > -NF2 > -NH2 > -ONO2. The contribution of the azido group (-N3) to Ed and HOF is the largest, and so its presence in energetic materials is favorable on thermodynamic grounds. The contribution of the -NF2 to F, D, and P is the largest, although it has little effect on HOF. This also indicates that D and P depend more on F than on HOF. -ONO2 leads to the decrease of HOF, which is disadvantageous to D and P, but it increases the value of F only inferior to -NF2, so the derivatives with -ONO2 substituents have the second largest D and P. NO2 will increase HOF and F moderately, which makes D and P of the derivatives with -NO2 substituents stand in the third. Whereas the contribution of -N3 to HOF is the largest, that to F is little, and thus its contribution to D and P is less than those of ONO2, -NF2, and -NO2. Although -NH2 decreases HOF, it can increase F to a certain extent, so the detonation property of NH2 derivatives will be enhanced. For -CN and -NC derivatives, a great increase of HOF cannot make up the loss of F, so their D and P valuees are smaller than those of HNAB. It is worthwhile to note that F, D, and P of all the title compounds are more than 1.80 g cm-3, 7.5 km s-1, and 26 GPa, respectively. As compared to the commonly used important explosives such as TATB, RDX, and HMX, almost all HNAB derivatives surpass TATB on D and P, which implies that the azo bridge (-NdN-) can dramatically increase the explosive properties. In addition, those with three or four -NO2 substituents (I-4, I-5), two to four -ONO2 substituents (V-2, V-3, V-4, V-5), four -N3 substituents (VI-5), and two to four -NF2 substituents (VII-2, VII-3, VII-4, VII-5) are superior to RDX, and that I-5, V-4, V-5, VII-4, and VII-5 excel HMX, which indicates that these compounds are potential HEDCs. 3.2. Sensitivity. Table 4 lists oxygen balance (OB%), charges on nitro group (QNO2), the energy of the highest occupied molecular orbital (EHOMO), the energy of the lowest unoccupied molecular orbital (ELUMO), the energy gaps between LUMO and HOMO (ΔE), and bond dissociation enthalpies (BDE) for HNAB derivatives. The available experimental values of impact sensitivity h50% are also presented in Table 4. It can be seen that h50% of TATB is much higher than that of HNAB. This is because in TATB six furcated hydrogen bonds are formed, which make the molecule more stable, while the -NdN- bridge group may decrease the stability of HNAB. 3.2.1. Electronic Structure. The effects of various groups on HOMO and LUMO are schematically shown in Figure 4, and it can be easily found that HOMO and LUMO energy levels decrease as compared to that of HNAB when the -NO2, -CN, -NC, -ONO2, or -NF2 group is attached to the ring, thereinto -NO2 and -CN make it decrease most. On the contrary, the introduction of -NH2 group will make the HOMO

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and LUMO energy levels increase gradually. This indicates that different substituents exert different effects on the HOMO and LUMO energy levels. Because the variation trends of the HOMO and LUMO energies versus the number of substituents n are accordant for the same substituent, the substituent has little effect on the energy gaps (ΔE). This implies that the substituents interact tantamountly with the HOMO and LUMO orbitals. Comparing EHOMO (-0.2580 eV), ELUMO (-0.1375 eV), and ΔE (0.1205 eV) of II-5 with that of TATB (-0.2648 eV, 0.1028 eV, 0.1621 eV), one sees that the bridge group -NdNincreases ELUMO (33.75%) more than EHOMO (2.57%), which indicates that the bridge group interacts mainly with the LUMO. It is noteworthy that the energy gaps of HNAB derivatives are much lower than that of TATB, which means HNAB derivatives are more sensitive than TATB. As is known, LUMO is related to molecular electron affinity, Badders’s study showed that the impact sensitivity of the aromatic explosives will increase with the decrease of the LUMO energy,42 so incorporation of NdN- group will decrease the sensitivity. It is obvious that only -NH2 can decrease the sensitivity; other substitutents increase the sensitivity except -N3, which has little effect on sensitivity, so II-5 may be the most insensitive one of all the title compounds. Because C-NO2, N-NO2, and O-NO2 bonds are usually the trigger bonds in nitro explosives, the net charges on nitro group (QNO2) may reflect the ability of -NO2 attracting electrons and therefore the stability of the molecule. From Table 4, it can be seen that QNO2 of TATB is much more than that of HNAB. In addition, the magnitudes of QNO2 decrease linearly with the increase in the number of substitutents including -NF2, -NO2, -ONO2, -NC, and -CN, which suggests these five substitutents will increase the sensitivity. -N3 group exerts little effect on QNO2, and only NH2 can promote the nitro group to attract more electrons linearly, which is accordant with experiment and is due to the formation of the intramolecular hydrogen bonds between the amino and nitro groups, which may make -NO2 possess more charges, and thus make the compound more stable. Hence, in the explosive molecule design, incorporation with -NH2 is an effective means to decrease the sensitivity despite its disadvantage to detonation performance. 3.2.2. Bond Dissociation Enthalpies. Usually the stronger are the weakest bonds, the more stable are the energetic materials; that is, the sensitivity and stability of the energetic compounds are directly relevant to bond strength, which is commonly described by BDE. Studies on BDEs are important and essential to understand the stability and decomposition process of the energetic materials. The possible initial steps in the pyrolysis route are considered for the title compounds by breaking the following bonds: RingNO2, Ring-NdN, and Ring-substituent including Ring-NH2, Ring-CN, Ring-NC, Ring-ONO2, Ring-N3, Ring-NF2, and O-NO2 for -ONO2 derivatives. The weakest bond among the same type of bonds is selected as the trigger bond based on the Mulliken bond population analyses.19-26 From Table 4, it can be seen that, for the nitro derivatives of HNAB, the BDE for removal of the -NO2 moiety decreases inch by inch with the more -NO2 substitution, indicating that the stability decreases and their sensitivities increase accordingly, which confirms that the nitro group has an effect of activity. Moreover, this case is consistent with that of the nitro group charges. The BDE for rupture of Ring-NdN increases gradually with the increase in the number of nitro group. When the number 1759



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Table 4. Oxygen Balance (OB%), Charges on Nitro Group (QNO2), the Energy of Highest Occupied Molecular Orbital (EHOMO), the Energy of Lowest Unoccupied Molecular Orbital (ELUMO), the Energy Gaps between LUMO and HOMO (ΔE), Bond Dissociation Enthalpies (BDE) for the Rupture of the Weakest Bonds, and the Available Experimental h50% BDE (kJ mol-1) OB%

QNO2 (e)

EHOMO (eV)

ELUMO (eV)

ΔE (eV)

Ring-NO2

TATB

-55.78

-0.560

-0.2648

-0.1028

0.1621

276.93

HNAB

-49.56

-0.344

-0.2866

-0.1607

0.1258

231.89

Ring-NdN

Ring-substituent

O-NO2

420.95

h50% (m) 4.90

192.28

0.37

RDX

-21.61

-0.112

-0.3118

-0.0881

0.2237

145.62

0.28

HMX

-21.61

-0.113

-0.3106

-0.0772

0.2334

160.41

0.32

-NO2 I-1

-37.02

-0.333

-0.2987

-0.1723

0.1264

208.84

193.24

I-2

-26.57

-0.327

-0.3076

-0.1812

0.1264

204.16

195.34

I-3

-26.57

-0.309

-0.3132

-0.1770

0.1362

207.98

226.35

I-4

-17.72

-0.302

-0.3233

-0.1942

0.1292

213.62

226.38

I-5

-10.13

-0.288

-0.3307

-0.2007

0.1300

199.08

232.73

-NH2 II-1

-49.68

-0.374

-0.2787

-0.1544

0.1243

217.20

181.55

450.96

II-2 II-3

-49.79 -49.79

-0.404 -0.408

-0.2682 -0.2692

-0.1505 -0.1491

0.1177 0.1201

238.04 226.52

177.30 165.76

449.51 430.61

II-4

-49.90

-0.437

-0.2631

-0.1453

0.1178

246.39

160.28

444.33

II-5

-50.00

-0.471

-0.2580

-0.1375

0.1205

245.72

162.57

429.10

-CN III-1

-51.97

-0.333

-0.3042

-0.1758

0.1284

230.24

210.29

503.7

III-2

-54.16

-0.328

-0.3122

-0.1879

0.1242

229.2

217.15

500.06

III-3

-54.16

-0.329

-0.3144

-0.1813

0.1330

213.58

215.04

503.63

III-4 III-5

-56.14 -57.94

-0.323 -0.321

-0.3234 -0.3293

-0.1952 -0.2001

0.1281 0.1291

211.6 209.86

230.47 235.29

499.4 496.12

IV-1

-51.97

-0.333

-0.3018

-0.1711

0.1307

229.35

212.86

418.38

IV-2

-54.16

-0.327

-0.3069

-0.1814

0.1256

229.21

220.7

415.02

-NC

IV-3

-54.16

-0.322

-0.3097

-0.1746

0.1351

217.64

234.16

418.44

IV-4

-56.14

-0.317

-0.3154

-0.1861

0.1293

217.98

233.37

418.44

IV-5

-57.94

-0.309

-0.3189

-0.1891

0.1298

216.78

235.63

416.07

-ONO2 V-1

-32.73

-0.332

-0.3005

-0.1745

0.1260

232.05

209.58

329.87

71.42

V-2

-19.50

-0.324

-0.3040

-0.1798

0.1242

237.81

213.28

326.9

54.52

V-3

-19.50

-0.331

-0.2933

-0.1524

0.1408

201.49

203.36

305.61

39.85

V-4

-8.82

-0.313

-0.3057

-0.1767

0.1289

223.82

226.24

320.42

50.29

V-5

0.00

-0.300

-0.3093

-0.1806

0.1287

225.92

232.68

329.54

49.53

-N3 VI-1

-43.79

-0.343

-0.2913

-0.1681

0.1233

210.22

222.32

310.57

VI-2 VI-3

-38.93 -38.93

-0.344 -0.338

-0.2914 -0.2902

-0.1699 -0.1673

0.1215 0.1229

221.94 223.82

229.85 231.16

308.66 300.74

VI-4

-34.76

-0.337

-0.2832

-0.1647

0.1185

223

239.13

299.22

VI-5

-31.15

-0.338

-0.2863

-0.1689

0.1174

222.75

215.87

299.26

-NF2 VII-1

-42.92

-0.325

-0.3041

-0.1750

0.1291

217.37

215.06

222.41

VII-2

-37.53

-0.311

-0.3080

-0.1836

0.1245

226.88

224.45

216.2

VII-3

-37.53

-0.312

-0.3093

-0.1712

0.1381

216.03

236.38

238.7

VII-4 VII-5

-33.04 -29.26

-0.296 -0.274

-0.3142 -0.3209

-0.1841 -0.1931

0.1301 0.1278

225.82 213.93

243.28 256.03

234.44 238.34

of substituting nitro group is 1 and 2, the BDE of Ring-NO2 is larger than that of Ring-NdN, but the contrary is true when n g 3. This shows that the Ring-NO2 bond may be the trigger bond during the thermolysis initiation process as n = 1 or 2, and the

homolysis of Ring-NdN is the first step in decomposition as n = 3 or 4. While for the amino derivatives of HNAB, BDE values for the homolysis of Ring-NO2 bonds increase with the number of -NH2 groups increasing, this accords with previous .that 1760



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Figure 4. Variations of HOMO and LUMO energies and QNO2 with the number of substituents for HNAB derivatives.

introduction of amino groups is an effective approach to increasing the thermal stability of explosive molecules due to the formation of a hydrogen bond between -NO2 and -NH2, which correspondingly makes molecules more stable. The greater is the number of substituted -NH2, the larger is the BDE, which similarly confirms that the amino group has an insensitizing effect, but unfortunately the BDEs for the rupture of both Ring-NdN and Ring-NH2 decrease with the introduction of -NH2. Furthermore, BDE of Ring-NdN is the least in these three series (Ring-NO2, Ring-NdN, and Ring-NH2), all below 182 kJ mol-1, which excludes the possibility of the RingNO2 bond being a trigger bond and also suggests that the formation of hydrogen bond results in rupture of the RingNdN easily. Hence, it could not simply conclude that introduction of amino groups is an effective approach to improve thermal stability of all explosives. It is true only under the condition that introduction of other groups does not change the initial homolysis bond. As for the -CN and -NC derivatives, the variational trend of BDE for Ring-NO2 and Ring-NdN versus the number of substituents is the same as that of NO2 derivatives, whereas for -ONO2 derivatives the O-NO2 bond pyrolyzes at first, which is different from other compounds. As for the -N3 derivatives, the Ring-NO2 bond may be the initiation bond except for n = 4, where Ring-NdN ruptures first. While the BDE values of Ring-NO2, Ring-NdN, and Ring-NF2 are close for the derivatives with one or two -NF2 substitutents, these three bonds probably rupture simultaneously. When more H atoms in benzene ring were substituted by -NF2 groups, the Ring-NO2 bond may be the trigger bond. It should be pointed out that BDEs of the trigger bonds in all these HNAB derivatives are lower than that of TATB (276.93 kJ mol-1), which implies the sensitivities of these compounds are high as compared to TATB. At the same time, BDEs of trigger bonds for the title compounds except -ONO2 derivatives are

relatively larger than those of RDX and HMX, which means these compounds suffice the stability request of explosives.

4. CONCLUSIONS On the basis of the theoretical studies of the structures and the performance for the HNAB derivatives, the following conclusions are drawn: (1) Different substituent groups exert diverse influence on detonation energy (Ed), and the effect of substituent on Ed is different from that on HOF. The order of the contribution of various substituent groups to Ed is -N3 > -NF2 > -NO2 > -ONO2 > -NC > -CN > -NH2, while that to HOF is -N3 > -NC > -CN > -NO2 > -NF2 > -NH2 > -ONO2. The good linear relationships between Ed and HOF and the number of substituents n indicate good group additivity of Ed and HOF for HNAB derivatives (2) Most of the substituents improve F, D, and P values except -CN and -NC; the order of the contribution of the substituent groups to D, P, and F is -NF2 > -ONO2 > -NO2 > -N3 > -NH2. The variation trends of D, P, and F with n are nearly the same for each substituent. F, D, and P of all title compounds are more than 1.80 g cm-3, 7.5 km s-1, and 26 GPa, respectively. Almost all HNAB derivatives surpass TATB on D and P; some derivatives of -NO2 (I-4, I-5), -ONO2 (V-2, V-3, V-4, V-5), -N3 (VI-5), and -NF2 (VII-2, VII-3, VII-4, VII-5) are superior to RDX, and I-5, V-4, V-5, VII-4, and VII-5 excel over HMX, which indicates that these compounds are potential HEDCs. (3) The HOMO and LUMO energy levels decrease when NO2, -CN, -NC, -ONO2, or -NF2 group is attached to the ring. On the contrary, the introduction of -NH2 group will make EHOMO and ELUMO increase gradually; however, the energy gaps (ΔE) are little affected. This indicates that the substituents interact tantamountly with 1761


The Journal of Physical Chemistry A the HOMO and LUMO orbitals. All the title HNAB derivatives are more sensitive than TATB. -NH2 decreases the sensitivity and -N3 has little effect on it, while other substitutents increase it. QNO2 values of the derivatives increase linearly with the increase in the number of -NF2, -NO2, -ONO2, -NC, and -CN, while -N3 group exerts little effect on QNO2, and only NH2 can promote the nitro group to attract more electrons linearly. (4) BDEs of the trigger bonds in all these HNAB derivatives are lower than that of TATB, which implies the sensitivities of these compounds are higher. At the same time, BDEs of trigger bonds for the title compounds except ONO2 derivatives are large enough to suffice the stability request of explosives. For the -NO2, -CN, and -NC derivatives, the Ring-NO2 bond may be the trigger bond as n = 1 or 2, while the homolysis of Ring-NdN is the first step as n = 3 or 4. For the -NF2 derivatives, RingNO2, Ring-NdN, and Ring-NF2 maybe rupture simultaneously as n = 1 or 2, and the Ring-NO2 bond may be the trigger bond as n g 3. For the -NH2 derivatives, BDE of Ring-NdN is the least. For -ONO2 derivatives, the O-NO2 bond pyrolyzes at first. As for the -N3 derivatives, the Ring-NO2 bond may be the initiation bond except for n = 4, where Ring-NdN ruptures first.

’ ASSOCIATED CONTENT

bS

Supporting Information. Calculated total energies (E0), zero-point energies (ZPE), thermal corrections (HT), and heats of formation (HOFs) for the title compounds, along with 10 reference compounds being enlisted in the isodesmic reactions at the B3LYP/6-31G(d) level. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We gratefully thank the National Natural Science Foundation of China (Grant No. 11076017) for the support of this work. ’ REFERENCES (1) Korkin, A. A.; Bartlett, R. J. J. Am. Chem. Soc. 1996, 118, 12244. (2) Leininger, M. L.; Sherrill, C. D.; Schaefer, H. J. Phys. Chem. 1995, 99, 2324. (3) Strout, D. L. J. Phys. Chem. A 2004, 108, 10911. (4) Fried, L. E.; Manaa, M. R.; Pagoria, P. F.; Simpson, R. L. Annu. Rev. Mater. Res. 2001, 31, 291. (5) Sikder, A. K.; Sikder, N. J. Hazard. Mater. 2004, 112, 1. (6) Xiao, H. M.; Xu, X. J.; Qiu, L. The Design of High Energy Density Materials; Science Press: Beijing, 2008. (7) Xiao, H. M. The Molecular Orbital Theory of Nitro Compounds; National Defence Industry Press: Beijing, 1993. (8) Pagoria, P. F.; Lee, G. S.; Mitchell, A. R.; Schmidt, R. D. Thermochim. Acta 2002, 384, 187. (9) Boddu, V. M.; Viswanath, D. S.; Ghosh, T. K.; Damavarapu, R. J. Hazard. Mater. 2010, 181, 1. (10) Zhang, C. Y. J. Phys. Chem. B 2007, 111, 14295. (11) Huynh, M. H. V.; Hiskey, M. A.; Hartline, E. L.; Montoya, D. P.; Gilardi, R. Angew. Chem., Int. Ed. 2004, 43, 4924.

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Substituent Effects on the Properties Related to Detonation

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