Prediction of crystalline densities of polynitro arenes for estimation of their detonation performance based on quantum chemistry

Journal of Molecular Structure: THEOCHEM 953 (2010) 163–169

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Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem

Prediction of crystalline densities of polynitro arenes for estimation of their detonation performance based on quantum chemistry Gui-xiang Wang *, Xue-dong Gong, Yan Liu, Hong-chen Du, He-ming Xiao ** Computation Institute for Molecules and Materials, Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, China

a r t i c l e

i n f o

Article history: Received 9 May 2010 Accepted 22 May 2010 Available online 27 May 2010 Keywords: Polynitro arenes Densities Quantum chemistry Correlation

a b s t r a c t Thirty nitro aromatic compounds are studied using the density functional theory B3LYP method with six basis sets (3-21G, 6-31G, 6-31G*, 6-31G**, 6-311G* and 6-31+G**) and semiempirical PM3 method. Based on the geometries optimized at various theoretical levels, the molecular volumes and densities are calculated. Compared with the experimental results, the densities estimated by the PM3 and B3LYP/321G methods are all systematically larger, and that obtained with the other five basis sets are better and quite accurate. Considering that a larger basis set demands more computer resource, B3LYP/6-31G or 6-31G* is recommended for rapid and reliable prediction of crystalline densities. The effect of various groups on the densities is discussed. Based on the theoretical densities, it is possible to estimate the detonation properties, which will be helpful to rapidly and effectively design and screen promising candidates of high energy density materials (HEDMs). Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Nowadays, with the rapid development of science, technology and new weapon systems, study of novel high energy density materials (HEDMs) has become one of the most activated regions and seems to be never ending because of their superior explosive performances over the currently used materials [1–5]. Among their performances, density has been considered as the primary physical parameter, which is closely related to the detonation performances, such as detonation velocity and pressure, explosion heat, specific volume, and so on. Moreover, detonation velocity and pressure increase proportionally with the packing density and the square of it, respectively [6,7]. Therefore, at present, improving the density has become the main approach to search HEDMs. Among the main methods previously used to predict the crystalline densities (qcry.) of the explosives, the simplest, earliest and most widely used ones are the group additivity methods of the molar refraction [7] and the molar volume [8–10], where the molar volume is obtained by summing up the volume of appropriate atoms or functional groups. These are truly the rapid methods to give the effective volume and density for a molecule. However, these methods have the drawback that it cannot readily account for the molecular conformation, isomerization and crystal packing

* Corresponding author. Fax: +86 25 84303919. ** Corresponding author. Fax: +86 25 84303919. E-mail addresses: [email protected] (G.-x. Wang), [email protected] (H.-m. Xiao). 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2010.05.023

efficiency. So, they are not efficient to predict the density of HEDMs. Meanwhile, many scientists [11–15] have been attempting to use the potential function method and the crystal chemistry method based on the dense packing theory, which are more accurate to predict crystalline densities. However, although these approaches effectively account for the influence of the molecular spatial arrangement, they require extensive computational works and takes relatively longer time and higher cost, which illustrates that it is difficult to be widely used. Therefore, a novel simple approach, which can be used to rapidly and reliably assess the crystalline densities, is urgently expected to come into being. In the recent years, our group has proposed a new method to calculate the theoretical densities (qcal.), i.e., qcal. (qcal. = M/V) is obtained from the molecular volume (V) divided by the molecular weight (M) based on the quantum chemistry. This method has been widely used to calculate the detonation properties of the organic cage compounds and heterocyclic nitramines, which plays a good role in carrying out a series of investigations on the ‘‘molecular design” of high energy density compounds (HEDCs) [16–31]. Recently, Qiu et al. [32] selected 45 energetic nitramines with experimental values of density qcry., and performed the quantum chemistry studies with different methods and basis sets. It was found that, on the whole, qcal. calculated at the B3LYP/6-31G level accords with qcry. and the corresponding correlation coefficient (R) is 0.8911. Whereas a larger basis set at the B3LYP level overestimates V and underestimates qcal.. And the densities predicted by the semiempirical MO methods are all systematically larger than the experimental ones.

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G.-x. Wang et al. / Journal of Molecular Structure: THEOCHEM 953 (2010) 163–169

NO2

NO2

NO2

NO2

NO2

NO2

1,2-DNB

NB

NO2 1,4-DNB

1,3-DNB

NO2 NO2 NO2

O2 N

O2N

NO2 HNB

PAM

NO2

NO2 NH2

NO2

NH2

H2N

NH2

H2 N

NO2

O2 N

NO2

O2N

NH2

NO2 NH2 TATB

DATB NO2

NO2 OH

OH

OH

HO

NO2

O2 N

NO2

O2N

1,3,5-TNB

NO2

NO2

O2 N

NO2

O2 N

NO2

NO2

O2 N

NO2

NO2 2,3,4,6-TetNA

TNP

2,4-DNP

TNR

NO2

NO2

NO2 CH3

CH3

CH3

CH3

H3C

O2N

NO2

O2N

NO2 CH3

2,4-DNCB

NH2

O2N

NO2

NO2

NO2

O2N

NO2 O2N TNCB

NO2

O2N

NO2

Cl

O2N

O2N

TNCr

NO2 O2N

H2N

NO2

Cl

NO2

O2N

NO2

NO2 CH3

HO

CH3 TNM

TNX

2,4,6-TNT

2,3,4-TNT

NO2

NO2 H3C

NO2

O2N

NO2

2,6-DNT

2,4-DNT

NO2

O2 N

NO2

O2 N

CH3

HNS

DAHNBP O2N

NO2

NO2

NO2

NO2

NO2

OCH3

OCH3

N N O2N

NO2

NO2

NO2

NO2

NO2 O

NO2

NO2 O2N

O2N

O2N

O2N

H N

NO2

NO2 O2N

NO2

HNDPA

HNDPO NO2

2,4,6-TNA

2,4-DNA

HNAB

NO2

O2N

O2N

NO2 S

NO2 O2N

NO2

HNDPS Fig. 1. Illustration of the molecular structures of the polynitro arenas.

But there also exist some questions. For example, is the abovementioned conclusion drawn by Qiu applicable for the other kinds

of explosives? For the various kinds of explosives, do the volumes and densities calculated by the different methods and basis sets

Table 1 The calculated densities and the molecular volumes based on the different methods and basis sets and the experimental crystalline densities.a No.

Chemical name

Group I 1 Nitrobenzene

Code design

qexp.b

NB

1.34

1,2-Dinitrobenzene

1,2-DNB

1.59

3

1,3-Dinitrobenzene

1,3- DNB

1.57

4

1,4-Dinitrobenzene

1,4- DNB

1.63

5

1,3,5-Trinitrobenzene

1,3,5-TNB

1.76

6

Hexanitrobenzene

HNB

2.01

7

1-Amino-2,4,6- trinitrobenzene

PAM

1.76

8

1,3-Diamino-2,4,6- trinitrobenzene

DATB

1.83

9

1,3,5-Triamino-2,4,6- trinitrobenzene

TATB

1.93

10

2,3,4,6-Tetranitroaniline

2,3,4,6-TetNA

1.87

11

2, 4-Dinitrophenol

2, 4-DNP

1.68

12

2,4,6-Trinitrophenol

TNP

1.77

13

2,4,6-Trinitroresorcinol

TNR

1.83

14

2, 4-Dinitrotoluene

2,4-DNT

1.52

15

2, 6-Dinitrotoluene

2,6-DNT

1.54

16

2,3,4-Trinitrotoluene

2,3,4-TNT

1.62

17

2,4,6-Trinitrotoluene

2,4,6-TNT

1.65

18

1,3-Dimethyl-2,4,6- trinitrobenzene

TNX

1.64

19

1,3,5-Trimethyl-2,4,6- trinitrobenzene

TNM

1.48

20

1-Methyl-3-hydroxy-2,4,6- trinitrobenzene

TNCr

1.69

21

1-Chloro-2,4- dinitrobenzene

DNCB

1.70

22

1-Chloro-2,4,6- trinitrobenzene

TNCB

1.80

23

3,30 -Diamino-2,20 ,4,40 ,6,60 - hexanitrobiphenyl

DAHNBP

1.79

24

2,20 ,4,40 ,6,60 - Hexanitrostilbene

HNS

1.74

HNAB

1.79

25

0

0

0

2,2 ,4,4 ,6,6 - Hexanitroazobenzene

Vd

PM3

3-21G

6-31G

6-31G*

6-31G**

6-311G*

6-31+G**

1.53 (0.19) 1.79 (0.20) 1.84 (0.27) 1.78 (0.15) 2.02 (0.26) 2.43 (0.42) 1.98 (0.22) 2.03 (0.20) 2.02 (0.09) 2.20 (0.33) 1.90 (0.22) 2.07 (0.30) 2.22 (0.39) 1.65 (0.13) 1.72 (0.18) 1.92 (0.30) 1.89 (0.24) 1.80 (0.16) 1.75 (0.27) 1.97 (0.28) 1.99 (0.29) 2.16 (0.36) 2.11 (0.32) 2.05 (0.31) 2.09 (0.30)

1.48 (0.14) 1.72 (0.13) 1.71 (0.14) 1.76 (0.13) 1.90 (0.14) 2.20 (0.19) 1.90 (0.14) 1.91 (0.08) 1.97 (0.04) 2.03 (0.16) 1.82 (0.14) 1.92 (0.15) 2.06 (0.23) 1.65 (0.13) 1.65 (0.11) 1.81 (0.19) 1.81 (0.16) 1.78 (0.14) 1.70 (0.22) 1.88 (0.19) 1.77 (0.07) 1.98 (0.18) 2.06 (0.27) 1.94 (0.20) 2.03 (0.24)

1.43 (0.09) 1.63 (0.04) 1.59 (0.02) 1.59 (0.04) 1.72 (0.04) 1.99 (0.02) 1.81 (0.05) 1.82 (0.01) 1.82 (0.11) 1.87 (0.00) 1.67 (0.01) 1.88 (0.11) 1.87 (0.04) 1.55 (0.03) 1.58 (0.04) 1.71 (0.09) 1.70 (0.05) 1.68 (0.04) 1.59 (0.11) 1.75 (0.06) 1.74 (0.04) 1.83 (0.03) 1.86 (0.07) 1.77 (0.03) 1.84 (0.05)

1.44 (0.10) 1.61 (0.02) 1.64 (0.07) 1.65 (0.02) 1.78 (0.02) 2.00 (0.01) 1.78 (0.02) 1.80 (0.03) 1.82 (0.11) 1.89 (0.02) 1.73 (0.05) 1.84 (0.07) 1.91 (0.08) 1.56 (0.04) 1.59 (0.05) 1.70 (0.08) 1.72 (0.07) 1.69 (0.05) 1.60 (0.12) 1.77 (0.08) 1.72 (0.02) 1.85 (0.05) 1.89 (0.10) 1.82 (0.08) 1.88 (0.09)

1.41 (0.07) 1.62 (0.03) 1.61 (0.04) 1.66 (0.03) 1.78 (0.02) 2.02 (0.01) 1.82 (0.06) 1.82 (0.01) 1.81 (0.12) 1.92 (0.05) 1.73 (0.05) 1.84 (0.07) 1.89 (0.06) 1.57 (0.05) 1.56 (0.02) 1.69 (0.07) 1.70 (0.05) 1.66 (0.02) 1.60 (0.12) 1.76 (0.07) 1.71 (0.01) 1.88 (0.08) 1.89 (0.10) 1.82 (0.08) 1.85 (0.06)

1.40 (0.06) 1.59 (0.00) 1.63 (0.06) 1.60 (0.03) 1.72 (0.04) 1.97 (0.04) 1.75 (0.01) 1.76 (0.07) 1.79 (0.14) 1.84 (0.03) 1.68 (0.00) 1.79 (0.02) 1.85 (0.02) 1.52 (0.00) 1.50 (0.04) 1.65 (0.03) 1.66 (0.01) 1.63 (0.01) 1.55 (0.07) 1.77 (0.08) 1.74 (0.04) 1.78 (0.02) 1.89 (0.10) 1.76 (0.02) 1.84 (0.05)

1.39 (0.05) 1.58 (0.01) 1.61 (0.04) 1.57 (0.06) 1.69 (0.07) 1.93 (0.08) 1.72 (0.04) 1.77 (0.06) 1.77 (0.16) 1.81 (0.06) 1.65 (0.03) 1.76 (0.01) 1.85 (0.02) 1.53 (0.01) 1.58 (0.04) 1.66 (0.04) 1.66 (0.01) 1.59 (0.05) 1.54 (0.06) 1.75 (0.06) 1.72 (0.02) 1.80 (0.00) 1.85 (0.06) 1.74 (0.00) 1.81 (0.02)

PM3

3-21G

6-31G

6-31G*

6-31G**

6-311G*

6-31+G**

80.57

83.33

85.98

85.71

87.59

88.22

88.47

93.95

97.98

103.32

104.29

103.71

105.49

106.23

91.55

98.17

105.74

102.75

104.36

102.92

104.18

94.18

95.36

105.62

101.86

101.40

104.92

107.29

105.75

112.30

124.17

119.40

120.06

123.98

126.17

143.36

158.09

175.34

174.16

172.37

176.75

180.46

115.35

119.75

126.33

128.22

125.44

130.05

132.84

120.00

127.30

133.45

135.37

133.77

137.93

137.49

127.59

130.71

142.04

141.53

142.27

144.53

145.92

123.98

134.74

145.96

144.18

142.58

148.70

150.56

96.94

101.09

110.18

106.60

106.17

109.56

111.25

110.84

119.51

122.10

124.69

124.85

127.95

130.17

110.63

119.21

130.80

128.00

129.94

132.29

132.38

110.11

110.29

117.32

117.07

115.99

119.47

119.20

106.17

110.66

115.63

114.80

116.76

121.14

115.40

118.15

125.52

132.69

133.83

134.26

137.29

137.19

120.10

125.15

133.77

132.42

133.33

137.14

136.99

133.61

135.42

143.71

142.38

145.70

147.86

151.20

145.80

150.02

160.54

159.77

159.93

164.19

165.95

123.11

129.22

138.61

137.68

137.90

137.56

138.70

101.82

114.75

116.20

117.51

118.52

116.53

117.48

114.70

124.79

135.51

133.53

131.94

138.90

137.29

215.16

220.83

243.65

240.09

239.72

240.26

246.13

219.76

232.45

254.25

247.57

247.35

255.75

258.15

215.95

223.20

245.82

241.81

243.79

246.05

250.11

G.-x. Wang et al. / Journal of Molecular Structure: THEOCHEM 953 (2010) 163–169

2

qcal.c

(continued on next page) 165

245.70

251.23

have some regularity? Could the structure-performance (density especially) relations be searched after having been further studied? And so on. The polynitro arenes is an important category of energetic materials widely used as explosives, and they have numerous important applications in both civilian and military fields for a long time. Therefore, in this paper, we have selected this kind of compounds (see Fig. 1 for the structural diagrams of the molecules) as the research object. The DFT-B3LYP and semiempirical PM3 methods are chosen to perform the calculations. Results from the different methods have been compared, and the effects of basis sets on the molecular volumes and densities have been discussed. The conclusions may provide useful information for the molecular design and further studies of novel HEDMs.

234.38

241.03

237.74

242.00

242.99

243.12 238.84

232.90 233.36

234.97

241.00 237.84

139.22 138.33

234.08

141.63

123.09 124.34

121.23

6-31G* 6-31G

137.37

126.09 125.58

6-311G* 6-31G**

145.62

G.-x. Wang et al. / Journal of Molecular Structure: THEOCHEM 953 (2010) 163–169

6-31+G**

166

117.27

130.26

218.37

220.56

227.49

114.56

125.36

202.01

205.77

211.56

1.57 (0.23) 1.67 (0.06) 1.83 (0.13) 1.81 (0.16) 1.82 (0.17) (0.15) (0.16) (0.02) (0.08) 1.58 (0.24) 1.72 (0.11) 1.85 (0.15) 1.84 (0.19) 1.86 (0.21) (0.18) (0.19) (0.03) (0.09)

c

d

Units: qexp./(g cm3), qcal./(g cm3), V/(cm3 mol1). The experimental values are taken from Refs. [43–48]. The bracketed values are error. Volume calculations are based on the different methods and basis sets optimized geometries. a

Average rms Total average Total rms

1.65 HNDPS 2,20 ,4,40 ,6,60 - Hexanitrodiphenyl sulfide 30

1.65 HNDPA 2,20 ,4,40 ,6,60 - Hexanitrodiphenylamine 29

1.70 HNDPO 2,2 ,4,4 ,6,6 - Hexanitrodiphenylether 28

1.61 2, 4,6-TNA

0 0 0

2, 4,6-Trinitroanisole 27

3. Results and discussion

b

1.61 (0.27) 1.75 (0.14) 1.89 (0.19) 1.89 (0.24) 1.89 (0.24) (0.22) (0.22) (0.07) (0.11) 1.59 (0.25) 1.76 (0.15) 1.89 (0.19) 1.85 (0.20) 1.89 (0.24) (0.21) (0.21) (0.06) (0.10) 1.69 (0.35) 1.87 (0.26) 2.02 (0.32) 1. 99 (0.34) 2.01 (0.36) (0.33) (0.33) (0.19) (0.20) 1.73 (0.39) 1.94 (0.33) 2.18 (0.48) 2.13 (0.48) 2.16 (0.51) (0.44) (0.44) (0.29) (0.30) 1.34 2,4-DNA Group II 26 2,4-Dinitroanisole

Average rms

The nitro aromatic compounds generated from Chem3D Ultra 8.0 software are fully optimized without any symmetry restrictions at the semiempirical PM3 [33] method and the DFT-B3LYP level [34,35] with 3-21G, 6-31G, 6-31G, 6-31G, 6-311G and 631+G basis sets [36–40]. To characterize the nature of the stationary points, harmonic vibrational analyses are performed subsequently on each optimized structure, which demonstrates that all the optimized structures are truly local energy minima on the potential energy surface (PES) without any imaginary frequency and are the lowest energy conformers. Then, the density of each compound is obtained from the molecular volume divided by the molecular weight, while the molecular volume (V) of each molecule was yielded from the statistical average of 100 single-point molar volume calculations on each optimized structure. The molar volume is defined as the space inside 0.001e/bohr3 electron density surface and estimated by Monte-Carlo method with the Gaussian03 program package. [41].

1.63 (0.29) 1.77 (0.16) 1.88 (0.18) 1.87 (0.22) 1.88 (0.23) (0.22) (0.22) (0.07) (0.11)

PM3 (0.01) (0.05)

6-31+G** 6-311G*

(0.01) (0.05) (0.04) (0.06) (0.05) (0.07) (0.03) (0.06) (0.16) (0.17)

6-31G** 6-31G* 6-31G 3-21G PM3

qcal.c Chemical name No.

Table 1 (continued)

Code design

qexp.b

(0.26) (0.27)

Vd

3-21G

2. Computational method

3.1. Selecting the appropriate methods and basis sets Table 1 collects the molecular volumes (V) and the theoretical densities (qcal.) at the different methods and the different basis sets. For ease of comparison, the corresponding experimental densities (qexp), the errors, and root mean square derivations (rms) are also presented in Table 1. As can be seen from Table 1, it is evident that, V obtained by the PM3 method is smaller than that of the DFT-B3LYP methods. And, for the B3LYP methods, the larger the basis set (from 3-21G to 631+G) is, the larger the molecular volume is, i.e., a larger basis set makes the occupied space of the electrons larger. In addition, we also found that the calculated V increases with the increasing number of –NO2, –NH2, –OH, –CH3 groups, etc., obviously showing good group additivity. To show the variation of V with the different methods and basis sets more clearly, Fig. 2 are drawn and presented, which shows the correlations among the structures and V by the seven kinds of methods. It is found from Table 1 that, for all the nitroaromatic compounds, the densities calculated (qcal.) by the semiempirical PM3 method and the B3LYP/3-21G method are all overestimated, i.e., the theoretical densities are larger than the experimental data. This result agrees with the previous study of Klapotke and Ang [42]. They estimated the maximum crystalline densities for a number of nitramines and some other energetic materials by utilizing the semiempirical PM3 method, and suggested a relationship between the maximum crystalline densities and predicted values for the energetic materials (qmax = 0.86/qPM3). However, qcal. at the

167

V/(cm3.mol-1)

G.-x. Wang et al. / Journal of Molecular Structure: THEOCHEM 953 (2010) 163–169 260 250 240 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90 80

PM3 3-21G 6-31G 6-31G* 6-31G** 6-311G* 6-31+G**

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

Fig. 2. Correlations among the volumes calculated at various levels of theory.

0.30 0.27

6-31G 6-31G* 6-31G** 6-311G* 6-31+G**

0.24 0.21 0.18 0.15

error

0.12 0.09 0.06 0.03 0.00

is within ±0.1 except for the five compounds (26–30, group II) containing –O–, –NH– and –S– groups, i.e., 2,4-DNA (2,4-dinitroanisole), 2,4,6-TNA (2,4,6-trinitroanisole), HNDPO (2,20 ,4,40 ,6,60 -Hexanitrodiphenylether), HNDPA (2,20 ,4,40 ,6,60 -Hexanitrodiphenylamine), HNDPS (2,20 ,4,40 ,6,60 -Hexanitrodiphenyl sulfide). The average errors and the rms derivations of the other 25 compounds without these five compounds, i.e., 0.03, 0.05, 0.04, 0.01, 0.01, and, 0.06, 0.07, 0.06, 0.05, 0.05, respectively, are obviously improved. For the compounds from 26 to 30, although the errors are more, there are relatively good correlations between them. As Table 2 shows their relationships, the corresponding correlation coefficients (R) are 0.9627, 0.9359, 0.9572, 0.9399 and 0.9073. The correlations between the predicted and experimental densities are listed in Table 2. Taking B3LYP/6-31G as an example, for the group I (1–25), there are not only small errors but also good correlations between the experimental and theoretical densities, the correlation equation is Y = 0.3397 + 0.8273X, R = 0.9482, SD = 0.0423. However, as is known to all, a larger basis expends more computer resources. We do not think it is necessary according to our results. Therefore, we suggest that using DFT-B3LYP/6-31G or 631G is a good choice to rapidly while accurately predict the crystalline densities of the nitro aromatic compounds. Previous studies have shown that the densities calculated at the B3LYP/6-31G level are in accord with the experimental densities for, such as the nitro, nitramine and nitrate derivatives of the organic cage compounds [17,18,22]. Taking B3LYP/6-31G as an example, Fig. 4 presents a comparison of the experimental and predicted densities for all titled compounds. It is obvious that there are good linear correlations between the calculated densities and experimental data if all titled compounds are separated into two groups.

-0.03 -0.06

3.2. The effect of the molecular structures or the substituted groups on the densities

-0.09 -0.12 -0.15 -0.18

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930

Fig. 3. Error analysis of the calculated densities at the B3LYP/6-31G, 6-31G, 631G, 6-311G and 6-31+G levels.

B3LYP level with 6-31G, 6-31G, 6-31G, 6-311G and 6-31+G basis sets are good correlated with qexp, their average errors are 0.06, 0.07, 0.07, 0.03, 0.02, respectively, and their rms derivations are 0.10, 0.11, 0.11, 0.09, 0.08, respectively, which indicates that the five basis sets all can reliably predict the crystalline densities. Fig. 3 presents error analysis of the calculated densities at the B3LYP/6-31G, 6-31G, 6-31G, 6-311G and 6-31+G levels. As can be seen from Fig. 3, it is evident that the range of the other errors

It can be seen from Table 1 that, on the whole, qcal. increase with the increase of –NO2, –OH and –Cl groups in the molecule. For example, at the DFT-B3LYP/6-31G level, the theoretical densities of NB(1), 1,2-DNB(2), 1,3,5-TNB(5), HNB(6) are 1.44, 1.61, 1.78, 2.00 g cm3, respectively, and the value of TNCB(22) is 1.85 g cm3. For the isomeric compounds, the difference between their values of qcal. is small, e.g., the theoretical densities of 2,4-DNT(14) and 2,6DNT(15) are 1.56 and 1.59 g cm3, respectively. Contrasting the compounds 7, 8 and 9, it is found that the variation of qcal. does not correlate with the number of –NH2 group due to the presence of intermolecular and intramolecular hydrogen bonds. Reviewing the compounds 17–19, when there are the same number of –NO2 groups (n = 3), their qcal. decrease with the increase of –CH3 and CH3O– groups.

Table 2 Correlation between the predicted and experimental densities.a Methods

All (1–30)

Group I (1–25)

Group II (26–30)

PM3

Y = 0.1188 + 1.0991X R = 0.8483, SD = 0.1060 Y = 0.3642 + 0.8933X R = 0.8607, SD = 0.0816 Y = 0.5227 + 0.7248X R = 0.8415, SD = 0.0719 Y = 0.5429 + 0.7216X R = 0.8478, SD = 0.0697 Y = 0.4835 + 0.7556X R = 0.8525, SD = 0.0716 Y = 0.4961 + 0.7256X R = 0.8346, SD = 0.0740 Y = 0.5529 + 0.6823X R = 0.8468, SD = 0.0662

Y = 0.1575 + 1.2426X R = 0.9306, SD = 0.0745 Y = 0.1169 + 1.0232X R = 0.9445, SD = 0.0543 Y = 0.3179 + 0.8310X R = 0.9441, SD = 0.9443 Y = 0.3397 + 0.8273X R = 0.9482, SD = 0.0423 Y = 0.2375 + 0.8860X R = 0.9530, SD = 0.0430 Y = 0.2759 + 0.8409X R = 0.9373, SD = 0.0477 Y = 0.3640 + 0.7814X R = 0.9371, SD = 0.0444

Y = 0.0260 + 1.2591X R = 0.9400, SD = 0.0756 Y = 0.4247 + 0.9380X R = 0.9609, SD = 0.0447 Y = 0.4420 + 0.8516X R = 0.9627, SD = 0.0396 Y = 0.5062 + 0.8175X R = 0.9359, SD = 0.0509 Y = 0.6512 + 0.7263X R = 0.9572, SD = 0.0363 Y = 0.5146 + 0.7895X R = 0.9399, SD = 0.0475 Y = 0.5794 + 0.7299X R = 0.9073, SD = 0.0560

B3LYP/3-21G B3LYP/6-31G B3LYP/6-31G* B3LYP/6-31G** B3LYP/6-311G* B3LYP/6-31+G** a

R and SD denote the correlation coefficient and standard deviation, respectively.

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2.0

ρ cal.

1.9

2.0

1-30 (a) Y=0.5227+ 0.7248X R= 0.8415, SD=0.0719

1.9

1.8

1.8

1.7

1.7

1.6

1.6

1.5

1.5

1.4

1.4

1.90

1-25 (b) Y=0.3179+0.8310X R=0.9441,SD=0.9443

1.85

26-30(c) Y=0.4420+0.8516X R=0.9627, SD=0.0396

1.80 1.75 1.70 1.65 1.60

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1 1.3

1.4

1.5

1.6

1.7

ρexp.

1.8

1.9

2.0

1.55 2.1 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75

Fig. 4. Comparison of the experimental and predicted densities at the B3LYP/6-31G level for: (a) the entire set of molecules; (b) group I; (c) group II.

For the polyarenes, the conclusion is that, the more the number of benzene ring is, the larger the density is, in theory, which is contrasted to the experimental results. Therefore, it is necessary to perform further study in future. In conclusion, the number of –NO2 group has the most influence on qcal., and the influence of other groups is also not neglectable, so in the molecular design of energetic materials, we are going to adjust regularly in terms of requirement. With the predicted densities and heats of formation, it is possible to further estimate the detonation velocity, detonation pressure and other detonation characteristics using the Kamlet–Jacbos equations [6,7], which helps to effectively screen target structures for further synthesis and study.

4. Conclusions From the above studies at the DFT-B3LYP and semiempirical PM3 levels, we can draw the following conclusions:

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

(1) Compared with experimental densities, the densities calculated by the semiempirical PM3 method and the B3LYP/321G method are all systematically larger. And the B3LYP method with 6-31G, 6-31G, 6-31G, 6-311G and 631+G basis sets are accurate enough for predicting the solid-state densities of the polynitro arenas. Although the densities of the compounds containing –O–, –NH– and –S– groups are overestimated to some extent, there are quite good correlations between the experimental and calculated densities. (2) DFT-B3LYP/6-31G or 6-31G are good enough to rapidly and accurately predict the crystalline densities of the nitro aromatic compounds. (3) Densities of the title compounds increase with the increase of the number of –NO2, –OH and –Cl groups, while decrease with the increase of the –CH3 and CH3O– groups. The variation of density does not correlate with the number of –NH2 group due to the presence of intermolecular and intramolecular hydrogen bonds.

Acknowledgements The authors are very grateful for the financial support from the Postdoctoral Foundation of China (No. 20090461122), Jiangsu Planned Projects for Postdoctoral Research Funds (No. 0901009B), National Natural Science Foundation of China (Nos. 10576016 and 10576030), and National ‘‘973” Project.

[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41]

P.S. Gilbert, A. Jack, J. Energetic Mater. 45 (1986) 5. P.J. Agrawal, Prog. Energy Combust. Sci. 24 (1998) 1. M.X. Zhang, P.E. Eaton, R. Gilardi, Angew. Chem. Int. Ed. 39 (2000) 401. A.T. Nielsen, P. Nissan, A Polynitropolyaza Caged Explosives, Naval Weapon Center Technical Publication, 1986. Z.S. Wang, Y.X. Ou, W.Z. Ren, Science and Technology of Explosives and Propellants, Beijing Institute of Press, People’s Republic of China, 2002. M.J. Kamlet, S.J. Jacobs, J. Chem. Phys. 48 (1968) 23. X.H. Zhang, Z.H. Yun, Explosive Chemistry, National Defence Industry Press, Beijing, People’s Republic of China, 1989. C.M. Tarver, J. Chem. Eng. Data 24 (1979) 136. J.R. Stine, Prediction of Crystal Densities of Organic Explosives by Group Additivity, Los Alamos National Laboratory’s Report, New Mexico, 1981. H.L. Ammon, Struct. Chem. 12 (2001) 205. H.R. Karfunkel, R.J. Gdanitz, J. Comput. Chem. 13 (1992) 1171. J.R. Holden, Z. Du, H.L. Ammon, J. Comput. Chem. 14 (1993) 422. T.S. Pivina, V.V. Shcherbukhin, M.S. Molchanova, N.S. Zefirov, Propel. Explos. Pyrotech. 20 (1995) 144. A.V. Dzyabchenko, T.S. Pivina, E.A. Arnautova, J. Mol. Struct. 378 (1996) 67. B.M. Rice, D.C. Sorescu, J. Phys. Chem. B 108 (2004) 17730. J. Zhang, H.M. Xiao, J. Chem. Phys. 116 (2002) 10674. X.J. Xu, H.M. Xiao, X.D. Gong, X.H. Ju, Z.X. Chen, J. Phys. Chem. A 109 (2005) 11268. X.J. Xu, H.M. Xiao, X.H. Ju, X.D. Gong, W.H. Zhu, J. Phys. Chem. A 110 (2006) 5929. L. Qiu, H.M. Xiao, X.D. Gong, X.H. Ju, W.H. Zhu, J. Phys. Chem. A 110 (2006) 3797. L. Qiu, H.M. Xiao, X.H. Ju, X.D. Gong, Int. J. Quantum Chem. 105 (2005) 48. H.M. Xiao, J. Zhang, Sci. China Ser. B 45 (2002) 21. X.J. Xu, H.M. Xiao, X.F. Ma, X.H. Ju, Int. J. Quantum Chem. 106 (2006) 1561. X.J. Xu, W.H. Zhu, X.D. Gong, H.M. Xiao, Sci. China Ser. B 51 (2008) 427. L. Qiu, X.D. Gong, X.H. Ju, H.M. Xiao, Sci. China Ser. B 51 (2008) 1231. H.M. Xiao, X.J. Xu, L. Qiu, Theoretical Design of High Energy Density Materials, Science Press, Beijing, 2008. G.X. Wang, C.H. Shi, X.D. Gong, H.M. Xiao, J. Phys. Chem. A 113 (2009) 1318. G.X. Wang, X.D. Gong, H.M. Xiao, Int. J. Quantum Chem. 109 (2009) 1522. L.M. Qiu, X.D. Gong, G.X. Wang, J. Zheng, H.M. Xiao, J. Phys. Chem. A 113 (2009) 2607. L.M. Qiu, X.D. Gong, J. Zheng, H.M. Xiao, J. Hazard. Mater. 166 (2009) 931. G.X. Wang, X.D. Gong, Y. Liu, H.C. Du, X.J. Xu, H.M. Xiao, J. Hazard. Mater. 177 (2010) 703. G.X. Wang, X.D. Gong, Y. Liu, H.M. Xiao, Int. J. Quantum Chem. 110 (2010) 1691. L. Qiu, H.M. Xiao, X.D. Gong, X.H. Ju, W. Zhu, J. Hazard. Mater. 141 (2007) 280. J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. A.D. Becke, J. Chem. Phys. 97 (1992) 9173. J.S. Binkley, J.A. Pople, W.J. Hehre, J. Am. Chem. Soc. 102 (1980) 939. V.A. Rassolov, M.A. Ratner, J.A. Pople, P.C. Redfern, L.A. Curtiss, J. Comput. Chem. 22 (2001) 976. P.C. Hariharan, J.A. Pople, Theor. Chim. Acta 28 (1973) 213. G.A. Petersson, M.A. Al-Laham, J. Chem. Phys. 94 (1991) 6081. A.D. McLean, G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery, J.T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A.

G.-x. Wang et al. / Journal of Molecular Structure: THEOCHEM 953 (2010) 163–169 Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. AlLaham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Gaussian 03, Gaussian, Inc., Pittsburgh, PA, 2003. [42] T.M. Klapotke, H.G. Ang, Propel. Explos. Pyrotech. 26 (2001) 221. [43] X.F. Zhang, Performance Manual of Raw and Processed Materials of Overseas Explosives, Weapon Industry Press, Beijing, People’s Republic of China, 1991.

169

[44] Y.P. Zhong, Y.D. Hu, H.Z. Jiang, Performance Manual of Overseas Explosives, Weapon Industry Press, Beijing, People’s Republic of China, 1991. [45] H.S. Dong, F.F. Zhou, High Energy Explosives and their Corresponding Performance, Science Press, Beijing, People’s Republic of China, 1989. [46] Available from: (CAS No: 51-28-5). [47] Z.H. Chen, X.W. Zhu, Explosives Manual, China Coal Industry Publishing House, 1979. [48] C.M. Tarver, J. Chem. Eng. Data 24 (1979) 136.