ARTICLE pubs.acs.org/JPCA
Theoretical Studies on the Heats of Formation, Detonation Properties, and Pyrolysis Mechanisms of Energetic Cyclic Nitramines Fang Wang, Guixiang Wang, Hongchen Du, Jianying Zhang, and Xuedong Gong* Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China
bS Supporting Information ABSTRACT: Density functional theory calculations were performed to find comprehensive relationships between the structures and performance of a series of highly energetic cyclic nitramines. The isodesmic reaction method was employed to estimate the heat of formation. The detonation properties were evaluated by using the KamletJacobs equations based on the theoretical densities and HOFs. Results indicate the NNO2 group and aza N atom are effective substituents for enhancing the detonation performance. All cyclic nitramines except C11 and C21 exhibit better detonation performance than HMX. The decomposition mechanism and thermal stability of these cyclic nitramines were analyzed via the bond dissociation energies. For most of these nitramines, the homolysis of NNO2 is the initial step in the thermolysis, and the species with the bridged NN bond are more sensitive than others. Considering the detonation performance and thermal stability, twelve derivatives may be the promising candidates of high energy density materials (HEDMs). The results of this study may provide basic information for the further study of this kind of compounds and molecular design of novel HEDMs.
1. INTRODUCTION With the development of national defense and economy, high energy density materials (HEDMs) have attracted increasing attention because of their superior energetic output over the currently used materials. Cyclic nitramines constitute a class of organic energetic compounds and have played important roles in the civil and military fields for a long time;18 for example, TNAZ (1,3,3-tirnitroazetidine), RDX (hexahydro-1,3,5-trinitro1,3,5-trizine), and HMX (1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane) are well-known explosives. Nowadays, polycyclic and caged nitramines compounds such as TNAD (trans-1,4,5,8-tetranitro1,4,5,8-tetraazadecalin)9 and CL-20 (2,4,6,8,10,12-hexanitro-2,4, 6,8,10,12-hexaazaisowurtzitane)10 have raised significant interest because they have a better combination of heat of formation, density, and detonation performance than HMX. cis-2,4,6,8-Tetranitro-1H,5H-2,4,6,8-tetraazabicyclo[3.3.0]octane, commonly called “bicycle-HMX” because of its structural analogy with HMX, is another important polycyclic nitramine and has been used in solid propellants.11,12 Bicycle-HMX, with a larger ring strain than HMX, exhibits explosive performance superior to HMX. To meet the continuing demand for improved energetic materials, it is of the great importance to design and develop new nitramines. It has been found that increasing the number of the nitro groups and replacing the CH group with a nitrogen atom to introduce more NN bonds into the cyclic nitramines can lead to an increase in mass density and heat of formation and hence enhance detonation performance.13,14 However, improved detonation performance may inherently raise the greater danger of the experimental study. In addition, nitramine compounds are normally toxic.15 Therefore, experimental synthesis of nitramines may be not only dangerous but also hazardous to humans and the r 2011 American Chemical Society
environment. Hence, computer simulation, an effective way in screening promising explosives without these shortcomings, has been used to design various new energetic materials including nitramines and to provide understanding of the relationships between the structures and performance.14,1622 To find new nitrogen-rich nitramines with excellent performance, in this work, a series of nitramines were designed on the basis of the structures of HMX, bicycle-HMX, and TNAD, and their heats of formation (HOFs), densities (F), and explosive performance were investigated using density functional theory (DFT) mtheod. The thermal stabilities and pyrolysis mechanisms were also evaluated from the bond dissociation energies (BDE). It is expected that our results could provide useful information for laboratory synthesis of these nitramines and for design and development of new novel HEDMs.
2. COMPUTATIONAL DETAILS Geometry optimizations of the molecular structures were performed with the Gaussian 03 package23 at the B3LYP/6311G(d,p) level. Previous studies have shown that the basis set 6-311G(d,p) is able to figure out the accurate energy, molecular structure, and vibrational frequency that are very close to their experimental results.20,2426 All optimized structures were characterized to be the local energy minimum on the potential energy surface by vibrational analysis. Thermodynamic properties were calculated using the vibrational frequencies scaled by 0.96.27 The natural bond orbital (NBO) calculations have also been carried out.28 Received: May 22, 2011 Revised: September 9, 2011 Published: October 17, 2011 13858
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Figure 1. Molecular frameworks of cyclic nitramine derivatives based on HMX (A series), bicycle-HMX (B1 series, B11B13; B2 series, B21B23; B3 series, B31B33), and TNAD (C1 series, C11C17; C2 series, C21C26; C3 series, C31C37). Series B and C are divided according to different numbers of aza atoms (0, 1, and 2) on the bridged bond of cyclic skeletons.
The DFT-B3LYP method was previously used to predict the HOFs of many organic systems via isodesmic reactions17,24,25 The isodesmic reaction progresses, in which the number of each kind of formal bond is conserved, must comply with the bond separation reaction (BSR) rules. The molecule is broken down into a set of two heavy-atom molecules containing the same component bonds. However, usual BSR rules cannot be applied to the molecules with delocalized bonds and cage skeletons because of the large calculated errors of HOF. Therefore, we design isodesmic reactions in which the numbers of all kinds of bonds are kept invariable to decrease the calculation errors. This is because the electronic environment of atoms in the reactants and products are very similar in isodesmic reactions, the errors of electronic correction energies can be counteracted, and then the errors of the calculated HOFs can be greatly reduced.29 In the designed reactions, the basic structural unit of the aza cyclic skeleton (X), i.e., 1,3,5,7-tetraazacyclooctane in HMX, 2,4,6,8-tetraazabicyclooctane in bicycle-HMX, and 1,4,5,8-tetraazadecalin in TNAD, is kept invariable. This approach has proved to be reliable.3033 The object molecules are classed into three groups (A, B, and C series), as shown in Figure 1.
The isodesmic reactions used to obtain the HOF of the cyclic nitramines at 298 K are as follows: XðNO2 Þn þ nCH4 f X H þ nCH3 NO2 ð4 e n e 8Þ
ð1Þ
For reaction 1, the heat of reaction (ΔH298) at 298 K can be calculated from the following equation:
∑
∑
ΔH298 ¼ ΔHf, P ΔHf , R ¼ ΔE0 þ ΔZPE þ ΔHT
ð2Þ
where ΔHf,P and ΔHf,R are the HOFs of the products and reactants at 298 K, respectively. ΔE0 is the change in total energy between the products and the reactants at 0 K, ΔZPE is the difference between the zero-point energy (ZPE) of the products and the reactants, and ΔHT is the thermal correction from 0 to 298 K. The experimental HOFs of the reference compounds CH4 and CH3NO2 in eq 1 are available.34 As the experimental HOFs of the aza cyclic skeleton (X) are unavailable, additional calculations were carried out for the atomization reaction CaHbOcNd f aC(g) + bH(g) + cO(g) + dN(g). Either the G2 theory35 or the complete basis set (CBS-Q) method36,37 has 13859
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Table 1. Calculated Total Energies (E0, au), Thermal Corrections (HT, kJ/mol), Zero-Point Energies (ZPE, au), and Heats of Formation (HOF, kJ/mol) for the Reference Compoundsa compd CH4 CH3NO2
E0
HT
ZPE
HOFb
HOFc
40.53374
10.03
0.04471
74.6
74.32
245.08220
14.15
0.04979
80.8
81.40
a
The scaling factor is 0.98 for ZPE and 0.96 for HT.27 b Experimental values taken from ref 34. c Calculated at the CBS-Q level.
Table 2. Calculated Total Energies (E0, au), Thermal Corrections (HT, kJ/mol), Zero-Point Energies (ZPE, au), and Heats of Formation (HOF, kJ/mol) for the Nitraminesa compd
HT
ZPE
HOF
A1
1196.87097
49.59
0.19039
263.70
A2
1417.38300
64.75
0.17824
525.91
A3
1637.89112
64.75
0.16596
761.54
A4
1637.88665
64.75
0.16565
774.70
A5
1858.38308
73.59
0.15295
1039.33
A6 B11
2078.87478 1195.66018
80.00 46.84
0.13998 0.16759
1335.66 286.73
B12
1416.16740
54.76
0.15497
532.87
B13
1636.67153
62.55
0.14243
788.85
B21
1211.63887
46.81
0.15386
493.21
B22
1432.14625
55.12
0.14120
733.66
B23
1652.65076
63.48
0.12847
982.10
B31
1227.59215
47.32
0.13908
766.88
B32 B33
1448.09983 1668.60473
55.87 64.54
0.12638 0.11350
1003.32 1247.33
C11
1274.30345
51.97
0.22706
278.19
C12
1494.83737
58.99
0.21590
454.10
C13
1715.32915
67.18
0.20254
734.31
C14
1715.37067
66.31
0.20452
624.64
C15
1715.37085
66.18
0.20465
626.63
C16
1935.86123
74.52
0.19115
911.08
C17 C21
2156.35040 1290.28913
82.91 52.56
0.17774 0.21290
1197.71 461.80
C22
1510.82466
59.72
0.20175
629.73
C23
1510.82137
59.61
0.20165
639.60
C24
1731.31850
67.72
0.18837
903.64
C25
1951.84125
75.17
0.17351
1104.78 1389.63
C26
2172.33482
83.10
0.16360
C31
1306.23909
53.57
0.19771
729.11
C32 C33
1526.77517 1747.26311
60.85 68.85
0.18643 0.17312
898.77 1185.84
C34
1747.30942
68.22
0.17517
1064.24
C35
1747.30794 1967.79560
67.96 76.43
0.17538 0.16175
1076.16 1363.64
2188.28028
85.21
0.14808
1865.92
C36 C37 a
E0
The scaling factor is 0.98 for ZPE and 0.96 for HT.27
been verified to be able to predict the HOFs accurately, whereas the G2 theory is more expensive and not yet practical to calculate the total energies of these aza cyclic skeletons due to the large ring size. Therefore, the CBS-Q method was used in this work.
Figure 2. Relations between HOFs and NNO2 numbers for series A, B, and C.
The detonation velocity (D) and pressure (P) were estimated by the empirical KamletJacobs equations38 as D ¼ 1:01ðNM 1=2 Q 1=2 Þ1=2 ð1 þ 1:30FÞ
ð3Þ
P ¼ 1:558F2 NM 1=2 Q 1=2
ð4Þ
where F is the density of explosive (g/cm3), N is the moles of gaseous detonation products per gram of explosive, M is the average molecular weight of gaseous products, and Q is the chemical energy of detonation (cal/g) defined as the difference between the HOFs of the products and reactants of the most exothermic reactions. For these cyclic nitramines, the theoretical density was obtained from the molecular weight divided by the average molecular volume of 100 single point calculations. The volume was defined as the space inside an electronic isodensity contour of 0.001 electron/bohr3 evaluated using a Monte Carlo integrator. This method has been successfully applied to various energetic molecules.39,40 The strength of bonding, which can be evaluated by bond dissociation energy (BDE), is fundamental to understanding chemical processes.41 The energy required for bond homolysis at 298 K and 1 atm, i.e., the enthalpy of reaction of AB(g) f A•(g) + B•(g), is the BDE of AB by definition.42 The terms “bond dissociation energy” (BDE) and “bond dissociation enthalpy” often appear interchangeably in the literature.43
3. RESULTS AND DISCUSSION 3.1. Heat of Formation. HOF is usually taken as the indicator of the “energy content” of an HEDM. Therefore, it is of great importance to predict HOF accurately. Table 1 lists the total energies, thermal corrections, zero-point energies, and HOFs for the reference compounds, and the calculated HOFs of the aza cyclic skeleton X are summarized in Table 1S as the Supporting Information for brevity. The HOFs of CH4 and CH3NO2 at the CBS-Q level are 74.32 and 81.40 kJ/mol, very close to the experimental values34 with the relative errors of only 0.37% and 0.74%, respectively. This is supported by the previous reports that CBS-Q theory can predict HOFs accurately.36 13860
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Table 3. Predicted Densities (G), Heats of Detonation (Q), Detonation Velocities (D), Detonation Pressures (P), and Oxygen Balances (OB) for the Nitraminesa compd F (g/cm3) Q (cal/g)
D (km/s)
P (GPa)
9.23 (9.10) 38.57 (39.00)
OBb (%) 21.62
A1
1.87 (1.90)
1629.22
A2
1.95
1836.90
10.05
46.91
4.68
A3
1.98
1978.98
10.55
52.25
24.74
A4
2.02
1987.09
10.70
54.27
24.74
A5 A6
2.09 2.14
2114.17 2232.70
11.29 11.76
61.61 67.65
40.55 53.34 16.32
B11
1.87 (1.86)
1622.46
9.19 (9.13) 38.40 (42.0)
B12
1.95
1820.99
9.98
46.28
9.41
B13
2.03
1978.31
10.69
54.36
29.02
B21
1.94
1765.99
9.82
44.70
2.71
B22
1.95
1963.88
10.34
49.75
21.11
B23
2.01
2091.75
10.86
55.69
39.28
B31 B32
1.91 2.00
1935.99 2092.82
10.12 10.83
47.13 55.30
10.81 32.75
B33
2.10
2222.81
11.54
64.39
C11
1.80 (1.80)
1541.82
49.49
8.60 (8.36) 32.83 (31.00)
44.71
C12
1.87
1704.33
9.35
39.74
19.56
C13
1.99
1864.93
10.14
48.23
3.86
C14
1.96
1801.63
9.97
46.36
3.86
C15
1.99
1802.77
10.07
47.70
3.86
C16 C17
2.04 2.07
1951.40 2074.04
10.62 11.03
53.73 58.52
20.87 34.78
C21
1.80
1656.23
8.92
35.33
32.19
C22
1.87
1784.28
9.54
41.26
6.50
C23
1.87
1790.68
9.58
41.66
6.50
C24
1.99
1942.19
10.38
50.68
13.49
C25
2.07
2035.92
10.96
57.74
29.50
C26
2.12
2149.81
11.43
63.55
42.61
C31 C32
1.81 1.91
1831.67 1941.84
9.32 10.04
39.01 46.21
19.75 4.32
C33
1.99
2089.51
10.72
54.10
23.08
C34
2.00
2019.65
10.65
53.41
23.08
C35
1.99
2026.50
10.62
53.01
23.08
C36
2.04
2153.78
11.13
59.02
38.10
C37
2.11
2359.09
11.77
67.19
RDX
1.79 (1.82)
1565.45
8.87 (8.75) 34.80 (34.00)
50.40 21.60
a
Data in parentheses are the experimental values taken from refs 5255. For the explosive CaHbOcNd: OB (%) = 1600 (c 2a b/2)/Mw, where Mw is the molecular weight. b
Table 2 summarizes the total energies, thermal corrections, zero-point energies, and HOFs of all cyclic nitramines. The HOFs of all cyclic nitramines (A, B, or C series) are larger positive relative to A1 (HMX) (HOF = 263.70 kJ/mol) and increase with the increasing number of NNO2 group as a whole. This is also why A6, B33, and C37 have the biggest HOFs in their corresponding series, and C37 possess the most energy content that is 530.26 and 618.29 kJ/mol larger than A6 and B33, respectively. The relative positions of the nitramine groups also have some effect on the HOFs; e.g., A4 has a somewhat larger HOF than A3, and the HOF of C35 is slightly higher than that of C34, which is caused by the larger static hindrance interactions of the nitro groups. For the isomers C33, C34, and C35, the HOFs
of the latter two compounds are very close, whereas that of C33 is about 109.67 kJ/mol larger. This is because C33 contains one more NN bond in the cyclic skeleton than C34 and C35. Thus, NN bonds also contribute to the heats of formation of highnitrogen compounds.44 To show the effect of the NNO2 groups or aza N atoms on the HOF more clearly, relations between HOFs and the number of NNO2 groups are plotted in Figure 2. It is found that there exists a good linear relationship between the HOFs and the numbers of nitramine group (n), e.g., for series A, HOF = 809.117 + 265.734n (R = 0.999, SD = 19.967). Introduction of one more nitramine group increases HOFs by 265.73 kJ/mol for series A, and 251.06 and 229.60 kJ/mol for series B1 and C1 on average, respectively. This shows a good group additivity of nitramine groups on HOFs. Additionally, for series B and C, the HOFs are in the order B3 (C3) series > B2 (C2) series > B1 (C1) series. This is because series B3 or C3 contains two more aza atoms on the bridged bond in cyclic skeleton, whereas series B1 or C1 do not. For instance, B11, B21, and B31 have four NNO2 groups but zero, two, and five NN bonds, respectively; B21 possesses 206.48 kJ/mol higher energy content than B11 and B31 is 263.17 kJ/mol larger than B21, which indicates that introduction of one more NN bond into the cyclic skeleton increases the HOF by more than 90 kJ/mol. Similar trends can also be found in series C, e.g., for C11, C21, and C31. This is also the reason that nitrogen-rich compounds are preferred as promising HEDMs and have been studied favorably.4547 As there are hindered internal rotations within nitramine molecules caused by nitro groups, the contribution of internalrotation partition50,51 to the internal thermal energy are evaluated. Take TNAD (C11) at 298 K for example; the calculated internal thermal energy is 644.07 kJ/mol, whereas it is only 0.14 kJ/mol larger when hindered internal rotations are considered. This shows that the internal-rotation partition contributes little to the energy content. The predicted HOFs can be used to assess the explosive performance of these cyclic nitramines but are not sufficient;48,49 therefore, the density and detonation velocity and pressure were also evaluated. 3.2. Detonation Properties. Detonation velocity and detonation pressure are two important parameters for energetic materials. Table 3 presents the calculated F, Q, D, P, and oxygen balance (OB) for these cyclic nitramines. For comparisons, the experimental detonation performance of HMX, bicycle-HMX, and TNAD is also tabulated in Table 3 together with another known explosive RDX. The calculated detonation velocities and pressures agree well with the available experimental data,5255 with the relative errors +1.43% and 1.10% for HMX (A1), +0.65% and 8.57% for bicycle-HMX (B11), +2.87% and +5.90% for TNAD (C11), and +1.37% and +2.35% for RDX, respectively. This reflects that our predictions for the title compounds are reliable and further confirms the reliability of the calculation method used for these molecular systems. As shown in Table 3, F, D, and P increase with the increasing number of NNO2 groups or aza nitrogen atoms generally. Besides, the relative positions of nitramine groups influence not only HOFs but also the explosive properties. For instance, C15 has slightly higher Q, F, D, and P than C14, whereas the isomer C13 with one more NN bond has the largest corresponding values. This supports the claim that introducing more nitro groups or aza atoms into an energetic molecule usually enhances its detonation performance.56 The detonation properties of the three series vary in the similar range; i.e., D is in the range 10.0511.76, 9.8211.54, and 8.9211.77 km/s, 13861
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Table 4. Bond Dissociation Energies (BDE, kJ/mol) and Bond Order (BO) of the Relatively Weak Bonds of the Cyclic Nitramines NNO2 compd
Figure 3. Correlations between F, D, P, and NNO2 numbers for series A and C.
and P is in the range 46.9167.65, 44.7064.39, and 35.3367.19 GPa for series A, B, and C, respectively. Figure 3 displays the correlations between F, D, and P and the number of NNO2 groups. Only series A and C are plotted because series B has a trend similar to that of series C. Obviously, F, D, and P are good linearly related with the number of NNO2 groups. Take series A for example; when one additional NNO2 is introduced, F, D, and P increase by 0.07 g/cm3, 0.63 km/s, and 7.29 GPa, respectively. This shows good group additivity on the detonation properties. For series C1, C2, and C3, it is seen that the compounds with the same number of NNO2 groups have more or less the same F, whereas D and P differ greatly and are in the order of C3 > C2 > C1. This is because replacing the CH with an aza N atom has not much impact on F because CH and N atom are isoelectronic, but it significantly affects the HOFs because the cyclic nitramines with more NN bond possess larger positive HOFs and generate more N2 gas and thus give off more energy during combustion.44,45 Therefore, series C3 with the most aza N atoms gives the best detonation performance, and series C1 with the least aza N atoms behaves the lowest. Oxygen balance is another important criteria for selecting potential HEDMs.57 Table 3 shows the performance (D and P) of the cyclic nitramines increase with the increasing OB. It is suggested that OB can be used to roughly predict the impact sensitivity of the explosives. The larger the OB is, the higher the impact sensitivity is. Therefore, it can be deduced roughly that the impact sensitivities of these nitramies increase with the increasing NNO2 groups. Considering the quantitative criteria of HEDM, that is, F ≈ 1.9 g/cm3, D ≈ 9.0 km/s, and P ≈ 40.0 GPa, it is found from Table 3 that all title compounds but C11 and C21 satisfy the requirement. Moreover, most derivatives of A, B, and C (A2A6, B12B33, C13C17, C24C26, and C32C37) have better detonation properties over the famous caged nitramine CL-20 (D = 9.4 km/s, P = 42 GPa).52 A6, B33, and C37 with the most number of NNO2 groups and aza N atoms perform best in their corresponding series (F > 2.1 g/cm3, D > 11.5 km/s, P > 64.0 GPa). If compared with another commonly used explosive RDX (F = 1.81 g/cm3, D = 8.75 km/s, P = 34.0 GPa), the cyclic nitramines all have much better explosive performance. Therefore, if these cyclic nitramines can be synthesized, they will have higher exploitable values and be worth investigating further. 3.3. Pyrolysis Mechanism and Thermal Stability. The bond dissociation energy (BDE) of the trigger bond is often a key factor in investigating the pyrolysis mechanism for energetic compounds.58 Generally, the smaller the energy is needed for breaking a bond, the weaker the bond is. Previous studies on nitro compounds such as nitroaromatic and nitramine molecules have shown that the breaking of RNO2 bond is usually the
BO
BDE
NN BO
BDE
CN BO
BDE
CC BO
BDE
A1
0.9951 175.31
A2
0.7974
0.9621 298.53
A3
0.7829 121.95 1.0835 195.70 0.9396 282.36
A4
0.7149
86.57 1.0744 138.03 0.9168 275.36
A5
0.7224
81.16 1.0666 117.41 0.9395 290.41
A6
0.7277
85.20 1.0692 153.32
B11
0.9601 155.01
B12
0.7182
72.24 1.0608 215.83 0.9406 306.84 0.9398 275.85
B13
0.7023
95.58 1.0609 208.58 0.9474 245.74 0.9458 309.78
B21
0.8388
99.81 1.0372 174.50 0.9013 219.12
B22
0.7082
74.96 1.0267 137.20 0.9078 232.61
B23
0.6923
72.78 1.0173 127.57 0.9182 251.17
B31
0.8207
98.10 0.8442 117.74 0.9538 244.74
B32
0.6828
67.23 0.8604 124.62 0.9528 284.41
B33
0.6697
66.04 0.8947 133.17
C11
1.0084 159.67
C12
0.8262
94.45 1.1067 217.49
C13
0.6924
68.38 0.9928 148.48
C14
0.8068
90.62 1.0793 218.85
C15
0.8186
91.76 1.1069 206.98
C16
0.6897
66.87 0.9916 125.83
C17
0.6807
61.96 0.9971 119.99
C21
0.8624 104.70 1.0495 147.87
C22
0.7007
75.67 1.0516 169.77
C23
0.8054
87.64 1.0569 174.21
C24
0.6789
75.33 0.9715 136.86
C25
0.6511
54.93 1.0301 124.81
C26
0.6549
78.24 0.9725 146.75
C31
0.8525
92.24 0.8502
43.92
C32
0.6572
61.24 0.8573
53.67
C33
0.5619
43.61 0.8693 113.96
C34
0.6624
63.27 0.8644
60.66
C35
0.6643
59.77 0.8699
55.19
C36
0.5711
44.56 0.8754
61.25
C37
0.5825
35.60 0.8885
60.00
96.80 1.0836 186.93 0.9208 270.54
0.9385 305.03 0.9375 256.46
initial step in decomposition or detonation and there is a parallel correlation between the BDE of the weakest RNO2 bond and compound’s sensitivity.40,59,60 However, this is only applicable to the molecule in which the RNO2 bond is the weakest one. For tetranitrotetraazaspiropentane, for example, the homolysis of the NN bond in the ring is the initial step in the thermolysis or explosion in the gas phase.14 Another example is octanitrocubane, for which the pyrolysis initiation reaction is the rupture of the CC single bond in the cube cage instead of the side chain CNO2 bond.61 Thereby, for these molecules, the strength of RNO2 cannot be used directly as an index of sensitivity. Similarly, the weakest bond in the cyclic nitramines studied here may not be the NNO2. To elucidate the pyrolysis mechanism and thermal stability of the title compounds, four possible bond dissociations have been considered: (1) the NNO2 bond on the side chain; (2) the NN bond in the ring; (3) the CN bond in the ring; (4) the CC bond in the ring. It should be pointed 13862
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The Journal of Physical Chemistry A out that among the same kind of bonds, the weakest bond was selected as the breaking bond on the basis of the results of natural bond population analysis. For series C, only the BDEs of NNO2 and NN bonds have been calculated because these two kinds of bonds are relatively weaker than other bonds as were found for series A and B. Table 4 presents the bond dissociation energies (BDE) and bond order (BO) of the relatively weaker bonds for the cyclic nitramines. The calculated BDEs of NNO2 (175.31 kJ/mol) and CN bonds (298.53 kJ/mol) for HMX agree well with the previous results (167.11 and 296.77 kJ/mol, respectively)14 obtained at the B3LYP/6-31G* level. According to the calculated BDE, the trigger linkage of series A and B appears to be the side NNO2 bond, which is consistent with the previously found pyrolysis mechanism of the nitramine compounds.59 But there are some differences for series C; that is, for C31, C32, C34, and 35, the initiation step tends to be the cleavage of the bridged NN bond on the ring rather than the side NNO2 bond. It is interesting to note that although C33, C36, and C37 have the bridged NN bond as well, the side NNO2 dissociation becomes easier. This may be due to the existence of the stronger electron-delocalization in N6 ring62 in these compounds, which makes the NN bond stronger and more difficult to break in thermolysis. The same trend can also be found from the bond order of the bridged NN bond; e.g., the bond order of the bridged NN bond is larger in C37 (0.8885) than in C31 (0.8502). Therefore, the rupture of the side NNO2 bond of series A and B is the initial step in the pyrolysis, whereas the bridged NN bond without a N6 ring in the chemical structures in series C appears to be the trigger bond in the thermolysis or explosion in the gas phase. The BDE values can be used to measure the relative order of thermal stability or sensitivity for energetic materials.60 Thus, for these cyclic nitramines, the stability decreases with the increasing NNO2 groups or aza N atoms, and the species with the bridged NN bond in the ring are more sensitive than others on the whole. The relative positions of nitramine groups also affect the BDE. For example, A3 has a much larger BDE (121.95 kJ/mol) than A4 (86.57 kJ/mol) due to the weaker repulsion of nitro groups in the former than in the latter. Hence, A3 is more stable than A4, which can also be achieved from their total energies or heats of formation (Table 2). Overall, it is found from Table 4 that the stability of the compounds of the three series decrease in the order A > B > C with the increasing nitro groups or aza N atoms. This is a consequence of the electrostatic interactions and the σ electron-withdrawing effect of NO2 substituents that increase ring tension and thus destabilize the system generally; e.g., the BDE values for the weakest bonds of A6, B33, and C37 are 85.20, 66.04, and 35.60 kJ/mol, respectively. In comparison with HMX, bicycle-HMX, and TNAD, all derivatives are less stable. According to the suggestion of Chung et al.63 that the molecule to be a viable candidate should have a dissociation barrier larger than 20 kcal/mol, A1A6, B13, B21, B31, C12, C14, C15, C21, and C23 are the possible candidates of HEDMs. In conjunction with the detonation performance of these cyclic nitramines (Table 3), A2A6, B13, B21, B31, C12, C14, C15, and C23 are the preferred candidates of HEDMs.
4. CONCLUSIONS In this work, 32 cyclic nitramine derivatives of HMX, bicycleHMX, and TNAD were designed and investigated using the
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DFT-B3LYP method with the 6-311G(d,p) basis set. The results show that all cyclic nitramines possess large positive HOFs that increase with the increasing number of NNO2 groups and aza N atoms on the whole. The predicted detonation velocities and detonation pressures indicate that the NNO2 group and aza N atom are effective substituents for enhancing the detonation performance. All nitramines except C11 and C21 exhibit better detonation performance than HMX. The thermal stability and pyrolysis mechanism of these cyclic nitramines were evaluated using the bond dissociation energies. The stability decreases with the increasing numbers of NNO2 groups or aza atoms. For most of these nitramines, the homolysis of NNO2 is the initial step in the thermolysis or explosion in the gas phase, whereas the species with the bridged NN bond in the ring are more sensitive than others. Considering the detonation performance and thermal stability, twelve derivatives may be the promising candidates of HEDMs.
’ ASSOCIATED CONTENT
bS
Supporting Information. Data for all calculated total energies (E0) and HOFs of the parent heterocyclic skeletons (X). Complete ref 23. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel.: + 86-25-84315947-803. E-mail:
[email protected]. edu.cn.
’ ACKNOWLEDGMENT We greatly thank the National Natural Science Foundation of China (NSAF grant no. 11076017) for the support of this work. ’ REFERENCES (1) Cobbledick, R. E.; Small, R. W. H. Acta Crystallogr. 1974, B30, 1918. (2) Cohen, N. S.; Strand, L. D. U.S. Patent 4,092,188, 1978. (3) Gilardi, R. D.; Karle, J. Chemistrv of Energetic Materials; Academic Press: San Diego, 1991. (4) Xiao, H. M. Molecular orbital theory for nitro compounds; National Defense Industry Press: Beijing, 1993. (5) Zenin, A. J. Propul. Power. 1995, 11, 752. (6) Manning, T.; Strauss, B.; Prezelski, J. P.; Moy, S. U.S. Patent 5,798,481. 1998. (7) Jalovy , Z.; Zeman, S.; Suceska, M.; Vavra, P.; Dudek, K.; Rajic, M. J. Energ. Mater. 2001, 19, 219. (8) Balakrishnan, V. K.; Halasz, A. J. Hawari. Environ. Sci. Technol. 2003, 37, 1838. (9) Willer, R. L. J. Org. Chem. 1984, 49, 5150. (10) Simpson, R. L.; Urtiew, P. A.; Ornellas, D. L.; Moody, G. L.; Scribner, K. J.; Hoffman, D. M. Propellants, Explos., Pyrotech. 1997, 22, 249. (11) Qiu, L.; Xiao, H. M. J. Hazard. Mater. 2009, 164, 329. (12) Koppes, W. M.; Chaykovsky, M. H.; Adolph, G.; Gilardi, R.; George, C. J. Org. Chem. 1987, 52, 1113. (13) Jaidann, M. S.; Abou-Rachid, R. H.; Lussier, L. S. J. Hazard. Mater. 2010, 176, 165. (14) Qiu, L.; Xiao, H. M; Gong, X. D; Ju, X. H.; Zhu, W. H. J. Phys. Chem. A 2006, 110, 3797. (15) Zhang, J.; Oxley, J.; Smith, J.; Bedford, C.; Chapman, R. J. Mass Spectrom. 2000, 35, 841. 13863
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