ARTICLE pubs.acs.org/JPCA
Computational Studies on the Crystal Structure, Thermodynamic Properties, Detonation Performance, and Pyrolysis Mechanism of 2,4,6,8-Tetranitro-1,3,5,7-tetraazacubane as a Novel High Energy Density Material Fang Wang, Hongchen Du, Jianying Zhang, and Xuedong Gong* Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China ABSTRACT: Studies have suggested that octanitrocubane (ONC) is one of the most powerful non-nuclear high energy density material (HEDM) currently known. 2,4,6,8-Tetranitro-1,3,5,7-tetraazacubane (TNTAC) studied in this work may also be a novel HEDM due to its high nitrogen content and crystal density. Density functional theory and molecular mechanics methods have been employed to study the crystal structure, IR spectrum, electronic structure, thermodynamic properties, gas-phase and condensedphase heat of formation, detonation performance, and pyrolysis mechanism of TNTAC. The TNTAC has a predicted density of about 2.12 g/cm3, and its detonation velocity (10.42 km/s) and detonation pressure (52.82 GPa) are higher than that of ONC. The crystalline packing is P212121, and the corresponding cell parameters are Z = 4, a = 8.87 Å, b = 8.87 Å, and c = 11.47 Å. Both the density of states of the predicted crystal and the bond dissociation energy of the molecule in gas phase show that the cage CN bond is the trigger bond during thermolysis. The activation energy of the pyrolysis initiation reaction obtained from the B3LYP/6-311++G(2df,2p) level is 125.98 kJ/ mol, which indicates that TNTAC meets the thermal stability request as an exploitable HEDM.
1. INTRODUCTION Cage compounds constitute an important category of high energy density materials (HEDMs)15 due to the large strain within the compact skeleton coupled with the high heat of formation and crystal density that, in turn, makes them superior explosives over the conventional ones. In this category, nitrocubanes have a significant potential for applications as promising HEDMs. Eaton et al. have reported the synthesis of nitrocubanes from dinitrocubane through octanitrocubane (ONC),6,7 and in the series of nitrocubanes, ONC is highly energetic and has better explosive performance than CL-20 (2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane), the most powerful explosive presently used.8 However, ONC is currently too difficult and expensive to be produced in quantities. Therefore, active efforts are continued to find new energetic compounds based on the highly symmetric cubic cage skeleton, for example, octanitrosocubane9 and octanitroxycubane.10 A driving force for the use of cubane is its high positive heat of formation (622.1 kJ/mol), high density (1.29 g/cm3), and good thermal stability (decomposition temperature >220 °C).11,12 Recently, studies of azacubanes by introducing nitrogen atoms into the cage instead of replacing the H atoms of cubane by NO2 groups have created an interest in designing a new class of energy-rich materials1315 in which the CC bond weakening associated with a “perpendicular” NO2 can be eliminated when an aza nitrogen is adjacent to the CNO2 because the aza nitrogen has an overall stabilizing effect through diminishing the molecular strain energy.16,17 Therefore, the potential high-energy molecule r 2011 American Chemical Society
2,4,6,8-tetranitro-1,3,5,7-tetraazacubane (TNTAC; Figure 1), which benefits from all the stabilizing effects and can in principle be prepared from amine precursors, has been studied in this work Computational study by highly accurate ab initio and density functional theory (DFT) methods has played an essential role in predicting the geometric and energetic properties for chemical systems. Owing to the difficulties in the synthesis of the molecule under consideration, computer simulation becomes an effective way to predict its structure and related properties. So far, there are several theoretical studies on TNTAC.1518 Recently, Fan et al. have predicted that the strain energy of TNTAC (992.95 kJ/mol) is very large but smaller than that of ONC (1103.03 kJ/mol).18 Investigations on the molecular electrostatic potential of nitroazacubanes reveal that TNTAC with face opposite nitrogen atoms in the cage is more delocalized than other conformers of tetranitroazacubane.15 In the present study, the density functional theory (DFT) and molecular mechanics (MM) methods were employed to evaluate the crystal structure and properties of the compound, such as infrared spectrum (IR), electronic structure, heat of formation (HOF), detonation performance, and pyrolysis mechanism. The calculation results show that TNTAC may be a very plausible HEDM target. Received: May 27, 2011 Revised: September 13, 2011 Published: September 15, 2011 11788
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The enthalpy of explosion (ΔHD) was calculated for the decomposition reaction: C4 N4 ðNO2 Þ4 f 4CO2 þ 4N2
ð3Þ
Detonation velocity (D) and pressure (P), two important parameters reflecting the explosive performance of energetic materials, were estimated by empirical Kamlet-Jacobs formula32 as follows:
Figure 1. Optimized structure of 2,4,6,8-tetranitro-1,3,5,7-tetraazacubane (TNTAC) and octanitrocubane (ONC) at the B3LYP/6-311 +G(2df,2p) level.
2. COMPUTATIONAL METHODS Geometry optimization for TNTAC was performed at the levels of DFT-B3LYP/6-311+G(2df,2p), B3PW91/6-311+G(2df,2p), and PBE1PBE/6-311+ G(2df,2p) with the Gaussian 03 package.19 It is known that the DFT has emerged as a very reliable theoretical method,20,21 and especially the DFTB3LYP functional with appropriate basis set is able to reproduce experimental molecular geometry, infrared spectrum, and heat of formation.2224 However, other two DFT level calculations were also carried out for the purpose of comparison. In addition, ONC was also optimized at the B3LYP level for comparison and testing of the reliability of the calculated results. Vibrational analysis showed that the optimized structures corresponded to local energy minima on the potential energy surfaces without any imaginary frequency. The natural bond orbital (NBO)25 and molecular electrostatic potential (MEP) were computed at the B3LYP level. Moreover, the single-point energy calculations were performed at the B3LYP level with the larger basis sets 6-311++G(2df,2p)26 and Dunning’s AUG-cc-PVDZ(5d).27 The method of isodesmic reaction at the DFT level has been employed successfully to calculate the gas-phase HOFs (ΔfH°gas) of many organic systems.2,23,2830 Hence, it was adopted to evaluate the ΔfH°gas of the title compound at 298 K using the following reaction:
For the isodesmic reaction 1, the heat of reaction (ΔH298) can be calculated from the following equation: ΔH298 ¼
∑Δf HP ∑Δf HR ¼ ΔE0 þ ΔZPE þ ΔHT þ ΔnRT
ð2Þ
where ΔfHP and ΔfHR are the HOFs of the products and reactants at 298 K, respectively. ΔE0 is the difference between the total energy of the products and the reactants at 0 K, ΔZPE is the difference between the zero-point energies (ZPE) of the products and the reactants, and ΔHT is the thermal correction from 0 to 298 K. Because the experimental HOFs of reference compounds NH3, CH4, CH3NO2, and CH3NH2 are 45.94, 74.40, 80.80, and 22.05 kJ/mol, respectively,31 then the HOF of the title compound can be figured out easily.
D ¼ 1:01ðNM 1=2 Q 1=2 Þ1=2 ð1 þ 1:30FÞ
ð4Þ
P ¼ 1:558 F2 NM 1=2 Q 1=2
ð5Þ
where N is the moles of gaseous detonation products per gram of explosive; M is the average molecular weight of gaseous products; Q is the chemical energy of denotation (kJ/g; Q = ΔHD); and F is the density of explosive (g/cm3). The strength of bonding, which can be evaluated by the bond dissociation energy (BDE), is fundamental to understanding chemical processes.33 The energy required for bond homolysis at 298 K and 1 atm, that is, the enthalpy of reaction AB(g) f A(g) + B(g), is the bond dissociation enthalpy of AB by definition.34 For many organic molecules, the terms “bond dissociation energy” and “bond dissociation enthalpy” are often used interchangeably in the literature.35 In this work, the BDEs of all possible initiation bonds were calculated using eq 6: BDEðA BÞ ¼ ½Δf HðAÞ þ Δf HðBÞ Δf HðA BÞ
ð6Þ
where ΔfH(AB), ΔfH(A), and ΔfH(B) stand for the enthalpies of the parent compound and the corresponding radicals, respectively. Because HEDMs are usually in agglomerate solids, we have predicted the possible polymorphs of the title compound by searching the possible molecular packings among seven most probable space groups (P21/c, P-1, P212121, P21, Pbca, C2/c, and Pna21)3638 using the Dreiding force field and the Polymorph module39 in Materials Studio.40 The nonlocal functional B3LYP incorporated in the CASTEP41 module was then employed to calculate the density of states (DOS) of the predicted crystal using the norm-conserving pseudopotentials42 and a plane-wave expansion of the wave functions. All-electron calculations are carried out for an isolated atom in a chosen electronic configuration (not necessarily in the ground state). This provides valence electron eigenvalues and valence electron wave functions for the atom. The electronic wave functions were obtained by the all-bands scheme43 that allows a simultaneous update of all wave functions. The self-consistent ground state of the system was determined by using a band-by-band conjugated gradient technique to minimize the total energy of the system with respect to the plan-wave coefficients. The cutoff energy of plane-waves was set to 380.0 eV. Brillouin zone sampling was performed by using the Monkhost-Pack scheme with a k-point grid of 3 3 3. The values of the kinetic energy cutoff and the k-point grid were determined to ensure the convergence of total energies.
3. RESULTS AND DISCUSSION 3.1. Molecular Geometry and Electronic Structure. Before discussing the various properties, it is useful to examine the geometric structure of the title compound. Table 1 lists the selected geometry parameters of the title compound and ONC at 11789
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Table 1. Selected Bond Lengths (Å), Bond Angles (°), Energies of HOMO (EH) and LUMO (EL) and Their Gap ΔE (eV), Electron Affinity EA (eV), and NBO Charges (e) at the B3LYP/6-311+G(2df,2p) Level for TNTAC and ONCa compound
CN
TNTAC
1.501
ONC a
CC
1.565,1.562 (1.567,1.563)
CNO2
ONO
EH
EL
ΔE
EA
qC
qNO2
qN 0.50
1.495
129.3
9.79
4.32
5.47
3.18
0.63
0.13
1.485 (1.482)
128.8 (128.9)
10.21
4.75
5.46
3.47
0.10
0.10
Values in parentheses are experimental data of ONC.
Figure 2. HOMO, LUMO, and electrostatic potentials mapped onto 0.001 electron/bohr3 contour of the electronic density at the B3LYP/6-311 +G(2df,2p) level. Potential color range: from red (negative) to blue (positive).
Figure 3. Simulated IR spectra for TNTAC and ONC at the B3LYP/6-311+G(2df,2p) level.
the B3LYP/6-311+G(2df,2p) level. To test the reliability of the calculated results, experimental values of ONC obtained from X-ray diffraction7 are also presented. Obviously, the B3LYP/6311+G(2df,2p) geometry of ONC is in excellent agreement with the experimental observations. The CN bond in the cage of TNTAC is longer than the normal CN bond (1.47 Å) due to the cage strain found in the system.18 The CNO2 bond of TNTAC is found to be longer than that of ONC, while the difference is not significant. Additionally, the natural charges obtained from NBO calculations reveal that when aza N atoms are introduced into the cage of ONC, the charges on the NO2 group become more negative and the positive charges on carbon atoms increase, owing to the electron-withdrawing effect of the aza N atoms. Analysis of the molecular orbital can provide useful information on electronic structures.44 It was proposed that the molecule
with a larger energy gap is expected to have a lower reactivity in the chemical or photochemical processes with electron transfer or leap.4547 As is evident in Table 1, the energies of HOMO, LUMO, and their gap ΔE of TNTAC are slightly higher than those of ONC, indicating TNTAC may have a comparable chemical reactivity with ONC. Figure 2 illustrates the 3D plots of HOMO, LUMO, and molecular electrostatic potentials (MEP) for the title compound and ONC. All the HOMO and LUMO levels are 2-fold degenerate, indicating that small changes in charge state could lead to minor JahnTeller distortions.48 For TNTAC and ONC, the skeleton CN or CC orbitals participate in both the HOMO and the LUMO levels, and removal of an electron from the HOMO level or addition of an electron to the LUMO level could weaken the skeleton framework. The estimated electron affinity of TNTAC (3.18 eV) is smaller 11790
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Table 2. Thermodynamic Properties of TNTAC and ONC at Different Temperaturesa compound TNTAC
ONC
a
T
200
298
300
400
500
600
700
800
C°p,m
181.43
241.48
242.57
296.17
337.88
368.95
391.93
409.06
S°m
451.32
535.01
536.51
613.9
684.69
749.18
807.86
861.37
H°m
23.74
44.51
44.96
71.99
103.79
139.21
177.31
217.4
C°p,m
318.06
408.65
410.27
490.21
553.4
601.27
637.12
664.09
S°m
615.44
759.56
762.09
891.45
1007.93
1113.26
1208.77
1295.69
H°m
39.91
75.63
76.39
121.55
173.87
231.72
293.72
358.84
Units: T, K; C°p,m, J/mol/K; ΔSQm, J/mol/K; H°m, kJ/mol.
Figure 4. Relationships between the thermodynamic functions (C°p,m: J/mol/K, S°m: J/mol/K, H°m: kJ/mol) and temperature (T: K) for TNTAC and ONC.
than that of ONC (3.47 eV), which suggest TNTAC may be slightly less easy to accept an electron, but it is much larger than that of cubane (1.5 eV) and C60 (2.74 eV, experiment).49 This indicates that, in analogy to the fullerene in the alkali-doped fullerene crystal, TNTAC could also act as an electron acceptor like ONC found by Kortus et al.49 Inspection of the MEP for the two compounds, the negative potentials appear to be distributed mostly on the oxygen atoms, and the positive ranges characterize at the center of the cage skeleton, which attributes some stabilization to the cube skeleton as was found in ONC.50 3.2. Thermodynamic Properties and Heat of Formation. Figure 3 provides the simulated IR spectrum of the title compound, together with the IR of ONC for comparison. A scaled factor of 0.96 is adopted on these frequencies because the DFTcalculated harmonic vibrational frequencies are usually larger than those observed experimentally.51 The frequencies are then used to calculated their thermodynamic properties. It has been shown that the calculated IR of ONC is in quite close agreement with the previous study.52 Obviously, the two compounds have similar IR spectra, and there are four main characteristic regions in the spectra. For TNTAC, the strong characteristic peak at 1597 cm1 corresponds to the NdO asymmetric stretch of nitro TNTAC :
C°p, m ¼ 31:246 þ 0:846T 4:696 104 T 2
groups, similar with that in ONC (1580 cm1). Another remarkable signal centering at 1326 cm1 is associated with a CN stretch and NdO symmetric stretch motion in CNO2 groups, not much different from that in ONC (1310 cm1). At 1036 cm1 for TNTAC, the strong peak is also caused by the CN stretch of the CNO2 groups, while the weak peak at 1170 cm1 for ONC corresponds to CC stretch modes. Finally, the weak peaks at less than 823 and 762 cm1 for TNTAC is mainly caused by the torsion of the cube skeleton and the bend vibration of nitro groups. While for ONC, the weak peaks at 840 cm1 correspond to the bending of nitro groups and a strong CN stretching motion of the CNO2 groups. The predicted IR for the title compound should be able to assist in identifying TNTAC. On the basis of vibrational analysis results and statistical thermodynamic method, thermodynamic properties, including standard molar thermal enthalpy (H°m), standard molar heat capacity (C°p,m), and standard molar thermal entropy (S°m) from 200 to 1000 K of the title compound and ONC are evaluated and tabulated in Table 2. The correlation equations between the thermodynamic functions and temperature in the range of 200800 K are shown as follows and can be expressed as in Figure 4. ðR 2 ¼ 0:9998, SD ¼ 1:3263Þ
S°m ¼ 311:362 þ 0:965T 2:842 104 T 2 ðR 2 ¼ 0:9999, SD ¼ 0:7035Þ Hm° ¼ 20:298 þ 0:177T þ 1:467 104 T 2 ðR 2 ¼ 0:9998, SD ¼ 1:1475Þ ONC :
C°p, m ¼ 94:339 þ 1:259T 6:8726 104 T 2
ðR 2 ¼ 0:9999, SD ¼ 1:7906Þ
S°m ¼ 299:961 þ 1:709T 5:884 104 T 2 ðR 2 ¼ 0:9999, SD ¼ 2:4386Þ Hm° ¼ 20:298 þ 0:177T þ 1:467 104 T 2 ðR 2 ¼ 0:9999, SD ¼ 1:6620Þ where R2 and SD are the correlation coefficient and standard deviation, respectively.
With the increase in temperature, H°m of TNTAC and ONC monotonically increase. This is because the main contributions 11791
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Table 3. Calculated Total Energies E0 (a.u.) and Gas-Phase Heats of Formation ΔfH°gas (KJ/mol) for the Reference Compoundsa E0 (CH4)
a
E0 (NH3)
E0 (CH3NH2)
E0 (CH3NO2)
E0 (TNTAC)
ΔfH°gas
PBE1PBE/6-311+G(2df, 2p)
40.4246
56.4749
95.7065
244.7829
1190.6082
968.43
B3PW 91/6-311+G(2df, 2p)
40.4715
56.5256
95.7934
244.9554
1191.3790
960.76
B3LYP/6-311+G(2df, 2p)
40.4885
56.5484
95.8315
245.0526
1191.8218
997.67
B3LYP/6-311++G(2df, 2p)b
40.5370
56.5865
95.8998
245.1067
1191.9319
998.03
B3LYP/AUG-cc-PVDZb
40.5204
56.5707
95.8737
245.0545
1191.7157
1015.81
E0 is after correction of the ZPE and HT. b Single point energy at the B3LYP/6-311+G(2df,2p) geometries.
Table 4. Molecular Packings for TNTAC Obtained with the Drieding Force Field in Seven of the Most Possible Space Groups Z
F (g/cm3)
E (kcal/mol/ asym 3 cell)
a (Å)
b (Å)
c (Å)
α (°)
β (°)
γ (°)
P-1 Pbca
2 8
2.09 2.08
178.10 177.99
7.58 25.16
7.58 5.66
11.96 12.94
80.13 90.00
90.15 90.00
43.51 90.00
Pna21
4
2.07
177.98
12.87
5.69
12.65
90.00
90.00
90.00
P21/c
4
2.07
177.98
12.65
12.87
13.87
90.00
155.79
90.00
C2/c
8
2.08
177.74
25.70
5.83
12.67
90.00
104.41
90.00
P21
2
2.11
177.51
5.73
8.87
8.87
90.00
90.00
90.00
P212121
4
2.12
176.78
8.87
8.87
11.47
90.00
90.00
90.00
space group
to the enthalpy are from the translations and rotations of the molecules at low temperature, whereas the vibration motion is intensified at higher temperature and makes more contribution to the enthalpy. Moreover, H°m of the ONC is greater than that of TNTAC, for example, at 298 K, H°m of the latter is 31.12 kJ/ mol larger than that of the former. The same is true for C°p,m and S°m. Because there are stronger interactions between the nitro groups in ONC, the vibrational motions of ONC make more contributions to C°p,m, H°m, and S°m as the temperature increase. This leads to ONC having higher C°p,m, H°m, and S°m compared to TNTAC. The relationship between the thermodynamic functions and the temperature makes the evaluation of the thermodynamic functions at different temperatures very easy and is necessary for predicting reactive properties at various temperatures. Take the decomposition reaction C4N4(NO2)4(g) f 4CO2(g)+ 4N2(g) of TNTAC for example, the enthalpy change and the free energy change (according to ΔG = ΔH TΔS) can be evaluated on the basis of the thermodynamic functions. At 298 K, the enthalpy change and the free energy change are 27.85 and 289.88 kJ/mol. While at 800 K, they are 6.80 and 715.51 kJ/mol, respectively. This indicates that the decomposition reaction becomes less endothermic with the increasing temperature. Moreover, the free energy changes appear to be much larger as the temperature increase and thus the reaction is more favorable at higher temperature. Our previous study on the thermodynamic properties of caged compounds has proved that the calculated results are in good accordance with the experimental values.53 Because there are no experimental values for ONC and the title compound, our results may be used as references for experimental work and further studies on the physical and chemical properties of TNTAC and ONC. The HOF is one of the most important thermochemical properties of energetic materials and is usually taken as an indicator of the “energy content” of an HEDM. It has been reported that the DFT is quite accurate for calculating the gasphase HOF (ΔfH°gas) of energetic compounds via isodesmic reaction.2830 Table 3 presents the total energies of the reference
compounds and the resulting predictions for ΔfH°gas of TNTAC at various levels of theory. It is found that ΔfH°gas calculated by B3LYP/6-311+G(2df,2p) is a little larger than those by PBE1PBE/6-311+G(2df,2p) and B3PW91/6-311+G(2df,2p), with the differences of 29.24 and 36.91 kJ/mol, respectively. Moreover, in comparison with the ΔfH°gas from the 6-311 +G(2df,2p) basis set at the B3LYP level, the 6-311++G(2df,2p) basis set gives a very close value and the AUG-cc-PVDZ basis set gives a higher value by 18.14 kJ/mol. The maximum discrepancy of ΔfH°gas is 36.91 kJ/mol due to using different functionals and basis sets. Therefore, ΔfH°gas is slightly affected by the functionals and basis sets. For assessment of the potential performance of the energetic material of interest, it is also important to know their condensedphase HOF (ΔfH°cond) because it is related directly with the detonation parameters. According to Hess’ law, ΔfH°cond can be obtained by Δf H°cond ¼ Δf H°gas ΔHsub
ð7Þ
where ΔHsub is the heat of sublimation and can be evaluated by the Byrd and Rice method54 in the framework of the Politzer approach,55 which has been successfully applied to many energetic compounds56,57 using the following empirical expression: ΔHsub ¼ β1 A2 þ β2 ðvσ2tot Þ0:5 þ β3
ð8Þ
where A is the area of the isosurface of 0.001 electrons/bohr3 electronic density, ν is the degree of balance between positive and negative potential on the molecular surface, σ2tot is a measure of variability of the electrostatic potential, and β1, β2, and β3 are determined through a least-squares with the experimental ΔfH°cond of a selected set of known materials.54 For the current estimates, the related electrostatic potential descriptors were calculated at B3LYP/6-311++G(2df,2p)//B3LYP/6-311+G(2df,2p) level. Thus, based on eq 8, the estimated ΔHsub of the title compound is 104.09 kJ/mol, and the resulting prediction for ΔfH°cond is 893.94 kJ/mol (3.10 kJ/g), using ΔfH°gas (998.03 kJ/mol) at the level of B3LYP/6-311++G(2df,2p)//B3LYP/6-311+ G(2df,2p), 11792
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Figure 6. Total DOS and PDOS of TNTAC. Figure 5. Most possible packing of TNTAC. 58
which is obviously larger than that of CL-20 (0.96 kJ/g) and ONC (1.09 kJ/g).52 This may be due to the large strain energy18 together with the energy content of the CN bonds in the rigid skeleton.14 Therefore, the high energy content of the title compound satisfies the necessary characteristic of energetic materials. 3.3. Crystal Structures. Molecular mechanics (MM) has been widely used to predict the molecular packing (crystal structure) of the energetic compounds.59,60 Dreiding force field,61 capable of predicting the condensed phase properties for a broad range of molecules such as polynitroadamantanes62 and hexaazaisowurtzitanes,30 has been employed to predict the crystal structure of the title compound in this paper. Table 4 collects the cell parameters and crystal densities of the seven possible packings with the lowest energy in each space group. It is found that the structure with the P212121 symmetry has the lowest energy. Therefore, the title compound tends to exist in the P212121 group (Figure 5) because the most stable polymorph usually possesses the least Gibbs free energy (or energy at 0 K). The corresponding cell parameters are Z = 4, a = 8.87 Å, b = 8.87 Å, c = 11.47 Å, and F = 2.12 g/cm3. In addition, the predicted crystal density of the P212121 packing is close to the density (2.11 g/cm3) obtained from the volume inside an electron density contour of 0.001 e/Bohr3 at the B3LYP/6-311+G(2df,2p) level. Thus, TNTAC has a high density comparable to that of ONC (2.10 g/cm3),6 indicating it may exhibit good detonation performance because density is the key factor affecting the detonation properties of energetic materials.32 Density of state (DOS) is a presentation of the band structure of a crystal. A better understanding of the band structure is its projection density of state (PDOS). PDOS can be used to investigate the constitution of energy bands.59,60 Figure 6 plots the DOS and PDOS of the predicted crystal structure of TNTAC, in which the origin of the energy is taken to be the Fermi level. In the upper valence band, the crystal has a sharp peak near the Fermi level. The top of the DOS valence band shows four main peaks, and these peaks are predominately from the p states of the N and C atoms in the cage. It is found that the states of N in the cage make more important contributions to the valence bonds than these of C atoms. As for the conduction band, it is also dominated by the p states of the N and C atoms in the cage. The N atoms in NO2 hardly contribute to the frontier energy bands. This indicates that the p states of the solid play a very important role in the chemical reaction, and the CN bond in the cage is the active center, which is consistent with the molecular orbital analysis in the gas phase that CN bond
Table 5. Bond Dissociation Energies (BDE, kJ/mol) and the Activation Energy (Ea, kJ/mol) for the Title Compound
TNTAC
BDE
Ea
CN CNO2
CN
PBE1PBE/6-311+G(2df,2p) 157.94 214.85
137.06
B3PW 91/6-311+G(2df,2p) 152.79 204.72
132.06
B3LYP/6-311+G(2df,2p)
125.95 (125.98,a 129.74b)
140.63 196.72
a
Calculated at the B3LYP/6-311++G(2df,2p)//B3LYP/6-311+G(2df,2p) level. b Calculated at the B3LYP/AUG-cc-PVDZ//B3LYP/6311+G(2df,2p) level.
participates in both the HOMO and LUMO frontier orbitals. Meanwhile, near the Fermi level, the p states of the N and C atoms in the cage are overlapped. Therefore, the CN bonds in the cage may be the trigger bonds during thermolysis. Similar conclusions can also be drawn from the BDE analysis below. 3.4. 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.35,63 Previous studies on the ring or caged nitro compounds such as RDX (hexahydro-1,3,5-trinitro-1,3,5-trizine), CL-20, and nitroxycubanes have shown that the breaking of the RNO2 bond is usually the initial step in decomposition and there is a parallel relationship between the BDE of the weakest RNO2 bond and the sensitivity.9,6365 For ONC, the CC bond in the cage is found to be the initial bond during thermolysis rather than the CNO2 bond.52 To elucidate the pyrolysis mechanism and thermal stability of TNTAC, two possible bond dissociations, that is, the rapture of the skeleton CN bond and side chain CNO2 bond were considered in this work. The related results are covered in Table 5. As is shown in Table 5, the BDE calculated by the B3LYP functional is somewhat smaller than those by the PBE1PBE and B3PW91 functionals, with the maximum difference of 18.13 kJ/ mol. Calculation results at various methods show that the skeleton CN bond has much smaller BDE than the side chain CNO2 bond, for example, 140.63 and 196.72 kJ/mol, respectively, at the B3LYP/6-311+G(2df,2p) level. Therefore, the breaking of the CN bond in the cage is much easier and is the pyrolysis initiation step during pyrolysis in gas phase. This is in accord with that drawn from the DOS calculation on the crystal structure. Besides, the BDE of the trigger bond for TNTAC is large enough and suffices the stability request suggested 11793
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Table 6. Detonation Properties of TNTAC and ONC compound
a
ΔfH°cond (kJ/g)
F (g/cm3)
D (km/s)
P (GPa)
Q (kJ/g)
TNTAC
3.10
2.12
10.42
52.82
8.57
ONC
1.09
2.19a (2.10)b
10.26a (10.10)b
52.08a (50.00)b
8.35a
b
Calculated data from ref 52. Estimated values from ref 6.
previously,66 that is, for a viable candidate of HEDM, BDE should be larger than 80 kJ/mol and for an exploitable HEDM, 120 kJ/mol. The activation energy (Ea) for the pyrolysis initiation reaction has the direct influence on the sensitivity and thermal stability of energetic compounds6772 and is a more important kinetic parameter than BDE. The larger the activation energy, the higher the thermal stability will be. Ea for the cleavage of the CN bond in the cage are also tabulated in Table 5. It is found that Ea from B3LYP/6-311+G(2df,2p) is slightly smaller than those from PBE and B3PW91 methods. Furthermore, Ea obtained at the B3LYP level with larger 6-311++G(2df,2p) (125.98 kJ/mol) and AUGcc-PVDZ (129.74 kJ/mol) basis sets, are very close to that from 6-311+G(2df,2p) basis set (125.95 kJ/mol). Though the title compound has smaller Ea for the pyrolysis initiation reaction than ONC (155.30 kJ/mol),52 its thermal stability meet the thermal stability request as an exploitable HEDM. 3.5. Detonation Properties. Together with the predicted crystal density and ΔfH°cond calculated by B3LYP/6-311++G(2df,2p), the detonation velocity (D) and pressure (P) are evaluated by the Kamlet-Jacobs equations.32 Table 6 summarizes the detonation properties of TNTAC as well as ONC. It can be seen that the D and P of TNTAC (10.59 km/s and 54.47 GPa) are larger than those of ONC. In comparison with another famous caged explosive CL-20 (F = 2.04 g/cm3, D = 9.4 km/s, P = 42 GPa),58 TNTAC exhibits much better detonation performance. In addition, TNTAC is perfectly oxygen balanced as ONC, that is, it does not need any atmospheric oxygen to combust and it gives off more energy than ONC during the explosion. This illustrate that the title compound has superior detonation performance and meets the requirements (i.e., F g 1.9 g/ cm3, D g 9.0 km/s, P g 40.0 GPa) as HEDMs.73 Therefore, if TNTAC can be synthesized, it will have higher exploitable values.
4. CONCLUSIONS In the present work, DFT and MM methods have been employed to study the geometry, electronic structure, IR spectrum, thermodynamic functions, gas-phase and condensed-phase heat of formation, detonation performance, and pyrolysis mechanism of a novel caged compound, 2,4,6,8-tetranitro-1,3,5,7tetraazacubane (TNTAC). Calculation results show that the density, heat of formation, and detonation performance of TNTAC are larger than that of ONC. Both the density of states of the predicted crystal and the bond dissociation energy of the molecule in gas-phase suggest that the cage CN bond is the trigger bond during thermolysis. Besides, the activation energy of the pyrolysis initiation reaction is 125.98 kJ/mol at the B3LYP/6311++G(2df,2p) level. This indicates that TNTAC meets the thermal stability request as an exploitable HEDM. In summary, TNTAC is expected to be a novel candidate of HEDM and has high exploitable values. This paper provides some basic information of physical chemistry and detonation properties for people interested in this compound.
’ AUTHOR INFORMATION Corresponding Author
*Tel.: + 86-25-84315947-803. E-mail:
[email protected].
’ ACKNOWLEDGMENT We greatly thank the National Natural Science Foundation of China (Grant No. 11076017) for the support of this work. ’ REFERENCES (1) Qiu, L.; Xiao, H. M.; Gong, X. D.; Ju, X. H.; Zhu, W. H. J. Phys. Chem. A 2006, 110, 3797. (2) Xu, X. J.; Xiao, H. M.; Gong, X. D.; Ju, X. H.; Chen, Z. X. J. Phys. Chem. A 2005, 109, 11268. (3) Vayalakkavoor, R. T.; Vedachalam, M.; Boyer, J. H. Heterocycles 1990, 31, 479. (4) Sun, C. H.; Zhao, X. Q.; Li, Y. C.; Pang, S. P. Chin. Chem. Lett. 2010, 21, 572. (5) Marchand, A.; Sharma, G. J. Org. Chem. 1987, 52, 4784. (6) Eaton, P. E.; Gilardi, R. L.; Zhang, M. X. Adv. Mater. 2000, 12, 1143. (7) Zhang, M. X.; Eaton, P. E.; Gilardi, R. Angew. Chem., Int. Ed. 2000, 39, 401. (8) Simpson, R. M.; Urtiew, P.; Ornellas, D.; Moody, G.; Scribner, K.; Hoffman, D. Propellants, Explos., Pyrotech. 1997, 22, 249. (9) Richard, R. M.; Ball, D. J. Hazard. Mater. 2009, 164, 1552. (10) Richard, R. M.; Ball, D. J. Hazard. Mater. 2009, 164, 1595. (11) Eaton, P. E. Angew. Chem., Int. Ed. 1992, 31, 1421. (12) Kybett, B. D.; Carroll, S.; Natalis, P.; Bonnell, D.; Margrave, J.; Franklin, J. L. J. Am. Chem. Soc. 1966, 88, 626. (13) Patil, U. N.; Dhumal, N. R.; Gejji, S. P. Theor. Chem. Acc. 2004, 112, 27. (14) Jursic, B. J. Mol. Struct.: THEOCHEM 2000, 530, 21. (15) Dhumal, N. R.; Patil, U. N.; Gejji, S. P. J. Chem. Phys. 2004, 120, 749. (16) Murray, J. S.; Seminario, J. M.; Politzer, P. Struct. Chem. 1991, 2, 153. (17) Murray, J. S.; Seminario, J. M.; Lane, P.; Politzer, P. J. Mol. Struct.: THEOCHEM 1990, 207, 193. (18) Fan, X. W.; Qiu, L.; Ju, X. H. Struct. Chem. 2009, 20, 1039. (19) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M .W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 03, Revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (20) Wei, T.; Zhu, W.H.; Zhang, J.; Xiao, H. M. J. Hazard. Mater. 2010, 179, 581. (21) Fan, X. W.; Ju, X. H.; Xiao, H. M. J. Hazard. Mater. 2008, 156, 342. 11794
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