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Quantum-Chemical Studies on Hexaazaisowurtzitanes V. D. Ghule,† P. M. Jadhav,‡ R. S. Patil,‡ S. Radhakrishnan,*,‡ and T. Soman‡ ACRHEM, UniVersity of Hyderabad, Hyderabad, and High Energy Materials Research Laboratory, Pune, India ReceiVed: July 28, 2009; ReVised Manuscript ReceiVed: NoVember 12, 2009
Highly nitrated cage molecules constitute a new class of energetic materials that have received a substantial amount of interest. Among them 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) is a powerful explosive with poor impact and friction characteristics. In the present study we aim to design novel energetic materials by tailoring the molecular structure of CL-20. Important characteristics such as the heat of formation and density have been predicted using density functional theory and packing calculations, respectively. Sensitivity correlations have been established for model compounds by analyzing the charge on the nitro groups. Molecules IDX1, IDX4, and IDX7 have been found to have comparable performance with better insensitivity characteristics and may be explored as CL-20 substitutes in defense applications. 1. Introduction Highly nitrated cage molecules constitute a new class of energetic materials that have gained great importance in recent years. These strained rings of cage compounds possess a concomitant increase in the heat of formation (∆Hf°) and a high density, which make them powerful explosives.1–5 In this class, caged nitramine 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) is one of the highest density and energy single components.6–8 This compound was first synthesized by Arnold Nielsen.9–11 Though the molecule is superior in performance, this molecule is highly sensitive to impact and friction. Hence, it would be desirable to tailor the molecular structure of CL-20 with improved sensitivity characteristics. Imidazole, triazole, and tetrazole are natural frameworks for energetic materials, as they have inherently high nitrogen contents. The introduction of an amino group is one of the simplest means to enhance the thermal stability of an energetic material.12,13 Adding these functionalities to the ring typically alters the ∆Hf°, making them more positive, which is a desired characteristic for most energetic materials.14 The key properties of energetic materials in relation to their electronic structure are the ∆Hf°, density, detonation pressure and velocity, and sensitivity. It is impractical to measure ∆Hf° for thermally unstable molecules and new energetic materials for which synthesis is difficult. There are several methods15 that predict the gas-phase ∆Hf° from quantum-mechanical calculations. The density functional theory methods, especially the B3LYP hybrid model, not only can produce reliable geometries and energies, but also require less time and computer resources.16,17 Similarly, density is being predicted by crystal structure packing calculations as they are superior to the group additive approaches.18 The explosive performance characteristics, viz., detonation velocity (D) and pressure (P), were evaluated by Kamlet-Jacobs empirical relations from their theoretical densities (Fo) and calculated ∆Hf°. Predicting sensitivity is of significant importance in deriving novel energetic molecules because safe handling is one of the most important issues. Among various aspects of sensitivity, impact sensitivity is measured by the drop * To whom correspondence should be addressed. E-mail: sradha78@ yahoo.com. Phone: +91 20 25869571. Fax: +91 20 25869031. † University of Hyderabad. ‡ High Energy Materials Research Laboratory.
weight impact test and experimental determination associated with large errors. Several simple relationships have been found that relate impact sensitivities with measured and predicted molecular properties, particularly within chemical families.19,20 Recently, Zhang et al. demonstrated the relationship between the impact sensitivities and electronic structures of some nitro compounds which can be established by the charge analysis of the nitro group.21,22 In the present study we aim to design novel insensitive energetic materials by systematic structure-property relationships. DFT techniques are used for the prediction of ∆Hf° by employing the isodesmic approach, while the crystal density is predicted by packing calculations. In this study we also explore the sensitivity correlations from the electronic structures. Molecular structures with diverse substituents (amino and triazole functional groups) at varying positions in the basic hexaazaisowurtzitane cage skeleton considered in the present study are shown in Figure 1. 2. Computational Details Geometry optimization of the molecular structures was carried out with the Gaussian 03 package.23 The hybrid density functional B3LYP24–26 method with the 6-31G* 27,28 basis set was used. The optimized structures were characterized to the relative energy minimum of the potential surface by frequency calculation. Thermal corrections to the enthalpy at 298.15 K were also obtained from frequency calculation. Those molecules that possess internal rotation and a thermodynamic degree of freedom have been treated in the default level as it is implemented in the Gaussian 03 package. The method of isodesmic reaction was used to calculate ∆Hf° from total energies obtained from the ab initio calculations. To obtain better calculation accuracy, the reference compounds for all isodesmic reactions are the same, and their total energies (E0), zero point energies (ZPEs), thermal corrections (HT°), and ∆Hf° values were calculated at the B3LYP/6-31G* level. ∆Hf° for the hexaazaisowurtzitane cage (C2A) and CL20 was evaluated by constructing the isodesmic reaction as shown in Figure 2. In addition, ∆Hf° for reference compound NH2NO2 was evaluated by the G3 theory based on the atomization approach.29 Density was predicted using crystal structure packing calculations implemented in the Polymorph
10.1021/jp9071839 2010 American Chemical Society Published on Web 12/10/2009
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Figure 1. Structures of the model compounds.
module of Accelrys’s Materials Studio 4.01 suite.30 B3LYP/631G*-optimized structures were taken as the input geometry, and the Dreiding force field was employed to predict the possible molecular packing.31 The calculation involves defining a molecule in an asymmetric cell unit, packing into a crystal under a given space group symmetry, geometry optimization to achieve an energy-minimized structure, and removal of duplicate crystal structures by the clustering process as implemented in the Polymorph module.32 The empirical Kamlet-Jacobs equations were employed to estimate the values of D and P for the high-energy materials containing C, H, O, and N:
D ) 1.01(NM1/2Q1/2)1/2(1 + 1.30Fo)
(1)
P ) 1.55Fo2NM1/2Q1/2
(2)
where D is the detonation velocity (km/s), P is the detonation pressure (GPa), N is the number of moles of gaseous detonation
products per gram of explosives, M is the average molecular weight of the gaseous products, Q is the chemical energy of detonation (kJ/mol) defined as the difference in ∆Hf° between the products and reactants, and Fo is the density of the explosive (g/cm3). Atomic charges have been computed for the optimized geometries of designed molecules by natural bond orbital (NBO) analysis at the MP2/6-31G* level. 3. Results and Discussion Polynitrogen compounds are environmentally acceptable highenergy materials.33–37 Recently, polynitrofullerenes, polynitro1,2-bishomopentaprismanes, and polynitroimidazoles have also been studied by quantum-chemical calculations.38–40 In the present paper we discuss the predicted performance characteristics of the hexaazaisowurtzitane family of compounds. A
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Figure 2. Isodesmic reaction scheme.
TABLE 1: Total Energy (E0) at the B3LYP/6-31G* Level and Experimental ∆Hf° for the Reference Compounds
a
compd
E0 (au)
∆Hf° (kJ/mol)
CH4 CH3CH3 NH3 CH3NH2 CH3NO2 NH(CH3)2 NH2NH2 C 2 H 2N 3 NH2NO2
-40.46935 -79.75076 -56.50961 -95.78444 -244.95385 -135.06455 -111.79616 -242.18480 -260.98726
-74.6 -84.0 -45.9 -22.5 -74.7 -18.6 95.2 199.3 8.0a
Value obtained from G3 atomization calculations.
systematic structure-property relationship has been established by varying different substituents on the hexaazaisowurtzitane cage. 3.1. Gas-Phase Heat of Formation. ∆Hf° of model compounds has been predicted using the B3LYP method in combination with the 6-31G* basis set in the present study through the appropriate design of isodesmic reactions.41 The isodesmic reaction, in which numbers of electron pairs and chemical bond types are conserved in the reaction,42 allows cancellation of errors inherent in the approximate treatment of electron correlation in the solutions to quantum-mechanical equations. In addition, reasonably accurate predictions of ∆Hf° are possible by utilizing isodesmic schemes, even at relatively low levels of theory. However, good experimental values must be available for all but one reaction component, and also it is known that the different isodesmic reactions will predict different values for the same ∆Hf°.43 Recently, the isodesmic approach has been demonstrated for determination of ∆Hf° within a few kilocalories per mole of the experimental value.44 The calculated gas-phase ∆Hf° values at 298.15 K using the isodesmic approach are shown in Table 1. The experimental ∆Hf° of the reference molecules used in the isodesmic approach is presented in Table 1, while for NH2NO2 it has been obtained from the atomization approach using the G3 theory. ∆Hf° values calculated by the isodesmic approach of model compounds (C2A, CL-20 and IDX1-IDX8) are shown in Table 2. It is evident from the data listed in Table 2 that the ∆Hf° values of all compounds are quite large and positive. They are significantly higher than that of the basic hexaazaisowurtzitane cage (C2A), which shows that introduction of a nitro group is the main origin of energy. The positive value of ∆Hf° for C2A shows that energy can be brought into the system by strained ring systems and introduction of a heteroatom in the ring
(replacement of the ring carbons). The gas-phase ∆Hf° of CL20 is calculated to be 691 kJ/mol; however, the condensedphase value will be lower due to the contribution of the enthalpy of sublimation.7 It is also clear from Table 2 that, with an increase in the number of nitro groups, ∆Hf° of the corresponding compound increases, which may be attributed to repulsion of the nitro groups. Compound C2A represents the basic skeleton (hexaazaisowurtzitane cage), while IDX8, IDX2, and CL-20 contain two, four, and six nitro groups, respectively. Figure 3 shows the graph of the number of nitro groups versus ∆Hf° and reveals that ∆Hf° increases linearly with an increase in the number of nitro groups. This indicates that the explosive performance of CL-20 is superior among the model compounds. Comparison of IDX2, IDX3, and IDX4 clearly indicates the introduction of a nitrotriazole group increases the energy content significantly, and IDX4 is calculated to have the highest ∆Hf° (1044.5 kJ/mol) compared to the others. 3.2. Density. The high densities in the compounds can be achieved if the molecular structure contains fused ring systems and energy can be brought into the system by strained ring systems.2 Crystal structure density is predicted by the rigorous molecular packing calculations. The approach is based on the generation of possible packing arrangements in all reasonable space groups to search for the low-lying minima in the lattice energy surface. It has been observed that most organic crystals crystallize in only a few space groups (P21/c, P212121, P1j, P21, C2/c, Pbca, Pna21, Pnma, Pbcn).45,46 Hence, in the present study the search is limited to these space groups. The B3LYP/6-31G*level-optimized ground-state geometry is considered as the input structure for the polymorph search. The high-density polymorph is sorted out from the large number of potential crystal structures, and the lattice parameters of the same are presented in Table 3. The results reveal that all the molecules fall under four space groups, viz., Pbca, P21/c, Pna21, and P1j. The density of CL-20 is calculated to be 1.9 g/cm3 and is comparable to the experimental density.6 C2A offers a density of 1.5 g/cm3, and further the packing efficiency in the condensed phase increased by the introduction of substituents to the basic cage skeleton. It is also clear from Figure 3 that an increase in the density is observed with an increase in the number of nitro groups (from two to six in IDX8, IDX2, and CL-20, respectively), while the density decreases with the introduction of an amino group. However, the role of the amino group cannot be clearly defined since the packing pattern is highly dependent on the electronic structure of the molecule.47 Comparison of IDX2, IDX3, and IDX4 reveals that there is no significant change in density by
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TABLE 2: Calculated Thermophysical and Explosive Characteristics C2A CL-20 IDX1 IDX2 IDX3 IDX4 IDX5 IDX6 IDX7 IDX8 a
E0 (au)
∆Hf° (kJ/mol)
Fo (g/cm3)
Q (cal/g)
D (km/s)
P (GPa)
OBa (%)
-564.08800 -1790.93586 -1492.59063 -1382.00320 -1827.50079 -2272.89415 -1194.25507 -1882.79267 -2031.96156 -973.05904
319.9 691.3 768.0 537.6 760.6 1044.5 819.9 867.3 859.0 386.4
1.57 1.97 1.96 1.87 1.87 1.84 1.72 1.84 1.90 1.79
839.7 1738.2 1623.2 1572.9 1510.1 1497.2 1444.1 1527.4 1597.5 1291.1
5.56 9.73 9.34 8.87 8.81 9.21 8.09 8.68 9.02 8.30
12.56 44.64 40.64 35.66 35.51 40.41 28.23 33.88 37.29 30.45
-171.2 -11.0 -38.1 -36.8 -34.8 -33.6 -75.4 -35.4 -23.8 -80.6
OB ) oxygen balance.
Figure 3. Effect of nitro groups on the ∆Hf° and density of the compounds.
the introduction of nitrotriazole. Overall, except the molecules IDX5 and IDX8, all molecular structures have a density of about 1.9 g/cm3. Some of the representative crystal structures are shown in Figure 4. 3.3. Detonation Characteristics. The velocity of detonation (VOD) and pressure of the molecules are computed by Kamlet-Jacobs empirical equations48,49 on the basis of their theoretical densities (Fo) and calculated gas-phase heats of formation. The detonation velocity is proportional to the density, while the Chapman-Jouguet detonation pressure is proportional to the square of the initial density.50,51 Table 2 summarizes the calculated total electronic energy (E0), density (Fo), chemical energy of detonation (Q), VOD (D), and detonation pressure (P) for the molecules. The chemical energy of detonation (Q) varies from 1450 to 1630 kJ/mol and is calculated to be high for IDX1. The model compounds (IDX1 to IDX8) have a VOD higher than 8 km/s and a pressure above 30 GPa. Though their ∆Hf° values are higher than that of CL-20, due to the lower
densities, all the compounds have VODs and P values that are less than those of CL-20. This is because the performance characteristics D and P are mainly dependent on the crystal density of the molecule rather than its ∆Hf°. IDX1 is calculated to have the highest VOD among the designed molecules, and the replacements of nitro groups in CL-20 by amino groups bring the VOD down in IDX1. It is also observed that an increase in the number of nitro groups (from two to six in IDX8, IDX2, and CL-20, respectively) increases the Fo, Q, D, and P values of the corresponding compounds. Figure 5 compares the VODs of the model compounds. Introduction of a nitro group in the hexaazaisowurtzitane cage increases the density of the molecules and therefore has a significant contribution to the D and P performance characteristics. Though the introduction of one nitrotriazole in IDX2 does not alter the VOD significantly in IDX3, further addition of nitrotriazole increases the VOD to 9.2 km/s in IDX4. Further, introduction of the nitrotriazole ring on the hexaazaisowurtzitane (IDX3, IDX4, IDX6, and IDX7) also reveals an improvement in the performance characteristics. Comparison of IDX2, IDX3, and IDX4 indicates that, in these cases, the VOD is also dependent on N and M in addition to Q and Fo. Overall, IDX1, IDX4, and IDX7 have moderately comparable performance characteristics. 3.4. Impact Sensitivity Correlations. The relationship between the impact sensitivity and electronic structures of some nitro compounds can be established by the charge analysis of the nitro group.52 Nitro compounds are very strong electron acceptors and have a strong ability to attract electrons. Such an ability can be represented by the net charges of the nitro group. The higher the negative charge on the nitro group, the lower the electron attraction ability and therefore the more stable the nitro compound. In nitro-containing covalent compounds, C-NO2, N-NO2, and O-NO2 bonds denoted as R-NO2 bonds are usually the weakest in the molecule, and their breaking is the initial step in the decomposition or detonation. In the present
TABLE 3: Density and Lattice Parameters of the Predicted Highly Dense Polymorph of the Designed Molecules length (Å) compd C2A CL-20 IDX1 IDX2 IDX3 IDX4 IDX5 IDX6 IDX7 IDX8
space group P1j Pbca Pna21 P1j P1j Pbca P21/c P21/c P1j P1j
angle (deg)
cell volume (Å3)
density (g/cm3)
a
b
c
R
β
γ
381.4 2989.3 1315.4 633.1 830.7 4188.9 1283.2 1747.9 894.6 496.5
1.57 1.97 1.96 1.87 1.87 1.84 1.72 1.84 1.90 1.79
6.8 15.1 12.3 6.1 12.9 8.4 23.1 9.9 7.1 7.1
10.8 12.8 8.0 18.2 10.7 36.2 13.2 19.8 16.9 7.0
6.5 15.4 13.4 8.2 6.9 13.8 13.9 12.2 9.0 11.2
98.6 90.0 90.0 101.5 94.1 90.0 90.0 90.0 115.1 104.7
54.9 90.0 90.0 68.1 110.7 90.0 162.4 47.1 110.2 107.0
100.9 90.0 90.0 59.7 107.9 90.0 90.0 90.0 90.5 72.2
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Figure 5. VOD and -QNO2 profile of the model compounds.
TABLE 4: Computed -QNO2 from Atomic Charges by NBO Analysis compd
CL-20
IDX1
IDX2
IDX3
IDX4
IDX5
IDX6
IDX7
IDX8
-QNO2(e)
0.075
0.115
0.118
0.108
0.088
0.137
0.099
0.099
0.134
increase in the strength of the adjacent N-NO2 bond by the introduction of the amino group. Comparison of IDX2, IDX3, and IDX4 reveals that introduction of a single nitrotriazole ring does not play any role in altering the sensitivity behavior, but this role increases with introduction of two nitrotriazoles. Overall, the designed model compounds were found to have less impact sensitivity than CL-20. 4. Conclusions
Figure 4. Crystal structures of (a) IDX1, (b) IDX4, and (c) IDX7.
study, the charge on the nitro group (-QNO2) is considered for its correlation to impact sensitivity:
QNO2 ) QN + QO1 + QO2
(3)
The charge on the nitro group (-QNO2) is calculated by the sum of atomic charges on the nitrogen (QN) and oxygen (QO1 and QO2) atoms in the nitro group. Computed -QNO2 values of the molecules are presented in Table 4. The higher the -QNO2, the larger the impact insensitivity, and hence, -QNO2 can be regarded as the criterion for estimating the impact sensitivities. -QNO2 is calculated to be 0.075 e for CL-20, and for the other compounds it ranges from 0.088 to 0.137 e. This shows that the designed model compounds are more insensitive than CL20 (Figure 5). An increase in the number of nitro groups (from two to six in IDX8, IDX2, and CL-20) increases the impact sensitivity. Similarly, replacement of a nitro group with an amino group decreases the sensitivity. This can be attributed to an
Structure-property studies have been performed on hexaazaisowurtzitanes to achieve energetic performance comparable to that of CL-20 with better insensitivity characteristics. The ∆Hf° values of the model compounds have been computed by constructing reasonable isodesmic reactions using the DFT B3LYP6/31G* method. It has been found that the nitrotriazolebearing hexaazaisowurtzitane cage possesses a very high positive ∆Hf°. The crystal density has been predicted using molecular packing calculations. The density of the designed molecules is predicted to be about 1.9 g/cm3 in general, and the introduction of nitrotriazoles does not affect the density significantly. The model compounds (IDX1 to IDX8) have VODs higher than 8 km/s and pressures above 30 GPa. The charge on the nitro group has been analyzed to correlate the impact sensitivity. The NBO study reveals that the designed molecules have better impact insensitivity than the CL-20 molecule. The computational study identified IDX1, IDX4, and IDX7 as potential replacements for CL-20 in various energetic formulations. Acknowledgment. We thank Dr. A. Subhananda Rao, Director, Mr. B. Bhattacharya, Associate Director, and Dr. R. K. Pandey, Joint Director, High Energy Materials Research Laboratory, for their approval to publish this work. We also acknowledge the computational resources provided by the Centre for Development of Advanced Computing, Bangalore, India. References and Notes (1) Pagoria, P. F.; Lee, G. S.; Mitchell, A. R.; Schmidt, R. D. Thermochim. Acta 2002, 384, 187. (2) Bircher, H. Chimia 2004, 58, 355. (3) Qui, L.; Xiao, H. M.; Gong, X. D.; Ju, X. H.; Zhu, W. H. J. Phys. Chem. B 2006, 110, 3797.
Quantum-Chemical Studies on Hexaazaisowurtzitanes (4) Xu, X. J.; Xiao, H. M.; Ju, X. H.; Gong, X. D.; Zhu, W. H. J. Phys. Chem. A 2006, 110, 5929. (5) Richard, R. M.; Ball, D. W. J. Mol. Struct. 2008, 858, 85. (6) Simpson, R. L.; Urtiew, P. A.; Ornellas, D. L.; Moody, G. L.; Scribner, K. J.; Hoffman, D. M. Propellants, Explos., Pyrotech. 1997, 22, 249. (7) Geetha, M.; Nair, U. R.; Sarwade, D. B.; Gore, G. M.; Asthana, S. N.; Singh, H. J. Therm. Anal. Calorim. 2003, 73, 913. (8) Isayev, O.; Gorb, L.; Qasim, M.; Leszczynski, J. J. Phys. Chem. B 2008, 112, 11005. (9) Nielsen, A. T.; Nissan, R. A.; Vanderah, D. J.; Coon, C. L.; Gilardi, R. D.; George, C. F.; Flippen-Anderson, J. J. Org. Chem. 1990, 55, 1459. (10) Nielsen, A. T. Caged Nitramine Compound. U.S. Patent 5,693,794, 1997. (11) Nielsen, A. T.; ChaWn, A. P.; Christian, S. L.; Moore, D. W.; Nadler, M. P.; Nissan, R. A.; Vanderah, D. J.; Gilardi, R. D.; George, C. F.; Flippen-Anderson, J. L. Tetrahedron 1998, 54, 11793. (12) Agrawal, J. P. Prog. Energy Combust. Sci. 1998, 24, 1. (13) Xue, H.; Gao, Y.; Twamley, B.; Shreeve, J. M. Chem. Mater. 2005, 17, 191. (14) Gutowski, K. E.; Rogers, R. D.; Dixon, D. A. J. Phys. Chem. A 2006, 110, 11890. (15) Keshavarz, M. H. J. Hazard. Mater. 2006, 136, 145. (16) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: Oxford, 1989. (17) Byrd, E. F. C.; Rice, B. M. J. Phys. Chem. C 2007, 111, 2787. (18) Peralta-Inga, Z.; Degirmenbasi, N.; Olgun, U.; Gocmez, H.; Kalyon, D. M. J. Energ. Mater. 2006, 24, 69. (19) Cho, S. G.; No, K. T.; Goh, E. M.; Kim, J. K.; Shin, J. H.; Joo, Y. D.; Seong, S. Bull. Korean Chem. Soc. 2005, 26, 399. (20) Badders, N. R.; Wei, C.; Aldeeb, A. A.; Rogers, W. J.; Mannan, M. S. J. Energ. Mater. 2006, 24, 17. (21) Zhang, C.; Shu, Y.; Huang, Y.; Zhao, X.; Dong, H. J. Phys. Chem. B 2005, 109, 8978. (22) ChaoYang, Z.; Yuanjie, S.; Yigang, H.; Xinfeng, W. J. Energ. Mater. 2005, 23, 107. (23) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, T., Jr.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision A.1; Gaussian, Inc.: Pittsburgh, PA, 2003.
J. Phys. Chem. A, Vol. 114, No. 1, 2010 503 (24) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (25) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (26) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1998, 37, 785. (27) Petersson, G. A.; Al-Laham, M. A. J. Chem. Phys. 1991, 94, 6081. (28) Rassolov, V. A.; Pople, J. A.; Ratner, M. A.; Windus, T. L. J. Chem. Phys. 1998, 109, 1223. (29) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. J. Chem. Phys. 1998, 109, 7764. (30) Materials Studio 4.01; Accelrys Inc.: San Diego, CA, 2004. (31) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. J. Phys. Chem. 1990, 94, 8897. (32) Wang, G. X.; Shi, C. H.; Gong, X. D.; Zhu, W. H.; Xiao, H. M. J. Hazard. Mater. 2009, 169, 813. (33) Chavez, D. E.; Hiskey, M. A.; Gilardi, R. D. Angew. Chem., Int. Ed. 2000, 39, 1791. (34) Fraenk, W.; Habereder, T.; Hammerl, A.; Klapotke, T. M.; Krumm, B.; Mayer, P.; Noth, H.; Warchhold, M. Inorg. Chem. 2001, 40, 1334. (35) Hammerl, A.; Holl, G.; Klapotke, T. M.; Kaiser, M.; Ticmanis, U.; Noth, H.; Warchhold, M. Inorg. Chem. 2001, 40, 3570. (36) Hammerl, A.; Holl, G.; Klapotke, T. M.; Kaiser, M.; Piotrowski, H. Propellants, Explos., Pyrotech. 2001, 26, 161. (37) Guo, Y. Q.; Greenfield, M.; Bhattacharya, A.; Bernstein, E. R. J. Chem. Phys. 2007, 127, 154301. (38) Slanina, Z.; Zhao, X.; Chiang, L. Y.; Osawa, E. Int. J. Quantum Chem. 1999, 74, 343. (39) Qiu, L. M.; Gong, X. D.; Zheng, J.; Xiao, H. M. J. Hazard. Mater. 2009, 166, 931. (40) Fan, X. W.; Ju, X. H.; Xiao, H. M. J. Hazard. Mater. 2008, 156, 342. (41) Hehre, W. J.; Ditchfield, R.; Radom, L.; Pople, J. A. J. Am. Chem. Soc. 1970, 92, 4796. (42) Hehre, W. J.; Radom, L.; Schleyer, P. V. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley and Sons: New York, 1986. (43) Foresman, J. B.; Frisch, A. Exploring Chemistry with Electronic Structure Methods, 2nd ed.; Gaussian, Inc: Pittsburg, PA., 1996; p 181. (44) Li, X. H.; Zhang, R. Z.; Yang, X. D.; Zhang, H. J. Mol. Struct. 2007, 815, 151. (45) Baur, W. H.; Kassner, D. Acta Crystallogr., Sect. B 1992, 48, 356. (46) Belsky, V. K.; Zorkii, P. M. Acta Crystallogr., Sect. A 1977, 33, 1004. (47) Li, J.; Huang, Y.; Dong, H. Propellants, Explos., Pyrotech. 2004, 29, 231. (48) Kamlet, M. J.; Jacobs, S. J. J. Chem. Phys. 1968, 48, 23. (49) Kamlet, M. J.; Huewitz, H. J. Chem. Phys. 1968, 48, 3685. (50) Mader, C. L. In Organic Energetic Compounds; Markinas, P. L., Ed.; Nova Science Publishers: Commack, NY, 1996; p 193. (51) Strehlow, R. A. Combustion Fundamentals; McGraw-Hill: New York, 1985; p 302. (52) Zhang, C.; Shu, Y.; Huang, Y.; Zhao, X.; Dong, H. J. Phys. Chem. B 2005, 109, 8978.
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