DFT Studies on the Four Polymorphs of Crystalline CL-20 and the

Feb 3, 2007 - DFT-D studies on structural variation and absorption properties of crystalline benzotrifuroxan under high pressure. Dong Xiang , Qiong W...
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J. Phys. Chem. B 2007, 111, 2090-2097

DFT Studies on the Four Polymorphs of Crystalline CL-20 and the Influences of Hydrostatic Pressure on E-CL-20 Crystal Xiao-Juan Xu,†,‡ Wei-Hua Zhu,† and He-Ming Xiao*,† Institute for Computation in Molecular and Materials Science and Department of Chemistry, Nanjing UniVersity of Science and Technology, Nanjing 210094, People’s Republic of China, and Department of Chemistry, Yancheng Teachers’ College, Yancheng 224002, Jiangsu ProVince, People’s Republic of China ReceiVed: October 17, 2006; In Final Form: December 18, 2006

Based on density functional theory (DFT), four different methods with the generalized gradient approximation (GGA) have been employed to investigate the structural and electronic properties of the four polymorphs (R‚H2O, β, γ, and  phases) of CL-20, which is a well-known high energy density compound (HEDC). The relaxed crystal structures compare well with experimental data. According to the constitution of the frontier energy bands and the Mulliken population analyses, the N-NO2 bond is predicted to be the trigger bond during thermolysis. The density of states (DOS) of R-CL-20‚H2O is somewhat different from those of the other three crystals for its inclusion of H2O molecules that contribute the frontier energy bands. The band gaps obtained from the four different methods are consistent with each other. According to the calculated values of band gaps, the sensitivity of the four polymorphs of CL-20 is predicted as  < β < γ < R‚H2O, which agrees well with the experimental result. The effects of hydrostatic compression on the most stable -CL-20 have also been investigated using the GGA-PBE method in the pressure range of 0-400 GPa. -CL20 has anisotropic compressibility at low or high pressure. The band gap is found to decease with increasing pressure, showing the corresponding sensitivity increase. Based on the changes of the band gap and DOS with pressure, 400 GPa is considered to be the critical pressure for the insulator-metal phase transition.

1. Introduction Crystal is one of the most common forms that a material exists as. The crystal structure of a material determines its physical and chemical properties. Thus, investigation of crystals is more approximate to real materials than that of molecules. On the other hand, the investigation of crystal structure plays an important role in following the chemistry development trend from “molecular chemistry” to “materials chemistry”. Hexanitrohexaazaisowurtzitane (HNIW or CL-20) is an important energetic compound. Its successful synthesis has been praised as a breakthrough in the history of explosive synthesis,1 and it has been characterized as a high energy density compound (HEDC) in a number of high-performance explosive, propellant, and propelling agent formulations. Due to the different extending orientations of nitro groups relative to the five- or six-membered rings, the different molecular packing models, and the different number of molecules in a cell, four pure crystal polymorphs of CL-20, denoted as R-CL-20‚H2O, β-CL-20, γ-CL-20, and -CL20, have been separated and differentiated. -CL-20 has the biggest density and the greatest stability among them.2 There have been a series of theoretical or experimental studies on gaseous CL-20 molecules,3,4 CL-20 crystals,5-13 and CL-20based PBXs (polymer-bonded explosives).14-18 The sensitivity of an energetic material to initiation by a heat, shock, light, impact, or electrical discharge stimulus is the product of various factors. As an energetic material, its sensitivity is one of the most important properties and determines its application. The sensitivity measure usually depends on * Corresponding author. E-mail: [email protected]. † Nanjing University of Science and Technology. ‡ Yancheng Teachers’ College.

experiments, while the preliminary temperature, the loading density and mode of an explosive, and external stimulus influence the measurements of sensitivities. Therefore, establishment of a uniform measure for evaluating explosive sensitivity is still a challenging question. It is well-known that the crystal structure of a material determines its band structure, physical properties, and chemical properties, which further affect its sensitivity. Thus, it is necessary to model the properties of a solid at the atomic level and correlate its band structure with explosive sensitivity. Previously, most of the understanding of sensitivity has been obtained on the semiempirical discrete variation XR (DV-XR) and extended Hu¨ckel-crystal orbital (EH-CO) methods using a cluster moldel.19-21 In addition, most of the empirical modeling has been focused on the properties of the molecule in question, generally in the ground-state configuration. With the development of theoretical chemistry and computer technology, the Hartree-Fock quantum chemical method has also been employed to reveal the essence of the phenomenon,22,23 but these studies do not include electron correlation. Recently, density functional theory (DFT) with pseudopotentials and a plane-wave basis set, often used within the generalized gradient approximation (GGA), has been well established and has been successfully applied to the study of structures and properties of solids.24 Until now, no theoretical work has been done to provide the band structure of CL-20 and to predict its sensitivity, including the sensitivity ordering of the different polymorphs of CL-20. In addition, it is important to understand the influence of external factors such as pressure on the properties of a material. Thus, in this paper, we performed a series of DFT calculations to study the electronic structures of the four polymorphs of CL-20 using four different methods. Based on the obtained band gaps and

10.1021/jp066833e CCC: $37.00 © 2007 American Chemical Society Published on Web 02/03/2007

Polymorphs of Crystalline CL-20

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Figure 1. Unit cells for the four polymorphs of CL-20: (a) R-CL-20‚H2O, (b) β-CL-20, (c) γ-CL-20, and (d) -CL-20. Gray, white, red, and blue spheres stand for C, H, O, and N atoms, respectively.

“principle of easiest transition” (PET),19 the ordering of the sensitivity of the four polymorphs was predicted. In addition, the most stable -CL-20 was chosen to investigate the influences of hydrostatic pressure on the bulk properties, band structure, density of states (DOS), and sensitivity. 2. Computational Methods Based on DFT, we use four different methods to estimate the electronic structures of the four polymorphs of CL-20. The single point and full relaxation calculations were performed for β-, γ-, and -CL-20 unit cells (but not R-CL-20‚H2O because of its large size exceeding the calculation capability), using the DFT25 method with the GGA-PBE (Perdew-Burke-Ernzerhof) exchange-correlation functional26 and Vanderbilt-type ultrasoft pseudopotentials27 in the CASTEP program.28 Considering the

resource requirement and comparison, the calculation quality was set to medium. When the crystal was fully optimized, the atomic positions and the unit cell parameters were allowed to relax to the minimum energy configuration. The self-consistent ground state of the system was determined using a band-byband conjugate gradient technique to minimize the total energy of the system with respect to the plane-wave coefficients. The electronic wave functions were obtained by the Pulay densitymixing scheme,29 and the structures were relaxed using the BFGS method.30 Correspondingly, the total energy of the system was converged to less than 2.0 × 10-5 eV/atom, the residual force to less than 0.05 eV/Å, the displacement of atoms to less than 0.002 Å, and the residual bulk stress to less than 0.1 GPa. The cutoff energy of plane waves was set to 300.0 eV, and

TABLE 1: Experimental and Relaxed Lattice Constants and Atomic Fractional Coordinates Using the GGA-PBE Method for Bulk E-CL-20a atomic fractional coordinateb lattice constant

atoms

u

V

w

a ) 13.884 (13.696)

C C C C C C N N N N N N N N N N N N O O O O O O O O O O O O

0.3740 (0.3741) 0.1835 (0.1854) 0.3664 (0.3659) 0.2218 (0.2251) 0.2135 (0.2158) 0.1925 (0.1961) 0.3373 (0.3381) 0.2972 (0.2976) 0.3046 (0.3078) 0.1791 (0.1850) 0.2833 (0.2842) 0.1336 (0.1393) 0.3729 (0.3718) 0.0393 (0.0422) 0.3289 (0.3280) 0.3018 (0.3012) 0.3957 (0.3973) 0.1473 (0.1464) 0.4583 (0.4601) 0.3884 (0.3931) 0.2286 (0.2312) 0.0104 (0.0133) 0.4873 (0.4900) 0.3216 (0.3183) 0.1191 (0.1168) 0.3517 (0.3530) 0.2259 (0.2238) 0.1476 (0.1443) 0.3918 (0.3918) -0.0082 (-0.0067)

0.0619 (0.0629) 0.1359 (0.1352) 0.1368 (0.1369) 0.1191 (0.1184) 0.2347 (0.2324) 0.0192 (0.0212) 0.1134 (0.1150) -0.0226(-0.0190) -0.1034 (-0.1028) 0.2122 (0.2115) 0.0965 (0.0998) 0.0550 (0.0556) 0.3310 (0.3287) 0.0123 (0.0135) 0.2405 (0.2387) 0.1057 (0.1013) 0.1974 (0.1934) 0.2976 (0.2926) 0.3191 (0.3191) -0.1121 (-0.1132) -0.1606 (-0.1603) -0.0626 (-0.0616) 0.1993 (0.1949) 0.4115 (0.4092) 0.2753 (0.2668) 0.2601 (0.2545) 0.1153 (0.1121) 0.3847 (0.3818) 0.0954 (0.0873) 0.0546 (0.0556)

0.7878 (0.7906) 0.8671 (0.8646) 0.9283 (0.9281) 0.5640 (0.5690) 0.7816 (0.7823) 0.6467 (0.6520) 0.6313 (0.6373) 0.7441 (0.7504) 0.8519 (0.8509) 0.6118 (0.6150) 0.9814 (0.9793) 0.7467 (0.7477) 0.9554 (0.9524) 0.7267 (0.7259) 0.8554 (0.8602) 1.1492 (1.1449) 0.6094 (0.6087) 0.5014 (0.5026) 1.0585 (1.0524) 0.9648 (0.9619) 0.8237 (0.8217) 0.6335 (0.6321) 0.6994 (0.6980) 0.9209 (0.9190) 0.3577 (0.3602) 0.5024 (0.4972) 1.1870 (1.1805) 0.5599 (0.5566) 1.2392 (1.2362) 0.8011 (0.8004)

b ) 12.741 (12.554) c ) 8.969 (8.833) R ) 90.00 (90.00) β ) 111.18 (11.305) γ ) 90.00 (90.00) F ) 1.969 (2.055)

a

The experimental values are in parentheses. b The fractional coordinates of H atoms are omitted.

2092 J. Phys. Chem. B, Vol. 111, No. 8, 2007

Figure 2. Structure and atomic numbering of -CL-20 molecule.

Brillouin zone sampling was performed using the MonkhorstPack31,32 scheme in reciprocal space. In solving the Schro¨dinger equation of a system, DMol3 33,34 uses the numerical integration method; thus it can more greatly accelerate the calculation for larger systems than CASTEP can. To make a complete comparison and give reliable results, the GGA-RPBE (Revised Perdew-Burke-Ernzerhof)35 method in DMol3 was used to calculate the electronic structures for the four polymorphs of CL-20. Whether single point or optimization calculations in DMol3, all electrons are treated in the same manner as valence electrons. However, in our current version of DMol3, only atomic position relaxation can be carried out. In the calculations, we use the experimentally determined structures of the four polymorphs of CL-20. The structures of the four unit cells are presented as Figure 1. The R-CL-20‚ H2O crystallizes in the orthorhombic space group PBCA with a ) 0.9603 nm, b ) 1.3304 nm, and c ) 2.3653 nm, and has eight R‚H2O molecules per unit cell.10 β-CL-20 crystal is in the orthorhombic space group PCA21 with a ) 0.9670 nm, b ) 1.1616 nm, and c ) 1.3032 nm, and has four molecules per unit cell.11 γ-CL-20 crystal belongs to the monoclinic space group P21/N with a ) 0.9670 nm, b ) 1.1616 nm, and c ) 1.3032 nm, and has four molecules.12 -CL-20 belongs to the monoclinic space group P21/A with a ) 1.3696 nm, b ) 1.2254 nm, c ) 0.8833 nm, and β ) 111.18°, and has four molecules per unit cell.13 3. Results and Discussion 3.1. DFT Studies on the Four Polymorphs of CL-20. To check the reliability of the used GGA-PBE method, we compared the calculated and experimental structural parameters of bulk -CL-20. Table 1 presents the experimental13 and optimized cell parameters for -CL-20 crystal. From Table 1, it is found that the calculated results are 1.5% or so larger than the measured lattice constants, which is typical for the GGA-PBE method. We also checked the effect of the relaxation on the atomic fractional coordinates in Table 1. The

Xu et al. internal parameters in our relaxed geometries compare well with the available experimental values. This shows that the effect of the relaxation on the atomic positions is very small. We note that the internal structure parameters of -CL-20 assigned by the bond lengths and bond angles are close to the corresponding experimental data, as shown in Table 2. For example, the calculated C-N bond lengths are in the range of 1.428-1.458 Å, which approximate the experimental values of 1.434-1.477 Å. In addition, the relaxed unit cell parameters of β-CL-20 in the same way well reproduce the experimental results. These results indicate that the GGA-PBE method is suitable for these crystals. It should be pointed out that, in our work, β- and -CL-20 were relaxed with the CASTEP program. However, for some unknown reason, γ-CL-20 cannot be optimized in this way, and the size of R-CL-20‚H2O is beyond the calculation capability. Thus, the single point calculations of β-CL-20, γ-CL-20, and -CL-20 by the GGA-PBE method with CASTEP were also performed to provide supplementary information for the electronic characteristics. 3.1.1. Density of States (DOS). In our calculations, single point and relaxation calculations of the four crystals are performed using the GGA-PBE in CASTEP and GGA-RPBE in DMol3. It was exciting to see that the four different methods resulted in very similar densities of states (DOS) for each crystal. In this paper, we present only the DOS and PDOS (projection of DOS on atom-centered orbitals) obtained from the single point calculation on the experimental cell unit of the four crystals, since it can perform direct calculations on the four experimental crystal structures for comparison. Figure 3 displays the DOS and corresponding PDOS for R-CL-20‚H2O, β-CL-20, γ-CL-20, and -CL-20 unit cells, respectively. The origin of the energy is taken to be the Fermi level. We observe several general features from Figure 3. First, the DOS and PDOS for the three crystals β-CL-20, γ-CL-20, and -CL-20 are similar; it is understood that the number of molecules in each crystal is equal and the molecules have similar structures and are different only in the special orientations of -NO2. Second, the DOS and PDOS of R-CL-20‚H2O are larger than those of the other three crystals because it has more valence electrons. Third, the H2O states in R-CL-20‚H2O are at the top of the valence band, while the DOS of the CL-20 molecules is still similar to those of β, γ, and , except the former slightly shifts to the lower energy region. Fourth, all four crystals have a greater presence in the states of the narrow region at the top of the valence band. It is understood that the overlap of the energy bands in the region is strong. The atom-resolved DOS and PDOS of the four crystals are also shown in Figure 3. The main characteristics can be summarized as follows: (i) For R-CL-20‚H2O, the s and p states of O and H atoms in H2O contribute mostly to the upper valence bands and lower conduction bands. This indicates that, during

TABLE 2: Experimental and Relaxed Bond Lengths (Å) and Bond Angles (deg) for E-CL-20 bond length

exptl13

calcd

bond angle

exptl13

calcd

bond angle

exptl13

Calcd

C1-N1 C1-N2 C6-N2 C4-N4 C6-N6 C1-C3 C4-C6 N2-N3 N3-O2 N3-O3

1.442 1.445 1.477 1.437 1.434 1.590 1.575 1.368 1.224 1.215

1.441 1.439 1.458 1.433 1.428 1.589 1.570 1.371 1.247 1.238

C3-C1-N1 C3-C1-N2 N1-C1-N2 C4-C6-N2 C6-C4-N1 C1-N1-C4 C1-N2-C6 C1-N2-N3 C6-N2-N3 N2-C6-N6

112.6 113.3 96.0 101.3 101.0 111.1 110.8 119.6 118.7 112.0

111.7 111.7 97.2 101.9 101.5 111.2 111.1 120.6 121.2 111.6

C6-N6-N8 C2-N6-C6 C2-N6-N8 N2-N3-O2 N2-N3-O3 O2-N3-O3

120.2 118.7 121.2 116.4 116.9 126.6

120.8 117.4 121.7 116.5 116.7 126.8

Polymorphs of Crystalline CL-20

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Figure 3. Total and partial densities of states (DOS) of the four polymorphs of CL-20: (a) R-CL-20‚H2O, (b) β-CL-20, (c) γ-CL-20, and (d) -CL-20.

TABLE 3: Mulliken Populations of β-CL-20, γ-CL-20, and E-CL-20 Crystals Using the GGA-PBE Method crystal

C-H

C-C

C-N

N-N

NdO

β-CL-20 γ-CL-20 -CL-20

0.80-0.81 0.80-0.82 0.80-0.82

0.66-0.70 0.67-0.70 0.67-0.70

0.68-0.74 0.67-0.73 0.67-0.74

0.56-0.66 0.57-0.65 0.56-0.68

0.75-0.82 0.77-0.82 0.76-0.82

the thermolysis process, the H2O molecules may be first lost from R-CL-20‚H2O. Then, in the energy range from -4.5 to -1.8 eV, the DOS of R-CL-20‚H2O is mostly controlled by the p states of the O atoms in -NO2 and the N atoms in the cage skeleton. The next lower conduction bands are mainly the contributions of the p states of N and O atoms in -NO2, as well as the p states of N in the cage skeleton. (ii) For β-CL-20, γ-CL-20, and -CL-20, the contributions of C, H, O, and N

atoms to the DOS of the three crystals are almost the same. For example, the upper valence bands of -CL-20 are mainly the contributions of the s and p states of the O atoms of -NO2 and the N atoms in the cage skeleton. The lower conduction bands are mainly the contribution of the p states of N and O atoms in -NO2 and the p states of N in the cage skeleton. Also, Figure 3b-d show that, in the frontier band regions, the p states of N in -NO2 overlap those of N in the skeleton. According to

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Xu et al.

TABLE 4: Calculated Band Gaps (eV) of the Four Polymorphs of CL-20 Using Different Methodsa methods I II III IV

R-CL-20‚H2O

β-CL-20

γ-CL-20

-CL-20

1.751 2.581

3.405 3.540 3.719 3.628

3.247 3.517 3.390

3.446 3.608 3.798 3.634

a Methods I and II are the full relaxation and single point calculations on the experimental crystal with GGA-PBE in CASTEP, and III and IV are single point and atomic fraction relaxation calculations on the experimental crystal with GGA-RPBE in DMol3, respectively.

TABLE 5: Variations of the Lattice Parameters, Unit Cell Volume, Density, and Band Gaps (∆E) of E-CL-20 as a Function of the Hydrostatic Pressurea lattice parameters P (GPa)

a (Å)

b (Å)

c (Å)

β (deg)

V (Å3)

F (g cm-3)

∆E (eV)

exptl13

13.696 13.884 (1.37) 13.596 (-0.73) 13.233 (-3.38) 12.204 (-10.89) 11.535 (-15.78) 10.859 (-20.71) 9.791 (-28.5)

12.554 12.741 (1.49) 12.419 (-1.08) 11.767 (-6.27) 10.410 (-17.08) 9.893 (-21.20) 9.468 (-24.58) 9.477 (-24.51)

8.833 8.969 (1.54) 8.692 (-1.60) 8.390 (-5.02) 7.793 (-11.77) 7.451 (-15.65) 7.065 (-20.02) 6.419(-27.33)

111.180 111.305 (0.11) 111.425 (0.22) 113.289 (1.90) 116.616 (4.89) 117.271 (5.48) 119.457 (7.44) 121.244 (9.05)

1416.150 1478.110 (4.38) 1366.10 (-3.53) 1200.040 (-15.26) 885.114 (-37.50) 755.807 (-46.63) 632.468 (-55.34) 509.191 (-64.04)

2.055 1.969 (-4.18) 2.131 (3.70) 2.425 (18.05) 3.288 (60.00) 3.851 (87.40) 4.602 (123.94) 5.716 (178.51)

3.663 3.492 3.450 3.323 2.742 2.102 1.401 0.085

0 5 10 50 100 200 400 a

The values in parentheses are the corresponding percentage differences relative to the experimental data.

the principle of energy matching, these p states constitute N-NO2 bonds, and the N-NO2 bonds are predicted to be the trigger bonds during thermolysis. This is consistent with experiment9,36 and our previous theoretical study on the thermolysis of gas CL-20.37 In addition, the thermolysis mechanism of CL-20 can further be shown by comparing bond strengths. Table 3 lists the Mulliken population of three polymorphs of CL-20 obtained from experiment using the GGA-PBE method in CASTEP. From Table 3, it is found that the N-NO2 bonds of CL-20 molecules in each crystal always have the smallest populations among different types of bonds. According to “a principle of smallest bond order” (PSBO),38 the N-NO2 bond should indeed be the trigger bond during thermolysis. Although the Mulliken population of R-CL-20‚H2O could not be calculated because of its larger size, from the DOS it is reasonable to believe that the breaking of the N-NO2 bond will be the next step after the loss of H2O during thermolysis. 3.1.2. Band Gaps. The band gap between the highest occupied crystal orbital and the lowest unoccupied crystal orbital has been suggested to be relative to the sensitivity of a material. In the past decade our search group has suggested a “principle of easiest transition” (PET) to predict the sensitivity of ionic metal azides.19 In the principle, the band gap (∆E) between the highest occupied crystal orbital (HOCO) and the lowest unoccupied crystal orbital (LOCO) is used as a criterion to predict the sensitivity of a material, and the smaller the ∆E, the easier the electron transits and the larger the sensitivity will be. Many experimental results have been well illustrated by the principle. For example, the alkali-metal azides are insensitive, but heavymetal azides are very sensitive.19-21 Here, Table 4 lists the band gaps of the four crystals obtained from different methods. From Table 4, it can be found that the band gaps of each crystal from the different methods are close each other except for those of R-CL-20‚H2O. It was exciting to us that these four methods can produce the same order of band gaps for these crystals. The orders of the band gaps drawn from methods I and II are  > β and  > β > γ, respectively, and the same ordering,  > β > γ > R‚H2O, is obtained from methods III and IV. It is obvious that band gap orderings of the four crystals obtained from the four different methods are parallel. Based on PET, it can be deduced that the impact sensitivity for these

Figure 4. Views of -CL-20 along different axes.

crystals should follow the sequence  < β < γ < R‚H2O. This conclusion is almost consistent with the experimental results,  < γ < β < R‚H2O,39 except that the ordering of γ and β is reverse. The experimental result is considered to deviate from the reality for some measurement errors caused by many factors, such as the particle size. In addition, the trivial difference among the sensitivity of the four crystals makes the measurement difficult. For the four crystals studied in this paper, their N-NO2 bonds have been proven to be the trigger bonds. It is wellknown, to a certain extent, that bond strength can be approximately represented by bond length. That is, usually, longer bond length corresponds to weaker bond strength, and the N-NO2 bond with the longest bond length (LBN-NO2) is predicted to be the trigger bond. Therefore, LBN-NO2 can be used as a complementary tool to estimate the sensitivity of energetic materials. The experimental LBN-NO2 values of the four crystals are 1.432, 1.434, 1.444, and 1.446 Å, respectively, and increase in the following sequence  < β < γ < R‚H2O. Thus, their sensitivity order is predicted to be the same as that drawn from PET. In all, from the above studies on the electronic structures of the four polymorphs of CL-20, it can be found that the DOS and PDOS can be used to understand the compositions of the

Polymorphs of Crystalline CL-20

J. Phys. Chem. B, Vol. 111, No. 8, 2007 2095

Figure 5. Calculated band structures for bulk -CL-20 at different hydrostatic pressures.

upper valence bands and lower conduction bands, and to predict the pyrolysis mechanism of the crystals. The band gaps may explain the sensitivity of the polymorphs of CL-20. However, in practical use, the external surroundings often affects the properties of a material, and people often modify the performance of a material by changing the environment, such as temperature and pressure. In the following section, the -CL20 crystal is chosen to investigate the effects of hydrostatic pressure on its structure and properties. To study the effects,

both the cell parameters and atomic fractional coordinates are relaxed with the GGA-PBE method in CASTEP. 3.2. Influences of Hydrostatic Pressure on E-CL-20. 3.2.1. Lattice Parameters. Table 5 lists the relaxed unit cell parameters of -CL-20 in the hydrostatic pressure (P) range of 0-400 GPa using the GGA-PBE method. It can be seen from Table 5 that the values of a, b, c, and V at 0 GPa are a little larger than the experimental values, correspondingly. This may be due to the experimental measure

2096 J. Phys. Chem. B, Vol. 111, No. 8, 2007 at normal pressure of 0.0001 GPa or so. The compressibility of -CL-20 is anisotropic at low or high P. The molecular distance is longest along the b-axis, then that along the c-axis, and the a-axis is the last, as shown in Figure 4. From this, it can be inferred that the molecular interaction along b is the weakest, the compressibility of b is the largest, and that of the c- or a-axis is smaller for the larger molecular repulsions caused by the shorter distance along these two directions. Thus, when P is in the lower range of 5-50 GPa, the compressibility along the three directions follows the sequence b > c > a. When P is in the range of 100-400 GPa, the compressibilities along all three directions increase with increasing pressure, but that along b is to the limit and changes little. However, the P is large enough to overcome the molecular repulsion along the c- and adirections; therefore, the compressibility along these two directions still gradually increases, and that along a is a little larger than that along c. From Table 5, it can also be found that in the lower pressure regime (below 10 GPa), the lattice parameters, cell volume (V), and crystalline density (F) change slightly and agree well with the experimental data. However, when the pressure is above 10 GPa, these parameters deviate greatly from the experimental values. The lattice dimensions are compressed greatly and the crystalline density increases significantly with pressure increase. When the pressure arrives at 400 GPa, the density increases to 5.716 g/cm3. According to the well-known Kamlet-Jacobs equation,40 the detonation parameters of an explosive, such as detonation velocity (D) and detonation pressure (P), increase tremendously with the increasing F and are proportional to F2. Therefore, increasing pressure is useful for improving the performance of an explosive or propellant. 3.2.2. Band Structure and Density of States. The selfconsistent band structure along different symmetry directions of the Brillouin zone for the optimized structure of bulk -CL20 was calculated by the GGA-PBE method at different pressures, as shown in Figure 5. To be explicit, only the six upper valence bands (the highest occupied crystal orbitals) and four lower conduction bands (the lowest unoccupied crystal orbitals) were magnified in Figure 5. From Figure 5, we can draw the following conclusions: (i) With pressure increase, the energy bands (valence and conduction bands) shift to lower energy regions. (ii) When the pressure is in the range 0-50 GPa, the energy bands are mostly flat and fluctuate little, because -Cl-20 is a molecular crystal and the molecular interactions are weak. When the pressure increases from 100 to 400 GPa, however, the energy bands fluctuate a lot, due to increasing molecular interactions caused by compression. (iii) Most importantly, with the pressure increasing, the direct band gaps between the LUCO and the HOCO decrease gradually, and are 3.423, 3.441, 3.324, 2.731, 2.103, 1.589, and 0.197 eV at 0, 5, 10, 50, 100, 200, and 400 GPa, respectively. According to the PET, it can be predicted that as the pressure increases the decreasing band gap may lead to the increasing sensitivity. This is completely consistent with Kuklja’s work.41,42 Therefore, from our studies, PET is able to not only identify the sensitivity of the various polymorphs of a crystal, but also interpret the increasing sensitivity of an energetic material with increasing pressure. In addition, when P is 400 GPa, the pressure is large enough to close the band gap (0.197 eV) so that the electrons can move freely and the transformation of -CL-20 crystal from an electrical insulator to a metal occurs. As for CL-20, its normal N-NO2 should be of the same plane, but when the pressure is at 400 GPa, some N-NO2 dihedral angles have deviated from

Xu et al.

Figure 6. Crystal structure of bulk -CL-20 at 400 GPa.

Figure 7. Calculated total DOS for bulk -CL-20 at different pressures.

the plane (see Figure 6), which usually occurs with the metallization of the crystal. It should be noted that the crystals may contain various defects due to the influences of the surroundings during growth, and these defects, such as impurities, vacancies, and dislocations, will greatly help narrow the band gap. Thus, it is deduced that the critical pressure for the insulator-metal transition may be much less than 400 GPa. Figure 7 presents the corresponding total densities of state at different pressures. It can be seen that when the pressure is less than 50 GPa the curves of DOS are characterized by obvious peaks, but with increasing pressure the peaks widen gradually. When the pressure is 400 GPa, the DOS becomes smooth and DOS at each energy region are very approximate. This indicates that the probabilities that electrons occur in different energy regions are comparable and the electrons trend to be free; thus the -CL-20 crystal trends toward being metallic. This is in good agreement with the band gap analysis. 4. Conclusions Based on ab initio studies on the four polymorphs of the wellknown high energy density compound CL-20 using the DFT GGA-(R)PBE method, several meaningful conclusions can be

Polymorphs of Crystalline CL-20 drawn. (i) It is possible to use the DFT method to perform reliable calculations on the four polymorphs of CL-20. (ii) In the frontier energy regions, the p states of the N atoms in -NO2 overlap those of the N atom in the cage skeleton, indicating that the N-NO2 bond may be the trigger bond for thermolysis; this is further proved by Mulliken population analyses. (iii) The density of states (DOS) of R‚H2O is somewhat different from those of other three crystals because of its inclusion of H2O molecules. (iv) Based on the “principle of easiest transition” (PET) and the calculated band gaps from the four methods, the sensitivity of the four polymorphs of CL-20 is predicted to be  < β < γ < R‚H2O, which is consistent with the experimental result. The investigations on the influences of hydrostatic pressure on -CL-20 crystal using the GGA-PBE method also provide us with some interesting information. First, the compressibility of -CL-20 is anisotropic at low or high pressure. Second, it is found that when the pressure is less than 10 GPa the cell parameters, band structure, and DOS change little, but when the pressure increases from 50 to 400 GPa, these parameters change greatly. The decreasing band gap predicts its increasing sensitivity with increasing pressure. It is most important that, based on the changes of the band gap and DOS with pressure, 400 GPa was considered to be the critical pressure for the insulator-metal phase transition. Acknowledgment. We gratefully acknowledge the National Natural Science Foundation (10576016 and 10576030) and the National 973 project for their financial support. References and Notes (1) Nielsen, A. T. Nissan, P. A. Polynitropolyaza caged explosiVes. Part 5; Naval Weapon Center Technical Publication; 1986; p 6692. (2) Foltz, M. F.; Coon, C. L.; Garcia, F.; Nichols, A. L. Propellants, Explos., Pyrotech. 1994, 19, 19. (3) Xiao, H. M. Structures and Properties of Energetic Compounds; National Defense and Industrial Press: Beijing, 2004; p 72. (4) Zhang, J.; Xiao, H. M.; Ji, G. F. Acta Chim. Sin. 2001, 59, 1265. (5) Foltz, M. F.; Coon, C. L.; Garcia, F.; Nichols, A. L. Propellants, Explos., Pyrotech. 1994, 19, 133. (6) Foltz, M. F. Propellants, Explos., Pyrotech. 1994, 19, 63. (7) Simpson, R. L.;Urtuew, P. A.; Omellas, D. L.; et. al. Propellants, Explos., Pyrotech.1997, 22, 249. (8) Patil, D. G.; Brill, T. B. Combust. Flame 1991, 87, 145.

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