J. Phys. Chem. B 2007, 111, 12715-12722
12715
First-Principles Study of the Four Polymorphs of Crystalline Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine Weihua Zhu,*,† Jijuan Xiao,† Guangfu Ji,‡ Feng Zhao,‡ and Heming Xiao*,† Institute for Computation in Molecular and Materials Science and Department of Chemistry, Nanjing UniVersity of Science and Technology, Nanjing 210094, China, and Laboratory for Shock WaVe and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China ReceiVed: June 28, 2007; In Final Form: August 15, 2007
The electronic structure and vibrational properties of the four polymorphs of crystalline octahydro-1,3,5,7tetranitro-1,3,5,7-tetrazocine (HMX) have been studied using density functional theory within the local density approximation. The results show that the states of N in the ring make more important contributions to the valence bands than these of C and N of NO2 and so N in the ring acts as an active center. From the low frequency to high-frequency region, the molecular motions of the vibrational frequencies for the four HMX polymorphs present unique features. It is also noted that there is a relationship between the band gap and impact sensitivity for the four HMX polymorphs. From the cell bond order per unit volume, we may infer the variation order of crystal bonding for the four polymorphs and so predict their impact sensitivity order as follows: β-HMX < γ-HMX < R-HMX < δ-HMX, which is in agreement with their experimental order.
1. Introduction Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine, known as HMX, is an important and commonly used energetic ingredient in various high performance explosives and propellant formulations due to its thermal stability and high detonation velocity relative to other explosives.1,2 HMX is known to exist in four crystalline phases, denoted as R, β, δ, and γ.3,4 Although β-HMX is the thermodynamically stable form under ambient conditions, post-mortem analysis5 of samples recovered from safety experiments involving low-velocity projectile impacts on the HMX-based plastic-bonded explosive (PBX)-95016 has shown the formation of δ-HMX in the vicinity of damaged regions within the material. It is also known that a layer of δ-HMX is formed at the solid-melt interphase in deflagrating HMX. These observations present a safety concern since δ-HMX is considerably more sensitive than β-HMX. Therefore, a detailed and comparative study of the four HMX polymorphs offers the possibility of determining microscopic properties and understanding their explosive properties. Materials such as propellants and explosives contain tightly bonded groups of atoms that retain their molecular character until a sufficient stimulus is applied to cause exothermic dissociation. This in turn triggers further dissociation leading to initiation or ignition. The macroscopic behavior is ultimately controlled by microscopic properties such as the electronic structure and interatomic forces. Thus, a desire to probe more fundamental questions relating to the basic properties of HMX as a solid energetic material is generating significant interest in the basic solid-state properties of such energetic systems. Although the detailed decomposition mechanisms by which energetic materials release energy under mechanical shock are * To whom correspondence should be addressed. Fax: +86-2584303919. E-mail:
[email protected];
[email protected]. † Nanjing University of Science and Technology. ‡ China Academy of Engineering Physics.
still not well understood, it has been suggested that these decompositions may result from transferring thermal and mechanical energy into the internal degrees of freedom of the molecules in energetic solids.7-9 It is thus very important to understand the electronic and vibrational properties of the four HMX polymorphs. Many experimental studies have been performed to investigate the vibrational spectra of the HMX polymorphs.10-14 The investigation of the microscopic properties of energetic materials, which possess a complex chemical behavior, remains to be a challenging task. Theoretical calculations can play an important role in investigating the physical and chemical properties of complex solids at the atomic level and the establishment of the relationships between their structure and function. Previously, density functional theory (DFT) calculations based on norm-conserving pseudopotentials and a local density approximation (LDA) were performed to examine the energetics of the three pure polymorphic HMX (R, β, δ).15 Afterward, Lewis16 used the same method to investigate the energetics of HONO formation in the three pure polymorphs of condensed-phase HMX, where intermolecular hydrogen transfer occurs. Recently, Ye and Koshi17 have evaluated the energy transfer rates of the three pure HMX polymorphs in terms of the density of vibrational states and the unharmonic vibronphonon coupling term, which were calculated by using a flexible potential containing both intra- and intermolecular terms. As the electronic structure and vibrational properties of the four HMX polymorphs are not systematically investigated and compared, there is a clear need to gain an understanding of those at the ab initio level. In this study, we report a systematic study of the electronic structure and vibrational properties of the four HMX crystalline phases (R, β, δ, and γ) from DFT. Our main purpose here is to examine the differences in the microscopic properties of the polymorphs and to understand their structure-function relationships.
10.1021/jp075056v CCC: $37.00 © 2007 American Chemical Society Published on Web 10/12/2007
12716 J. Phys. Chem. B, Vol. 111, No. 44, 2007
Zhu et al.
Figure 1. Unit cell of R-HMX (a), β-HMX (b), δ-HMX (c), and γ-HMX (d). Gray, blue, red, and white spheres stand for C, N, O, and H atoms, respectively.
The remainder of this paper is organized as follows. A brief description of our computational method is given in section 2. The results and discussion are presented in section 3, followed by a summary of our conclusions in section 4. 2. Computational Method The calculations performed in this study were done within the framework of DFT,18 using Vanderbilt-type ultrasoft pseudopotentials19 and a plane-wave expansion of the wave functions. The self-consistent ground state of the system was determined by using a band-by-band 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 a density-mixing scheme20 and the structures were relaxed by using the Broyden, Fletcher, Goldfarb, and Shannon (BFGS) method.21 The LDA functional proposed by Ceperley and Alder22 and parametrized by Perdew and Zunder23 named CA-PZ, was employed. The cutoff energy of plane waves was set to 300.0 eV. Brillouin zone sampling was performed by using the Monkhost-Pack scheme with a k-point grid of 3 × 3 × 3, 4 × 2 × 3, 3 × 3 × 1, and 2 × 3 × 2 for R-, β-, δ-, and γ-HMX, respectively. The values of the kinetic energy cutoff and the k-point grid were determined to ensure the convergence of total energies. The R phase of HMX crystallizes in an orthorhombic Fdd2 space group and contains eight H8C4N8O8 molecules per unit cell.24 The β phase contains two H8C4N8O8 molecules per unit cell in a monoclinic lattice with space group P21/c.25 The δ phase crystallizes in a hexagonal P61 space group with six H8C4N8O8 molecules per unit cell.26 The γ phase contains two 2H8C4N8O8·0.5H2O molecules per unit cell in a monoclinic lattice with space group Pn.4 The γ phase is a hydrate and not a true polymorph. When the explosive decomposition of this HMX hydrate occurs water does not work. Strictly speaking only three HMX phases should be named polymorphs. Figure 1 displays the unit cell of the four HMX crystalline phases, and conformation and atomic numbering of H8C4N8O8 molecule in the β-HMX phase is shown in Figure 2. Starting from the above-mentioned experimental structures, the geometry relaxation was performed to allow the ionic configurations, cell shape, and volume to change. In the geometry relaxation, the total energy of the system was converged less than 2.0 × 10-5 eV, the residual force less than 0.05 eV/Å, the displacement of atoms less than 0.002 Å, and the residual bulk stress less than 0.1 GPa. The Mulliken charges and bond populations were investigated using a projection of the plane wave states onto a linear combination of atomic
Figure 2. Conformation and atomic numbering of H8C4N8O8 molecule in β-HMX.
TABLE 1: Experimental and Relaxed Lattice Constants (Å) for β-HMX this work a b c β
LDA
PBE
PW91
experimental25
6.539 11.030 8.689 123.9°
6.625 11.202 8.824 124.3°
6.617 11.188 8.810 124.2°
6.540 11.050 8.700 124.3°
orbitals (LCAO) basis set,27,28 which is widely used to perform charge transfers and populations analysis. The phonon frequencies at the gamma point have been calculated from the response to small atomic displacements.29 3. Results and Discussion 3.1. Bulk Properties. As a base for studying other HMX phases and as a well-studied benchmark, we apply three different functionals to bulk β-HMX as a test. The LDA (CA-PZ) and generalized gradient approximation (GGA) (PBE30 and PW9131) functionals were selected to fully relax the β phase without any constraint. The calculated lattice parameters are given in Table 1 together with their experimental values.25 It is found that the errors in the LDA (CA-PZ) results are slightly smaller than that in the GGA (PBE and PW91) results in comparison with the experimental values. This shows that the accuracy of LDA is better than that of the GGA functionals. Table 2 presents the bond lengths and bond angles of the β phase along with the corresponding experimental data. It is seen that the bond lengths and bond angles compare well with experimental values. The comparisons confirm that our computational parameters are reasonably satisfactory. We thus used LDA in all subsequent calculations.
Four Polymorphs of Crystalline HMX
J. Phys. Chem. B, Vol. 111, No. 44, 2007 12717
TABLE 2: Experimental and Relaxed Bond Lengths (Å) and Bond Angles (deg) for β-HMX bond length N2-C1 N2-C2′ N3-C1 N3-C2 N2-N1 N3-N4 N1-O1 N1-O2 N4-O3 N4-O4 C1-H1 C1-H2 C2-H3 C2-H4
bond angle
LDA
expt25
1.435 1.461 1.440 1.421 1.358 1.374 1.253 1.245 1.246 1.243 1.106 1.108 1.107 1.106
1.448 1.471 1.455 1.437 1.354 1.373 1.233 1.222 1.210 1.204 1.111 1.091 1.101 1.095
O1-N1-O2 N2-N1-O1 N2-N1-O2 N1-N2-C2′ N1-N2-C1 C1-N2-C2′ N2-C1-N3 N2-C1-H1 N2-C1-H2 N3-C1-H1 N3-C1-H2 H1-C1-H2 O3-N4-O4 N3-N4-O3 N3-N4-O4 N4-N3-C1 N4-N3-C2 C1-N3-C2 N2′-C2-N3 N3-C2-H4 N3-C2-H3 N2′-C2-H4 N2′-C2-H3 H3-C2-H4
LDA
expt25
125.7 118.5 115.8 115.8 118.7 123.7 111.4 106.8 111.8 107.3 111.6 108.0 126.5 116.5 117.0 117.9 118.2 123.5 110.6 108.2 109.9 109.9 109.0 109.1
125.9 118.0 116.1 115.2 118.2 122.4 113.5 108.5 109.8 106.6 111.8 106.2 126.7 115.9 117.4 117.4 118.2 123.8 110.2 107.3 110.5 110.1 109.2 109.6
3.2. Electronic Structure. The calculated total density of states (DOS) and partial DOS (PDOS) for the four HMX phases are displayed in Figures 3-6, respectively. The DOS of the four HMX phases are finite at the Fermi energy level. This is because the DOS contain some form of broadening effect. In the upper valence band, all of the four HMX phases have a sharp peak near the Fermi level, which shows that the top valence bands of their band structures are flat. The top of the DOS valence band shows three main peaks for R- and δ-HMX and two main peaks for β- and γ-HMX. These peaks are predominately from the p states. After that, several main peaks in the upper valence band are superimposed by the s and p states. The conduction band of each phase is dominated by the p states. This indicates that the p states for each HMX phase play a very important role in its chemical reaction. The atom-resolved DOS and PDOS of the four HMX phases are also shown in Figures 3-6, respectively. The main features can be summarized as follows. (i) In the upper valence band, the PDOS of the states of N in the ring are far larger than that of the states of C and N of NO2. It is expected that the states of N in the ring make more important contributions to the valence bands than these of C and N of NO2. This shows that N in the ring acts as an active center. (ii) Some strong peaks occur at the same energy in the PDOS of a particular C atom and a particular N atom in the ring. It can be inferred that the two atoms are strongly bonded. Similarly, a particular N atom of NO2 and a particular N atom in the ring are strongly bonded. (iii) There are some differences in the PDOS of the C atoms for the four HMX phases. This is due to the differences in their local molecular packing. The same is true of the N atoms in the ring and the N atoms of NO2. (iv) In the conduction band region of DOS, the peaks are dominated by the N-p states of ring and the N-p states of NO2. (v) In the energy range from -5.0 to 0 eV, the DOS of R-, β-, and γ-HMX are superimposed by the states of C and N in the ring, whereas that of δ-HMX mainly arises from the states of N in the ring. It is inferred that the C-N bond fission in the ring may be favorable in the decomposition of crystalline R-, β-, and γ-HMX. This is consistent with the previous conclusion32 that in a bulk
Figure 3. Total and partial density of states (DOS) of C-states, N in ring-states, N of NO2-states, and R-HMX. The Fermi energy is shown as a dashed vertical line.
Figure 4. Total and partial density of states (DOS) of C-states, N in ring-states, N of NO2-states, and β-HMX.
Figure 5. Total and partial density of states (DOS) of C-states, N in ring-states, N of NO2-states, and δ-HMX.
condensed phase the C-N bond scission reaction of the ring for R-HMX may be energetically favorable because of the steric constrains that will disfavor N-NO2 bond dissociation. Of
12718 J. Phys. Chem. B, Vol. 111, No. 44, 2007
Figure 6. Total and partial density of states (DOS) of C-states, N in ring-states, N of NO2-states, and γ-HMX.
course, near areas with large surfaces or voids there is no confining environmental and N-N bond dissociation would likely be more favorable. This is in agreement with the previous reports33,34 that the N-N bond scission reaction of hexahydro1,3,5-trinitro-1,3,5-triazine (RDX) in the gas-phase would be favorable. For the N-NO2 and C-N bond fission reactions of δ-HMX, it is difficult to judge which one is more favorable since the contribution of the states of C and of NO2 to the total DOS from -5.0 to 0 eV is very small. Recently, Feng and Li35 have investigated two polymorphs of flufenamic acid and elucidated the difference in the solid-state reaction of the two polymorphs based on their electronic structures. 3.3. Vibrational Properties. Here we investigate the vibrational properties of the four HMX phases. β-HMX contains a ring conformation that the NO2 groups adopt a chairlike arrangement. This gives the entire molecule a center of symmetry.24,25 The ring conformation of R-, δ-, and γ-HMX is a “boat” form that the NO2 groups are positioned on one side of the molecule.24,26 It is interesting to note that the R-, δ-, and γ-HMX phases have similar vibrational spectra, whereas the β phase has a significantly different vibrational spectrum.10-14 Therefore, the calculated vibrational frequencies for β-HMX are presented in Table 3, whereas these for R-, δ-, and γ-HMX are presented in Table 4. The corresponding experimental values are also listed for comparison. The lattice mode spectra of β-, δ-, and γ-HMX displays unique features in the region 27-80 cm-1, whereas there is only one librational vibration mode at 31.2 cm-1 in the R-HMX spectrum. β-HMX has five frequencies in this region, which are in agreement with the experimental reports.13 The lattice mode spectra of the other three phases were not reported in this region by the experiments because their lattice region spectra could not be routinely obtained. In the region of 80-500 cm-1, the molecular motions of the first four frequencies are the twisting of NO2 about N-N bonds, denoted γNN(NO2), and the motions corresponding to the following frequencies is concentrated in the distortions of C4N4 rings. In the region of 500-730 cm-1, the molecular motions of the frequencies are the bending of N-N-O angles, denoted b(NNO), and the stretching of N-N bonds, denoted V(NN). The 637.8 cm-1 mode corresponding to the bending of N-N-O and N-N-C angles and the stretching of C-N bonds appears in γ-HMX but not in any of the other three polymorphs. The modes in the range of 730-760 cm-1 are the wagging of N
Zhu et al. atoms out of the NO2 plane, denoted σ(NO2). We note that R, δ, and γ-HMX share similarities in band separation, whereas β has a different spectral pattern. This is because the crystal structures of R, δ, and γ-HMX differ from one another primarily through small differences in the relative positioning of the NO2 groups, while β-HMX has a different ring conformation from the other phases. In the region of 760-1260 cm-1, the molecular motions of the frequencies are mainly the stretching of C4N4 rings including the symmetric stretch of C-N-C and N-NC2 bonds, the asymmetric stretch of C-N-C, N-C-N, and N-N-C2 bonds, and the rocking in the CH2 plane. The modes of 1220.4 cm-1 in R, 1234.2 cm-1 in δ, and 1228.2 cm-1 in γ correspond to the stretching of only one N-O bond in NO2 moieties, denoted V(NO), plus the stretching of N-N bonds and the bending of C-N-C angles, which do not appear in β-HMX. The R-HMX phase has the smaller motion modes of the frequencies in this region than any of the other three polymorphs. In the region of 1260-1350 cm-1, the molecular motions of the frequencies involve the symmetric stretching of O-N-O bonds, denoted Vs(NO2), and the twisting about bisector of H-C-H angles, denoted γ(CH2). The modes of the four frequencies in the range of 1350-1500 cm-1 involve the wagging of H atoms out of the CH2 plane, denoted ω(CH2), and the bending of H-C-H angles, denoted b(HCH), which does not appear in R-HMX but appears in the other three polymorphs. In the region of 1500-1750 cm-1, the molecular motions of the frequencies are the asymmetric stretching of O-N-O bonds, denoted Vas(NO2). The calculated frequencies for the β-HMX phase in this region are much larger than the corresponding experimental values. The motions of these frequencies is concentrated in the NO2 moieties; thus, this discrepancies may be due to intermolecular hydrogen bonding interactions present in the crystal lattice, which are not well described by DFT. In the region of 2900-3100 cm-1, the molecular motions of the frequencies are divided into two separate groups. The motions of the first four frequencies involve the symmetric stretching of H-C-H bonds, denoted Vs(CH2), whereas these of the next four frequencies are concentrated in the asymmetric stretching of H-C-H bonds, denoted Vas(CH2). These modes do not appear in R-HMX but appear in the other three polymorphs. Recently, Stevens et al.36 has reported the single-crystal polarized Raman spectra for β-HMX. It can be seen from Table 3 that our calculated frequencies are in agreement with their experimental ones. They have also presented complete symmetry assignments for the Raman-active modes of β-HMX. This is useful for understanding the proposed vibrational mechanisms for the initiation of detonation. In a word, the β-HMX phase has clearly very different vibrational properties from R-, δ-, and γ-HMX. This is supported by previous experimental studies.10,12,14 From the low frequency to high-frequency region, the molecular motions of the frequencies for the four HMX polymorphs present unique features, which could be used to distinguish the polymorphs easily from one another. At lower (below 120 cm-1) or higher (above 1150 cm-1) frequencies, the motions seem very localized in certain atom groups, whereas elsewhere the motions are diffusely distributed among different atom groups. Since the torsional motions of the molecule’s functional groups are usually supposed to be highly coupled to the other moiety of the molecule,37 it is possible that the torsion motions of the NO2 groups act as doorways through which kinetic energy can flow into the molecule from its surroundings. These suggestions show
Four Polymorphs of Crystalline HMX
J. Phys. Chem. B, Vol. 111, No. 44, 2007 12719
TABLE 3: Vibrational Frequencies (cm-1) for β-HMX experimental infrared (IR) mode
assignmenta
1
librational vibration translational vibration rotational lattice vibration librational vibration translational vibration γNN(NO2) γNN(NO2) γNN(NO2) γNN(NO2) σ(CNC) b(NNC) σ(CNC) b(NNC), b(CNC) b(NNC), b(NCN) b(NNC), b(NNO) b(NNC) ν(CN), ν(NN), b(CNC) ν(NN), b(CNC), b(NNC) b(NNO), b(NNC) b(NNO), b(NNC) b(CNC), b(NNC) b(CNC), b(NNO), b(NNC) b(NNO) b(NNO) b(NNO), ν(NN) b(NNO), ν(NN) b(NNO), ν(NN) b(NNO), ν(NN) b(ONO), ν(CN) σ(ONO) σ(ONO) σ(ONO) σ(ONO) b(NCN) νs(NC2) νs(NC2) νs(NNC2) νs(NNC2) νas(NNC2)
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
experimental
Raman (R)
this work ref 14 ref 10 ref 13 ref 12 ref 13
950
953
41
νas(CNN), F(CH2)
930.9
965
966
42
νas(CNN), F(CH2)
938.4
65
43
79
81
1090
1088
90 110 126 140 152
97
1168 1190
1170 1192
1248 1268
1251 1270
1312
1310 1318
1350 1368
1351 1369
1418 1438
1420 1438
1460
1461
1532
1535
1558
1560
2992 3028
2994 3028
3037
3038
63.2 65.9
224
369.4 398.8 404.0 424.8 426.1 593.3 595.5 629.0 630.4 641.0 658.6 722.4 750.2 750.9 751.0 752.7 774.4 837.9 838.2 878.8 879.6 920.7
419
385 420
438
441
600
605
627
754
230
231
281 312
282 318
752
755
758 769
762 773
832 872
827 871
833 872
945
967
965
966
ν(NN), F(CH2)
1071.2 1088
1090
1089
44
νas(NNC2)
1086.1
45 46 47 48 49 50 51 52 53 54 55 56
νas(CNN), F(CH2) νas(CNN), F(CH2) νas(NC2) νas(NC2) νas(NC2) νas(NC2) νs(NO2) νs(NO2) νs(NO2) γ(CH2) νs(NO2) γ(CH2)
1146.1 1150.0 1196.9 1213.9 1228.0 1228.4 1275.3 1280.6 1293.4 1309.0 1329.2 1332.0
1325
1320
1325
1348
1348
1146 1204 1239 1279 1296
358
364
57
γ(CH2)
1344.9 1349
412
417
432
437
58 59 60 61
γ(CH2) ω(CH2) ω(CH2) ω(CH2)
1346.4 1367.8 1390.8 1385 1394.5 1395
597
600
638
640
62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78
ω(CH2) b(HCH) b(HCH) b(HCH) b(HCH) νas(NO2) νas(NO2) νas(NO2) νas(NO2) νs(CH2) νs(CH2) νs(CH2) νs(CH2) νas(CH2) νas(CH2) νas(CH2) νas(CH2)
1423.8 1426.8 1442.8 1446.5 1459.5 1700.4 1704.0 1706.9 1715.2 2955.4 2955.5 2955.6 2955.7 3029.9 3030.3 3030.8 3031.1
658
760 772
947
149 155
630 660
ref 14 ref 10 ref 13 ref 12 ref 13
923.2
59
84.0 96.1 111.9 112.9 147.6 156.2 217.0 217.6 256.1 295.6 332.0 337.5
assignmenta
Raman (R)
ν(NN), F(CH2)
36
78.8
mode
this work
40
38.8 57.3
infrared (IR)
662 721 759
663 722 762 763
834
834
881
884
948
1146 1205 1240 1280
1397
1145 1203
1281 1298
1395 1401
1433
1433
1434
1462
1465
1463
1534
1540
1538
1563
1570
1565
2985 2992 3027 3037
2978 2983 3027 3037
a
γNN(XY2): twist of XY2 about NN bond; σ(XY2): wag of X atom out of XY2 plane; b(XYZ): bend of X-Y-Z angle; νs(XY2): symmetric stretch of Y-X-Y bonds; νs(XXY2): symmetric stretch of X-X-Y2 bonds; νas(XY2): asymmetric stretch of Y-X-Y bonds; νas(XXY2): asymmetric stretch of X-X-Y2 bonds; F(XY2): rocking in XY2 plane; γ(XY2): twist about bisector of Y-X-Y angle; ω(XY2): wag of Y atoms out of XY2 plane.
that the NO2 groups play a very important role in the decomposition and detonation of HMX. 3.4. Electronic Structure and Impact Sensitivity. In this section, an attempt is made to correlate the impact sensitivity of the four HMX phases with their electronic structure. Band gap is an important parameter to characterize the electronic structure of solids. Table 5 presents the energy gaps between valence and conduction bands for R-, β-, δ-, and γ-HMX. This shows that the band gap decreases in the sequence of β-, γ-, R-, δ-HMX, whereas their experimental impact energy (shown in Table 5) increases in the following order: β-HMX < γ-HMX ∼ R-HMX < δ-HMX.38 Therefore, there is a relationship between the band gap and impact sensitivity for the four HMX polymorphs. This indicates that the smaller the band gap is,
the easier the electron transfers from the valence band to the conduction band, and the more the HMX phase becomes decomposed and exploded. In the previous studies,39,40 a “principle of the easiest transition” (PET) was put forward to investigate the relationship between the band gap and impact sensitivity for the metal azides. Although these calculations are performed at the semiempirical discrete variational XR (DVXR) and extended Hu¨ckel-crystal orbital (EH-CO) levels, the results have shown that their band gap could be correlated with their explosive characters. Our recent study on the heavy-metal azides within the framework of periodic DFT41 has also confirmed the relationship between the band gap and impact sensitivity. In several papers,42-45 Gilman has emphasized that the role of HOMO-LUMO (highest occupied molecular orbital-
12720 J. Phys. Chem. B, Vol. 111, No. 44, 2007
Zhu et al.
TABLE 4: Vibrational Frequencies (cm-1) for r-HMX, δ-HMX, and γ-HMX R-HMX
δ-HMX
experimental mode
assignmenta
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71
librational vibration translational vibration rotational lattice vibration librational vibration translational vibration γNN(NO2) γNN(NO2) γNN(NO2) γNN(NO2) σ(CNC) b(NNC) σ(CNC) b(CNC) b(NNC), b(CNC) b(NNC) ν(CN), ν(NN), b(NCN) ν(NN), ν(CN), b(CNC) ν(NN), b(NNO) b(NNC), b(NNO), F(CH2) b(NNO), b(NNC), F(CH2) b(NNO), b(NNC), F(CH2) b(CNC), F(CH2) b(NNO) b(NNO) b(NNO), ν(NN) ν(NN), b(ONO) ν(NN), b(ONO) b(NNO), b(NNC), ν(CN) ν(NN), b(ONO) σ(ONO) σ(ONO) σ(CNC) σ(ONO) σ(ONO) νs(NC2) νs(NC2) b(ONO), νs(NNC2) b(ONO), νs(NNC2) b(ONO), νs(NNC2) νs(NNC2) ν(NN), b(ONO) ν(CN), F(CH2) νs(NNC2) νs(NNC2), F(CH2) νs(NNC2), F(CH2) νas(NC2) νas(NC2) ν(NO), ν(NN), b(CNC) νas(NC2) νas(NC2) νs(NO2) νs(NO2) νs(NO2) γ(CH2) νs(NO2) γ(CH2) ω(CH2) γ(CH2) γ(CH2) ω(CH2) ω(CH2) b(HCH) ω(CH2) b(HCH) b(HCH) b(HCH) νas(NO2) νas(NO2) νas(NO2) νas(NO2) νs(CH2)
this work
IR14
IR10
R12
31.2
214.0 248.2 332.5 344.1
451
450
603 622
603 625
594 620
646
648
646
691.5 732.4 736.9 741.9 747.7 759.4
714 741 751
714 742 753
712 740 750 758
766 770
768
856.9 867.2 868.8
847 864 878 915
848 862
944
846 878
920 945
928 945
1032 1090 1110
1030 1085
1220
1215
936.3 1075.7 1095.8 1155.8 1208.0 1220.4 1247.9 1250.1 1268.0 1273.0 1310.6 1314.1 1330.5 1335.6
1030 1089 1109 1148 1215 1259 1268 1280 1319 1364 1370 1386 1393 1414 1432 1451 1441
1559.6 1570.3 1574.4
this work 32.6 46.5 55.6 56.2 70.9 92.5 95.4 105.8 105.8 124.9 186.9 187.8 216.6 241.8 339.2 359.7 374.3 395.8 395.9 396.0
90.1 92.0 104.9 108.8 128.3 175.1
406.8 409.9 450.2 454.9 587.0 591.1 611.5 619.1 649.5
1541 1561
1258 1280
1280
1320
1318
1370
1368 1385 1391
1394 1416 1432
1412 1422 1448
IR14
IR10
400
696.6 727.8 733.2 742.5 742.6 751.4 824.1 835.8 866.6 869.1 888.3 906.3 911.6 912.1 989.4 1036.6 1089.5 1154.1 1206.5 1234.2 1254.9 1255.3 1281.5 1293.0 1304.3 1305.2 1344.2 1360.5 1385.4 1390.8 1400.3 1400.3 1400.9 1400.9
599 621
605 625
646
655
654
711 733 750
713 740 750
713 735 751 763
763 767 830 841 867
765 848 866
846 870
913 930 941
910 925 940
930 943
1016 1087 1109 1147 1204 1222
1040 1088 1110
1092 1111
1249 1257 1274 1290
1225
1270
1256 1275 1291
1325 1340
1317 1332
1370 1383 1395
1370
1371 1382 1393
1419
1420
1545 1562 1611.8
1215
1320 1341
1451 1539 1561
experimental R12
392 446 473 590 601 622
470 585.8 589.9 610.4 637.6 639.1
1468 1550
γ-HMX
experimental
1393
1415 1422 1422
this work 27.2 43.7 51.9 53.3 68.6 89.2 93.3 101.4 105.8 129.2 191.6 191.7 216.6 255.4 329.7 347.1 386.9 392.7 404.2 408.9 450.2 457.9 579.7 592.8 610.9 632.2 632.3 637.8 712.6 730.3 730.8 744.7 745.6 759.0 843.8 844.1 863.1 864.6 885.4 905.6 910.8 920.0 1013.9 1081.2 1097.1 1153.3 1208.5 1228.2 1249.4 1249.4 1274.9 1275.9 1296.7 1321.5 1330.2 1336.7 1359.8 1377.2 1382.1 1383.5 1403.0 1420.8 1423.4 1442.5 1442.9
IR10
R12
205 224 328 365 402 458
658
592 618 636 648
712
710
622
735 751 768 845
753 840 847 878
918 941 1016 1090 1112 1149 1221 1255
928 940 995 1090 1112 1166 1190 1225 1259 1271
1280 1320
1375 1398
1294 1319 1330
1422
1375 1385 1392 1411 1419
1454
1440 1452
1545.3
1550
1557
1586.2 2923.7
1570
1563 1573 2918
1455 1560
1536 1562
Four Polymorphs of Crystalline HMX
J. Phys. Chem. B, Vol. 111, No. 44, 2007 12721
TABLE 4: Continued R-HMX
δ-HMX
experimental mode 72 73 74 75 76 77 78
assignmenta
this work
νs(CH2) νs(CH2) νs(CH2) νas(CH2) νas(CH2) νas(CH2) νas(CH2)
IR14
IR10
2970
γ-HMX
experimental R12
2975 3047
3049 3056
this work
2963.3
IR14
IR10
2970
experimental R12
2974
3058 3058 3053
3058
this work 2923.7 2935.5 2935.5 3061.1 3061.2 3070.8 3071.0
IR10
R12 2928 2982 3032 3045
a
γNN(XY2): twist of XY2 about NN bond; σ(XY2): wag of X atom out of XY2 plane; b(XYZ): bend of X-Y-Z angle; νs(XY2): symmetric stretch of Y-X-Y bonds; νs(XXY2): symmetric stretch of X-X-Y2 bonds; νas(XY2): asymmetric stretch of Y-X-Y bonds; νas(XXY2): asymmetric stretch of X-X-Y2 bonds; F(XY2): rocking in XY2 plane; γ(XY2): twist about bisector of Y-X-Y angle; ω(XY2): wag of Y atoms out of XY2 plane.
TABLE 5: Experimental Impact Energy and Calculated Band Gap and Cell Bond Order per Unit Volume for r-HMX, β-HMX, δ-HMX, and γ-HMX impact energy (Kg/cm2)38 band gap (eV) cell bond order per unit volume
R-HMX
β-HMX
δ-HMX
γ-HMX
0.20 2.42 0.073
0.75 3.62 0.080
0.10 0.021 0.057
0. 20 3.38 0.078
lowest unoccupied molecular orbital) gap closure in molecules suffering shear strain. Further reports34,46 on the excitonic mechanism of detonation initiation show that the pressure inside the impact wave front reduces the band gap between valence and conducting bands and promotes the HOMO-LUMO transition within a molecule. Although these studies have suggested that the HOMO-LUMO gap in molecules suffering shear strain, impact wave, or distortion relates directly to the sensitivity, they further support our conclusion here that there is the relationship between the band gap and sensitivity. It has been suggested that initiation of combustion or detonation in energetic solids is associated with small regions of the solid termed “hot spots”.47-49 In general, the initiation of explosion in HMX is concerned with the decomposition of a small volume of material in the region of the “hot spot” at a high temperature and in a short time. The thermal decomposition of the energetic material is prior to its detonation; thus, the information of the thermal decomposition seems to provide an important basis for understanding the explosive characteristics. For the crystal as a whole, a more meaningful quantity is the total cell bond order that is the sum of all bond order values in the crystal.50 Since the four HMX polymorphs contain different number of atoms and bonds within the unit cell of each phase, a much more useful concept is the cell bond order per unit volume. These numbers are listed in Table 5. It turns out that β-HMX has the highest value of 0.080 for the cell bond order per unit volume. The R-, δ-, and γ-HMX phases have the values of 0.073, 0.057, and 0.078, respectively. Therefore, we may conclude that the β-HMX crystal has the strongest crystal bonding among the four polymorphs. This is consistent with the fact that β-HMX is the thermodynamically most stable form under ambient conditions among the HMX polymorphs. The crystal bonding for the HMX phases weakens in the following order: β-HMX > γ-HMX > R-HMX > δ-HMX, so the activation order for thermal decomposition of the four polymorphs is as follows: β-HMX < γ-HMX < R-HMX < δ-HMX. From these discussions, we may infer that the impact sensitivity for the HMX phases increases in the following sequence: β-HMX < γ-HMX < R-HMX < δ-HMX, which is in agreement with their experimental sensitivity order.38
4. Conclusions In this study, we have performed a detailed density functional theory study of the electronic structure and vibrational properties of the four HMX polymorphs in the local density approximation. Then an attempt has been made to correlate the impact sensitivity of the four phases with their electronic structure. From the density of states for the four HMX phases, it is found that the states of N in the ring make more important contributions to the valence bands than these of C and N of NO2 and so N in the ring acts as an active center. The β-HMX phase has clearly very different vibrational properties from R-, δ-, and γ-HMX. From the low frequency to high-frequency region, the molecular motions of the frequencies for the four HMX polymorphs present unique features, which could be used to distinguish the polymorphs easily from one another. It is also noted that there is a relationship between the band gap and impact sensitivity for the four HMX polymorphs. From the cell bond order per unit volume, we may infer the variation order of crystal bonding for the four polymorphs and so predict their impact sensitivity order. Acknowledgment. We thank the funding from Key Laboratory for Shock Wave and Detonation Physics. This work was partly supported by National Natural Science Foundation of China (Grant No. 10576016) and National “973” Project. References and Notes (1) Cooper, P. W.; Kurowski, S. R. Introduction to the Technology of ExplosiVes; Wiley: New York, 1996. (2) Akhaven, J. The Chemistry of ExplosiVes; Royal Society of Chemistry: Cambridge, U.K., 1998. (3) Cady, H. H.; Smith, L. C. Los Alamos Scientific Laboratory Report LAMS-2652 TID-4500; Los Alamos National Laboratory: Los Alamos, NM, 1961. (4) Main, P.; Cobbledick, R. E.; Small, R. W. H. Acta Crystallogr., Sect. C 1985, 41, 1351. (5) Skidmore, C. B.; Phillips, D. S.; Idar, D. J.; Son, S. F. In Conference Proceedings: Europyro 99 Vol. I; Association Francaise de Pyrotechnie: Brest, 1999; p 2. (6) Idar, D. J.; Lucht, R. A.; Straight, J. W.; Scammon, R. J.; Browning, R. V.; Middleditch, J.; Dienes, J. K.; Skidmore, C. B.; Buntain, G. A. In Proceedings of the EleVenth International Detonation Symposium; Snowmass Village, CO, Aug 31-Sept 4, 1999; Naval Surface Warfare Center: Indian Head, 1999; p 335. (7) Dlott, D. D.; Fayer, M. D. J. Chem. Phys. 1990, 92, 3798. (8) Tokmanoff, A.; Fayer, M. D.; Dlott, D. D. J. Phys. Chem. 1993, 97, 1901. (9) Tarver, C. M. J. Phys. Chem. A 1997, 101, 4845. (10) Goetz, F.; Brill, T. B.; Ferraro, J. R. J. Phys. Chem. 1978, 82, 1912. (11) Yoo, C.-S.; Cynn, H. J. Chem. Phys. 1999, 111, 10229. (12) Goetz, F.; Brill, T. B. J. Phys. Chem. 1979, 83, 340. (13) Iqbal, Z.; Bulusu, S.; Autera, J. R. J. Chem. Phys. 1974, 60, 221.
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