Insights into the roles of two constituents CL-20 and HMX in the CL-20:HMX cocrystal at high pressure: a DFT-D study

Abstract

Density functional theory with dispersion corrections (DFT-D) was used to study pressure-induced effects in a novel energetic CL-20:HMX cocrystal and to understand what role its constituents CL-20 and HMX have. The structural, electronic, absorption, and mechanical properties of the cocrystal and its constituents were compared and analyzed in detail. The results indicate that the two constituents produce different effects on the crystal structure of the cocrystal in different directions. This distinct energy distribution in the cocrystal suggests that electron transitions may take place between the HMX and CL-20 molecules. The CL-20 in the cocrystal plays a leading role in the electronic structure of the cocrystal. The cocrystal has quite similar absorption spectra to ε-CL-20 but very different ones from β-HMX. Compared with the pure crystals, the mechanical properties of the cocrystal present a great anisotropy, which not only greatly strengthens the stiffness but also affects the preference of the stiffness towards different directions. Our results may provide fundamental insight into the roles of the two constituents in the cocrystal and may be helpful for developing new cocrystals with high energy and good safety.

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1. Introduction

High-energy density materials (HEDMs) have attracted considerable attention due to their potential applications in civilian and military fields. As we know, a combination of high detonation performance and good safety is still a challenging task for HEDMs. Besides great efforts in searching for novel insensitive high explosives (IHE),¹ the cocrystallization to generate novel solids comprised of two or more pure energetic compounds has proven to be an effective way to meet this requirement.^2–10 In this way, the cocrystallization offers great advantages to decrease the sensitivity of the existing energetic compounds without significantly reducing their energetic properties. Among the energetic cocrystals, a series of new cocrystals containing 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) have high density and improved mechanical and thermal stability.¹¹ For example, an energetic cocrystal composed of CL-20 and 2,4,6-trinitrotoluene (TNT) in a 1 : 1 molar ratio was presented by Bolton et al.³ recently. Another novel cocrystal with better energetic performance is CL-20 and 1,3,5,7-tetranitro-1,3,5,7-tetrazacyclooctane (HMX) cocrystal in a 2 : 1 molar ratio.⁴ The CL-20 : HMX cocrystal takes advantages of the single explosives and exhibits excellent power as well as good mechanical sensitivity. Thus, it is expected to be a promising candidate for IHEs because it greatly avoids the disadvantages of the CL-20 possessing high sensitivity to impact¹² and retains powerfully energetic performance (high density, high detonation velocity, and favorable oxygen balance) in general.

Now the cocrystallization strategy can be used to tune the density, thermal stability, or impact sensitivity of existing explosive components, but the fundamental questions relating to the roles of different components (such as CL-20 and HMX) in the cocrystals (such as CL-20:HMX) are little known. The macroscopic similarities between the cocrystal and pure energetic components are ultimately controlled by their microscopic properties such as electronic structures and intermolecular interactions. Therefore, an investigation on the microscopic relationships of different energetic constituents turns out to be an urgent task. In addition, the explosives also experience enormous pressure effects during detonation process. To well understand their behaviors at different pressures and during the detonation process, it is thus important to investigate their pressure-induced effects. An alternative method is the atomistic simulation to interpret both physical and chemical properties of the cocrystals as a complement to experiments. Recent density functional theory method with dispersion-correction (DFT-D) has been rationally applied to study energetic nitroamine compounds under hydrostatic compression.¹³

In this work we performed periodic DFT-D calculations to compare the structural, electronic, optical, and mechanical properties of the CL-20:HMX cocrystal and its components (β-HMX and ε-CL-20) under hydrostatic pressure of 0–100 GPa. The atomic positions and the lattice parameters of the three crystals were allowed to relax to the minimum energy configurations in the whole pressure range. Then a detailed comparison of the pressure effects on the cocrystal and β-HMX and ε-CL-20 single crystals was conducted. Our studies may shed light on how the two constituents CL-20 and HMX affect the structure and properties of their cocrystal.

2. Computational methods

The calculations performed in this study were done by DFT-D with Vanderbilt-type ultrasoft pseudopotentials and a plane-wave expansion of the wave functions as implemented in the CASTEP code.¹⁴ 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 the Pulay density-mixing scheme¹⁵ and the structures were optimized by the Broyden, Fletcher, Goldfarb, and Shannon (BFGS) method.¹⁶ The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional¹⁷ and dispersion correction using Grimme scheme^18,19 was employed. The cutoff energy of plane-waves was set to 380.0 eV. Brillouin zone sampling was performed by using the Monkhost–Pack scheme with the k-point grid of 3 × 1 × 2 for β-HMX, 2 × 1 × 1 for ε-CL-20, and 1 × 1 × 1 for CL-20:HMX cocrystal, respectively.

The experimental crystal structures of the three explosives^4,20,21 were first relaxed to allow the ionic configurations, cell shape, and volume to change at zero pressure. Then from these relaxed structures, we applied hydrostatic pressure from 0 to 100 GPa. During the geometry relaxation, the total energy of the system was converged less than 5.0 × 10⁻⁶ eV, the residual force less than 0.01 eV Å⁻¹, the displacement of atoms less than 5.0 × 10⁻⁴ Å, and the residual bulk stress less than 0.02 GPa. The values of the kinetic energy cutoffs and the k-point grids were used to ensure the convergence of the total energies.

3. Results and discussion

3.1. Crystal structures

The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional and dispersion corrections using Grimme scheme was used to fully relax the bulk crystals without any constraints at different pressures (Table 1). The three crystals crystallize in the primitive monoclinic forms with P2₁/c space group for β-HMX and CL-20:HMX cocrystal and with P2₁/n space group for ε-CL-20. The irreducible molecules per unit cell in β-HMX, ε-CL-20, and CL-20:HMX cocrystal are 2, 4, and 6 (2 for HMX and 4 for CL-20), respectively. Fig. 1 displays the side views of the three crystals along the a axis.

Table 1 Selected N–N bond lengths of the β-HMX, ε-CL-20, and CL-20:HMX cocrystal at various pressures (in Å)

Pressure (GPa)	β-HMX		HMX in cocrystal		ε-CL-20	CL-20 in cocrystal
	Equatorial	Axial	Equatorial	Axial	Average	Average
a The experimental data are taken from ref. 20.b The experimental data are taken from ref. 21.c The experimental data are taken from ref. 4.
0	1.387 (1.374)^a	1.375 (1.354)^a	1.399 (1.387)^c	1.378 (1.371)^c	1.411 (1.401)^b	1.403 (1.399)^c
20	1.346	1.336	1.36	1.343	1.365	1.358
40	1.327	1.325	1.334	1.34	1.343	1.347
60	1.313	1.319	1.319	1.325	1.326	1.331
80	1.302	1.312	1.307	1.314	1.316	1.32
100	1.293	1.305	1.299	1.305	1.311	1.31

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Fig. 1 Side view of the unit cells for (a) β-HMX, (b) ε-CL-20, and (c) CL-20:HMX cocrystal along the a axis.

To validate the reliability of the DFT-D method for studying the nitroamine explosives, the lattice parameters of both β-HMX, ε-CL-20, and CL-20:HMX cocrystal under hydrostatic compression together with available experimental data^22–24 are shown in Fig. 2. The results show that both the variation trends of the lattice constants of β-HMX and ε-CL-20 are well reproduced the experiments especially in the low pressure region. As the pressure increases, the lattice constants of the cocrystal gradually decrease. Its structure is much stiffer in the a axis than along the b and c direction. This indicates that the compressibility of the cocrystal is anisotropic. In the a direction, the cocrystal have quite different lattice constant from its constituents HMX and CL-20, suggesting that the two constituents produce collective effects on the lattice constant a of the cocrystal. However, the lattice constant b of the cocrystal approaches that of its constituent CL-20, while its lattice constant c is very close to that of its constituent HMX under compression. This indicates that CL-20 in the cocrystal plays main role in the b, while HMX has dominant effects on the c. Accordingly, the two constituents produce different effects on the crystal structure of the cocrystal in different directions.

Fig. 2 Lattice constants of the β-HMX, ε-CL-20, and CL-20:HMX cocrystal as a function of pressure.

Fig. 3 displays the compressed unit cell volumes of the two single crystals and cocrystal together with experimental values. Our results well reproduce the experimental variation trends. Since the numbers of the irreducible molecules in the CL-20:HMX cocrystal are equivalent to those in β-HMX and ε-CL-20, a direct comparison of the unit cell volume between the cocrystal and two single crystals can be given as

ΔV = V_AB − (V_A + V_B) (1)

where V_AB represents the unit cell volume of the cocrystal, V_A and V_B represent the unit cell volumes of the pure crystals A and B, respectively. It is found in Fig. 3 that the formation of the CL-20:HMX cocrystal costs more space over the volume sum of the two constituent crystals. The volume of the unit cell peaks at 10 GPa and then gradually decreases and levels off at about 10 ų (ca. 0.9% of V_A + V_B) in the high pressure region (above 40 GPa). This means that below 40 GPa, the molecules in the cocrystal CL-20:HMX are less densely packed and can be more compressible than the pure crystals. Although there are no available experimental compression studies on the CL-20:HMX cocrystal, the GGA/PBE functional with dispersion corrections appears to be adequate for studying the nitroamine explosives HMX and CL-20 weakly bonded by van der Waals forces. Therefore, the extensively existing hydrogen bondings in the cocrystal could be well described by using the DFT-D method in the whole pressure range.

Fig. 3 Unit cell volumes of the β-HMX, ε-CL-20, and CL-20:HMX cocrystal as a function of pressure. ΔV denotes the difference of the unit cell volumes between the cocrystal and two pure crystals.

3.2. Electronic structures

To understand the non-covalent interactions among the individual molecules in the CL-20:HMX cocrystal, the electron density difference (EDD) maps between the delocalized and localized wave functions were investigated.²⁵ For convenience, the cocrystal unit cell is divided into three molecular layers (two CL-20 layers and one HMX layer) parallel to the bc plane. The electron density difference (Δρ) were obtained by eqn (2).

Δρ = ρ_total − ρ_layer1 − ρ_layer2 − ρ_layer3 (2)

where ρ_AB is the electron density of the total system. ρ_layer1, ρ_layer2, and ρ_layer3 are the unperturbed electron densities of the three layers in the system. The electron delocalization between different layers in the cocrystal at zero pressure is shown in Fig. 4, where the blue color denotes a gain and the yellow color a loss of electron density. It is found that the electron density of the atoms participating in hydrogen bondings flows into the regions between two adjacent molecules in different molecular layers. For instance, Fig. 4a shows the electronic redistribution between the HMX and CL-20 molecules, where the O atoms of nitro group delocalize their lone pairs towards the adjacent H atoms and result in the polarization and elongation of the C–H bonds along with the reduction of electron densities on the N–NO₂ groups. It is obvious that both the nitro groups of the HMX and CL-20 molecules participate in forming hydrogen bonds with neighboring hydrogen atoms. The electron redistribution can also be found in the regions between the CL-20 molecules in Fig. 4b. Comparatively speaking, the electron density accumulating between the CL-20 molecules is significantly low compared with that between the CL-20 and HMX molecules (see Fig. 4a), suggesting that the hydrogen bonds between the CL-20 molecules are weaker than those between the CL-20 and HMX molecules. The existence of distributed hydrogen bonding nets is also supported by recent theoretical studies.^9,26 They are also suggested to greatly contribute to the low mechanical sensitivity.

Fig. 4 Spatial electron density difference (EDD) displaying electron delocalization between bulk crystal and different molecular layers in the CL-20:HMX cocrystal at 0 GPa. The blue and yellow color denotes a gain and a loss of electron density, respectively (isovalue is 0.015).

Fig. 5 compares the total density of states (DOS) of the three crystals at zero pressure. The total DOS of the CL-20:HMX cocrystal is resolved into two parts originating from the CL-20 and HMX states, respectively (see Fig. 5b and c). Each partial DOS of the pure constituent was plotted from the contribution of the selected pure molecules in the unit cell. The CL-20- and HMX-resolved DOS in the cocrystal can be directly compared with those of the pure crystals due to the same numbers of irreducible molecules per unit cell as mentioned above. Compared with the total DOS of the pure ε-CL-20 in Fig. 5a, both the valence bands and the conduction bands of CL-20 in cocrystal present a noticeable blue shift, suggesting that there is the extensive hybridization of the energy bands between CL-20 and HMX. Moreover, the peaks in the valence bands are significantly sharper than those in the pure crystal, implying that the intermolecular interactions among the CL-20 molecules in the cocrystal are considerably weaker than those in the pure ε-CL-20 crystal. But for HMX, as illustrated in Fig. 5c, there are few differences between the HMX-resolved DOS in the cocrystal and the DOS of the pure HMX especially with respect to the valence bands, despite of the significant disparities of the molecular packings in different crystals. While the conduction bands of the HMX molecules in the cocrystal almost disappear. Instead, the lower conduction bands of the cocrystal are dominated from the contributions of the CL-20 molecules. We note that the shape of the CL-20-resolved DOS in the cocrystal is essentially identical to that of the cocrystal. Therefore, the rigidity of the CL-20-resolved DOS implies that the modifications in the DOS are mainly due to the effects of the partial DOS of the HMX-states. This indicates that the CL-20 in the cocrystal plays a leading role on the electronic structure of the cocrystal.

Fig. 5 DOS of the same molecular species in the pure crystals with those in the cocrystal at zero pressure.

Fig. 6 displays the effect of pressure on the band gaps of the three crystals. Their band gaps gradually decrease as the pressure increases. The energy reduction is more pronounced in the low pressure region compared to the high pressure region. This indicates that there is an increase of charge overlap in the systems under compression. Previous studies^27–31 and the first-principles band gap criterion of impact sensitivity³² reported that for energetic crystals with similar structure or with similar thermal decomposition mechanism, the smaller the band gap is the easier the electron transfers from the valence band to the conduction band and the more they becomes decomposed and exploded. Thus, it may be inferred that the cocrystal becomes more and more sensitive with the increment of pressure. It is seen in Fig. 6 that overall, the band gap of the cocrystal is comparable to those of the two constituent pure crystals but presents a larger decreasing rate especially in the high pressure range. This implies that the CL-20:HMX cocrystal can be more favorable for the electron excitation than the pure explosives under external compression.

Fig. 6 Band gaps of the pure crystals and CL-20:HMX cocrystal versus pressure.

There are considerable intermolecular interactions in the CL-20:HMX cocrystal. To understand how the intermolecular interactions affect the electronic structure, Fig. 7–9 compare the band structures and frontier energy levels of the pure crystals and cocrystal. As shown in Fig. 7a, the pure β-HMX has a direct band gap of 3.29 eV at G point. In Fig. 7c, the valence band maxima (VBM) and conduction band minima (CBM) of ε-CL-20 are located at Z and D points, respectively, suggesting an indirect band gap of 3.23 eV. The band gap value is slightly smaller than that of β-HMX. Since both the two crystals are typical molecular solids, the bands are flat to some extent. The ε-CL-20 has much more flat band structure than the β-HMX, implying that the overlap between the energy levels of neighboring molecules is weaker in the ε-CL-20 crystal.

Fig. 7 Band structure and partial charge densities of β-HMX (a and b) and ε-CL-20 (c and d) at 0 GPa. The Fermi energy is shown as a dashed line. The blue energy levels represent for the valence band maxima and the red for the conduction band minima. The isovalue is defined by 0.03.

Fig. 8 Band structure of the CL-20:HMX cocrystal at 0, 20, 40, and 100 GPa. The Fermi energy is shown as a dashed line.

Fig. 9 Partial charge densities of the valence band maxima and conduction band minima of the cocrystal versus pressure. The blue energy levels represent for the VBM and the red for the CBM. The isovalue is defined by 0.01.

Fig. 7b and d display the partial charge densities of VBM and CBM for the pure crystals. From Fig. 7b, the VBM in β-HMX are localized mainly on the 2p-states of the axial N–NO₂ groups and partially on the 1s-states of the neighboring hydrogen atoms, but the CBM are localized solely on the equatorial N–NO₂ groups. It is found that the VBM and CBM in β-HMX and ε-CL-20 are alternately parallel to each other. Thus, we may expect that the alternative distribution of the frontier energy levels in the bulk β-HMX produces a specified direction for the electron transfer between the upper valence and lower conduction bands. A similar trend of the localization of VBM and CBM is also found in the solid ε-CL-20 (see Fig. 7d). The VBM possessing the parallel arrangements are surrounded by the CBM from adjacent CL-20 molecules. Both the VBM and CBM are localized on the NO₂ groups. The spatial distribution of the frontier energy levels suggests that the N–NO₂ groups in both the pure crystals can play a decisive role in the initial chemical decomposition. Our results are in agreement with previous studies^27,31,33,34 that the N–NO₂ bond cleavage may be energetically favorable in some condensed phase traditional nitroamine explosives.

The band structures of the CL-20:HMX cocrystal versus pressure are listed in Fig. 8. At 0, 20, 40, and 100 GPa, the VBMs are at the G point, while the CBMs are located between the G and F point, indicating that the cocrystal has an indirect band gap except for the situation at 40 GPa. However, at 40 GPa, comparable to its detonation pressure of 39.5 GPa,¹¹ the cocrystal possesses a direct band gap of 2.68 eV at the G point. It may thus be inferred that the electron excitation in the cocrystal is more direct in the vicinity of its detonation pressure. Next we turn to examine the distributions of the frontier energy levels in the CL-20:HMX cocrystal. Fig. 9 compares the partial charge densities of its VBM and CBM under different pressures. It is found that both the VBM and CBM are arranged into a homogeneous alignment parallel to the molecular layers. This indicates that the hydrostatic compression induces the significant delocalization of both the VBM and CBM energy levels. The VBM are dominantly contributed by the 2p-states of the axial N–NO₂ group of HMX in the whole pressure range. However, the CBM in the bulk cocrystal are originated mainly from the 2p-states of the N–NO₂ groups in CL-20. As the pressure increases, the CBM are delocalized on the N–NO₂ groups throughout the CL-20 molecular layers. The increasing pressure enhances the overlaps of the energy levels and leads to the frontier energy levels to disperse to the adjacent molecules, suggesting that the electron transfer becomes more favorable when the hydrostatic pressure is applied to the system. This redistribution of the frontier energy levels in the cocrystal is expected to produce periodic planar regions localized between the HMX and CL-20 molecules, where the electron transitions from the HMX to CL-20 molecules become easier.

3.3. Optical absorption properties

In this section, the optical absorption coefficients of the three crystals at different pressures were investigated and shown in Fig. 10. The absorption spectra often results from the photon-induced electron transitions between the occupied and unoccupied states in the molecular systems. It can give valuable information on the optical transition probability corresponding to specific light wavelength. The absorption coefficient α(ω) can be evaluated from the real part ε₁(ω) and imaginary part ε₂(ω) by eqn (3). The imaginary part ε₂(ω) of the dielectric function can be obtained from the momentum matrix elements between the occupied and unoccupied wave functions within the selection rules, and the real part ε₁(ω) of the dielectric function can be calculated from the imaginary part ε₂(ω) by the Kramer–Kronig relationship.³⁵

Fig. 10 A comparison of the absorption coefficients α(ω) for the three crystals at 0, 20, and 40 GPa.

It is found in Fig. 10 that the pure crystals and cocrystal at 0 GPa display optical absorption in the visible light range from about 2 eV. This value is obviously smaller than the band gaps of the crystals, suggesting that there is a considerable optical transition probability below the band gaps due to the attractive interaction between electrons and holes. As the pressure increases, the absorption peaks become wider and higher. It is thus inferred that both the three crystals have relatively high optical activity under high pressure. At zero pressure, the evolution patterns of absorption spectra for the CL-20:HMX cocrystal are quite similar to those of the ε-CL-20 pure crystal but exactly different from those of β-HMX. Both the three crystals have only one strong wide peak at about 5.76 eV in the absorption range from 0 to 20 eV. This value is in good agreement with the theoretical studies²⁹ that the first absorption peak of β-HMX at ambient pressure is found at 5.73 eV. Both the cocrystal and ε-CL-20 pure have very weak absorption bands above 7 eV. However, for β-HMX, there are four stronger absorption bands covering from 0 to 20 eV compared with the cocrystal and ε-CL-20. The calculated results here present that the absorption spectra of the cocrystal at high pressure display a few strong bands in the fundamental absorption region.

3.4. Mechanical properties

The general relation between stress and strain can be given by the generalized Hooke's law: σ_i = C_ijε_j(i,j = 1–6), where C_ij are the elements of the elastic constant matrix. Since all the crystals are monoclinic, there are only 13 non-zero independent elastic coefficients. According to statistics, a heteromorphy consisting of micro-crystals with random orientation can be considered to be isotropic. Based on the obtained bulk modulus B and shear modulus G by Reuss mean method,³⁶ the tensile modulus E and Poisson's ratio ν can be calculated from the following equations:

E = 2G(1 + ν) = 3B(1 − 2ν) (4)

Both the elastic coefficients and Cauchy pressure of the β-HMX, ε-CL-20, and CL-20:HMX cocrystal at different pressures are listed in Fig. 11 along with available experimental and theoretical data. Since there are no experimental elastic coefficients for the CL-20:HMX cocrystal, we only compared our calculated results with the experimental data of pure β-HMX and ε-CL-20 at 0 GPa here. Since the experimental studies used the P2₁/n space group for the β-HMX, the sign of experimental elastic coefficients of C₁₅, C₂₅, C₃₅, and C₄₆ were translated from P2₁/n to P2₁/c in our study.³⁷ Qualitatively speaking, the stiffness to the uniaxial compression can be described by the diagonal elements C_ii, while the biaxial compression and distortion can be judged by the off-diagonal elements C_ij. As seen in Fig. 11a, the CL-20:HMX cocrystal possesses considerable anisotropy in the diagonal elements C_ii (i = 1–6). The stabilities of the cocrystal and two pure crystals to the external compression are greatly strengthened as the elastic coefficients (C₁₁, C₂₂, C₃₃, C₁₂, C₁₃, and C₂₃) monotonically increase. For simplicity, the evolution patterns of elastic coefficients for β-HMX and ε-CL-20 at 0 GPa are not presented in Fig. 11a and b. At zero pressure, the comparison of C₁₁, C₂₂, and C₃₃ suggests that the cocrystal has better stiffness to the c axis than to other two axes. The increasing hydrostatic pressure can also affect the preference to the stiffness towards different directions. Fig. 11c compares the C₁₅, C₂₅, C₃₅, C₄₆, and Cauchy pressure (C₁₂–C₄₄) of the three crystals. For all the three crystals, both the four coefficients possess negative values in a wide pressure range. It is seen in Fig. 11c that the cocrystal has similar variation trends with β-HMX but quite different ones from ε-CL-20, especially on behalf of C₂₅. In addition, the ductibility and brittleness estimated by Cauchy pressure (C₁₂–C₄₄) are also shown in Fig. 11d. Since a positive value of Cauchy pressure represents for a ductile material and a negative for a brittle material. Thus, it may be deduced that the two pure explosives and cocrystal are easier to break under zero pressure than under compression. This is consistent with previous studies.³⁸ As the pressure increases, the Cauchy pressure changes into positive, implying less fragile properties and better ductibility for the solids.

Fig. 11 Elastic coefficients of the β-HMX, ε-CL-20, and CL-20:HMX cocrystal at different pressures.

Fig. 12 gives the tensile modulus (E), bulk modulus (B), shear modulus (G), Poisson's ratio (ν), and B/G for the three crystals versus pressure. These values are capable to measure the ability of the materials to resist against the shape deformation or volume change by the external stress. The shear modulus G indicates the resistance to plastic deformation and the bulk modulus B is proportional to the fracture strength for a material. It is seen from Fig. 12 that the present results tend to overestimate the experimental results.^39,40 When the pressure increases from 0 to 100 GPa, the moduli of E, B, and G in the three crystals increases in general, implying the increasing rigidity. It is also suggested that the pressure-induced densely molecular packings in the molecular crystals can significantly lead to the decrease of the elasticity. At 0 GPa, the B value of the cocrystal is almost the same as that of the pure crystals, indicating that their compressibilities are almost the same. From 20 to 40 GPa, the cocrystal has a lower B value than the pure CL-20 or HMX, so it is more compressible in this pressure range. The Poisson's ratio values in Fig. 12 represent the plasticity of the crystals. The Poisson's ratio values are in the range of 0.2 to 0.5 in the whole pressure range except for the cocrystal at 0 GPa with a abnormal negative value of −0.3. Thus, it may be inferred that all the three crystals have some plasticity over the entire pressure range. The analysis of B/G of β-HMX indicates that the tenacity increases as the pressure increases and reaches a maximum at 40 GPa. The cocrystal possesses the smallest B/G value of 0.3 at zero pressure, suggesting that it has a brittle character. However, the applied pressure is expected to noticeably enhance the ductility due to the B/G value increasing from 0.3 to 13.0.

Fig. 12 Mechanical properties of the β-HMX, ε-CL-20, and CL-20:HMX cocrystal as a function of pressure.

4. Conclusions

In this work, the structural, electronic, absorption, and mechanical properties of the Cl-20:HMX cocrystal and its constituting pure crystals β-HMX and ε-CL-20 under hydrostatic pressure of 0–100 GPa were comparatively studied to understand how the constituents affect the performance of the cocrystal using DFT-D. A comparison of the crystal structure of β-HMX and ε-CL-20 with available experimental data indicates that the GGA/PBE functional with dispersion corrections is adequate for describing the weakly bonded van der Waals forces in the molecular crystals in the whole pressure range. The compressed unit cell volume of the cocrystal displays a lesser densely molecular packings especially below 40 GPa than those of the pure crystals, indicating that the cocrystal can be more compressible in the low pressure region. The two constituents produce different effects on the crystal structure of the cocrystal in different directions.

An analysis of the electron density differences indicates that there is extensively electron delocalization between the O atoms of nitro groups and adjacent H atoms in the cocrystal, which may greatly contribute to its mechanical stability. The decreasing rate of the band gap for the cocrystal is more pronounced than those of β-HMX and ε-CL-20 under compression. Both the density of states and frontier orbitals analysis of the cocrystal suggest that the upper valence bands are mainly localized on the 2p-states of axial N–NO₂ groups of the HMX molecules and partially on the 1s-states of their neighboring hydrogen atoms, while the lower conduction bands are dominantly localized on the 2p-states of the NO₂ groups of the CL-20 molecules. The spatial distribution of the frontier energy levels is expected to produce a periodic planar region localized between the HMX and CL-20 molecular layers. This distinct energy distribution in the cocrystal suggests that the electron transitions may take place between the HMX and CL-20 molecules. The CL-20 in the cocrystal plays a leading role on the electronic structure of the cocrystal.

The three crystals have higher absorption coefficients in the high pressure region, indicating a shift toward higher frequencies in their absorption spectra. The cocrystal has quite similar absorption spectra to ε-CL-20 but exactly different ones from β-HMX. Compared with the pure crystals, the mechanical properties of the cocrystal present a great anisotropy. The anisotropy significantly depends upon the applied pressure which not only greatly strengthens the stiffness but also affects the preference of the stiffness to different directions. The tensile modulus (E), bulk modulus (B), shear modulus (G), Poisson's ratio (ν), and B/G indicate that the cocrystal is more capable to resist against the shape deformation or volume change than its constituents especially in the high pressure region.

Our results may provide fundamental insight into the roles of the two constituents in the cocrystal and may be helpful for developing new cocrystals with high energy and good safe.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant no. 21273115) and the project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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