Energetic materials (explosives, propellants, and pyrotechnics) that rapidly detonate and release heat or gaseous products when stimulated by impact or shock have attracted the attention of researchers for several decades because of their wide civilian and military applications.^[1,2] Among energetic materials, 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) is a secondary high explosive with extraordinary insensitivity to thermal, impact, or shock stimuli because of its strong intralayer intramolecular and intermolecular hydrogen bond interactions and weak interlayer van der Waals (vdW) interaction.^[3] The extended hydrogen bond network of TATB is evidence of its profound chemical stability, especially under high-temperature and high-pressure conditions.

For the safe storage, transport, and use of TATB, it is crucial to elucidate its compression behavior. In this regard, the variations in physical/chemical properties of TATB under high pressure should be characterized, such as polymorphic behavior, decomposition reaction, and detonation process. To date, TATB has been extensively investigated from both theoretical and experimental points of view, especially focusing on its high-pressure behavior. In 1976, Olinger et al.^[4] obtained the P–V relationship of TATB under hydrostatic compression by x-ray diffraction. Stevens et al.^[5] later measured the hydrostatic compression curve of TATB at ambient pressures up to 13 GPa using powder x-ray diffraction in conjunction with a diamond anvil cell.

Infrared and Raman spectroscopies are useful tools to characterize the geometric and bonding features and to disclose the initiation mechanism of shock-compressed energetic materials. Previously, the Raman and IR spectra of TATB crystal under ambient pressure and room temperature, as well as low temperature, have been measured by various groups.^[6–8] Under high-pressure conditions, Satija et al.^[9] reported the effect of static pressure on the Raman spectra of TATB up to 16 GPa. Pravica et al.^[10] performed an infrared spectroscopic study of TATB and found no phase transition under high pressures up to 10 GPa. Soon thereafter, Pravica et al.^[11] extended their synchrotron infrared measurements in the mid- and far-IR region up to 40 and 30 GPa, respectively. They found that the peak frequencies of the NH₂ symmetric and antisymmetric modes steadily decreased with increasing pressure, indicating the strengthening of the intermolecular hydrogen bonds. Davidson et al.^[12] performed Raman spectroscopic analyses on TATB solid and reported an unusually high chemical stability under extremely high static pressures up to 150 GPa, where two subtle structural phase transitions were observed at 28 and 56 GPa. Recently, using in-situ Raman spectroscopy and high-speed photography, Saint-Amans^[13] investigated the behavior of a TATB-based explosive under shockwave loading up to 30 GPa, in which a complete loss of Raman signal was observed around 9 GPa.

In reality, the detonation process of an energetic material generates a shock wave that represents a high-pressure and high-temperature condition and presents a great challenge for real-time experimental measurement. Alternatively, theoretical calculations provide an effective way to understand the detonation mechanism and decomposition reaction of energetic materials under high pressure and/or high temperature. To date, TATB crystal has been widely explored by ab initio calculations based on density functional theory (DFT). Wu et al.^[14] studied the uniaxial compression effect on the electronic structure of crystalline TATB solid. Liu and co-workers^[15,16] investigated the vibrational properties and compression behavior of TATB crystal under hydrostatic pressure up to 10 GPa using DFT within local density approximation and generalized gradient approximation. With PW91, PBE, and local density approximation functionals, Byrd and Rice^[17] calculated the crystal structures of five common energetic molecular crystals (including TATB) within the pressure range 0–10 GPa. They pointed out that the disagreement between experimental crystal structures and theoretical results arises from the inadequate description of non-covalent intermolecular interactions by conventional DFT methods. Subsequently, various dispersion correction methods have been implemented into the DFT framework, such as semi-empirical DFT-D^[18,19] and non-empirical vdW functionals,^[20,21] which provide a better description of the non-covalent interaction of energetic materials. For instance, Sorescu and Rice^[22] used DFT-D to further compute the crystallographic properties of 10 energetic molecular crystals including TATB. Their results indicated that the DFT-D method significantly improved the description of intermolecular interactions in molecular crystals under both ambient and high-pressure conditions compared to the conventional DFT. Landerville^[23] obtained the equations of state for various energetic materials using DFT calculations with the inclusion of vdW interactions, thermal effects, and zero-point energy corrections, which were able to predict the thermophysical properties of energetic materials within a wide pressure and temperature range. Using the van der Waals-density functional theory (vdW-DFT) approach, Budzevich^[24] investigated hydrostatic and uniaxial compressions of TATB and showed that the equilibrium structural and elastic properties and the hydrostatic equations of state were in good agreement with available experimental data. Wu et al.^[25] performed DFT and DFT-D-based MD simulations to investigate the lattice parameters, electronic structures, and P–V isotherm of TATB within the pressure range 0–100 GPa at room temperature. Their DFT-D results were consistent with experimental results, but the DFT results without vdW correction misestimated these parameters. They also performed ab initio molecular dynamics simulations to investigate the initiation mechanisms and subsequent decompositions of TATB crystal at an initial decomposition temperature of 623 K coupled with different pressures (1–20 GPa).^[26] Rykounov^[27] systematically considered the pressure effects on the thermodynamic, elastic, and acoustic properties of TATB using dispersion-corrected DFT. Manaa and Fried^[28] also observed the nearly equivalent inter- and intramolecular hydrogen bonds within TATB crystal under high pressure. Ojeda and Cagin^[29] observed a similar behavior of hydrogen bonds and analyzed the variation of vibrational spectra as a function of pressure.

Despite the extensive theoretical efforts devoted to the pressure effects of TATB, most have focused on the changes of hydrogen bonds and electronic structures. However, the detailed changes in spectroscopic characteristics, possible phase transformations, and the energy transfer mechanism of TATB under extreme conditions are still insufficiently investigated. In this work, we performed dispersion-corrected DFT calculations to examine the changes in crystal/molecular structures and vibrational modes of TATB under pressures of 0–30 GPa. In particular, our simulated Raman and infrared spectra of TATB under high pressure showed minor changes in the molecular conformation at about 3 GPa and 5 GPa.

According to x-ray diffraction data, the polymorph of TATB crystal at ambient conditions is a triclinic structure with a space group.^[3] Its unit cell contains two molecules of C₆H₆N₆O₆ with a total of 48 atoms (Fig. 1). All DFT calculations within the periodic boundary condition were carried out using the Cambridge Sequential Total Energy Package.^[30] The exchange–correlation interaction was treated within the generalized gradient approximation parameterized by the Perdew–Burke–Ernzerhof (PBE) functional.^[31] Norm-conserving pseudopotentials were used to describe the ion-electron interactions.^[32] From our previous benchmark calculations,^[33] it was confirmed that intermolecular non-covalent interactions play a significant role in energetic molecular crystals and must be properly accounted for. Thus, the empirical dispersion correction scheme by Grimme,^[19] PBE-D2, was employed to describe the non-covalent interactions. As a compromise between computational cost and accuracy, a 2×2×2 Monkhorst–Pack k grid for sampling the Brillouin zones^[34] and a kinetic energy cutoff of 1000 eV for plane-wave basis were adopted. The unit cell parameters and atomic coordinates were fully relaxed by the Broyden, Fletcher, Goldfarb, and Shannon algorithm.^[35] The convergence criteria of maximum total energies of 5×10⁻⁶ eV/atom, the maximum force of 0.01 eV/Å, the maximum stress of 0.02 GPa, and the maximum displacement of 5×10⁻⁴ Å were employed throughout all calculations. Hydrostatic pressure was applied from 0 to 30 GPa in steps of 0.5 GPa.

Fig. 1.

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	Fig. 1. (color online) (a) Molecular structure of TATB (C6H6N6O6) and crystal structures of TATB crystal at (b) 0 GPa and (c) 30 GPa. Color scheme: C, green; N, blue; O, red; H, white.

Based on the optimized crystal structures, Raman and infrared spectra were computed with the density functional perturbation theory.^[36] Intensities of Raman peaks were calculated by the linear response formalism. The experimental factors of temperature (10 K) and incident light wavelength (514.5 nm) were taken into account for simulating the Raman intensity. The spectrum peak was broadened by a 20-cm⁻¹ wide Lorentzian functional.

First, we optimize the lattice parameters of TATB crystal at zero pressure and compare them with the experimental XRD data and previous DFT calculations with and without dispersion correction. As shown in Table 1, our computed lattice parameters were reasonably close to the experimental values,^[3] that is, lattice parameters a and b were overestimated by 1.19% and 1.12%, respectively, while the lattice parameter c and unit cell volume V were underestimated by 2.68% and 1.11%, respectively. After a comprehensive assessment of lattice constants and lattice angles, the current PBE-D2 scheme provided more reasonable and accurate results than the previous computational results,^{[16,17,22,24,28]} especially for those from pure DFT calculations. However, it should be noted that the computed lattice constant of the c axis had a relatively large deviation from the measured value by 0.18 Å, suggesting that DFT-D2 is not accurate for describing the interlayer vdW interaction.

Table 1.

Table 1.

Table 1. Comparison of experimental (Ref. [3]) and computational (DFT-D2) lattice parameters and unit cell volumes V of TATB crystal at zero pressure. . Cell parameter a/Å b/Å c/Å α/(°) β/(°) γ/(°) V/Å3 Exp.[3] 9.010 9.028 6.812 108.59 91.82 119.97 442.49 DFT-D2 9.118 9.129 6.629 109.54 91.52 119.98 437.57 Error/% 1.19 1.12 2.68 0.87 0.32 0.01 1.11

Table 1. Comparison of experimental (Ref. [3]) and computational (DFT-D2) lattice parameters and unit cell volumes V of TATB crystal at zero pressure. .

Figure 2 shows the variation of lattice parameters as a function of pressure up to 30 GPa. Overall, the lattice parameters of TATB crystal from our theoretical calculation are in reasonable accordance with experimental data^[4] and previous calculations.^[17,27] Our computed lattice parameter c was consistent with the experimental data^[4] and our DFT-D result^[27] was better than the pure DFT result,^[17] further confirming the importance of dispersion correction within DFT for describing the weak interlayer interaction in TATB along the c axis. In Fig. 2, note that lattice parameters a and b exhibited a nearly identical decrease with increasing pressure, whereas the lattice parameter c reduced drastically with increasing pressure. This can be explained by the fact that the weaker interlayer vdW interaction along the c axis is more compressible than the relatively stronger hydrogen bonds within the ab plane. Figure 2 also shows the pressure-induced volume compression of TATB up to 30 GPa, together with previous experimental^[4] and computational^[17,27] results. Similar to the lattice parameters, our DFT-D2 calculations approximately reproduced the trend of pressure-induced reduction of volume by experiment, in which the volume reduction at up to 30 GPa was 67%.

Fig. 2.

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	Fig. 2. (color online) (a)–(c) Lattice parameters and (d) unit cell volume compression of TATB crystal as a function of pressure. Experimental results are from Ref. [4] and computational results are from Refs. [17] and [27].

We further examined the changes of molecular conformation in a TATB crystal under high pressure. With increasing pressure, the TATB molecules gradually approached each other and transformed from a flat to a curved configuration because of the large compressible intermolecular spacing, significant intralayer hydrogen bonds, and weak interlayer vdW interaction as shown in Figs. 1(b) and 1(c). Figure 3 displays the pressure dependences of the bond lengths for two C–N bonds (both nitro and amino) and the intramolecular and intermolecular hydrogen bonds of the amino and nitro groups. The lengths of intermolecular hydrogen bonds between adjacent molecules decreased continuously with a compression rate of −0.018 Å/GPa. In contrast, the bond lengths of two C–N bonds and intramolecular hydrogen bonds between the hydrogen of the amino and the oxygen of the nitro group showed little pressure-induced change within the entire pressure range, i.e., compression rates of about −0.0018 Å/GPa, −0.0011 Å/GPa (C–N bonds of nitro and amino), and −0.0019 Å/GPa ( of intra), respectively. The intermolecular hydrogen bond decreased from about 2.33 Å at 0 GPa to 1.80 Å at 30 GPa with a noticeable 0.53 Å reduction of amplitude. In contrast, the intramolecular bond changed by only 0.06 Å within the same pressure range (i.e., from about 1.71 Å at 0 GPa to 1.65 Å at 30 GPa), indicating a much stronger compression of the intermolecular hydrogen bonds.

Fig. 3.

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	Fig. 3. (color online) Evolution of bond lengths of two C–N bonds (both nitro and amino) and intramolecular and intermolecular hydrogen bonds of amino and nitro groups with pressure.

Mulliken population analysis further supports the trend of bond variations and reveals the pressure-induced charge transfer in TATB. As shown in Table 2, as pressure increases, the on-site charges of amino H, amino C, nitro N, and nitro O continuously increased, whereas the on-site charges of nitro C and amino N were significantly reduced. Overall, under external pressure, charges are transferred from the amino group to the nitro group; the average charges on the amino and nitro group were and , respectively, at zero pressure, while they became and at 30 GPa, respectively. Variation of the covalent bond lengths with pressure affects the charge density distributions as demonstrated in Fig. 4. Enhanced interactions in the intra- and intermolecular hydrogen bonds are clearly seen from the contour plots in Fig. 4. In particular, the overlap of electron densities between amino H and the nearest neighboring nitro O in TATB increase with increasing pressure, indicating the occurrence of inter-group charge transfer.

Fig. 4.

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	Fig. 4. (color online) Contour plots of charge density distribution of TATB crystal under (a) 0 and (b) 30 GPa.

Table 2.

Table 2.

Table 2. Mulliken charges (e) on every atom of TATB crystal under 0, 15, and 30 GPa. . Pressure C (NH2) N (NH2) H(NH2) C (NO2) N (NO2) O (NO2) 0 GPa 0.203 –0.707 0.460 0.053 0.360 −0.415 15 GPa 0.203 –0.647 0.435 0.067 0.350 −0.421 30 GPa 0.196 –0.616 0.425 0.073 0.343 −0.423

Table 2. Mulliken charges (e) on every atom of TATB crystal under 0, 15, and 30 GPa. .

In addition, the pressure-induced shrinkage of bond lengths results in a variation of the band gap and increases the sensitivity of energetic materials because a decreasing band gap leads to increased impact sensitivity.^[37] Table 3 presents the band gaps of TATB crystal under selected pressures. As the pressure increased, the band gap of TATB gradually decreased, which was also observed in Wuʼs calculations.^[25] This can be ascribed to the decrease of intermolecular spacing under compression leading to the approaching of different groups and charge density overlap and electron delocalization. At up to 30 GPa, the compressed TATB crystal had an appreciable band gap of 1.61 eV, indicating high chemical stability. Note that there is no structural phase transition in TATB within the considered pressure region from both our theoretical calculations and experiments.^[12] In contrast, most energetic materials undergo amorphization or phase transformation at relatively low pressures as well as band gap closure; for example, FOX-7 exhibits a molecular conformational change at 2 GPa and a structural phase transition at 4.5 GPa.^[38]

Table 3.

Table 3.

Table 3. Band gaps (eV) of TATB crystal under pressures of 0, 10, 20, and 30 GPa from this calculation (DFT-D2) and Ref. [25] (DFT-D). . Pressure 0 GPa 10 GPa 20 GPa 30 GPa DFT-D2 2.36 1.97 1.77 1.61 DFT-D 2.60 2.16 1.97 1.73

Table 3. Band gaps (eV) of TATB crystal under pressures of 0, 10, 20, and 30 GPa from this calculation (DFT-D2) and Ref. [25] (DFT-D). .

The electronic structures of the compressed TATB crystal can be further analyzed by the partial density of states (PDOS) and total density of states. Figure 5 shows the PDOS for TATB under 0 and 30 GPa. One can see that the 2p states of O, C, and amino N atoms contribute mostly to the conduction bands, while the 2p states of O, C, and nitro N atoms dominate the valence bands near the Fermi level. Therefore, we suggest that the nitro O atom and amino N atom mainly contribute to the relative reactivity of TATB under shock, which coincides well with the experimental and computational results showing that the loss of oxygen is assisted by an intramolecular/intermolecular NH₂ group of TATB under external stimuli.^[39–41] Under 30 GPa, the variation of the PDOS for the O atom is more pronounced than the other atoms, verifying the possible charge transfer from the amino group to the nitro group in TATB.

Fig. 5.

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	Fig. 5. (color online) Partial density of states of TATB at (a) 0 and (b) 30 GPa. The blue vertical dotted line indicates the Fermi level.

Raman and infrared spectra are critical for understanding the strength of chemical bonds, intermolecular interactions, and vibrational coupling of a molecular crystal at high pressure. Thus, vibrational frequencies of Raman and infrared spectra for TATB under hydrostatic compression were calculated and analyzed. Table 4 lists the computed vibrational frequencies of TATB crystal and the assignment to different modes, together with previously measured data at ambient pressure.^[7] Our computational frequencies excellently reproduced the experimental peak positions in which the mean square error of frequency was only 9 cm⁻¹. Figure 6(a) displays the evolution of Raman spectra of TATB as a function of pressure over a broad frequency range. The lower frequency peaks below approximately 200 cm⁻¹, including internal modes and lattice modes, corresponding to the skeletal deformation of TATB. The intermediate frequency modes in the range 200–1600 cm⁻¹ have a rather complicated character and mainly consist of C–NH₂ stretching, NO₂ stretching and scissoring, C–NO₂ twisting, and NH₂ scissoring, wagging, and rocking modes. The highest frequency modes in the range 3200–3400 cm⁻¹ have been assigned to the symmetric and asymmetric NH₂ stretching vibrations. As seen in Fig. 6(a), most vibrational frequencies shift gradually toward higher frequencies (i.e., blue shift) with increasing pressure as a result of the reduced interatomic distances, except for the NH₂ rocking vibration mode. This behavior is consistent with previous high-pressure Raman experiments of TATB crystals.^[13] The observed blue shift of most vibrational frequencies is caused by the strengthening of chemical bonds, especially the inter- and intramolecular hydrogen bonds enhanced by compression.

Fig. 6.

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	Fig. 6. (color online) Variations of simulated (a) Raman and (b) infrared spectra with pressure (0–30 GPa) over a broad frequency range.

Table 4.

Table 4.

Table 4. Calculated and experimental vibrational frequencies (in cm−1) of TATB crystal at ambient pressure. . Mode This work Exp.[7] Assignment M1 3346 NH2 asym. stretch M2 3343 NH2 asym. stretch M3 3333 3302 NH2 asym. stretch M4 3236 NH2 sym. stretch M5 3227 3213 NH2 sym. stretch M6 3220 3203 NH2 sym. stretch M7 1554 1566 C–NH2 stretch M8 1545 C–NH2 stretch M9 1535 1526 C–NH2 stretch M10 1498 1493 NH2 scissor M11 1492 1485 NH2 scissor M12 1437 1430 NH2 scissor M13 1437 1420 NH2 scissor M14 1394 1378 NH2 scissor + C–NO2 stretch + Ring breath M15 1374 1368 NH2 scissor + NO2 asym. stretch M16 1344 1341 Ring stretch + NH2 rock M17 1286 NH2 scissor M18 1280 1279 NH2 scissor M19 1199 Ring breath + NO2 stretch + NH2 scissor M20 1196 Ring stretch + NO2 stretch + NH2 scissor M21 1192 1191 Ring stretch + NO2 stretch + NH2 stretch M22 1149 1144 NH2 scissor M23 1147 NO2 stretch + NH2 scissor M24 1120 1134 NH2 rock + C–NH2 stretch M25 1114 NH2 rock M26 1027 1028 NH2 rock M27 1026 1023 NH2 rock M28 864 874 NO2 stretch + NH2 rock M29 862 878 NO2 stretch + NH2 rock M30 831 833 NH2 twist M31 820 818 NH2 twist M32 814 811 NH2 twist M33 808 806 NH2 twist + NO2 stretch M34 777 780 NH2 wag M35 763 761 NH2 wag + ring wag M36 744 749 NH2 wag M37 730 729 NH2 twist M38 726 729 NH2 wag M39 715 709 NH2 wag M40 696 696 NO2 scissor + NH2rock M41 695 C–NH2 stretch + C–NO2 scissor M42 694 NH2 rock M43 680 670 C–NH2 wag + C–NO2 wag M44 646 C–NH2 wag M45 645 C–NH2 wag M46 605 614 C–NH2 stretch M47 511 NH2 rock + NO2 rock M48 511 506 NH2 rock M49 490 NH2 rock + NO2 rock M50 441 449 NH2 rock + NO2 rock M51 440 445 NH2 rock M52 391 390 NH2 rock + NO2 rock M53 384 C–NO2 stretch M54 367 370 C–NH2 stretch + C–NO2 rock M55 364 369 C–NH2 stretch + C–NO2 twist M56 338 333 NH2 twist M57 331 332 NH2 twist M58 289 297 C–NH2 stretch + C–NO2 twist M59 288 296 C–NH2 stretch + C–NO2 twist M60 225 231 C–NH2 wag

Table 4. Calculated and experimental vibrational frequencies (in cm−1) of TATB crystal at ambient pressure. .

To further illustrate the pressure-dependent change of vibrational frequencies, the peak positions for selected modes as a function of pressure are depicted in Fig. 7. Interestingly, some abnormal frequency changes for a few vibrational modes are observed at pressures around 3 and 5 GPa, whereas the experimental Raman spectra of TATB revealed no phase transition up to at least 28 GPa.^[12] Nonetheless, our DFT-D calculations also show that the crystal structure is basically retained and there is no phase change within the pressure range 0–30 GPa. Thus, the abnormal Raman frequency changes are attributed to minor changes in molecular conformation, mainly because of the rotation of the NH₂ groups of TATB. Specifically, the NH₂ groups of TATB continuously undergo distortions and rotations and move away from their original locations under the compression process but exhibit reverse twisting around 3 and 5 GPa, triggering abnormal frequency changes.

Fig. 7.

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	Fig. 7. (color online) Pressure-induced frequency shift of selected Raman frequency modes (see Table 4 for definition).

Further analysis shows that the frequencies for NH₂ stretching (M1, M4) and NH₂ twisting (M30, M56, M57) modes monotonically increase with increasing pressure, both showing a subtle saltation around 3 GPa. In addition, NH₂ stretching frequencies present minor changes at about 5 GPa. More complex behaviors were observed for other modes. Modes 14, 15, and 28 contributed NH₂ scissoring, NH₂ rocking, and NO₂ stretching vibrations, respectively, a gradual red shift at less than 5 GPa, and a blue shift with increasing pressure. In particular, with increasing pressure, the vibrational character of pure NH₂ scissoring mode 14 was gradually mixed with C–NO₂ stretching and ring breathing vibrations, whereas the combinational mode 28 included less NO₂ stretching vibrations and gradually became a pure NH₂ rocking vibration. All these behaviors reveal strong coupling between NO₂ and NH₂ groups resulting from intra- and intermolecular hydrogen bonds and imply a transfer of energy among these vibrational modes. In contrast, as the pressure increases, the frequency of mode 16 consisting of NH₂ rocking and ring stretching first rose at a pressure less than 5 GPa and then dropped at up to 15 GPa. Meanwhile, it should be emphasized that there is no crossing of Raman vibrational peaks of these modes under all pressures up to 30 GPa. Similar behaviors were observed in the simulated infrared spectra of TATB in Fig. 6(b), showing as pressure-dependent anomalous spinodal around 3 and 5 GPa.

We carried out systematical DFT calculations to gain insight into the high-pressure molecular conformations and spectroscopic characters of the TATB insensitive explosive. Compared with the available experimental data and previous DFT calculations, it was shown that dispersion-corrected DFT is necessary to describe the TATB crystal. Under hydrostatic pressures up to 30 GPa, the changes of the lattice structure, cell volume, and the electronic band gap of TATB suggest unusually high chemical stability. Mulliken population analysis and density of states of TATB reveal possible charge transfer from NH₂ groups to NO₂ groups with increasing pressure. The simulated Raman and infrared spectra of TATB indicate the strengthening of hydrogen bonds and a strong coupling between NO₂ and NH₂ groups. Abnormal changes of selected vibrational modes are also observed at approximately 3 and 5 GPa, which are associated with minor changes of molecular conformation without changes in crystal symmetry. The present study provides a comprehensive understanding of the pressure dependence of crystal structures and vibrational spectra of insensitive energetic crystal, and may trigger further experiments to explore the high-pressure behavior of TATB and other energetic materials.