High-Pressure Studies of Hydrogen-Bonded Energetic Material 3,6-Dihydrazino-s-tetrazine Using DFT.

Hydrogen bonding is an important noncovalent interaction that plays a key role in most of the CHNO-based energetic materials, which has a great impact on the structural, stability, and vibrational properties. By analyzing the structural changes, IR spectra, and the Hirshfeld surfaces, we investigated the high-pressure behavior of 3,6-dihydrazino-s-tetrazine (DHT) to provide detailed description of hydrogen bonding interactions using dispersion-corrected density functional theory. The strengthening of hydrogen bonding is observed by the pressure-induced weakening of covalent N-H bonds, which is consistent with the red shift of NH/NH2 stretching vibrational modes. The intermolecular interactions in DHT crystals lead to more compact and stable structures that can increase the density but diminish the heat of detonation, Q. The calculated detonation properties of DHT (D = 7.62 km/s, P = 25.19 GPa) are slightly smaller than those of a similar explosive 3,6-bis-nitroguanyl-1,2,4,5-tetrazine (D = 7.9 km/s, P = 27.36 GPa). Overall, the crystallographic and spectroscopic results along with Hirshfeld surface analysis as a function of pressure reveal the presence of strong hydrogen bonding networks in the crystal structure of DHT.

Introduction

In the world of advanced technology, researchers are still digging deep down the track to obtain the balance between high performance and good molecular stability in order to design high-energy-density materials. However, the major goal in the field of energetic materials is to develop more powerful and insensitive explosives, propellants, pyrotechnics, and oxidizers. To construct these types of explosives, many factors need to be considered (e.g., safety, energy, cost, etc.) before they are applied for practical applications.[1] One among such parameters is sensitivity, which is a major problem of energetic materials and has to be taken into account during production, storage, and transportation. The best approach to improve the performance of an explosive without compromising safety is to choose the material that can form hydrogen bonding networks.[2] These noncovalent interactions, especially hydrogen bonding interactions, have a remarkable influence on the physical and chemical properties of explosives giving rise to efficient packing in the crystal, which in turn improves the density and stability of the material.[3] In addition, the low solubility in water is an extra advantage for strongly bonded energetic materials, which can provide better sensitivity together with low toxicity.[4] Various hydrogen-bonded energetic materials have been extensively studied in the recent years to understand the nature of intermolecular iterations.[5−8] For instance, the strong hydrogen bonding networks in 2,4,6-trinitro-1,3,5-benzenetriamine (TATB) not only enable higher density (ρ = 1.937 g/cm3) but also are responsible for its insolubility in most of the common solvents.[9] Recently synthesized ecofriendly energetic material hydrazine 5,5′-bitetrazole-1,1′-diolate (HA·BTO) exhibits higher crystal density (ρ = 1.913 g/cm3)[10] than that of 1,3,5-trinitro-1,3,5-triazinane (RDX, ρ = 1.806 g/cm3)[11] due to the influence of strong hydrogen bonding networks. The huge number of intermolecular hydrogen bonds not only play a crucial role in the formation of an interesting structure but also improve the stability of HA·BTO. Our previous results also showed that the presence of strong hydrogen bonding in ammonium dinitramide (ADN) is responsible for more hygroscopic nature than that of ammonium perchlorate (AP).[12]

Pressure on the scale of gigapascals can cause remarkable changes in the intermolecular interactions and reveals the hidden phenomena lying behind the extreme conditions.[13−15] Moreover, the effect of pressure on the crystal structure of energetic materials can facilitate an efficient crystal packing and tune the noncovalent hydrogen bond interactions, thereby improving the detonation properties. These types of studies provide a better understanding about the nature of hydrogen bonding and structural stability of the energetic materials under pressure. Li et al. carried out high-pressure studies on energetic material acetamidinium nitrate[16] (C2N2H7+·NO3–) using a diamond anvil cell. Their results show a deviation in the ideal hydrogen-bonded arrays along with a small slippage between adjacent ion pairs, which is responsible for the fabrication of new high-energy-density materials for better detonation performance. The pressure-induced rearrangement of hydrogen-bonded networks causes a phase transition in the carbohydrazide (CON4H6) energetic material.[17] The reported high-pressure phase with space group P1 exhibits almost 23.1% higher density than that of the ambient structure (P21/n). However, the influence of pressure can change the direction of atoms and molecules in hydrogen-bonded structures, allowing the explosive properties (such as sensitivity) to be modified. Therefore, it is particularly interesting to study the high-pressure behavior of hydrogen-bonded systems for exploring high-energy-density materials.

Nitrogen-rich energetic materials, especially tetrazine-based compounds, have attracted special attention due to their high positive heat of formation (HOF), higher densities, and better oxygen balance (OB).[18] As a component of gun and rocket propellant,[19] ecofriendly smoke ingredient of pyrotechnic composition, 3,6-dihydrazino-s-tetrazine (DHT) is considered to be a nitrogen-rich energetic material with the measured HOF and H50 values of +536 kJ/mol and 65 cm (2.5 kg, type 12), respectively.[19] It can detonate with a rate of 7.54 km/s in the unconfined pressed pellets of 0.50 in. in diameter. The carbon-free combustion and hot flames of DHT have made it an ideal for the new-generation ecofriendly firework.[20] Furthermore, it has been used to design a variety of other nitrogen-rich energetic materials, such as 3,6-di-azido-1,2,4,5-tetrazine.[21] DHT was first synthesized by Hiskey et al. in 1990s[22,23] and later recognized by several experimental groups,[24−29] but very few theoretical studies were reported.[30−33] Hu et al. studied the intermolecular interactions of DHT using computational modeling and found that the strong intermolecular hydrogen bonding networks dominantly contributed to the dimers.[33] Consequently, the variations identified on a microscopic level can also affect the macroscopic properties like density, which may further improve the performance of an explosive. Therefore, the increase in density of DHT under pressure may greatly influence the detonation properties and applications. Herein, we report the high-pressure investigation of structural and vibrational properties of DHT using first-principles calculations. Its axial and bond compressibilities and pressure–volume equation of state have been calculated. In addition, the effect of pressure on NH/NH2 stretching frequencies is crucial in understanding the behavior of hydrogen bonding. More information about the variations in packing patterns were obtained from Hirshfeld surfaces and the fingerprint plots. The present study explores the pressure-induced changes in intermolecular interactions to provide valuable information about the stability of hydrogen-bonded energetic materials.

Results and Discussion

Structural Properties

DHT crystallizes in the monoclinic P21/c symmetry with lattice parameters a = 4.043 Å, b = 5.644 Å, c = 12.129 Å, β = 99.124°, and Z = 2 at 173 K.[49] The molecular geometry and crystal structure of DHT are presented in Figures and 2, where the nitrogen atoms attached to the hydrazino group and the tetrazine ring are nearly coplanar with an axial symmetry. Each molecule in the crystal structure connects with the neighboring molecules to form three-dimensional N–H···N hydrogen bonding networks in the form of herringbone-like pattern. The presence of 12 hydrogen bonds in each molecule can strengthen the stability of the compound. The relaxed lattice parameters and the optimized volume obtained using various exchange–correlation functionals are presented in Table along with the experimental values. It is found that the calculated lattice parameters using local-density approximation (LDA) are smaller than the experimental results, whereas the generalized gradient approximation (GGA) values are overestimated. The well-known tendency of LDA/GGA calculations to underestimate/overestimate the lattice constants is precisely reflected in the obtained volumes (242.5/320.3), which fall below/above the experimentally measured volume of 272.9, respectively. In contrast, the correction to the Perdew–Burke–Ernzerhof (PBE) functional (TS and D2) provides reasonable improvement with small deviations when compared with experimental unit cell parameters. Especially, by the TS method, the error in the calculated volume is reduced to 0.01%, indicating the necessity of van der Waals (vdW) interactions while studying the structure of a DHT crystal.

Figure 1

Molecular geometry of DHT. Green dashed lines represent hydrogen bonding.

Figure 2

Crystal structure of DHT along the (a) x-axis and (b) y-axis and (c, d) significant H−π stacking interactions stacked in columns parallel to the c-axis.

Table 1

Calculated Lattice Parameters (a, b, c in Angstrom), Lattice Angle (β, in Degrees), and Volume (V in Å3) of DHT Using PBE-GGA and Dispersion-Corrected (TS, D2) Functionals Along with Experimental Data[49],a

	LDA	PBE	TS	D2	expt[49]
a	3.996 (−1.18%)	4.798 (+18.64%)	4.178 (+3.31%)	4.036 (−0.17%)	4.043
b	5.364 (−4.97%)	5.340 (−5.39%)	5.506 (−2.45%)	5.541 (−1.83%)	5.644
c	11.532 (−4.92%)	12.501 (+3.06%)	11.984 (−1.19%)	11.855 (−2.25%)	12.129
β	101.23 (+2.12%)	88.9 (−10.31%)	98.22 (−0.9%)	99.9 (0.78%)	99.12
V	242.51 (−11.31%)	320.32 (17.37%)	272.95 (0.01%)	261.19 (4.29%)	272.91

The relative errors (in percentage) with respect to experiments are given in parentheses; here, “+” and “–” signs indicate overestimation and underestimation of the calculated values, respectively, when compared with experiments.

To understand the origin of the response of DHT as a function of pressure, we carried out a detailed investigation of its crystal structure at different pressures up to 30 GPa in a step size of 5 GPa at 0 K. Remarkably, DHT exhibits anisotropic behavior along three crystallographic directions under pressure (see Figure a). The compressibility in the a-direction is markedly greater than that in the b- and c-directions. At 30 GPa, lattice parameters a and b decrease by 28.6 and 8.17%, respectively, whereas c first increases and then slightly decreases by 0.17% from its ambient pressure value. This indicates that the structure of DHT is much softer in the a-axis than in the b- and c-directions. Furthermore, as pressure increases, the unit cell volume decreases monotonically and reaches 85% of its ambient volume by 30 GPa (Figure c), which in turn enhances the density from 1.72 to 2.67 g/cm3. The resulting P–V data is used to calculate the bulk modulus (B0) and its pressure derivatives (B0′) by fitting with the third-order Birch Murnaghan equation of state and are found to be 20.72 GPa and 5.47, respectively. The obtained results show that DHT is a more harder material than ADN and AP whose experimental bulk modulus values are reported as 16.4[50] and 15.2 GPa,[51] respectively.

Figure 3

Calculated pressure dependence of (a) unit cell parameters (a, b, c), (b) normalized unit cell parameters (a/a0, b/b0, c/c0), (c) volume (V), and (d) normalized volume (V/V0) of DHT. The solid red line represents the compression data fit to the third-order Birch Murnaghan equation of state.

The applied pressure is not only responsible for the changes in the unit cell of DHT but also affects the molecular geometry such as bond lengths and bond angles. Especially, there exist strong N–H···N hydrogen bonding networks between neighboring molecules within the crystal structure. Under ambient conditions, the bond lengths of N4–H4A, N4–H4B, and N3–H3 are 1.038, 1.038, and 1.048 Å, respectively. The three N–H bonds of the DHT molecule points to the three neighboring molecules. These intermolecular hydrogen bond distances can be measured using the N···H distance. For instance, DHT molecule connects with neighboring molecules in the direction of N1, N2, and N4 atoms and the corresponding N···H distances are 2.157, 2.166, and 1.872 Å, respectively. The average distances of the intermolecular N···H pairs and N–H covalent bonds are 2.06 and 1.04 Å, respectively. These hydrogen bonds exhibit vast changes in the bond strength as a function of pressure. The calculated pressure dependence of the intramolecular N–H (dN–H) bond length, intermolecular N···H (dN···H) and N···N (dN···N) distances, and N–H···N (∠N–H···N) bond angles are shown in Figure . The obtained N–H bond lengths show anisotropic behavior as a function of pressure (see Figure a); especially, the covalent N3–H3 bond length is enlarged and increased from 1.044 Å at 0 GPa to 1.111 Å at 30 GPa. The increase of the dN–H bond length represents the weakening of covalent N–H bonds by facilitating the release of hydrogen atom. In general, the N–H covalent bond becomes larger under compression, whereas the H···N interaction shrinks due to reducing repulsive force, leading to shortening of the total N–N distance. From Figure b, the average distances between the intermolecular N···H contacts at 0 GPa (2.06 Å) and 30 GPa (1.97 Å) are found to be less than the sum of the vdW radii of H and N (2.7), which supports the strengthening of hydrogen bond due to shortening of intermolecular N···H contact distance under pressure. The fundamental criteria to determine the strengthening or/and weakening of hydrogen bonding mainly depend on the above analyzed intermolecular distance and the frequency of the corresponding vibrational stretching modes, which will be discussed in the next section.

Figure 4

Calculated (a) intramolecular N–H (dN–H) bond length, (b) intermolecular N···H (dN···H) and (c) N···N (dN···N) distances, and (d) N–H···N (∠N–H···N) bond angle as a function of pressure in DHT.

Vibrational Properties

The vibrational spectroscopy study of hydrogen-bonded energetic materials under compression can tune the range of frequencies due to weak intermolecular interactions and explains the effect of hydrogen bonding on the stability of crystal structure. Usually, the weakening or strengthening of hydrogen bonds can be visualized based on the shift in the D–H vibrational frequency. For any material containing D–H···A hydrogen bonds (D and A represent donor and acceptor, respectively), the IR spectra corresponding to a particular frequency shift toward lower energies by decreasing the D–A distance. This can be explained in terms of electrostatic attraction between the proton and acceptor atom. When a system is compressed, the distance between the donor and acceptor atoms reduces, enhancing the electrostatic attraction between H and A. This leads to lengthening of D–H bond distance by reducing the D–H stretching frequencies toward lower energies. This is in accord with the aforementioned N–H bond length, where the H···N distance decreases as a function of pressure, which strengthens the hydrogen bonding. As discussed above, DHT crystallizes in the monoclinic structure containing 32 atoms in the primitive cell, resulting in 96 vibrational modes. From the group analysis of the P21/c space group, the representation of symmetry decomposition isGroup theoretical analysis of 93 optical modes shows that 24Ag ⊕ 24Bg are Raman-active modes and 23Au ⊕ 22Bu are IR-active modes. The obtained optical modes along with corresponding vibrational assignments are presented in Table . Of these 93 optical modes, 18 were under the frequency of 300 cm–1. However, in remaining 75 modes, 24 pairs of modes (48 modes) were under 10 cm–1 from each other (15 pairs of the 24 were below 5 cm–1 and 9 of the 24 were below 3 cm–1). The pressure-induced IR spectral variations of DHT in the frequency range of 70–470, 465–655, 750–1435, 1420–1680, and 1800–3300 cm–1 are presented in Figure . The lattice modes between the vibrational frequencies of 58 and 322 cm–1 are mainly due to translational and/or rotational motion of the tetrazine ring and the NH2 group. As pressure increases, lattice modes shift monotonically toward higher frequencies due to the reduction of intermolecular separation, which results in strengthening of interactions between adjacent molecules.[52,53]Figure b shows the rotation and bending modes of the NH2 group and bending and breathing modes of the tetrazine ring, whereas NH (wagging, stretching, rocking, and bending); NH2 (wagging and twisting); ring breathing; and C–N, C=N, and N–N stretching modes are shown in the Figure c. These modes display a blue shift up to the studied pressure range. The most pronounced one is the significant splitting of the NH bending mode (1550 cm–1) into two distinguishable bands at around 20 GPa (see Figure d). One of these modes shows a negative pressure dependence, whereas the other displays a positive dependence.

Table 2

Calculated Phonon Frequencies Along with the Corresponding Assignment of DHT at the DFT-TS Equilibrium Volume Using the Norm-Conserving Pseudopotentials (NCP) Approach under Ambient Pressure

mode	frequency (cm–1)	assignment
M4–M22	58–322	lattice modes
M23, M24	364–365	ring lib
M25–M28	374–463	ring lib, NH2 rot
M29	477	NH2 rot
M30, M31	480–490	NH2 wagg
M32–M34	496–526	NH2 rot
M35	527	NH2 bend, N–C=N wagg
M36	544	NH2 rot
M37, M38	636–642	ring breath
M39, M40	665–686	ring bend, NH2 wagg
M41–M44	763–802	NH wagg
M45	809	NH2 wagg, NH str
M46	813	NH wagg
M47	845	ring breath
M48–M50	846–869	NH rock
M51–M58	987–1074	NH2 wagg, C–N, C=N, N–N str
M59–M62	1157–1178	NH2 wagg
M63, M64	1269–1274	N–C=N asy str, NH2 twist
M65–M68	1284–1292	NH2 twist
M69, M70	1330–1335	NH bend
M71, M72	1379.02–1379.77	C–N, C=N str, NH bend
M73–M80	1444–1557	NH bend
M81–M84	1648–1659	NH2, NH scissor
M85–M88	2966–3064	NH str
M89–M92	3211–3215	NH2 sym str
M93–M96	3271.49–3271.78	NH2 asym str

Figure 5

Calculated IR spectra in the frequency range of (a) 70–470 cm–1, (b) 465–655 cm–1, (c) 750–1435 cm–1, (d) 1420–1680 cm–1, (e) 1800–3030 cm–1, and (f) 3010–3300 cm–1 of DHT as a function of pressure.

The application of pressure to N–H stretching modes provides a vital information regarding the variations in hydrogen bonding networks. As shown in Figure e,f, the N–H stretching bands located between 2950 and 3300 cm–1 are composed of three modes: the highest-intensity mode at 2986 cm–1 is assigned to the stretching of the NH group. Further, the peaks at 3215 and 3271 cm–1 correspond to the symmetric and asymmetric stretching modes of the NH2 group (see Figure ), respectively. In contrast to other bands, the two lowest-frequency modes located at 2986 and 3215 cm–1 move toward lower frequencies with increasing intensities as a function of pressure. The highest-frequency mode appears to reduce and eventually disappears at the maximum pressure of 30 GPa. The frequency lowering is more pronounced in the NH and NH2 symmetric stretching groups than in the NH2 asymmetric stretching mode. The observed decreasing activity in NH/NH2 vibrational modes agrees with generalized rules of pressure-induced strengthening of N–H···N hydrogen bonding in the DHT crystal. As shown in Figure , the N–H groups of various molecules serve as proton donors and nitrogen atoms in the tetrazene ring act as proton acceptors to form hydrogen bonding networks. The adoption of pressure will reduce the N–H···N hydrogen bond lengths and the separation between neighboring molecules along hydrogen-bonded chains. The observed variation trends of NH/NH2 vibrational modes as a function of pressure are quantitatively similar to those in the previous studies of hydrogen-bonded energetic materials.[54]

Figure 6

Few simulated vibrational modes of the DHT crystal.

Hirshfeld Analysis

The Hirshfeld surface analysis has made it possible to explore the nature of intermolecular interactions that can provide a direct insight into the molecular crystal. Recently, Ma and his co-workers[55] used the Hirshfeld surface theory to study the intermolecular interactions of 10 existing impact-sensitive highly energetic (SHE) materials including RDX, 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX), CL-20, and octanitrocubane. Subsequently, they found that the covalent O···O interactions are the predominant intermolecular interactions in SHE, whereas less sensitive highly energetic materials (LSHE) are governed by intermolecular hydrogen bonding. The lack of intermolecular hydrogen bonding networks and planar big π-conjugated molecular geometric structures in SHE crystals are responsible for their low molecular stability when compared to that of LSHE. They also reported that the intermolecular O···O interactions in SHE can break more readily and thus are more sensitive compared with LSHE.

To have a clear visualization of the molecule, the Hirshfeld surfaces were shown in a transparent mode. The strong N–H···N hydrogen bonding networks between the respective donor and acceptor atoms are seen as deep red spots on the Hirshfeld surfaces mapped over dnorm (see Figure a) with adjacent molecules connected by N3–H3···N4, N4–H4A···N1, and N4–H4B···N2 hydrogen bonds. These observations are further confirmed by the electrostatic potential (see Figure b) mapped on Hirshfeld surfaces that clearly demonstrates the presence of an electropositive (blue) region around hydrogen atoms, whereas a strong negative electrostatic potential (red) surrounding the nitrogen atoms. Furthermore, the breakdown of the fingerprint plot into specific atom types reveals that 58.3% of the total Hirshfeld surfaces are due to N···H/H···N interactions, which appear as a pair of distinct sharp spikes in the bottom left/right region of the two-dimensional (2D) fingerprint plot, representing the characteristics of strong hydrogen bonding. The participation of H···H contacts is shown in the middle region of the fingerprint plot with overall 26.3% of the Hirshfeld surfaces (see Figure a,b).

Figure 7

(a) Hirshfeld surface of the DHT crystal for visualizing the intermolecular interactions. (b) Electrostatic potential mapped on the Hirshfeld surface. The green dashed lines represent the hydrogen bonds.

Figure 8

(a, c) Hirshfeld surfaces and (b, d) 2D fingerprint plots of the DHT crystal, showing the percentages of close intermolecular contacts contributing to the total Hirshfeld surface area at 0 and 30 GPa, respectively. The graphical plots are mapped onto the Hirshfeld surfaces with dnorm using red (shorter intermolecular contacts), white (contacts around the vdW separation), and blue (longer intermolecular contacts) colors.

As pressure increases, the blue region decreases and becomes almost invisible at 30 GPa (see Figure c,d). However, the red region spreads all over the Hirshfeld surfaces, indicating an increase in the number of closer contacts under pressure. In general, the pressure-induced variations in the intermolecular interactions will tend to bring the molecules together, enabling a denser molecular packing. However, the structure of fingerprint has been compressed and drawn toward the origin due to shortening of longer intermolecular contacts, which is related to the decrease of de value at elevated pressures (0 GPa = 1.54 Å; 30 GPa = 1.26 Å). Furthermore, the orange and red points in the fingerprint plots of 30 GPa indicate the closest contacts in this crystal structure. Overall, the applied pressure increases the contribution of N···H/H···N and N···N interactions whereas decreases the H···H interactions to the total Hirshfeld surfaces (see Figure ).

Figure 9

Pressure versus percentage contributions to the Hirshfeld surface area for the various intermolecular interactions of the DHT crystal.

Detonation Properties

The performance of explosives is exclusively determined by their detonation properties: the higher the detonation velocity and pressure, the greater the detonation performance. These detonation characteristics can be calculated using various computer codes through density and HOF. Foremostly, the condensed phase HOF of CHNO-based explosives can be predicted by the following equation[57]where ΔfHθ is the condensed phase HOF (kJ/mol) and ΔfHIECθ and ΔfHDECθ are the increasing and decreasing energy content parameters of an explosive, respectively. From eqs and 2, the value of ΔfHθ can be increased by adding more number of carbon and nitrogen atoms as well as by reducing the number of hydrogen and oxygen atoms. However, the calculated ΔfHθ value for DHT (+501.7 kJ/mol) is found to be higher than that for BNT (+336.1 kJ/mol) due to the absence of oxygen atoms in the former. Subsequently, the obtained crystal density and HOF were used to predict the detonation characteristics through Kamlet–Jacobs equations[58]where D and P are the detonation velocity (km/s) and detonation pressure (GPa), respectively, which can be determined by substituting ρ, the crystal density (g/cm3); M, the average molecular weight of gaseous products (g/mol); N, the moles of detonation gas products per gram of explosive; and Q, the heat of detonation (cal/g) values according to the largest exothermic principle.[59] Furthermore, the sensitivity and performance of an explosive can be roughly predicted by computing the oxygen balance (OB) using the following formula[60]where M represents the molecular weight and a, b, and c are the number of C, H, and O atoms, respectively. Generally, the higher OB leads to greater detonation pressure and velocity and thus superior performance of an explosive.[61] At the same time, the negative OB can also be used to predict the shock sensitivity, where the energetic materials with zero oxygen balance are highly sensitive to shock.[62] The calculated HOF, Q, D, P, and OB of DHT along with BNT are presented in Table . Moreover, the detonation characteristics of DHT (D = 7.62 km/s, P = 25.19 GPa) are smaller than those of BNT (D = 7.9 km/s, P = 27.36 GPa). This inadequacy in the performance is due to negative OB of DHT that may significantly reduce the amount of velocity and pressure released during detonation. The negative oxygen balance also indicates that DHT is less sensitive than BNT. It is worth noting that the heat of detonation (Q) for DHT is less than that for BNT. The hydrogen-bonded N–H···N intermolecular interactions serve as a stabilizing factor that reduces the heat of detonation, Q.[63−65]

Table 3

Calculated Detonation Properties of DHT Compared with the Values of 3,6-Bis-Nitroguanyl Tetrazine (BNT)[56]

	ρ (g/cm3)	HOF (kJ/mol)	Q (cal/g)	D (km/s)	P (GPa)	OB (%)
DHT (C2H6N8)	1.729	501.76 (536)[19]	1072.68	7.62 (7.54)[19]	25.19	–78.80
BNT (C4H6N10O4)	1.76[56]	336.1	1165.61	7.90	27.36	–55.78

Conclusions

In summary, we have systematically investigated the structural and vibrational properties of a hydrogen-bonded energetic material 3,6-dihydrazino-s-tetrazine (DHT) under high-pressure up to 30 GPa via dispersion-corrected DFT. The obtained ground-state properties using standard exchange–correlation functionals (LDA/GGA) show drastic variations from experimental values, whereas the vdW-TS method provides an accurate description of the intermolecular interactions for the DHT crystal. The linear compressibility curves along the crystallographic a- and c-axes are shown to be the most and least compressible, respectively. The predicted bulk modulus values reveal that DHT is more harder than the well-known energetic oxidizers ammonium dinitramide (ADN) and ammonium perchlorate (AP). The existence of strong hydrogen bonding networks in the high-pressure region weakens the covalent N–H bond lengths, which is consistent with the decreasing activity of NH/NH2 stretching vibrational modes. The 2D fingerprint plots reveal that 58.3% of the total Hirshfeld surfaces are due to N···H/H···N interactions, indicating the significance of hydrogen bonds as primary intermolecular interactions in the DHT crystal. The calculated heat of formation (+501.7 kJ/mol) and detonation properties (D = 7.62 km/s, P = 25.19 GPa) of DHT are found to be higher and slightly smaller, respectively, than those of the similar explosive BNT.

Computational Details

All calculations were performed using the plane-wave pseudopotential method based on DFT, which is implemented through the Cambridge Series of Total Energy Package.[34,35] The exchange–correlation potentials were described within the generalized gradient approximation (GGA) by the Perdew–Burke–Ernzerhof (PBE) functional.[36] The Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization scheme[37] was used to obtain the equilibrium crystal structure. The ultrasoft pseudopotentials (USP) have been utilized to calculate the structural properties, whereas norm-conserving pseudopotentials (NCP) for obtaining zone-center IR spectra of DHT under pressure up to 30 GPa. The plane-wave cut-off energies of 600 eV for USP and 950 eV for NCP were used to expand the wave functions. A 6 × 5 × 2 Monkhorst–Pack grid[38] was used for Brillouin zone integration. The self-consistent energy convergence criterion was set to 5.0 × 10–6 eV/atom, and the force per atom diminished to 0.01 eV/Å. The maximum stress and displacement were set to 0.02 GPa and 5.0 × 10–4 Å, respectively. The vibrational spectra of DHT were calculated using the linear response method as implemented in density functional perturbation theory.

The accurate description of weak intermolecular interactions (e.g., hydrogen bonding, van der Waals (vdW) forces) has been the subject of interest from many decades. The conventional exchange–correlation functionals (e.g., LDA, GGA) in DFT are unable to accurately capture the long-range vdW forces. For instance, LDA underestimates the volume by 7–30%, whereas GGA overestimates by 10–15% for CL-20,[39] RDX,[40] HMX,[41] PETN,[42] TATB,[43] FOX-7,[44] and TNAD.[45] The inadequacies in describing the intermolecular interactions not only affect the prediction of accurate crystal geometry but also lead to errors in the computed properties such as density, elastic modulus, cohesive energy, and band gap. Recently, various improvements were made to extend standard DFT to include these types of weak dispersive forces. Particularly, the empirical vdW corrections such as the Grimme (DFT-D2)[46] and Tkatchenko and Scheffler (DFT-TS)[47] corrections to PBE are most successful methods. Within the DFT + D framework, the total energy including vdW correction is given bywhere EDFT is the normal self-consistent Kohn–Sham energy and Edisp is the empirical dispersion correction expressed aswhere R, C, and s6 represent the interatomic distance, dispersion coefficient for the pair of ith and jth atoms, and a global scaling factor that only depends on the density functional used, respectively. The damping function, , is introduced to avoid divergence for small R.

The Hirshfeld surfaces of DHT were calculated using CrystalExplorer,[48] which is a powerful tool for exploring the nature of intermolecular interactions within the crystal. The strength of the interactions can be described by dnorm (normalized contact distance)where di and de denote the internal and external separations from the nearest atoms and ri and re represent the vdW radii of the two atoms inside and outside the Hirshfeld surfaces. These close intermolecular contacts were identified by a three-dimensional dnorm surface in which the positive/negative values represent the intermolecular contacts that are longer/shorter than the vdW separations. The graphical plots are mapped onto the Hirshfeld surfaces with dnorm using red (shorter intermolecular contacts), white (contacts around the vdW separation), and blue (longer intermolecular contacts) colors. In addition, the 2D fingerprint plots associated with Hirshfeld surfaces can provide a summary of intermolecular interactions in the molecule.