First principle study and Hirshfeld surface analysis on the effect of type, number, and position of small molecules on the structural stability and optical property of a powerful energetic crystal 6-nitro-7-azido-pyrazol[3,4-d][1,2,3]triazine-2-oxide

Abstract

In the present study, the detailed functions of three small molecules, H₂O, NH₃, and H₂S, on the structural stability of a novel high energy compound 6-nitro-7-azido-pyrazol[3,4-d][1,2,3]triazine-2-oxide (ICM-103) with high application value were investigated by the first principle study and Hirshfeld surface analysis. The effects of type, number, and position of small molecules on the molecular, crystal and electronic structures, close contacts and sensitivity, and optical properties of ICM-103 were also studied. First, the relatively high sensitivity feature used as initiating explosives of ICM-103 was confirmed, but H₂O, NH₃, and H₂S all could stabilize the structure of ICM-103 to reduce sensitivity by enhancing close contacts such as hydrogen bonding and increasing the ratio of red dots located on the block edge of Hirshfeld surface. This function could be further improved with the increment of number, and small molecules in two different positions were found to have a synergistic effect on stabilizing the structure. The stabilization ability of NH₃ was found to be stronger than H₂O and H₂S due to the highest stabilization energy and strongest close contacts. Then, H₂O and NH₃ reduced the absorption intensity to ultraviolet light but enhanced the absorption to visible light and infrared light. Three molecules all increased the dielectric constant and static refractive index with the order of H₂S, and H₂O, NH₃. NH₃ eliminated the region, in which light could not be transmitted in other crystals. Finally, the position of NH₃ was found to have significant effects on the structure and properties of ICM-103, while this is not obvious for H₂O and H₂S.

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1. Introduction

The energetic compound is one kind of active, special but very important energy material that releases huge power in an extremely short time when stimulated by external energy factors including impact, heat, friction, and electricity. Thus, it can be applied in many fields including national defence, aerospace and tunneling, in which it may be used as a high explosive, gun, solid rocket propellant, primary explosive, etc. Among different kinds of energetic compounds, the high energy density compound has attracted lot of attention from researchers due to its outstanding performance such as high detonation properties. Lately, some good representatives including all-nitrogen pentazole series (N₅),^1–7 ICM series,^8–10 and high energy cage compounds¹¹ have been designed and synthesized successfully. However, due to their high energy, many of them have low stability and high sensitivity. However, at the same time, an interesting phenomenon was observed in which a different number of small molecules such as H₂O (or H₃O⁺) and NH₃ (or NH₄⁺) coexisted with energetic molecules in the crystal. For example, these reported pentazole energetic compounds include [M(H₂O)₄(N₅)₂]·4H₂O (M = Mn, Fe, Co, Zn)¹ and (N₅)₆(H₃O)₃(NH₄)₄Cl.² For the ICM series, in the crystal of an insensitive compound 2,4,6-triamino-5-nitropyrimidine-1,3-dioxide (ICM-102),⁹ or in the crystal of a fused-ring initiating substance 6-nitro-7-azido-pyrazol[3,4-d][1,2,3]triazine-2-oxide (ICM-103),¹⁰ a different number of H₂O were observed. For the high energy cage compound, H₂O was also found in the crystal of one of the most powerful compounds 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazatetracyclo[5.5.0.0.0]dodecane (CL-20).¹¹ Thus, it is necessary to clearly learn and understand the reason for these small molecules coexisting with energetic molecules in the crystal as well as their functions and effects on the structures and properties of different energetic crystals. Based on the quantum mechanical calculation, Luo¹² has found that two kinds of H₂O are in the [M(H₂O)₄(N₅)₂]·4H₂O (M = Mn, Fe, Co, Zn) system, and they can participate in both the coordination and hydrogen bonding to stabilize the whole structure. In addition, the hot H₂O was found that can catalyze the decomposition of pentaerythritol tetranitrate¹³ and furoxan¹⁴ by transporting oxygen between reaction centers under extremely high temperature/pressure, and the content of H₂O was found to affect the thermal decomposition of ammonium dinitramide.¹⁵ Our previous work¹⁶ found that the H₂O can stabilize the crystal structure and reduce the impact insensitivity of ICM-102 by enhancing the hydrogen bonding and other intermolecular interactions. H₂O will also improve the density, mechanical performance, and thermodynamics parameters of ICM-102. In all, since energetic compounds are dangerous materials and sensitive to the internal/external environment, these above mentioned studies may show the effects of small molecules on the structure and property under different conditions. Thus, in order to increase the safety in operation, processing and usage, enhance the application value, and guide the design of new advanced energetic compounds, it is important and necessary to investigate and understand these clearly and deeply.

ICM-103 (as seen in Fig. 1) is a new synthetic high energy compound,¹⁰ whose heat of formation (744.8 kJ mol⁻¹), heat of combustion (739.4 kJ mol⁻¹), density (1.86 g cm⁻³), detonation velocity (D = 9.1 km s⁻¹), and detonation pressure (P = 35.1 GPa) are apparently higher than 2-diazo-4,6-dinitrophenol (D = 6.9 km s⁻¹)¹⁷ and lead azide (D = 5.9 km s⁻¹),¹⁸ showing its outstanding detonation performance. While its impact sensitivity, friction sensitivity, and electrostatic discharge sensitivity are 4 J, 60 N, and 130 mJ, respectively, which are also obviously superior to those of 2-diazo-4,6-dinitrophenol (1 J, 24.7 N, and 1.8 mJ)¹⁷ and lead azide (2.5–4 J, 0.1–1 N, and <5 mJ).¹⁸ The excellent combination performance of ICM-103 shows its tremendous application foreground as an initiating explosive device to replace 2-diazo-4,6-dinitrophenol and lead azide. As an initiating explosive, ICM-103 is even more sensitive to various structural and environmental factors than secondary explosives like CL-20 and insensitive compounds like ICM-102, and clearly understanding its structure and property will be essential to accelerate the application. From the crystal structure, two kinds of H₂O molecules at two different positions (positions 1 and 2) were found (as seen in Fig. 1b), and each one has two H₂O molecules. Thus, in the present work, using the first principle calculation and Hirshfeld surface analysis method, the molecular, crystal and electronic structures, the safe and optical properties of ICM-103 were studied. Effects of three kinds of small molecules (H₂O, NH₃, and H₂S) with a different number (0, 2, and 4) at two different positions on the structure and properties were investigated and explored comprehensively.

Fig. 1 The single molecule structure and atomic number (a) and crystal structure (b) of ICM-103.

2. Computational methods

First of all, all first-principle calculations on the ICM-103 crystal were performed using the CASTEP module.¹⁹ The norm-conserving pseudopotential,²⁰ GGA-PW91 with the OBS correction (labeled as GGA-PW91-OBS),²¹ and the BFGS²² optimization method were used. The cutoff (750 eV), k-point (3 × 5 × 1), and SCF tolerances (fine grade) were set. There are four H₂O molecules in the crystal of ICM-103, two H₂O are in position 1 while the other two are in position 2, as seen in Fig. 1b. The original experimental crystal structure¹⁰ of ICM-103 (labeled as ICM-103-4H₂O) was used as the input structure and relaxed. Then, based on this relaxed structure, all four H₂O, two H₂O in positions 1 and 2 were deleted to form the ICM-103-0H₂O and the other two H₂O-crystals (ICM-103-2H₂O-1 and ICM-103-2H₂O-2), respectively. All four H₂O, two H₂O in positions 1 and 2, were replaced by a corresponding number of NH₃ and H₂S to form three NH₃-crystals (ICM-103-4NH₃, ICM-103-2NH₃-1, ICM-103-2NH₃-2) and three H₂S crystals (ICM-103-4H₂S, ICM-103-2H₂S-1, and ICM-103-2H₂S-2), respectively. Since H₂O, NH₃, and H₂S can act as both the donor and acceptor of hydrogen bonds, their size and function are similar to each other. Thus, it may be supposed that they will occupy similar initial lattice sites in the crystal structure of ICM-103. These 9 newly formed crystals were then relaxed using the same method and set as ICM-103-4H₂O to obtain their corresponding stable crystals. The small molecules were allowed to diffuse freely during the relaxation simulation. Based on the relaxed crystals, the band structure, band gap, density of states (DOS), and optical properties were calculated and estimated. The optimization and energy calculations of single H₂O, NH₃, and H₂S were performed in a big periodic cell, which has the same scale as the corresponding ICM-103 crystal. The stabilization energy (ΔE) was predicted by the following equation: ΔE = E_cry − (n × E_sm + E_NW). E_cry means the energy of ten crystals, n is the amount of the corresponding small molecules, E_sm is the energy of the corresponding single small molecule, and E_NW represents the energy of crystal ICM-103-0H₂O. Finally, the Hirshfeld surface analysis calculations of ten ICM-103 crystals were performed using the CrystalExplorer 3.0 program.²³

3. Results and discussion

3.1. Crystal structure

The GGA-PW91-OBS method was used to relax and optimize the crystal structure of ICM-103-4H₂O at ambient conditions without any constraint, and the predicted lattice constants are listed in Table 1. It can be found that the calculated values are close to the experimental results, and the errors ranged from 0.7% to 3.8%. A comparison of the bond length of main chemical bonds between the theoretical and experimental results has been made, and the errors are very small, as seen in Table 2. The above results show the high accuracy of the used method. Thus, the GGA-PW91-OBS method was also used to relax other newly formed crystals, and the results have been listed in Table 1. It is found that the lattice parameters are sensitive to the type, number, and position of three small molecules. First of all, since three small molecules will occupy the space in crystals, the volume (V) enlarges with the increased number of small molecules in each series. Then, the length of the S–H bond is obviously larger than those of the N–H and O–H bonds, thus, leading to a larger volume and lower density apparently for H₂S-crystals. As density is an important parameter related to the energy performance of energetic crystals and for energetic compounds with similar structures, the lower the density is, the lower the energy. Therefore, H₂S may be less helpful for obtaining higher energy compared with the other two small molecules. Finally, due to the fact that small molecules are mainly occupied in the space along the b and c directions, the crystals within small molecules all have longer b and c than crystals without small molecules or within fewer small molecules. As a result, generally, H₂S-crystals have longer a, c, and volume than NH₃-crystals than H₂O-crystals, while this is just the opposite for b.

Table 1 Relaxed lattice parameters of all ten ICM-103 crystals with the experimental data at ambient conditions

Parameter	a (Å)	b (Å)	c (Å)	β (°)	V (Å^3)
a The absolute values in parentheses correspond to the percentage differences relative to the experimental data.
ICM-103-4H2O/Expt.	9.931	5.210	19.767	116.4	916.0
ICM-103-4H2O/GGA-PW91-OBS	10.038 (1.1%)^a	5.409 (3.8%)^a	19.611 (0.7%)^a	117.7 (1.1%)^a	943.1 (3.0%)^a
ICM-103-0H2O	10.414	5.107	19.486	117.3	921.0
ICM-103-2H2O-1	10.146	5.296	19.624	117.2	937.3
ICM-103-2H2O-2	10.104	5.324	19.547	117.1	934.9
ICM-103-4NH3	10.464	5.075	22.178	123.7	979.8
ICM-103-2NH3-1	10.122	5.282	21.321	124.4	931.4
ICM-103-2NH3-2	10.309	5.127	20.275	118.3	943.2
ICM-103-4H2S	10.855	5.082	22.529	119.2	1085.0
ICM-103-2H2S-1	10.688	5.000	21.794	118.3	1025.2
ICM-103-2H2S-2	10.668	5.003	21.741	118.2	1022.4

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Table 2 A comparison of the bond length of main chemical bonds between the theoretical and experimental results for ICM-103-4H₂O

Bond	Expt. (Å)	GGA-PW91-OBS (Å)	Absolute error (Å)	Relative error (%)
N1–N2	1.291	1.287	0.004	0.3
C1–N1	1.372	1.392	0.02	1.5
C1–N4	1.346	1.348	0.002	0.1
C1–C2	1.403	1.411	0.008	0.6
N5–N4	1.346	1.375	0.029	2.2
N5–O1	1.253	1.265	0.012	1.0
N5–N6	1.308	1.349	0.041	3.1
N6–C3	1.352	1.348	0.004	0.3
C3–C2	1.393	1.414	0.021	1.5
C3–N7	1.338	1.363	0.025	1.9
N7–N8	1.352	1.366	0.014	1.0
N8–C4	1.313	1.339	0.026	2.0
C4–C2	1.399	1.418	0.019	1.4
C4–N9	1.447	1.450	0.003	0.2
N9–O3	1.222	1.241	0.019	1.6
N9–O2	1.214	1.242	0.028	2.3

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The bond length of various bonds in ICM-130 molecules was found to be also affected by small molecules. For the ICM-103 molecule, the NO₂ and N₃ groups may be the most sensitive sites to stimulus and have the main effects on sensitivity and safety. The C–NO₂ bond is easy to break, while the C1N1–N2N3 bond (as seen in Fig. 1) in the N₃ group is also easy to break to release N₂ gas. Thus, the effects of small molecules on the bond length of these two bonds (C–NO₂ and N1–N2 bonds) were studied and are listed in Table 3. It is found that ICM-103-4H₂O, ICM-103-2H₂O-1, and ICM-103-2H₂O-2 have shorter C–NO₂ bonds than ICM-103-0H₂O, especially for ICM-103-4H₂O, whose two C–NO₂ bonds are both 0.6% shorter than ICM-103-0H₂O. This is even more obvious for NH₃-crystals, with the two C–NO₂ bonds of ICM-103-4NH₃ being about 1.7% shorter than those of ICM-103-0H₂O. This is because the small molecules in the crystal of ICM-103 will help generate the hydrogen bonds between NO₂ and small molecules, which increases the stability of NO₂ groups and leads to stronger and shorter C–NO₂ bonds. The N1–N2 bonds of NH₃-crystals are also about 0.4–1.1% shorter than ICM-103-0H₂O. For the three H₂S-crystals, their C-NO₂ and N1–N2 bonds are slightly shorter than ICM-103-0H₂O in general. In each series, the crystals with four small molecules have the shortest C–NO₂ and N1–N2 bonds. Fig. 2 displays the optimized structures of 9 newly formed crystals. It is found the relative positions of energetic molecules and small molecules in H₂O-crystals and H₂S-crystals are not changed obviously compared to ICM-103-4H₂O. But it is interesting to find the H atom linked with N7 in ICM-103 molecules has transferred from ICM-103 to the N atom in NH₃ to form NH₄, which is different from that of H₂O and H₂S. This may suggest that NH₃-crystals may transform from neutral to ionic type energetic compounds, as NH₃ usually tends to exist in the form of NH₄ when contained in energetic crystals. Many NH₄-related energetic compounds like ammonium dinitramide (ADN), ammonium perchlorate (AP), and (N₅)₆(H₃O)₃(NH₄)₄Cl have been synthesized and reported before.

Table 3 The bond lengths (Å) of C–NO₂ and N1–N2 bonds, stabilization energy (ΔE, eV), band gap (GAP, eV), dielectric constant [ε₁(0)], and refractive indices (n₀) of ten ICM-103 crystals

Crystal	C–NO2		N1–N2		ΔE	GAP	ε 1(0)	n 0
ICM-103-0H2O	1.459	1.459	1.288	1.288	0	2.287	1.941	1.393
ICM-103-4H2O	1.450	1.450	1.287	1.287	−5.01	2.217	2.047	1.431
ICM-103-2H2O-1	1.459	1.450	1.291	1.291	−2.36	2.182	1.950	1.396
ICM-103-2H2O-2	1.459	1.450	1.289	1.284	−2.38	2.182	1.950	1.396
ICM-103-4NH3	1.434	1.434	1.274	1.274	−7.56	2.133	2.039	1.428
ICM-103-2NH3-1	1.460	1.427	1.280	1.279	−3.74	1.595	2.062	1.436
ICM-103-2NH3-2	1.459	1.437	1.283	1.280	−3.37	1.955	2.126	1.458
ICM-103-4H2S	1.458	1.458	1.286	1.286	−2.38	2.059	2.011	1.418
ICM-103-2H2S-1	1.459	1.456	1.289	1.282	−1.03	2.040	1.979	1.407
ICM-103-2H2S-2	1.459	1.459	1.289	1.282	−1.03	2.040	1.979	1.407

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Fig. 2 The optimized crystal structures of nine newly formed ICM-103 crystals.

3.2. Electronic structure

The small molecules were found to influence the electronic structure of ICM-103 crystals. First, the estimated band gap values of ten crystals have been listed in Table 3. It is found that ICM-103-0H₂O has the highest band gap, showing that the electron transfer from the valence band to the conduction band is more difficult than in other crystals. Since three small molecules have different effects on the crystal and molecular structures, the band gap is changed to different degrees. For example, the band gap decreases with the order of ICM-103-0H₂O, H₂O-crystals, and H₂S-crystals in general. The energy levels in band structures for H₂O and H₂S molecules are located between 0–−20 eV rather than between the HOMO and LUMO of ICM-103. Thus, the band gap values of H₂O-crystals and H₂S-crystals have not reduced obviously and are close to ICM-103-0H₂O. But for NH₃-crystals, due to the change from neutral to ionic crystals and forming of NH₄, the electronic structures have been affected more obviously compared to others. As a result, their band gap values are different from each other and all lower than ICM-103-0H₂O. The band gap of ICM-103-2H₂O-1/2 and ICM-103-2H₂S-1/2 are the same, respectively. But the band gap of ICM-103-2NH₃-1 is obviously lower than that of ICM-103-2NH₃-2, showing that the effects of the position and type of small molecules on the band gap coupled with each other. The band gap values of ICM-103 crystals are generally small, showing that the electron-related chemical reaction is easy to occur and is in agreement with the feature of initiating explosives.

Fig. 3 displays the band structures of ten ICM-103 crystals. When compared with ICM-103-0H₂O, it is observed from Fig. 3a that ICM-103-4H₂O, ICM-103-4NH₃, and ICM-103-4H₂S all have more energy levels due to the contribution and effect of the corresponding small molecules. But the effects of small molecules on the energy levels at the valence band and conduction band are different. H₂O and NH₃ will induce the energy level at the valence band and conduction band to red-shift and blue-shift, respectively, while H₂S will induce some of the energy levels at the valence band to blue-shift. The number of H₂O and H₂S also affects the band structure to some degree, but their positions have negligible influence, as seen in Fig. 3b and d. The position and number of NH₃ both have significant effects on the band structure. The energy levels in ICM-103-2NH₃-1 are lower than those in ICM-103-2NH₃-2 and ICM-103-4NH₃, especially at the conduction band, as seen in Fig. 3c.

Fig. 3 A comparison of the band structure of ten ICM-103 crystals.

Finally, Fig. 4 further depicts the DOS of ten ICM-103 crystals. From Fig. 4a, it can be seen that H₂O, NH₃, and H₂S all make contributions to different DOS peaks. For H₂O, it makes contributions to peaks at energies of −19 eV and −8–0 eV. For NH₃, its contributions occur at energies −17 and −8–−5 eV. H₂S makes significant contributions to peaks around Fermi level (−3–0 eV) and two other peaks at −16 eV and −8.5 eV, which may be because ICM-103-4H₂S has more energy levels than ICM-103-0H₂O at 0–3 eV. As a result, ICM-103-4H₂O, ICM-103-4NH₃, and ICM-103-4H₂S have different DOS compared to ICM-103-0H₂O. The effects of the number on DOS are mainly on the peak intensity, while the position of small molecules on DOS is not obvious, as seen in Fig. 4b–d. In all, it is found that the type, number, and position of small molecules indeed can influence the molecular, crystal, and electronic structures of ICM-103. These effects are different from each other and may be coupled with each other sometimes, which may indicate that they will also affect the properties of ICM-103.

Fig. 4 A comparison of the DOS of ten ICM-103 crystals.

3.3. Hirshfeld surface

Hirshfeld surface^16,24–26 can provide a lot of useful information for understanding the intermolecular contacts and impact the sensitivity of energetic crystals. Table 4 lists the predicted d_norm mapped on Hirshfeld surface (HS) for visualizing intermolecular and ratio of red dots located on the block edge (E%) of ten ICM-103 crystals. Generally, it is observed that all other 9 crystals have more red spot areas than ICM-103-0H₂O, showing that H₂O, NH₃, and H₂S can strengthen close contacts in ICM-103 crystals obviously, and this may be helpful for increasing the close contact intensity and stabilizing the system. Then, it has been reported that when more red dots are located on the block edge, the impact sensitivity of energetic compounds will be lower. As seen in Table 4, the E% value of ICM-103-0H₂O is 50%, showing that half of the red hot dots are not located on the edge area, and ICM-103 is a relatively sensitive energetic compound, which conforms to its characteristic as an initiating explosive. However, this can be improved to some degree, as found for all other 9 crystals, with higher E% than ICM-103-0H₂O, especially for the crystals containing four small molecules, whose E% values are higher than 80%. This indicates that H₂O, NH₃, and H₂S in the ICM-103 system may be good for decreasing the impact sensitivity, and this positive effect will be more obvious with the increment of the number of molecules. The effects of the position of small molecules on the E% are not obvious.

Table 4 The d_norm mapped on Hirshfeld surface (HS) for visualizing intermolecular and ratio of red dots located on the block edge (E%) of ten ICM-103 crystals

	ICM-103-0H2O	ICM-103-4H2O	ICM-103-2H2O-1	ICM-103-2H2O-2
HS
E%	50	86	54	56
	ICM-103-4NH3	ICM-103-2NH3-1	ICM-103-2NH3-2
HS
E%	83	76	71
	ICM-103-4H2S	ICM-103-2H2S-1	ICM-103-2H2S-2
HS
E%	83	6%	66

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For a deeper understanding of the detailed close intermolecular contacts in different ICM-103 crystals, Fig. 5 displays the fingerprint plots of contacts of ten crystals. Generally, a smaller d_i (the distances from the surface to the nearest atom inside the surface) + d_e (the distances from the surface to the nearest atom outside the surface) will lead to a closer atom–atom contact, and the contact being stronger and stronger when the color changes from blue to blue-green and green. Therefore, from Fig. 5, it can be seen that the contribution to the whole picture within lower d_i (2.0 Å) + d_e (2.0 Å) in all 9 small molecule-containing crystals is much larger than in ICM-103-0H₂O, and the green and blue-green regions are also wider than ICM-103-0H₂O, showing that all three small molecules H₂O, NH₃ and H₂S can increase close contacts in ICM-103 crystals apparently. Then, it is found that this decreases with the order of NH₃-crystals, H₂O-crystals, and H₂S-crystals, indicating that NH₃ is the most favourable molecule for enhancing the close contacts and may also be true for stabilizing the system. One main reason is that the small molecules can increase the intermolecular hydrogen-bonding contact (N/O/S⋯H), as seen from Fig. 6. It can be found that the O⋯N, N⋯N, and N/O/S⋯H are three main contacts in each crystal, but their percentage values are different. In ICM-103-0H₂O, the percentage of O⋯N contact is the highest among all close contacts, but this is N/O/S⋯H for other small molecule containing crystals, in which the percentage of the N/O/S⋯H increases in the order of ICM-103-0H₂O (20.6%), ICM-103-4H₂S (31.8%), ICM-103-4H₂O (32.2%), and ICM-103-4NH₃ (46%), leading to the stronger hydrogen bonding and better stabilizing function on the crystal structure. More information is further supported by Fig. 7, in which it can be clearly seen that the number of intermolecular contact network lines and strength of N/O/S⋯H contacts also increase in the same order as mentioned above. However, this is different from that of ICM-102 crystal,¹⁶ in which the H₂O is the most favourable one to stabilize the system, showing that the stabilization effect of small molecules is also related to the energetic molecule. Finally, the number and position of small molecules also affect close contact. In each series, the crystals with four small molecules have stronger close contacts than crystals with two. In addition, it is found that ICM-103-2H₂O-2 has stronger close contacts than ICM-103-2H₂O-1, while this is just the opposite for ICM-103-2NH₃-1 and ICM-103-2NH₃-2. The difference in close contacts between ICM-103-2H₂S-1 and ICM-103-2H₂S-2 is not obvious. This shows that the effect of the position on close contacts is coupled with the type of small molecules.

Fig. 5 Fingerprint plots for ten ICM-103 crystals. The points on the plot with no contribution on the surface are uncolored, and points with a contribution to the surface are colored blue for a small contribution through blue-green to green for a higher contribution.

Fig. 6 The percentage of main close contacts in four ICM-103 crystals.

Fig. 7 The intermolecular contact network (dash line) and fingerprint plots for N/O/S⋯H contacts in four ICM-103 crystals. The points on the plot with no contribution on the surface are uncolored and colored gray, and points with a contribution to the surface are colored blue for a small contribution to blue-green for a big contribution.

Table 3 lists the calculated stabilization energy (ΔE) for nine crystals with small molecules. It is seen that all of them have negative ΔE values, showing that the H₂O, NH₃, and H₂S can decrease the total energy and stabilize the whole ICM-103 crystal. ICM-103-4H₂O has a negative ΔE value than ICM-103-2H₂O-1 and ICM-103-2H₂O-2, and this is true for NH₃-crystals and H₂S-crystals. Besides, it is interesting to find the ΔE value of ICM-103-4H₂O is even lower than the sum of ICM-103-2H₂O-1 and ICM-103-2H₂O-2, indicating that the two H₂O molecules in position 1 and position 2 may have synergy to stabilize the system in ICM-103-4H₂O, and this is also true for ICM-103-4NH₃ and ICM-103-4H₂S, showing that the stabilization effect on crystals of small molecules can be further strengthened with the increasing number. But the effect of the position on ΔE is controlled by the type of small molecules, and the ΔE of ICM-103-2H₂O-2 is 0.2 eV lower than ICM-103-2H₂O-1, while ICM-103-2NH₃-1 has negative ΔE than ICM-103-2NH₃-2, ICM-103-2H₂S-1, and ICM-103-2H₂S-2 have the same ΔE, showing that the two H₂O molecules in position 2 are more helpful for stabilizing the ICM-103 crystal, while for NH₃, it is position 1. The result obtained by stabilization energy is in agreement with those by Hirshfeld surface and fingerprint plots. In all, three small molecules can stabilize the ICM-103 crystal and increase in the order of H₂S, H₂O, and NH₃. This effect is further enhanced with the increment of the number by the synergy between small molecules in positions 1 and 2.

3.4. Optical properties

Light is also one kind of energy and stimulus, and many energetic crystals are sensitive to light and respond to its stimulus differently. Therefore, important optical properties, including the absorption spectra, dielectric function, and refractive index of ICM-103 crystals, were studied in this section, and the effects of the number of H₂O, NH₃ and H₂S in positions 1 and 2 were also investigated. Firstly, absorption coefficient α(ω) was calculated by the equation:²⁷ (ε₁ and ε₂ are the real part and imaginary part of the dielectric function, respectively), as it is a common parameter used to estimate the absorption intensity under different wavelengths of light. Fig. 8 depicts the predicted absorption spectra of ten ICM-103 crystals. First, it is found that the absorption spectra of ICM-103-2H₂O-1 and ICM-103-2H₂O-2 are almost the same, making their absorption spectra overlap each other in Fig. 8. This is also true for ICM-103-2H₂S-1 and ICM-103-2H₂S-2, showing that the position of H₂S and H₂O affect the absorption spectra. But this is not true for NH₃-crystals, as seen from Fig. 8 that the absorption intensity of ICM-103-2NH₃-2 is obviously stronger than that of ICM-103-2NH₃-1 to light in the range of 200–600 nm. Then, it can be seen that different types and numbers of small molecules have different effects on the absorption spectra at a different wavelength range of light. For H₂O-crystals, three peaks occur at around 320 nm (strongest), 135 nm and 85 nm, which are located in the ultraviolet region. The difference in the position of the peak is small, but and the absorption coefficient decreases with the order of ICM-103-0H₂O, ICM-103-2H₂O-1/2 and ICM-103-4H₂O in this region (10–400 nm), showing that H₂O will reduce the absorption intensity to ultraviolet light, and this is also true for NH₃ and H₂S. While this order is just the opposite to the light with a longer wavelength (>400 nm), indicating that H₂O can enhance the absorption to visible light and infrared light, which is also true for NH₃. For NH₃-crystals, the number and position of main adsorption peaks are similar to those of H₂O-crystals, but the absorption intensity and order for the three NH₃-crystals are obviously different from those of H₂O-crystals. Generally, the absorption coefficient decreases in the order of ICM-103-2NH₃-2, ICM-103-2NH₃-1, and ICM-103-4NH₃ in the region of 10–400 nm, but the order is ICM-103-4NH₃, ICM-103-2NH₃-2, and ICM-103-2NH₃-1 in the 400–750 nm region, and ICM-103-2NH₃-1, ICM-103-4NH₃ and ICM-103-2NH₃-2 in the 750–1200 nm region, respectively. This shows that two NH₃ in position 2, four NH₃, and two NH₃ in position 1 are more favourable for absorbing ultraviolet light, visible light, and infrared light, respectively. Finally, different from H₂O and NH₃, three peaks at around 300 nm, 125 nm, and 82 nm in the absorption spectra for H₂S-crystals indicate the blue-shift. The difference in absorption spectra for three H₂S-crystals is negligible, showing that the number and position of H₂S almost have no effects on the absorption to different wavelengths. In all, small molecules H₂O, NH₃, and H₂S influence the α(ω) and absorption strength to different wavelengths of light, and effects are also related to their number and position.

Fig. 8 The predicted absorption spectra of ten ICM-103 crystals.

Fig. 9 displays the real part ε₁ and imaginary part ε₂ of the dielectric function of ten ICM-103 crystals. The whole shape and changing trend of the dielectric function for ten crystals are similar to some degree, but differences caused by the small molecules have been observed and cannot be neglected. Previous works have used the first principle method to predict the dielectric constant ε₁(0) of several energetic compounds (like AP and NaN₃) and found that the theoretical values are in agreement with the experimental results.^28,29 As seen from Fig. 9 and Table 3, first, the ε₁(0) value of all ICM-103-0H₂O crystal is 1.941, showing its small electron binding ability and electric polarization ability. But this can be slightly increased by three small molecules, as the other nine crystals all have higher ε₁(0) than ICM-103-0H₂O. For the crystals with four small molecules, ε₁(0) decreases in the order of ICM-103-4H₂O, ICM-103-4NH₃, and ICM-103-4H₂S. But this is different for crystals with two small molecules, and ε₁(0) decreases in the order of ICM-103-2NH₃-1/2, ICM-103-2H₂S-1/2, and ICM-103-2H₂O-1/2. The position also has effects on ε₁(0) and is related to the type of small molecules. For example, ε₁(0) values for ICM-103-2H₂O-1 and ICM-103-2H₂O-2 are the same, and this is also true for ICM-103-2H₂S-1 and ICM-103-2H₂S-2, and their values are both lower than the corresponding crystal with four small molecules, respectively. But ICM-103-2NH₃-2 has higher ε₁(0) than ICM-103-2NH₃-1, which in turn is higher than ICM-103-4NH₃. Generally, the ε₁(0) values of ten ICM-103 crystals are between the value of energetic compounds AP and metal-azides, which conforms to the characteristic of energetic crystals. Then, ε₁ of ICM-103-0H₂O reaches the three largest peak values at the energy of 2.85 eV (the strongest peak), 9.51 eV (weak peak), and 14.33 eV (weak peak). But these three peaks will shift to lower energy in general due to the existence of small molecules, especially for the NH₃-crystals, and the strongest peak of its three related crystals occur at energies 1.72 eV (ICM-103-4NH₃), 1.62 eV (ICM-103-2NH₃-1), and 2.19 eV (ICM-103-2NH₃-2), respectively. The ε₁ within the 4.24–5.06 eV of ICM-103-0H₂O is lower than zero, indicating that light cannot be transmitted in its solid crystals in this region. This is similar for ICM-103-2H₂O-1 and ICM-103-2H₂O-2, ICM-103-4H₂S, ICM-103-2H₂S-1 and ICM-103-2H₂S-2. But this region is changed to 3.96–4.79 eV and 4.06–4.72 eV, respectively. While for ICM-103-4NH₃ and ICM-103-2NH₃-1, the ε₁ values are all positive, and this untransmittable region is eliminated completely.

Fig. 9 The predicted dielectric function of ten ICM-103 crystals.

Then, the imaginary part ε₂ can reflect the information of electron transition, as seen from Fig. 9. For ICM-103-0H₂O, it increases gradually from 0 eV and peaks at 3.78 eV with the strongest intensity, and another two weak peaks occur at 10.02 eV and 15.43 eV. The first strong peak is due to the electron transition mainly from the high valence band into the low conduction band, while the rest are caused by transmitting other different valence electrons into the conduction band. The shapes of ε₂ for the other nine crystals are similar to ICM-103-0H₂O, and the position and intensity of peaks are different to some degree. For instance, the position of the first peak is shifted to lower energy with lower intensity for all nine crystals compared to ICM-103-0H₂O, which is consistent with the fact that their band gap values are lower than ICM-103-0H₂O. The ε₂ of NH₃-crystals at low energy (<2.5 eV) is higher than other crystals, showing that NH₃-crystals can adsorb more photons in the long wavelength region like infrared and visible light, which is in agreement with the results of absorption spectra. Finally, the refractive index (n) and extinction coefficient (k) are obtained by these two equations: ε₁ = n² − k² and ε₂ = 2nk, as depicted in Fig. 10. The theoretical static refractive index n₀ () values of ten ICM-103 crystals are listed in Table 3. The n₀ value increases in the order of ICM-103-0H₂O, ICM-103-2H₂O-1/2, ICM-103-2H₂S-1/2, ICM-103-4H₂S, ICM-103-4NH₃, ICM-103-4H₂O, ICM-103-2NH₃-1, and ICM-103-2NH₃-2, showing that the three small molecules can enhance the ability to refract light and increases in the order of H₂S, H₂O, and NH₃ in general, and the position and number of molecules also has an influence. Then, the shapes and changing trends of n and k for each ICM-103 crystal are similar to those of ε₁ and ε₂, respectively. The energy regions within k > n for some crystals correspond to those of ε₁ < 0. In all, these results show that the type, number, and position of three small molecules do have a significant effect on the optical properties of ICM-103 crystals.

Fig. 10 The predicted refractive index of ten ICM-103 crystals.

4. Conclusions

In this work, the functions of three molecules H₂O, NH₃, and H₂S on stabilizing the crystal structure of the high energy compound ICM-103 were investigated using the first principle calculation and Hirshfeld surface analysis. The effects of type, number, and position on the molecular, crystal and electronic structures, safety and optical properties were also studied. The results show that H₂O, NH₃, and H₂S can stabilize the crystal structure and have different effects on the structure and properties. (1) They change the lattice parameter of ICM-103 crystals and shorten the bond length of weak C–NO₂ bonds and N–N bonds in the N₃ group. (2) The NH₃ transforms the crystal from neutral to ionic type energetic compounds by the hydrogen transition from the ICM-103 molecule to NH₃. (3) They all contribute to DOS at different energy regions and generate new energy levels in the band structure. The number and position of these molecules also have different effects on the electronic structure, especially in the case of NH₃. (4) The low band gap, relative high E% value, and low percentage of hydrogen bonding in close contacts show the sensitive feature of ICM-103, which is used as initiating explosives. (5) H₂O, NH₃, and H₂S can stabilize the crystal structure of ICM-103 and reduce the sensitivity by increasing the E% value, enhancing and enriching the close contacts, especially the hydrogen-bonding contact. (6) The stabilization energy of crystals with four small molecules is obviously higher than the sum of the corresponding two crystals with two small molecules, showing that the small molecules in the two positions can cooperate with each other to better stabilize the crystal structure. (7) This stabilization effect increases in the order of H₂S, H₂O and NH₃, and the NH₃ in position 1 is more favorable for stabilizing the crystal structure than that in position 2, but the position of H₂S and H₂O almost has a negligible effect. (8) H₂O and NH₃ reduce the absorption intensity to ultraviolet light but enhance the absorption to visible light and infrared light, and the number and position of H₂S almost have no effects on the absorption to light of different wavelengths. (9) They all increase the dielectric constant and static refractive index in the order of H₂S, and H₂O, NH₃. NH₃ can eliminate the region in which the light cannot be transmitted in H₂O-crystals, H₂S-crystals, and ICM-103-0H₂O. This work may be helpful for understanding the stabilizing effect of small molecules on unstable high energy crystals. Since H₂O, NH₃, and H₂S are non-energy or low-energy molecules whose presence will harm the energy performance of high energy compounds, studies on searching for new small molecules with higher energy to stabilize and adjust the unstable energetic crystal system may be needed.

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgements

The present work was supported by the National Natural Science Foundation of China (51802156), Natural Science Foundation of Jiangsu (BK20170761, BK20181302), Postdoctoral Research Funding Program of Jiangsu (2021K192B), and Outstanding Scientific and Technological Innovation Team in Colleges and Universities of Jiangsu Province.

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