3.1 Molecular geometry and electronic structure
The molecular structures of A1 to A5 and B1 to B5 were optimized via the method introduced above. As can be seen in Fig. 2, The combination of pentazole and ANTA, pentazole and NTO have not changed the original structures. The target molecules have the C1 point group by calculation. The order of dipole moment of the designed molecules are as follows: A2 > A1 > A4 > A3 > A5 (9.44 to 4.26 Debye) and B2 > B1 > B5 > B3 > B4 (4.45 to 3.14 Debye), that is, NH2 group has a positive correlation to the molecular dipole moment, while NF2 and NO2 group are reversed.
Table 1 displays the predicted bond lengths of relevant structures. As shown in Table 1, the N-N bond length in the triazole ring is between 1.342 Å and 1.369 Å, and the C-N bond length is 1.280 ~ 1.435 Å. In other words, the bond length of the triazole ring is between the corresponding N-N and C-N single bond (~1.41 Å and ~1.45 Å, respectively) and double bond (~1.23 Å and ~1.27 Å respectively) [33], indicating that the triazole rings of ANTA, NTO and their derivatives have certain aromaticities. Similarly, PZ has aromaticity, where the N-N bond length in the ring ranges from 1.278 Å to 1.377 Å. According to research findings, in the derivative (A1) consisting of an ANTA and a PZ ring, the difference of bond lengths in PZ ring is smaller than that of parent PZ, reflecting that the combination of PZ and ANTA enhances the conjugate effect in PZ. The same phenomenon occurs when the NH2 or NO2 group is introduced to A1. However, for the corresponding NTO derivatives, an opposite trend occurs, showing that the introduction of groups could weaken the conjugation effect of PZ. Overall, the derivatives bound by ANTA and PZ are more insensitive than those bound by NTO and PZ.
Table 1. The predicted bond lengths (Å) of ANTA, NTO and designed compounds.
Comp.
|
C-N in ANTA
|
N-N in triazole
|
NANTA-NH2/NO2/NF2
|
NANTA-NPZ
|
N-N in PZ
|
(C-N in NTO)
|
(NNTO-NH2/NO2/NF2/PZ)
|
(NNTO-NNH-PZ)
|
ANTA
|
1.311-1.364
|
1.362
|
¾
|
¾
|
¾
|
NTO
|
1.291-1.403
|
1.358
|
¾
|
¾
|
¾
|
PZ
|
¾
|
¾
|
¾
|
¾
|
1.294-1.354
|
A1
|
1.310-1.365
|
1.357
|
¾
|
1.366
|
1.303-1.334
|
A2
|
1.319-1.360
|
1.342
|
1.374
|
1.365
|
1.303-1.333
|
A3
|
1.305-1.399
|
1.355
|
1.443
|
1.367
|
1.299-1.339
|
A4
|
1.303-1.378
|
1.369
|
1.368
|
1.360
|
1.280-1.374
|
A5
|
1.303-1.375
|
1.367
|
¾
|
1.353-1.365
|
1.278-1.377
|
B1
|
1.288-1.415
|
1.363
|
¾
|
1.394
|
1.284-1.368
|
B2
|
1.291-1.400
|
1.365
|
1.403
|
1.393
|
1.284-1.368
|
B3
|
1.283-1.427
|
1.365
|
1.487
|
1.390
|
1.283-1.370
|
B4
|
1.280-1.435
|
1.367
|
1.383
|
1.390
|
1.283-1.370
|
B5
|
1.281-1.424
|
1.363
|
1.351
|
1.389
|
1.278-1.375
|
For the designed compounds, the energies of the highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO) and energy gaps (ΔE) were illustrated in Fig. 3. The energy of HOMO and LUMO decreases with the increase of the number of PZ attached to nitrogen in ANTA or NTO, showing that the addition of PZ could make the electron acceptance of ANTA or NTO easier and the electron loss more difficult. Since NH2 is an electron-donor group and NO2 and NF2 are electron withdrawing groups, the introduction of NH2 group increases the energy of HOMO and LUMO, while the introduction of NO2 and NF2 groups has an opposite effect. Conceptual density functional theory is a significant theory for the study of chemical reaction activities and sites. In this framework, there is a quantity called softness. Softness does not refer to the rigidity of the system, but reflects the activity of electrons and the distribution of easy deformation degree. For a series of similar systems, it is generally believed that the softer the molecule is, the more active its reactivity is. The softness is approximately equal to the reciprocal of HOMO-LUMO gap. In the chemical or photochemical process of electron transfer or transition, the energy gap is an important parameter to evaluate the reactivity. Thus, the smaller the Energy gap, the higher the reactivity. As shown in Fig. 3, all of the designed compounds have relatively large energy gaps, ranging from 4.14 eV to 5.31 eV, which indicates that these molecules show good stability in the chemical process. Moreover, A3 has the largest energy gap, while A5 has the smallest one among these compounds.
3.2 Density and heat of formation
For high-energy materials, density plays a significant role in detonation performance, since higher density means more energy per unit volume. Specifically, the density can directly affect the detonation performance shown in the Kamlet−Jacobs equation. In this part, based on the combination of PZ and ANTA (A1 to A5)/NTO (B1 to B5), the effect of introducing different substituents on the density of energetic compounds with appropriate positions were studied. The density of the designed compounds ranges from 1.81 g/cm3 to 1.97 g/cm3 (Table 2). In view of the second substitution site of NTO is adjacent to C-NO2, while that of ANTA is meta-substitution. When the same substituent is introduced, the repulsive force between substituents of series B derivatives is larger, and the corresponding substituents contribute more to the volume, so that the densities of series B derivatives are slightly lower than those of series A derivatives. It is found that the density increases in the order of A1 to A4, exhibiting that the introduction of NH2, NO2 and NF2 into the system increases the density. Since the above groups can significantly increase the molar mass of the compound, but have relatively little effect on the molecular volume. One should note that A5 (consisting of an ANTA and two PZ rings) has lower density, compared with A1, as a result of less coplanarity of its structure, reducing the packing regularity and increasing the spatial volume of the molecule with the addition of another PZ ring. In short, its contribution to volume is much greater than that to molecular weight. The change trend of the density of B and A series compounds is similar (except B2). Obviously, the influence of the introduction of amino group on the volume is greater than that on molecular weight for B2.
Nitrogen content and oxygen balance (OB) are two momentous parameters for screening energetic compounds. The higher the nitrogen content of energetic materials is, the better the detonation performance is. Explosive reactions can release maximum heat when the oxygen balance is zero. Lower OB stands for more oxygen being needed from external surroundings during combustion transitioning to detonation, which could result in the decrease of detonation performance. Therefore, the energetic compounds with high nitrogen content and zero oxygen balance would have better detonation performance. For the designed molecules, the nitrogen content is higher than 58%, and the oxygen balance is between –26.29 % and 3.09 %. This displays that these molecules have good detonation properties.
Table 2. The calculated values of solid-phase HOF, density, N-content and OB.
Properties
|
A1
|
A2
|
A3
|
A4
|
A5
|
B1
|
B2
|
B3
|
B4
|
B5
|
ρ (g/cm3)
|
1.90
|
1.91
|
1.92
|
1.97
|
1.85
|
1.83
|
1.81
|
1.89
|
1.96
|
1.85
|
HOFg (kJ/mol)
|
876.92
|
1027.14
|
981.98
|
940.76
|
1524.38
|
737.42
|
870.63
|
902.98
|
870.10
|
1432.21
|
ΔHsub (kJ/mol)
|
130.24
|
145.71
|
134.27
|
134.96
|
149.75
|
115.75
|
124.76
|
130.81
|
131.12
|
151.47
|
HOFs (kJ/mol)
|
746.68
|
881.43
|
847.71
|
805.81
|
1374.63
|
621.66
|
745.86
|
772.17
|
738.98
|
1280.74
|
OB (%)a
|
–24.24
|
–26.29
|
–3.29
|
–12.85
|
–14.98
|
–14.95
|
–17.47
|
–3.09
|
–6.04
|
–8.48
|
N-content (%)
|
70.71
|
72.30
|
63.37
|
61.85
|
78.65
|
65.42
|
67.25
|
59.46
|
58.11
|
74.20
|
a OB (%) for CaHbOcNdFe: 16 × (c – 2a – b/2 – e)/M × 100%; M is molecular weight of the title compounds.
Heat of formation (HOF) is one of the most crucial quantities used to evaluate the energetic properties of HEDMs. To demonstrate the reliability of the calculated HOFs, the gas-phase HOF, solid-phase HOF and heat of sublimation of NTO, being –14.18 kJ/mol, –95.31 kJ/mol and 81.13 kJ/mol respectively, were calculated (see Computational methods for details). The calculated value of solid-phase HOF is comparable to the experimental values of –100.8 kJ/mol [34]. Thus, the methods we chose are reasonable. The range of solid-phase HOF is from 621.66 kJ/mol to 1374.63 kJ/mol. According to research findings, the addition of another PZ ring could increase the solid-phase HOF of the system by about 640 kJ/mol. For A series compounds, the solid-phase HOF of A2, A3, A4 or A5 is larger than A1, indicating that the introduction of the NH2, NO2, NF2 groups or consisting of an ANTA and two PZ rings could enhance HOF. While this positive influence of NH2, NO2 or NF2 group is weaker than that of addition of another PZ ring, since A2 to A4 all have lower solid-phase HOFs than A5 to varying degrees. An analogical situation occurs in series B derivatives. Meanwhile, the similar solid-phase HOF values of series A and B show that the introduction of NF2 (A4 and B4) cannot significantly increase the HOF. Therefore, in the formation of such compounds, in order to obtain high HOF, the introduction of NH2 or NO2 group as a substituent or combining with two PZ rings is a good choice.
3.3 Energetic properties
The detonation heat (Q), detonation pressure (P), and detonation velocity (D) of the title compounds have been assessed by the semi-empirical Kamlet-Jacobs formula, which has been proved to be applicable for predicting the explosive properties of energetic high-nitrogen compounds based on the predicted density and heat of formation. P and D are the most important parameters for evaluating energetic materials.
The P and D for two known explosives RDX and HMX were also calculated by above method. The calculated values (RDX: P = 34.8 GPa, D = 8.9 km/s; HMX: P = 39.2 GPa, D = 9.3 km/s) are comparable to the experimental values (RDX: P = 34.7 GPa, D = 8.8 km/s; HMX: P = 39.0 GPa, D = 9.1 km/s) [35]. Hence, our predictions for the designed compounds are reliable. For the purpose of comparison, the experimental detonation performances of RDX and HMX were also showed in Fig. 4a. Since densities and HOFs play a crucial role for detonation performances, it is pleasant to see that the trends of Q, P and D are basically the similar. Therefore, combined with the above analysis of the density and HOF of A and B series derivatives, it is reasonable that the detonation performances of A series is larger than those of B series on the whole. Judged by the Q, P and D values, all of the designed compounds have good detonation performances.
For molecules A1 to A4 and B1 to B4, with increasing sequence number, both corresponding P and D increases gradually, indicating that the introduction of NH2, NO2 or NF2 is beneficial for improving energetic properties. What’s more, the molecule with NF2 group (A4 or B4) has the best detonation performances while the compound with the NH2 substituent (A2 or B2) has the worst detonation performances, indicating that the contribution of NF2 group to the detonation performance of an energetic compound is greater than that of NH2 group. When an NTO is combined with two PZ rings, both P and D are larger than those of B1 and B2. The reason is that the density and HOF of B5 advantage over those of B1 and B2. It is further proved that density and HOF are the decisive factors for evaluating the detonation performance of energetic materials. Both P and D of compounds A3, A4 and B4 are superior to HMX, A2, A5, B3 and B5 have approximate or exceeded P and D over HMX, whereas those of B1 and B2 are approximate or inferior to RDX, exhibiting that they can be taken as promising candidates of HEDMs apart from B1 and B2. These predictions further verify that modifying energetic molecules with appropriate substituents is a meritorious method to improve the energetic properties.
3.4 Sensitivity
The core problem in designing new explosives is to achieve the desired balance between high performance and low sensitivity. Therefore, in order to further investigate the practical application, an admissible sensitivity value is essential for a new high-energy compound. It is therefore significant to have some means of evaluating the likely sensitivities of compounds that have not yet been synthesized. In this part, the free space per molecule in the unit cell, designated ΔV, has been used to evaluate sensitivity of the proposed compounds, which has been proved to be reliable for predicting the sensitivity of energetic compounds [31, 36]. The smaller value of ΔV is, the lower sensitivity of the explosive is.
In Fig. 4b, the second substitution site of NTO is adjacent to C-NO2, whereas that of ANTA is the meta-potition from C-NO2. When the same substituent is introduced, the repulsive force between substituents of B series derivatives is larger, resulting in the sensitivities of B series derivatives being slightly higher than those of A series derivatives. Compared with A1 (43.51 Å3) and A5 (56.26 Å3), B1 (45.73 Å3) and B5 (58.07 Å3), the ΔV values are significantly increased, showing that merging two PZ rings into one structure increases the sensitivity. The increased sensitivity is probably caused by the weakening interactions between the ring of PZ and ANTA/NTO. ΔV values of A5, B3, B4 and B5 were larger than HMX (49.20 Å3) [36], indicating that they are more sensitive than HMX. When PZ of the second site in A5 or B5 is replaced by NH2, NO2 or NF2 groups, the ΔV value is significantly reduced. It displays that NH2, NO2 or NF2 groups can effectively adjust the sensitivity properties of the compounds to an acceptable level. Among them, the addition of NH2 group reduced the sensitivity of compounds significantly. The reason is that NH2 is an electron-donating group, which can offset the imbalance of surface potential caused by electron-withdrawing components. Secondly, the existence of NH2 substituent can generate intermolecular and intramolecular hydrogen bonds, thus stabilizing the system. Moreover, Compounds A1, A2, A3, A4 and B2, all have exceed or approximate P and D to RDX, lower or approximate sensitivity to HMX, indicating that these five novel compounds have good performance, which reveals the great potential of the parent compounds (formed by PZ and ANTA/NTO) used as HEDMs. Additionally, both molecules A3 and A4 are superior to HMX in detonation performance and are good candidates to HEDMs.