Combination High Energy with Stability : Polynitrogen Explosives N 14 and N 18

Novel high energy density materials N14 (1,6-dihydro-1,2,3,3a,4,5,5a,6,7,8,8a,9,10,10atetradecazapyrene) and N18 (1,2,2a,3,4,4a,5,6,6a,7,8,8a,9,10,10a,11,12a-octadecazacoronene) were designed, and their structures, detonation performance and stabilities were calculated employing density functional theory (DFT). Calculations reveals that they have a good balance between high energy and stability. Their energy gaps between LUMO and HOMO are all lower than that of TATB, while their impact sensitivity h50% is estimated close to that of RDX. Concerning energy, detonation performance of the N14 (P = 43.6 GPa, D = 10040 m/s, Q = 2214 cal/g) and the N18 (P = 37.4 GPa, D = 9400 m/s, Q = 2114 cal/g) are comparable to CL-20.


Introduction
High energy density materials (HEDMs), which possess not only perfect detonation performance but also good thermal stability and low sensitivity, have attracted considerable interests for some potential applications in propellants, explosives and pyrotechnic agents in recent years [1][2][3][4][5].
In order to meet main requirements in safety and power, much effort has been taken by lots of research groups [6][7][8][9].However, in most cases, it is very difficult to concentrate both desired properties into one substance, whether traditional energetic compounds and rich nitrogen energetic salts, or polynitrogen materials.
On the other hand, polynitrogen materials have received much more attention on their high energy content due to the deviation of bond energy of N2 triple bond and N-N single bonds or double bonds [14].However, most of them are unstable.Since 1999, a series of N5 + -containing salts are investigated and the most stable N5 +containing salt N5 + SbF6 -is only stable at about 60 o C [15,16].In 2004, polymeric nitrogen with cubic gauche structure was produced by Eremets [17].Its power is five times more than that of the most powerfully energetic materials, whereas it is disappeared at ambient pressure.In 2017, two significant breakthroughs in the bulk synthesis and characterization of the pentazolate anion cyclo-N5 -salts were achieved by Hu [18,19] and Lu [20], respectively.Recently, the most stable cyclo-N5 -salt Na24N60 and Na20N60 occurs only below 148 o C [21].Besides, some other all nitrogen materials can`t exist under room temperature for a long time [14,22].
New high energy density materials are considered under the circumstances.Two novel covalent compounds, N14 and N18, are designed in this paper with the characteristics of great power and high safety, whose chemical structures are shown in Figure 1.There are 14 nitrogen atoms closely linked in N14, and 18 nitrogen atoms in N18.In these structures, that several nitrogen atoms connected directly can enhance energy.However, in most cases, high nitrogen content and stability tend to be mutually exclusive [23].Thereby olefin and benzene ring are expected to form a large π bond with nitrogen atoms to improve its stability thought the large conjugated bonds do not appear at last.A structure C12N12 being similar to N18 was reported, Mondal [24] indicates that are slightly aromatic in nature, but Tursungul [25] doesn`t agree with him.

N14
N18 Figure 1 Chemical structure of the title compounds Theoretical studies of N14 and N18 make it not only possible to provide forecast of properties of candidate compounds, but also possible to compare them.This paper presents the molecular geometries structures, frontier molecular orbitals, electrostatic potential (ESP), impact sensitivity h50% to illustrate their insensitivities.At the same time, the theoretical density (ρ), the heat of formation (HOF), and the detonation performance is emphasized to explain their high energy.These results can also be used for comparison with property of other familiar explosives, and provide theoretical supports for molecular design of novel high energetic density compounds.

Computational details
Computations were performed with Gaussian 09 package at B3LYP level [26] method with 6-311++G (d, p) basis set.The molecular geometries and electronic structures were obtained with the density functional theory (DFT) method.The geometric parameters of these two structures were allowed to be optimized, and no constraints were imposed on molecular structures during optimization process.Structures were identified to be local minima without imaginary frequencies.
The geometric structure refers to bond length and bond angle in this paper.Bond length is one important parameter for a molecular.Commonly, the bond length is closely related with the bond stability: the longer the bond length is, the less stable the bond is [27].Bond angle is another important parameter for a molecular and 108 o is an excellent value [28].
The frontier molecular orbitals include the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO).The energy gap (∆ELUMO-HOMO) is essential for kinetic stability and chemical reactivity during the chemical processes with electron transfer or leap.Previous studies have also proved that the higher energy gap, the lower chemical reactivity and vice versa [29].
Molecular electrostatic potentials (ESP) are used to describe the interaction of static electricity in molecules, and to predict chemical reactivity sites.With the help of VMD program, the very nice color-filled molecular surface maps with surface extrema can be plotted based on the output of the Multiwfn program [30].In the map, the green and orange spheres correspond to significant minima and maxima ESP surfaces respectively.These spheres are labeled by dark blue and brown-red texts with the unit kcal/mol.At the same time, the global minima and maxima on the surface are labeled by larger and italic font.
Impact sensitivity is an important index to evaluate explosives, and h50% is a common value to assess the index.The h50% is the height where 50% probability of the "drop" result in reaction of the sample.The shorter the drop height is, the greater the impact sensitivity is.There are four methods to estimate the impact sensitivity h50% [28], shown in Equation ( 1) ~ (4).Where is the difference between magnitudes of average values of the positive and negative electrostatic potential (kJ/mol), v is balance parameter, and Q is heat of detonation (kJ/g).

Method 1:
(1) Method 2: (2) Method 3: (3) Method 4: (4) The isodesmic reactions were used to predict the heat of formation (HOF) of compounds, and isodesmic reactions of N14 and N18 are shown in Scheme 1 and 2. The enthalpy of reaction (ΔrH298) at 298 K can be calculated according to equation (5) in the isodesmic reaction.The ∆fHP and ∆fHR of following equation are the HOFs of products and the reactants, respectively.Similarly, ∆E0, ∆EZPE, ∆HT are the difference between products and reactants.Furthermore, E0, EZPE and ∆HT are total energy at 0 K, the zero-point energy and the thermal correction from 0 K to 298 K, respectively.

Scheme 1 The isodesmic reaction of N14
Scheme 2 The isodesmic reaction of N18 According to Equation ( 5), the heat of formation of the gaseous N14 and N18 ∆fH(g) can be calculated, while the heat of formation in the condensed phase ∆fH(c) is determined by Equation ( 6).In order to estimate ΔHsub, the electrostatic potential method [31] can be used, shown in Equation ( 7).In the equation, As and νσ 2 tot is derived from the molecular electrostatic potential calculation by Multiwfn software [30].
(5) (6) (7) In the high energy density material, the crystal density (ρ) is an important parameter for predicting performance.Equation (8) proposed by Politzer et al [32] was used to calculate the crystal density of compounds where M is the molecular weight and Vm is the molecular volume defined as inside a contour of 0.001 au density that was evaluated using a Monte Carlo integration.Finally, α, β and γ here is 0.9183, 0.0028, and 0.0443, respectively.

Geometrical Structures
The structure of N18 is similar to that of coronene, with periphery nitrogen atoms replacing carbon atoms.Some of periphery nitrogen atoms form double bonds while some form single bonds, and the middle carbon forms the benzene ring.We hope that the nitrogen atoms with single bond, which carry lone pair electrons, form more large conjugated system with the benzene ring and lots of azo bonds.However, the output result at B3LYP method shows that all atoms are not on coplanar, so N18 may be not an aromatic compound.The structure output of N18 is shown in Figure 2. Six carbon atoms of the benzene ring form large π bond in the input structure, but they are linked together with double bonds in output structure.It is not corrected for keeping raw data.
In this structure, all carbon atoms are in the same plane and each C-C bond length is 1.3707 Å, which is shorter than that of benzene (1.3945 Å).All of the double bond nitrogen atoms are also in the same plane and the distance of N-N double bond (each one is 1.2389 Å) shorter than that of cazobenzene (1.2522 Å).Similarly, six single bond nitrogen atoms are placed on the same plane while N-N single bond of the compound(1.4398Å) is  The structure of N14 is similar to that of pyrene, with periphery nitrogen atoms replacing carbons atoms.Moreover, it possesses two additional hydrogen atoms because nitrogen has three valence bonds.We hope that the nitrogen atoms with single bond, which carry lone pair electrons, form more large conjugated system with the C-C double bond and many azo bonds.Just like N18, the output result at B3LYP method shows that all atoms are on not coplanar, so N14 may be not an aromatic compound.The structure output of N14 is shown in Figure 3.  1.Some of them are shorter than that of hydrazine, and some of them are longer slightly but close to it.In the structure of N14, some bond angles are listed in Table 2 and other bond angles have same value for symmetry structure.From the table, it can be seen that all bond angles are closed to 108 o .As the situation in N18, not all atoms in N14 are on the same plane and form a large conjugated system, but they have special interactions to become a stable structure.The LUMO (a) and HOMO (b) orbits of N14 and N18 are show in Figure 4.The positive phase is red and the negative one is green.Either LUMO or HOMO doesn't locate on H atom of N14, and the two orbits locate approximately on all the atoms of N18.Energy gaps of some compounds were calculated with the same method listed in Table 3.In general, the smaller the value is, the more stable the compound is.In the table, the value of energy gap is in order HMX ≈ RDX > FOX7 > TATB.So their stability is in order TATB > FOX7 > RDX ≈ HMX, consistent with experimental values [33].Similarly, the value of energy gap is in order TATB > N14 > N18, therefore their stability is in order N18 > N14 > TATB.
Table 3 Energy Gaps of some compounds  5.The surface minima of ESP is distributed near some N atoms due to these atoms with double bonds or lone pair electron, which are the primary electrophilic sites.The global minima site of ESP is present near the N3 atom, with the value -24.03 kcal/mol.The global maxima site of ESP is +52.67 kcal/mol, which is close to that of H18 atom since nitrogen atoms attracted a great deal of electrons.However, it may be not easy to be attacked by nucleophile.Because H18 with maxima in a monomer and N with surface minima in neighbor monomer product hydrogen-bond, which will result electrostatic potentials cancelled each other out.The same is to H17, other global maxima site with +52.62 kcal/mol.From Figure 5(b), it can be seen that a large portion has a small ESP value from -25 to +25 kcal/mol.The negative part mainly corresponds to the surface above and below the several N atoms with the effect of the abundant lone pair electron or π-electron cloud.The biggest positive area mainly arises from C-C double bond, and the smaller ones with remarkable positive ESP value correspond to C-H bond though that is not nucleophilic sites.Electrostatic potentials map on molecular surface (a) and the surface areas in each ESP range (b) of N18 is plotted and shown in Figure 6.The surface minima of ESP are distributed in the peripheral of N atoms ring and their values range from -17.16 to -17.15 kcal/mol which is close to global minima.The N25 is near the global minima site, with the value -17.16 kcal/mol.Just like the minima, the surface maxima range from +42.00 to +42.14 kcal/mol, which is close to the global maxima +42.17 kcal/mol.They are located in the peripheral of benzene ring and on the same side of the global minima site.It can be seen that positive and negative potential distributed more evenly over surface.It is reported [34,35] that the more evenly the electron is distributed over the surface of the molecule, the more insensitive the molecule is.There is a large portion ESP distributing from -20 to +30 kcal/mol as shown in Figure 6 The values (cm) of h50% are estimated through four methods and the results of some compounds are summarized in Table 4.The experimental values of TNT, RDX, HMX, PETN, TATB, FOX7 and CL-20 are also shown in the table for comparison.It can be seen that values obtained from method 4 can`t reflect the one of experiment, methods 1-3 show relatively consistent results.From the table the h50% of title compounds may be closed to that of RDX.This result is different to the Frontier Molecular Orbitals theory because the accuracy of the predictions from the models can`t be assured entirely [36].

Heats of Formation
The gas phase heat of formation of N14 and N18 can be calculated according to Scheme 1, 2 and Equation ( 5).The experimental gas phase heat of formation of NH3, CH4, C6H6, CH3NH2, N2H2 and N2H4 are available [37].They are all shown in Table 5 and the gas phase heat of formation of N14 and N18 is 2142.17 and 2959.60 kJ/mol, respectively.Due to lots of nitrogen which are connected directly, their enthalpy of formation is much higher than RDX, HMX or CL-20 [38], shown in Table 8.The heat of formation in the condensed phase of N14 and N18 can be calculated according to Equation ( 6) and ( 7), and they are 2048.49and 2846.46 kJ/mol, respectively.Related parameters are shown in Table 6.

Crystal Densities
The crystal densities of N14 and N18 can be calculated according to Equation ( 8), and they are 1.784 and 1.817 g/cm 3 .Related parameters are shown in Table 7.As these two compounds contain mainly C and N, and don`t contain O, their densities are lower than HMX and CL-20, shown in Table 8.

Detonation Performance
The detonation velocity (D), detonation pressure (P) and heat of detonation (Q) of N14 and N18 are computed based on their crystal densities (ρ) and condensed phase heats of formation ∆fH(c).Their detonation performance, including RDX, HMX and CL-20 [39] are shown in Table 8.It reveals that detonation performance of the N14 (Q = 2214 cal/g and D = 10040 m/s) and N18 (Q = 2114 cal/g and D = 9400 m/s) are higher than that of CL-20 while their detonation pressures (43.6 GPa and 37.4 GPa) are lower.The detonation performance values are computational data from reference [39].4.

Conclusions
In this work, N14 and N18 are calculated by Gaussian 09 package at B3LYP method with 6-311++G (d, p) basis set to investigate their detonation performance and stability.The results show that detonation performance of N14 (P = 43.6GPa, D =10040 m/s, Q = 2214 cal/g) and N18 (P = 37.4 GPa, D = 9400 m/s, Q = 2114 cal/g) are comparable to the value of CL-20.What`s more, their energy gaps (∆ELUMO-HOMO) are superior to TATB`s and their impact sensitivity h50% may be close to RDX.Considering both the detonation properties and stabilities, they are all likely to be used as candidates of high energy density materials with low sensitivity and high performance, and these results can also be used for comparison with property of other familiar explosives, and provide theoretical supports for molecular design of novel high energetic density compounds.Further work on route optimization and practical synthesis is being carried out by our team.

Figure 2
Figure 2 Structure of the N18

Figure 3
Figure 3 Structure of the N14 In the structure of N14, C-C double bond has a bond length of 1.3122 Å, which is shorter than that of ethylene (1.3288 Å).The Distance of N3-N4 and N9-N10 are 1.2523 Å while N6-N7 and N12-N13 are 1.2324 Å, and they are close to counterpart of cazobenzene.Two C-N bond lengths are 1.3922 and 1.3921 Å, respectively, which are shorter than C-NO2 of TATB.The N-H bond length is 1.0151 Å, which is closed to that of NH3 (1.0147 Å) calculated with same method and basis set.All N-N single bond length of N14 are listed in Table1.Some of them are shorter than that of hydrazine, and some of them are longer slightly but close to it.In the structure of N14, some bond angles are listed in Table2and other bond angles have same value for symmetry structure.From the table, it can be seen that all bond angles are closed to 108 o .As the situation in N18, not all atoms in N14 are on the same plane and form a large conjugated system, but they have special interactions to become a stable structure.Table1N-N single bond length of the N14

Figure 4
LUMO (a) and HOMO (b) orbitals of N14 and LUMO (c) and HOMO (d) orbitals of N18 3.3 Electrostatic Potentials Electrostatic potentials map on molecular surface (a) and the surface areas in each ESP range (b) of N14 are plotted and shown in Figure

Figure 5
Figure 5 Electrostatic potentials map (a) and the surface areas (b) of N14

Figure 6
(b).Obviously, positive part arises from N atom and negative one comes from C atom.Electrostatic potentials map (a) and the surface areas (b) of N18 3.4 Impact sensitivity

Table 1 N
-N single bond length of the N14 Preprints (www.

Table 5
Related parameters for predicting gas phase heat of formation by isodesmic reactions

Table 6
Related parameters for predicting condensed phase heat of formation

Table 7
Related parameters for predicting crystal densities

Table 8
Detonation performance of HEDM