#
Novel All-Nitrogen Molecular Crystals Composed of Tetragonal N_{4} Molecules

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Computational Details

#### 2.1. Method

#### 2.2. Characterization of Atomic Structure

## 3. Results and Discussion

#### 3.1. Properties under Hydrostatic Pressures

#### 3.2. Properties of Kinetics and Thermodynamics

#### 3.3. Prediction of Detonation Performance

**N${}_{6}$**molecular crystal, about 185 kcal/mol [22] but higher than that of bipentazole and N${}_{8}$, about 81.6 and 89.4 kJ/mol atom${}^{-1}$, respectively [38]. The enthalpy of formation of Td-N${}_{4}$ that we used to calculate detonation velocity and detonation pressure was 180.8 kcal/mol.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of trihedral angle S-ABC; $\alpha ,\beta ,\gamma $ are three face angles; $\theta $ is the dihedral between two planes △SAB and △SAC.

**Figure 2.**Crystal structures, with little gray balls representing nitrogen atoms. (

**a**) This crystal contains 2 Td-N${}_{4}$ molecules, lattice parameters are a = 6.58 $\stackrel{\u02da}{\mathrm{A}}$, b = 8.52 $\stackrel{\u02da}{\mathrm{A}}$, c = 6.60 $\stackrel{\u02da}{\mathrm{A}}$, $\alpha $ = 92.6${}^{\circ}$, $\beta $ = 89.3${}^{\circ}$, $\gamma $ = 92${}^{\circ}$. (

**b**) This crystal contains 8 Td-N${}_{4}$ molecules; lattice parameters are a = 8.21 $\stackrel{\u02da}{\mathrm{A}}$, b = 8.36 $\stackrel{\u02da}{\mathrm{A}}$, c = 8.02 $\stackrel{\u02da}{\mathrm{A}}$, $\alpha $ = 116${}^{\circ}$, $\beta $ = 117${}^{\circ}$, $\gamma $ = 96${}^{\circ}$. (

**c**) This crystal contains 64 Td-N${}_{4}$ molecules; lattice parameters are a = 16.42 $\stackrel{\u02da}{\mathrm{A}}$, b = 16.72 $\stackrel{\u02da}{\mathrm{A}}$, c = 16.04 $\stackrel{\u02da}{\mathrm{A}}$, $\alpha $ = 116${}^{\circ}$, $\beta $ = 117${}^{\circ}$, $\gamma $ = 96${}^{\circ}$.

**Figure 3.**Statistical distribution of components of the unit vector in the normal direction on the surface of tetrahedron N${}_{4}$ for 2-Td-N${}_{4}$ under 0 GPa and 200 GPa: (

**a**) ${n}_{x}$, (

**b**) ${n}_{y}$, (

**c**) ${n}_{z}$; (

**d**) statistical distribution of the heights of the tetrahedron N${}_{4}$.

**Figure 4.**Energy as a function of pressure for the 2-Td-N${}_{4}$, 8-Td-N${}_{4}$ and 64-Td-N${}_{4}$. Black square represents 2-Td-N${}_{4}$, red triangle represents 8-Td-N${}_{4}$, and blue circles represent 64-Td-N${}_{4}$.

**Figure 5.**Density as a function of pressure for 2-Td-N${}_{4}$, 8-Td-N${}_{4}$, and 64-Td-N${}_{4}$. Black square represents 2-Td-N${}_{4}$, red circle represents 8-Td-N${}_{4}$, and blue triangle represents 64-Td-N${}_{4}$.

**Figure 6.**Ratio of lattice constants as a function of pressure for (

**a**) 2-Td-N${}_{4}$, (

**b**) 8-Td-N${}_{4}$, (

**c**) 64-Td-N${}_{4}$.

**Figure 7.**Pair distribution functions for 64-Td-N${}_{4}$ under 0, 100, 200, and 380 GPa. (

**a${}_{\mathbf{1}}$**) Pair distribution function (PDF). (

**a${}_{\mathbf{2}}$**) Angle distribution function (ADF). (

**a${}_{\mathbf{3}}$**) Dihedral distribution function (DDF).

**Figure 8.**Band structures and DOS of 2-Td-N${}_{4}$: (

**a**) 0 GPa, (

**b**) 100 GPa, (

**c**) 200 GPa, (

**d**) 430 GPa. Fermi level E${}_{F}$ was set at zero; horizontal green dashed line denotes the energy positions of the conduction band minimum.

**Figure 9.**DOS of 8-Td-N${}_{4}$: (

**a**) 0 GPa, (

**b**) 100 GPa, (

**c**) 200 GPa, (

**d**) 390 GPa, (

**e**) 400 GPa. Fermi level E${}_{\mathrm{F}}$ was set to be zero.

**Figure 10.**DOS of 64-Td-N${}_{4}$: (

**a**) 0 GPa, (

**b**) 100 GPa, (

**c**) 200 GPa, (

**d**) 370 GPa, (

**e**) 380 GPa. Fermi level E${}_{\mathrm{F}}$ was set at zero.

**Figure 11.**Molecular dynamics simulation was carried out for 8-Td-N${}_{4}$. Figure (

**a${}_{\mathbf{1}}$**–

**a${}_{\mathbf{4}}$**) show the total energy (△E${}_{\mathrm{tot}}$(t) = E${}_{\mathrm{tot}}$(t) − E${}_{\mathrm{tot}}$(t${}_{0}$)), kinetic energy (E${}_{\mathrm{k}}$), temperature (T) and pressure (P) of the system as a function of time under 1 GPa and 10 GPa, respectively.

**Figure 12.**(

**a**–

_{1}**a**) Pair distribution functions at 15, 25, 35, and 50 ps under 1 GPa in the MD simulations.

_{3}**Figure 13.**(

**a**–

_{1}**a**) Pair distribution functions at 15, 25, 35, and 50 ps under 10 GPa in the MD simulations.

_{3}**Table 1.**Density of the crystal structure consisting of 8 Td-N${}_{4}$ molecules. This structure was optimized by applying external pressure on the basis of a PWmat code.

Pressure (GPa) | Density (g/cm${}^{3}$) | Energy (eV) |
---|---|---|

30 | 2.79 | −8549.92 |

50 | 3.11 | −8518.47 |

80 | 3.48 | −8476.25 |

100 | 3.67 | −8450.27 |

**Table 2.**Detonation pressure and detonation velocity calculations for Td-N${}_{4}$ compared with solid C–H–N–Q explosives [42] using the K–J equation.

Explosive | ${\mathit{\rho}}_{0}{(\mathbf{g}/{\mathbf{cm}}^{3})\phantom{\rule{0.166667em}{0ex}}}^{1}$ | ${\u25b3}_{\mathit{f}}{\mathit{H}}^{0}{(\mathbf{kcal}/\mathbf{mol})\phantom{\rule{0.166667em}{0ex}}}^{2}$ | ${\mathit{P}}_{\mathit{pro}}\phantom{\rule{0.166667em}{0ex}}{}^{3}/{\mathit{P}}_{\mathit{ref}}\phantom{\rule{0.166667em}{0ex}}{}^{4}\left(\mathbf{GPa}\right)$ | ${\mathit{D}}_{\mathit{pro}}\phantom{\rule{0.166667em}{0ex}}{}^{5}/{\mathit{D}}_{\mathit{ref}}\phantom{\rule{0.166667em}{0ex}}{}^{6}(\mathbf{km}/\mathbf{s})$ |
---|---|---|---|---|

TNT | 1.65 | −14.17 | 20.7/19.4 | 7.01/6.92 |

RDX | 1.80 | 16.79 | 34.4/34.9 | 8.80/8.82 |

HMX | 1.91 | 17.87 | 38.5/39.1 | 9.15/9.15 |

CL-20 | 2.04 | 95.04 | 44.3/45.9 | 9.64/9.60 |

N${}_{4}$ | 2.09 | 180.8 | 74.2 | 12.27 |

N${}_{4}$ | 2.20 | 180.8 | 81.0 | 12.78 |

^{1}${\rho}_{0}$ is the loading density of explosives.

^{2}${\u25b3}_{f}{H}^{0}$ is the enthalpy of formation calculated by the atomization energy method.

^{3}${\mathrm{P}}_{\mathrm{pro}}$ is the detonation pressure calculated by our program.

^{4}${\mathrm{P}}_{\mathrm{ref}}$ is the detonation pressure in the reference.

^{5}${\mathrm{D}}_{\mathrm{pro}}$ is the detonation velocity calculated by the program we wrote.

^{6}${\mathrm{D}}_{\mathrm{ref}}$ is the detonation velocity in the reference.

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**MDPI and ACS Style**

Pang, S.; Wang, F.
Novel All-Nitrogen Molecular Crystals Composed of Tetragonal N_{4} Molecules. *Int. J. Mol. Sci.* **2022**, *23*, 5503.
https://doi.org/10.3390/ijms23105503

**AMA Style**

Pang S, Wang F.
Novel All-Nitrogen Molecular Crystals Composed of Tetragonal N_{4} Molecules. *International Journal of Molecular Sciences*. 2022; 23(10):5503.
https://doi.org/10.3390/ijms23105503

**Chicago/Turabian Style**

Pang, Suna, and Feng Wang.
2022. "Novel All-Nitrogen Molecular Crystals Composed of Tetragonal N_{4} Molecules" *International Journal of Molecular Sciences* 23, no. 10: 5503.
https://doi.org/10.3390/ijms23105503