Predicted Pressure-Induced High-Energy-Density Iron Pentazolate Salts

Chuli Sun(孙矗丽)$^{2}$, Wei Guo(郭伟)$^{1,2,3\hyperlink{s}{*}}$, and Yugui Yao(姚裕贵)$^{1,2,3}$

doi:10.1088/0256-307X/39/8/087101

⇦Chinese Physics Letters, 2022, Vol. 39, No. 8, Article code 087101⇨ Predicted Pressure-Induced High-Energy-Density Iron Pentazolate Salts Chuli Sun (孙矗丽)2, Wei Guo (郭伟)1,2,3*, and Yugui Yao (姚裕贵)1,2,3 Affiliations 1Frontiers Science Center for High Energy Material (MOE), Beijing Institute of Technology, Beijing 100081, China 2Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China 3State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China Received 26 April 2022; accepted manuscript online 6 July 2022; published online 18 July 2022 ^*Corresponding author. Email: weiguo7@bit.edu.cn Citation Text: Sun C L, Guo W, and Yao Y G 2022 Chin. Phys. Lett. 39 087101 Abstract Metal-pentazolate compounds as candidates for novel high-energy-density materials have attracted extensive attention in recent years. However, dehydrated pentazolate salts of transition metal iron are rarely reported. We predict two new iron pentazolate salts $Fdd2$-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ using a constrained crystal search method based on first-principles calculations. We propose that the stable $Fdd2$-FeN$_{10}$ crystal may be synthesized from FeN and N$_{2}$ above 20 GPa, and its formation enthalpy is lower than the reported iron pentazolate salt (marked as $P\bar{1}$(No.2)-FeN$_{10}$). Crystal $P\bar{1}$(No.1)-FeN$_{10}$ is composed of iron bispentazole molecules. Formation enthalpy, phonon spectrum and ab initio molecular dynamics calculations are performed to show their thermodynamic, mechanical and dynamic properties. Moreover, the high energy density (3.709 kJ/g, 6.349 kJ/g) and good explosive performance indicate their potential applications as high-energy-density materials.

DOI:10.1088/0256-307X/39/8/087101 © 2022 Chinese Physics Society Article Text Dinitrogen is one of the most inert gases under ambient conditions due to its strong bond energy (N$\equiv$N, $\sim $954 kJ/mol), while the bond energy of N–N ($\sim $160 kJ/mol) or N=N ($\sim $418 kJ/mol) is weaker. Therefore, a large amount of energy is released when a single bond (double bond) transforms into a triple bond. Polymeric nitrogen containing single or double bonds has been extensively studied by researchers as an eco-friendly new energetic material, among which the pentazolate anion (cyclo-N$_{5}^{-}$) has attracted wide attention due to its potential applications in high-energy-density materials (HEDM). Previous research achievements of pentazolate anion (cyclo-N$_{5}^{-}$) are mainly the synthesis of metal or metal-free pentazolate hydrates under ambient conditions, such as [Mg(H$_{2}$O)$_{6}$(N$_{5})_{2}$]$\cdot$4H$_{2}$O, [Na(H$_{2}$O)(N$_{5})_{2}$]$\cdot$2H$_{2}$O, [$M$(H$_{2}$O)$_{4}$(N$_{5})_{2}$]$\cdot$4H$_{2}$O ($M$ = Fe, Co, Zn) and (N$_{5})_{6}$(H$_{3}$O)$_{3}$(NH$_{4})_{4}$Cl.[1-4] However, the non-energetic groups (H$_{2}$O and Cl) reduce the nitrogen content, energy density and explosive properties of those complexes, making them less interesting in terms of performance. Therefore, the design of stable pentazolate salts that contains fewer non-energetic groups has become a hot-spot in HEDM. In recent years, pentazolate salts containing alkali metals, alkaline earth metals, trivalent metals and transition metals have been discovered through high-pressure experiments or theoretical predictions.[5-15] Transition metal element iron, as the second most common metal element in nature, has a moderate atomic mass and can also provide more electrons. However, the related research on dehydrated iron pentazolate salt is rarely reported. The coordination form of iron with the pentazolate anion (cyclo-N$_{5}^{-}$) and the energetics of iron pentazolate salts have intrigued us to investigate their potential synthesis condition, stability and detonation performance. In this work, through a constrained crystal search combined with density functional theory (DFT) calculations, we find two FeN$_{10}$ pentazolate salts at 40 GPa, i.e., Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$. Fdd2-FeN$_{10}$ is more energetically favorable than the reported iron pentazolate structure $P\bar{1}$(No.2)-FeN$_{10}$. Their stability is confirmed by formation enthalpies, phonon spectrum and ab initio molecular dynamics (AIMD) simulations. The research of electronic structure and energetics reveals that Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ are semiconductors and insulators with high energy density (3.709 kJ/g, 6.349 kJ/g), respectively. Moreover, their better explosive properties also make them good candidates in the field of high-energy powerful explosives. Computational Methods. Structural predictions were performed by the CALYPSO code, which is an efficient structure prediction method based on particle swarm optimization algorithm to achieve the global or local minimizations in the potential energy surface.[16-18] In our structure search, the cyclo-N$_{5}^{-}$ is constrained as a unit of the initial structure, and the stoichiometric Fe$_{2}$(N$_{5})_{4}$ is used to directly search for thermodynamically stable structures under 40 GPa. During the structure search, first-principles calculations were performed in the framework of DFT to obtain the total energy of the systems, as implemented in the Vienna ab initio simulation package (VASP).[19] The electron exchange-correlation effects were described by the Perdew–Burke–Ernzerhof generalized gradient approximation (GGA).[20] The projector-augmented wave method[21] was adopted, and 3$d^{7}4s^{1}$ and 2$s^{2}2p^{3}$ were treated as valence electrons of Fe and N, respectively. In structural optimization, a cut-off energy of 600 eV and a force convergence of 0.02 eV$\cdot$Å$^{-1}$ were set. Since the optimized ground state structures are non-magnetic, we did not consider the magnetic properties of iron pentazolate salts in subsequent calculations. Meanwhile, the van der Waals interaction was included by using the PBE-D3 method.[22] The effects of PBE-D3 and optB88-vdW[23] methods on crystal energy are shown in Fig. S1 of the Supplemental Material. In order to study the mechanical stability of the structure, phonon dispersion calculations were performed in the PHONOPY code using the density functional perturbation theory.[24] Ab initio molecular dynamics (AIMD) simulations with the NPT ensemble can reflect the dynamic stability of structures under different pressures and temperatures, in which $1 \times 1\times 2$ (176 atoms) and $3 \times 2\times 2$ (132 atoms) supercells of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ were used, respectively. The AIMD simulation time at each temperature was set to 10 ps with a step size of 1 fs. The formation enthalpy of iron pentazolate salts relative to solid Fe and N was calculated by the formula $\Delta H_{\rm f}=[{H(({\rm FeN}_{10})_{x})-xH({\rm Fe})-5xH({\rm N}_{2})}]/11x$ to characterize the thermodynamic stability of structures, in which bcc-Fe, hcp-Fe, $\alpha$-N$_{2}$, $P4_{1}2_{1}$2-N$_{2}$ and cg-N[25] are taken as the reference states in the corresponding pressures. Fe–N structures in Fig. 2(a) except the FeN$_{10}$ phase are obtained from the work of Jiao et al.,[26] and their enthalpies were recalculated in Fig. 2(a). Energy density is of great significance in the study of energetic materials. When (FeN$_{10})_{x}$ is decomposed into $F\bar{4}3m$-FeN[27] and dinitrogen gas under ambient conditions, the released energy density $E_{\rm d}$ was calculated by the following formula $E_{\rm d}=[{E(({\rm FeN}_{10})_{x})-E(x{\rm FeN})-E(\frac{9}{2}x{\rm N}_{2})}]/x(55.8+140)$, where the energy of dinitrogen gas is $\sim $0.25 eV/atom lower than $\alpha$-N$_{2}$.[11,28] Results and Discussion—Crystal Structures and Stability. Through the restrained crystal search, we focus on two FeN$_{10}$ compounds, namely Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$, as shown in Fig. 1. Their lattice parameters and atomic positions under ambient conditions can be seen in Table S1 of the Supplemental Material. From Fig. 1(a), we can see that each iron atom forms an octahedral configuration with its neighboring nitrogen atoms, and the N–N bond length of $\eta^{3}$-N$_{5}$ ring is around 1.32 Å, which is between the N–N single bond (1.45 Å) and the N=N double bond (1.25 Å). Here, $\eta^{n}$ shows the coordination mode of the cyclo-N$_{5}^{-}$ ligand and the metal atom, where $n$ represents the hapticity of the cyclo-N$_{5}^{-}$. Figure 1(b) shows a metallocene-like crystal structure with atomic coordination quite different from Fdd2-FeN$_{10}$, where each iron atom is located between two parallel N$_{5}$ rings, and the N–N bond length is $\sim $1.38 Å. The Fe–N bond length of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ is about 1.96–2.00 Å. Compared with the bond length of Fe–N in [Fe(H$_{2}$O)$_{4}$(N$_{5})_{2}$]$\cdot$4H$_{2}$O (2.17 Å),[4] Fe–N in the two compounds forms a stronger coordination bond. Meanwhile, we also find a crystal structure with space group $P\bar{1}$ which is denoted here as $P\bar{1}$(No.2)-FeN$_{10}$ (Fig. S2), whose local atomic coordination is similar to Fdd2-FeN$_{10}$, but their crystal structures are quite different. The $P\bar{1}$(No.2)-FeN$_{10}$ has also been reported by Huang et al.,[29] and its structural information can also be obtained in Table S1 of the Supplemental Material. The three pentazolate salts may undergo phase transition under certain conditions, but phase transition in solid is rather complicated. The LASP software developed by Liu et al. may attack this problem by a stochastic surface walking method to predict the crystal phase transition pathway,[30,31] and the research is beyond the scope of this work.

Fig. 1. The crystal structures of (a) Fdd2-FeN$_{10}$ and (b) $P\bar{1}$(No.1)-FeN$_{10}$ under ambient pressure. Fe–N and N–N bond lengths are shown in black and blue numbers, respectively.

Formation enthalpy can be used to evaluate the thermodynamic stability of crystal phases, where negative values represent exothermic formation of compounds from elements. Since Fdd2-FeN$_{10}$ is more energetically favorable than $P\bar{1}$(No.1)-FeN$_{10}$ and $P\bar{1}$(No.2)-FeN$_{10}$ (Fig. S1), we use Fdd2-FeN$_{10}$ for the calculation of formation enthalpy at the Fe:N ratio 1:10. As shown in Fig. 2(a), the convex hulls connect the stable phases by solid lines, and the dashed lines above the solid lines connect the metastable phases. The formation enthalpies of Fdd2-FeN$_{10}$ are located on the convex hulls at 30 GPa, 40 GPa, 60 GPa and 70 GPa, respectively, indicating the thermodynamic stability of Fdd2-FeN$_{10}$ under high pressure. Figure 2(b) shows that Fdd2-FeN$_{10}$ is still the most favorable phase in known FeN$_{10}$ in terms of energy relative to the FeN+4.5N$_{2}$ system, and it may be synthesized by $P6_{3}$/mmc-FeN and $P4_{1}2_{1}$2-N$_{2}$ overcoming a certain dynamic barrier at high temperature and $> 20$ GPa. So, we encourage experimental group to try to synthesize this high-nitrogen content metal nitride since 20 GPa is feasible in many high-pressure devices with large volume. In order to further evaluate the mechanical and dynamic stability of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$, phonon dispersion curves and AIMD simulations at 0 GPa and 40 GPa were performed. At 0 GPa, the calculated phonon spectra of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ are shown in Figs. 3(a) and 3(c), respectively. The results for $P\bar{1}$(No.2)-FeN$_{10}$ is also shown in Fig. S3(a) for comparison. The absence of imaginary phonon frequencies indicates their mechanical stability under ambient pressure. It is unsurprising that their mechanical stabilities are improved at 40 GPa, which can be seen in Figs. S4(a), S4(c) and S4(e) of the Supplemental Material.

Fig. 2. (a) Formation enthalpies of Fe$_{x}$N$_{y}$ phases with respect to elemental iron and nitrogen solids at different pressures. Except for the FeN$_{10}$ phase, the crystal structures at other ratios are from the work of Jiao et al.,[26] and their enthalpies are recalculated. The solid lines connect stable phases, and the dashed lines connect metastable phases. FeN$_{10}$ under different pressures remains Fdd2 symmetry, only the volume changes. (b) The enthalpy difference of Fdd2-FeN$_{10}$, $P\bar{1}$(No.1)-FeN$_{10}$ and $P\bar{1}$(No.2)-FeN$_{10}$ relative to the FeN+4.5N$_{2}$ system. $F\bar{4}3m$-FeN, $P6_{3}/mmc$-FeN,[26] $\alpha$-N$_{2}$, $P4_{1}2_{1}$2-N$_{2}$ and cg-N[25] are used in the corresponding pressures.

In AIMD simulations, 300 K is used as the initial temperature applied to the crystals, then the structures are heated at 200 K intervals to observe evolutions with increasing temperature. Figures 3(b) and 3(d) reveal that Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ can remain stable at about 900 K and 500 K, respectively, under ambient pressure for 10 ps. However, their structures lose stability when the temperature increases to 1000 K and 600 K, which is shown in Fig. S5 of the Supplemental Material. As the temperature rises, the Fe–N bond in Fdd2-FeN$_{10}$ breaks first, which is similar to the dynamic characteristics of LiN$_{5}$[32] and CuN$_{5}$.[13] However, the fracture mode of $P\bar{1}$(No.1)-FeN$_{10}$ is different, where the N$_{5}$ ring breaks first with increasing temperature, which is consistent with the pyrolysis mechanism proposed by Zhang et al.[33] Under high pressure, the stability of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ is greatly enhanced, and their dynamic stability temperatures are raised to $\sim $2500 K and $\sim $800 K, respectively.

Fig. 3. [(a), (c)] Phonon dispersion curves of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ at 0 GPa. [(b), (d)] Total free energy fluctuations of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ in AIMD simulations. Here, 900 K and 500 K are the highest temperature at which Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ can remain stable at ambient pressure respectively, and the illustrations show their structural snapshots after 10 ps.

Fig. 4. [(a), (b)] Electron localization function and Bader charge of Fdd2-FeN$_{10}$ at 0 GPa, respectively. [(c), (d)] Electron localization function and Bader charge of $P\bar{1}$(No.1)-FeN$_{10}$ at 0 GPa, respectively.

Bond Characteristics. In Order to study the bond characteristics of crystal structures, we calculate and analyze their electron localization function (ELF), charge distribution, and crystal orbital Hamilton population (COHP). The ELF can clearly show their bonding properties, in which the color indicates the possibility of detecting localized electrons. As the color bar changes from blue to red, the detected electrons are more localized. As shown in Figs. 4(a) and 4(c), we can see that there is a strong covalent bond between N atoms in cyclo-N$_{5}^{-}$, and a coordination bond between Fe–N of Fdd2-FeN$_{10}$. The coordination bond is a special covalent bond in which the shared electron pair and empty orbital are provided by N atoms and Fe atoms, respectively. Furthermore, we can also see lone-pair electrons existing at the vertex of the pentagon in cyclo-N$_{5}^{-}$. The metal cation and cyclo-N$_{5}^{-}$ of $P\bar{1}$(No.1)-FeN$_{10}$ involve a $\pi$-bond, about half ionic and half covalent, which has been widely reported in the study of iron bispentazole molecule Fe($\eta^{5}$-N$_{5})_{2}$.[34-36] Bader charge analysis[37] is used to measure the charge transfer. As shown in Figs. 4(b) and 4(d), iron atoms donate electrons to nitrogen atoms, where the iron atoms in Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ have about 1.20$e$ and 1.10$e$ transferred to two N$_{5}$ rings, respectively. Moreover, the charge distribution on each N atom in the cyclo-N$_{5}^{-}$ of $P\bar{1}$(No.1)-FeN$_{10}$ is more homogeneous than that of Fdd2-FeN$_{10}$, indicating that the aromaticity of N$_{5}$ rings in $P\bar{1}$(No.1)-FeN$_{10}$ is less disturbed.

Fig. 5. [(a), (b)] Projected COHP (pCOHP) curves and density of states (DOS) of Fe–N and N–N bonds in Fdd2-FeN$_{10}$. [(c), (d)] Projected COHP (pCOHP) curves and density of states (DOS) of Fe–N and N–N bonds in $P\bar{1}$(No.1)-FeN$_{10}$. ICOHP denotes integrated COHP.

The COHP[38] can quantitatively characterize the bonding strength of Fe–N and N–N bonds, which is implemented in the LOBSTER program.[39] The –pCOHP (negative projected COHP) is usually employed, with a positive value indicating a bonding state, and a negative value indicating an antibonding state. As shown in Fig. 5, the –pCOHP curves show that the occupied states of Fe–N and N–N bonds in Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ are mainly bonding states, only a few occupied states of N–N bonds exist on antibonding orbitals, and the p-wave electrons of nitrogen contribute to the strong covalent bond in cyclo-N$_{5}^{-}$. In addition, we also calculate the integrated COHP (ICOHP), which is the energy integral up to the highest occupied energy level. The larger the -ICOHP, the stronger the covalent bonding. From the ICOHP values, we can see that the Fe–N and N–N bonds in Fdd2-FeN$_{10}$ have a stronger chemical bond than the corresponding bonds in $P\bar{1}$(No.1)-FeN$_{10}$. Also, the –ICOHP of N–N bond in Fdd2-FeN$_{10}$ is much larger than the Fe–N bond, indicating that the chemical bond of N–N is stronger, which verifies the result of dynamics simulation. Although the –ICOHP of a single Fe–N bond in $P\bar{1}$(No.1)-FeN$_{10}$ is relatively small, the Fe–N bond is not easy to break due to its unique coordination mode, which is also consistent with the MD simulation. Electronic Structures. Electronic property is essential for the characterization of materials. Here we first focus on electronic band structures and density of states (DOS) of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$. From Fig. 6, we can see that Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ show semiconducting nature under ambient pressure with band gaps of 1.592 and 2.192 eV, respectively. Moreover, the partial density of states (pDOS) and partial charges (Fig. S6) intuitively show that the valence band maximum (VBM) and the conduction band minimum (CBM) of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ are mainly contributed by $d$ state of Fe atoms. The distribution of electronic states is mainly related to the atomic coordination mode in the crystal structure. Under the action of crystal field, due to the negative charge of the N atom, all $d$ electrons are subject to its Coulomb repulsion, resulting in the splitting of degenerate electronic states in the $d$ level. As shown in Fig. S7, the octahedral configuration formed by central ion Fe and neighboring N atoms in Fdd2-FeN$_{10}$ makes the VBM mainly composed of $dz^{2}$ and $dx^{2}-y^{2}$ electrons, while the CBM mainly from the dyz orbital of Fe atoms. The VBM of $P\bar{1}$(No.1)-FeN$_{10}$ is mainly contributed by the $dz^{2}$ state, and the CBM is mainly derived from the dyz and dxz orbitals. It is worth noting that GGA or LDA functionals usually underestimate the band gap, while the GW method[40] has a more reliable description of the band gap of semiconductors and insulators.[41,42] The band gaps of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ are calculated to be 2.573 and 4.913 eV using the GW method, so $P\bar{1}$(No.1)-FeN$_{10}$ should exhibit insulating behavior under ambient pressure. Meanwhile, the pressure dependence of band gaps is also an important electronic property. The band gap of $P\bar{1}$(No.1)-FeN$_{10}$ decreases as the pressure increases, and the pDOS can be seen in Fig. S8 of the Supplemental Material. Significantly, the band gap of Fdd2-FeN$_{10}$ increases with the compression at 0–10 GPa. By comparing and analyzing the pDOS of Fdd2-FeN$_{10}$ under different pressures [Fig. 7(b)], we infer that the enhanced coupling between Fe–N and the covalency of N atoms lead to the enhancement of electronic localization, which in turn leads to an increase in the band gap at 0–10 GPa. The trend of band gap increasing with compression is also found in the NeN$_{10}$ and NeN$_{22}$ systems.[43] The pDOS of Fdd2-FeN$_{10}$ at 20–100 GPa are also included in Fig. S9 of the Supplemental Material.

Fig. 6. (a) Band structures and the partial density of states of Fdd2-FeN$_{10}$ at 0 GPa. (b) Band structures and the partial density of states of $P\bar{1}$(No.1)-FeN$_{10}$ at 0 GPa.

Explosive Performance. For energetic materials, energy density and detonation properties are key parameters to characterize their performance. As shown in Table 1, when the decomposition products of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ are FeN and N$_{2}$(g) under ambient conditions, their energy densities $E_{\rm d}$ are calculated to be 3.709 kJ/g and 6.349 kJ/g, respectively, and the value of $P\bar{1}$(No.1)-FeN$_{10}$ exceeds the standard energetic material TNT (2,4,6-trinitrotoluene) and HMX (cyclotetramethylene tetranitramine).[27] In addition, the calculated gravimetric energy densities $\rho$ (3.211 g/cm$^{3}$, 2.197 g/cm$^{3}$) are also higher than TNT and HMX.[44] Detonation velocity and detonation pressure are two important parameters for designing high-performance explosives. Therefore, we calculate the detonation velocity $D$ and detonation pressure $P$ of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ through the popular empirical Kamlet–Jacobs equations.[44] In the formulas $D=1.01(NM^{0.5}E_{\rm d}^{0.5})^{0.5}(1+1.30\rho)$ and $P=15.58\rho^{2}NM^{0.5}E_{\rm d}^{0.5}$, $N$ is the moles of gas produced per gram of compounds, and $M$ is the molar mass of gas products. Table 1 shows that the detonation velocity (14.220 km/s, 12.119 km/s) and detonation pressure (1189.372 kbar, 728.108 kbar) of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ are much higher than those of HMX and TNT,[10,11,44] and the $D$ and $P$ of Fdd2-FeN$_{10}$ are even about 2–3 times of TNT and HMX, indicating the potential applications of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ in high explosives.

Fig. 7. (a) Pressure dependence of electronic band gaps. (b) Partial density of states of Fdd2-FeN$_{10}$ at 0 GPa and 10 GPa, respectively.

**Table 1.** Detonation properties of *Fdd*2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$. The reported values of TNT and HMX serve as a comparison. The results are calculated with the Kamlet–Jacobs equations.
Compounds	$E_{\rm d}$ (kJ/g)	$\rho$ (g/cm$^{3}$)	$D$ (km/s)	$P$ (kbar)
Fdd2-FeN$_{10}$	3.709	3.211	14.220	1189.372
$P\bar{1}$(No.1)-FeN$_{10}$	6.349	2.197	12.119	728.108
TNT	4.30	1.64	6.90	190
HMX	5.70	1.90	9.10	393

In summary, through the combination of first-principles calculations and a molecular crystal search method, we find two new iron pentazolate salts, namely Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$. The energy density (3.709 kJ/g) of Fdd2-FeN$_{10}$ with the lowest enthalpy is close to TNT, while the energy density of $P\bar{1}$(No.1)-FeN$_{10}$ is as high as 6.349 kJ/g, which exceeds that of HMX. Formation enthalpy and phonon spectrum indicate the thermodynamic and mechanical stability of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$, and Fdd2-FeN$_{10}$ may have a relatively low synthesis pressure ($\sim $20 GPa). AIMD simulations demonstrate that the two compounds can maintain stable within 10 ps under ambient conditions. Meanwhile, the research of electronic properties reveals semiconducting and insulating behavior of Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$. In addition, Fdd2-FeN$_{10}$ and $P\bar{1}$(No.1)-FeN$_{10}$ also show good explosive performance, indicating their potential application prospects in the field of high-energy explosions. This work not only predicts a more stable dehydrated iron pentazolate salt, but also explores the crystal structure of iron bispentazole, providing a reference for subsequent experimental and theoretical works. Acknowledgments. This work was supported by the National Natural Science Foundation of China (Grant No. 51971037), and the National Key Research and Development Program of China (Grant No. 2017YFB0701603). We gratefully acknowledge HZWTECH for providing computation facilities. References A series of energetic metal pentazolate hydratesSynthesis and characterization of the pentazolate anion cyclo -N₅ ˉ in (N₅ )₆ (H₃ O)₃ (NH₄ )₄ ClA Symmetric Co(N₅ )₂ (H₂ O)₄ ⋅4 H₂ O High-Nitrogen Compound Formed by Cobalt(II) Cation Trapping of a Cyclo-N₅⁻ AnionDual Functions of Water in Stabilizing Metal-Pentazolate Hydrates [M(N₅ )₂ (H₂ O)₄ ]·4H₂ O (M = Mn, Fe, Co, and Zn) High-Energy-Density MaterialsCrystalline LiN₅ Predicted from First-Principles as a Possible High-Energy MaterialSodium pentazolate: A nitrogen rich high energy density materialHigh-Pressure Synthesis of a Pentazolate SaltHigh-Pressure Synthesized Lithium Pentazolate Compound Metastable under Ambient ConditionsSimple Route to Metal cyclo -N₅^– Salt: High-Pressure Synthesis of CuN₅Predictions on High-Power Trivalent Metal Pentazolate SaltsPressure-Stabilized High-Energy-Density Alkaline-Earth-Metal Pentazolate SaltsModerate Pressure Stabilized Pentazolate Cyclo-N₅^– Anion in Zn(N₅ )₂ SaltStabilization of the High-Energy-Density CuN₅ Salts under Ambient Conditions by a Ligand EffectPacking high-energy together: Binding the power of pentazolate and high-valence metals with strong bondsHigh-energy-density pentazolate salts: CaN10 and BaN10Crystal structure prediction via particle-swarm optimizationCALYPSO: A method for crystal structure predictionCALYPSO structure prediction method and its wide applicationEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setGeneralized Gradient Approximation Made SimpleProjector augmented-wave methodEffect of the damping function in dispersion corrected density functional theoryChemical accuracy for the van der Waals density functionalFirst principles phonon calculations in materials scienceHigh-Pressure Phases of NitrogenHigh-Pressure FeN _x : Stability, Phase Transition, and Energetic CharacteristicCrystal structure and magnetic properties of the compound FeNPressure-stabilized hafnium nitrides and their propertiesPredicted Polymeric and Layered Covalent Networks in Transition Metal Pentazolate M( cyclo -N₅ ) _x Phases at Ambient and High Pressure: Up to 20 Nitrogen Atoms per MetalLASP: Fast global potential energy surface explorationStochastic surface walking method for crystal structure and phase transition pathway predictionCrystalline Structures and Energetic Properties of Lithium Pentazolate under Ambient ConditionsTheoretical studies on stability and pyrolysis mechanism of salts formed by N5 − and metallic cations Na+, Fe2+ and Ni2+Review of the Current Synthesis and Properties of Energetic Pentazolate and Derivatives ThereofIron Bispentazole Fe(η5-N5)2, a Theoretically Predicted High-Energy Compound: Structure, Bonding Analysis, Metal-Ligand Bond Strength and a Comparison with the Isoelectronic FerroceneUnderstanding the nature of the bonding in transition metal complexes: from Dewar's molecular orbital model to an energy partitioning analysis of the metal–ligand bondImproved grid-based algorithm for Bader charge allocationCrystal Orbital Hamilton Population (COHP) Analysis As Projected from Plane-Wave Basis SetsLOBSTER: A tool to extract chemical bonding from plane-wave based DFTNew Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas ProblemSelf-consistent

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