⇦Chinese Physics Letters, 2022, Vol. 39, No. 5, Article code 056102Express Letter Pressure-Driven Ne-Bearing Polynitrides with Ultrahigh Energy Density Lulu Liu (刘璐璐)1,2, Shoutao Zhang (张守涛)3*, and Haijun Zhang (张海军)1,2* Affiliations 1National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China 2Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China 3Centre for Advanced Optoelectronic Functional Materials Research and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China Received 23 March 2022; accepted 15 April 2022; published online 23 April 2022 *Corresponding authors. Email: zhanghj@nju.edu.cn; zhangst966@nenu.edu.cn Citation Text: Liu L L, Zhang S T, and Zhang H J 2022 Chin. Phys. Lett. 39 056102    Abstract Neon (Ne) can reveal the evolution of planets, and nitrogen (N) is the most abundant element in the Earth's atmosphere. Considering the inertness of neon, whether nitrogen and neon can react has aroused great interest in condensed matter physics and space science. Here, we identify three new Ne–N compounds (i.e., NeN$_6$, NeN$_{10}$, and NeN$_{22}$) under pressure by first-principles calculations. We find that inserting Ne into N$_2$ substantially decreases the polymeric pressure of the nitrogen and promotes the formation of abundant polynitrogen structures. Especially, NeN$_{22}$ acquires a duplex host-guest structure, in which guest atoms (Ne and N$_2$ dimers) are trapped inside the crystalline host N$_{20}$ cages. Importantly, both NeN$_{10}$ and NeN$_{22}$ not only are dynamically and mechanically stable but also have a high thermal stability up to 500 K under ambient pressure. Moreover, ultra-high energy densities are obtained in NeN$_{10}$ (11.1 kJ/g), NeN$_{22}$ (11.5 kJ/g), tetragonal t-N$_{22}$ (11.6 kJ/g), and t-N$_{20}$ (12.0 kJ/g) produced from NeN$_{22}$, which are more than twice the value of trinitrotoluene (TNT). Meanwhile, their explosive performance is superior to that of TNT. Therefore, NeN$_{10}$, NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ are promising green high-energy-density materials. This work promotes the study of neon-nitrogen compounds with superior properties and potential applications.
cpl-39-5-056102-fig1.png
cpl-39-5-056102-fig2.png
cpl-39-5-056102-fig3.png
cpl-39-5-056102-fig4.png
 DOI:10.1088/0256-307X/39/5/056102 © 2022 Chinese Physics Society Article Text Exploring the behavior of inert elements including He, Ne, Ar, Kr, and Xe is the key to understanding the formation and evolution of planets.[1,2] These inert elements generally exist in gaseous form since they have typical closed-shell structures and can hardly react with other elements or compounds under ambient conditions. However, Dong et al. have successfully synthesized a stable Na$_2$He compound under high pressure.[3] Recently, many theoretical works reported that the inert gas may react with other elements or compounds under high-pressure conditions (such as iron,[4] iron peroxide,[5] alkali metal oxide, sulfide compound,[6] alkaline earth metal fluoride,[7] or H$_2$O[8–11]), which indicate that inert-element-stored compounds may exist in the planet's interior. Moreover, these compounds exhibit interesting properties, such as plastic and superionic states, which lead to potential applications in materials science.[8–11] Thus, an increasing number of theoretical and experimental studies have been committed to investigating the compounds with inert elements.[12–15] Nitrogen is the most abundant element in the Earth's atmosphere and exists as the stable gaseous form of N$_2$ molecules with the strong triple N bond (N$\equiv$N) under ambient conditions. Because of the energy difference between a single bond ($\sim $160 kJ/mol) and a triple bond ($\sim $1 MJ/mol),[16] it is difficult to convert N$_2$ molecules into polymeric nitrogen. On the other hand, polynitrogens with N–N single bonds can produce a large amount of energy and N$_2$ when they are thermally decomposed. Meanwhile, the rapid release of N$_2$ causes high pressure. Therefore, polynitrogens with N–N single bonds as high-energy-density materials may have important potential applications for military, industry, and engineering,[17,18] and have become a hot spot in the field of new green energy sources. Numerous efforts have been made to obtain polymeric nitrogen. The single-bonded cubic gauche phase (cg-N) of nitrogen was first predicted,[19] and then was confirmed by experiments using laser-heated diamond anvil cells at a temperature above 2000 K and under the pressure above 110 GPa.[20] Subsequent works also reported various polynitrogens under high-pressure conditions, such as layered $Pba2$,[21] cage-like diamond N$_{10}$,[22] metallic $P4/nbm$ nitrogen,[23] single-bonded nitrogen,[24] and black-phosphorus-structure polynitrogen.[25,26] However, synthesizing these polynitrogens require extremely high pressure and some are thermally metastable under ambient conditions. So far, much attention has been focused on the lower-pressure limits of thermodynamic stability of metal nitrides.[27–32] Unfortunately, these metal nitrides do not contain pure nitrogen covalent bonds, but a mixture of ionic bonds and nitrogen covalent bonds. The result is that the energy density is not enough high for industrial applications. A remarkable observation is that inserting noble elements into the nitrogen system can significantly change the long-range Coulomb interactions and reduce the synthesis pressure of polynitrogen compounds.[7] For instance, solid van der Waals (vdW) compound He(N$_2$)$_{11}$ was synthesized under a low pressure (9 GPa) at room temperature.[33] Thereafter, many inert elements-nitrogen compounds with high-energy densities have been predicted, including HeN$_4$,[34] HeN$_{10}$,[35] and XeN$_6$.[15] As an important member of inert elements, Ne atoms not only can trace the internal evolution of stars and the formation of solar nebulae,[2] but also have an electronic structure similar to nitrogen, which allows Ne atoms to possibly occupy vacancies in the nitrogen polymer network. The solid vdW compound (N$_2$)$_6$Ne$_7$ with guest-host structure was successfully synthesized at the room temperature and at pressure of 8 GPa,[36] but not found to contain polymeric nitrogen. It is still uncertain whether Ne and N can form new compounds with polymeric nitrogen under pressure. In this work, to search for Ne-containing polynitrides, we systematically explored the Ne–N system under pressure via swarm-intelligence structure search. Three new Ne–N compounds with polymeric nitrogen are found: $R\bar{3}m$ NeN$_{6}$, $P6_3/m$ NeN$_{10}$, and $I4/m$ NeN$_{22}$. The ab initio molecular dynamics (AIMD) simulations and phonon spectra indicate that $P6_3/m$ NeN$_{10}$ and $I4/m$ NeN$_{22}$ are mechanically and dynamically stable above 500 K under the ambient pressure. In particular, after removal of Ne or Ne and N$_2$ dimers from NeN$_{22}$, the unique pure tetragonal polymeric nitrogen structures, t-N$_{22}$ and t-N$_{20}$ are obtained, and they are dynamically and thermally stable upon decompression to the ambient pressure. Remarkably, the energy densities of $P6_3/m$ NeN$_{10}$, $I4/m$ NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ are found to be 11.1, 11.5, 11.6, and 12.0 kJ/g, respectively, indicating that they are promising high-energy-density materials. Calculation Details. For the crystal structure search, we employed the unbiased swarm intelligence structure prediction method as implemented in the CALYPSO code.[37,38] Its validity has been widely confirmed by a variety of systems, from element solids to binary and ternary compounds.[39–42] Structural optimizations and electronic property calculations were performed in the framework of the density functional theory within the Perdew–Burke–Ernzerhof (PBE)[43] of generalized gradient approximation[43] as implemented in the VASP package.[44] The PBE functional was applied to all the calculations, and we have optimized the NeN$_{22}$ at 1 atm with the local-density-approximation functional. The resulting lattice parameters of NeN$_{22}$ are $a = b = c = 6.0054$ Å, which are smaller than those ($a = b = c = 6.0869$ Å) calculated using the PBE exchange-correlation functional. The electron-ion interaction was described by means of the all-electron projector augmented wave (PAW)[45] with $2s^22p^6$ and $2s^22p^3$ valence electrons for Ne and N atoms, respectively. A kinetic-energy cutoff of 750 eV and a Monkhorst–Pack scheme[46] with a $k$-point grid of $2\pi \times 0.03$ Å$^{-1}$ were adopted to ensure that total energy calculations converged to less than 1 meV per atom. To verify the dynamical stability of predicted structures, we carried out the phonon calculations via the finite displacement approach[47] as performed in the Phonopy code.[48] The vdW interactions are also taken into consideration by using DFT-D3 functional[49,50] in VASP. Using AIMD within the NPT ensemble with a Langevin thermostat.[51] The AIMD simulations were carried out within the $2 \times 2 \times 2$ (176 atoms), $2 \times 2 \times 1$ (184 atoms), $2 \times 2 \times 1$ (176 atoms), and $2 \times 2 \times 1$ (160 atoms) supercells for NeN$_{10}$, NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$, respectively. AIMD simulation lasted for 7 ps with a time step of 1.0 fs, and the equilibrium structures were obtained from the last step of AIMD simulations. The electron localization function (ELF) was utilized to measure the degree of electron localization.[52] Crystal orbital Hamilton populations (COHPs)[53] as implemented in the LOBSTER program[54] was used to quantitatively characterize the chemical bonding properties. The noncovalent interactions (NCIs) in molecular structures were analyzed by the CRITIC2 code.[55,56] The steric NCIs are visualized through the Visual Molecular Dynamics software.[57] Results and Discussion. To determine the stable Ne–N phases, we focus on nitrogen-rich NeN$_x$ ($x = 1$–10, 22) compounds and perform structure search at 1 atm, 50 GPa, and 100 GPa. It has been shown that nitrides containing noble elements can be stabilized under high pressure mainly due to the participation of the vdW effects.[34,35] Therefore, the vdW interactions are also considered to calculate the formation enthalpies of each NeN$_x$ structure with the lowest enthalpy at the corresponding pressure, where the formation enthalpy $\Delta H$ is defined as $$ \Delta H({\rm NeN}_x) = [H({\rm NeN}_x) - H({\rm Ne}) - xH({\rm N})]/(1 + x).~~ \tag {1} $$ Here, $H = U + PV$ is the enthalpy of each composition with $U$, $P$, and $V$ being internal energy, pressure, and volume, respectively; $H$(NeN$_x$) is the enthalpy per formula unit of NeN$_x$; $H$(Ne) and $H$(N) represent the enthalpy per atom of elemental Ne and N, respectively; $\alpha$-nitrogen and $P4_12_1$2 structures are used for pure nitrogen.[58,59] Meanwhile, $Fm\bar{3}m$ Ne as a reference phase is taken for the computation of formation enthalpy.[60] Then, the resulting $\Delta H$ of each NeN$_x$ at selected pressure is used to build the convex hull as shown in Fig. 1(a). The thermodynamically stable compounds are located on the convex hull (solid lines), whereas compounds lying on the dotted lines are energetically unstable. According to the convex hulls shown in Fig. 1(a) and the pressure-composition phase diagram illustrated in Fig. 1(b), we found three new stable phases: $R\bar{3}m$ NeN$_{6}$, $P6_3/m$ NeN$_{10}$, and $I4/m$ NeN$_{22}$. At 1 atm, there are no compounds showing negative formation enthalpies with respect to the mixture of Ne and N$_2$. With an increase in pressure, NeN$_{6}$ is found to be stable at 69 GPa. As pressure further increases, NeN$_{10}$ becomes energetically more favorable than NeN$_{6}$ or Ne and N$_2$ mixtures above 70 GPa, as shown in Fig. S1 in the Supporting Information. For the stoichiometry NeN$_{22}$ with the highest N content, it becomes thermodynamic stable at a higher pressure of 76 GPa, as shown in the inset of Fig. 1(b). In addition, it should be mentioned that (N$_2$)$_6$Ne$_7$ was successfully synthesized under high pressure,[36] which offers the possibility of synthesizing our predicted Ne–N phases.
cpl-39-5-056102-fig1.png
Fig. 1. (a) Convex hulls for formation enthalpies ($\Delta H$, with respect to pure Neon and pure nitrogen) calculated by considering the DFT-D3 functional under different pressures of 1 atm, 50 GPa, and 100 GPa. (b) Pressure-composition phase diagram of the Ne–N compounds up to 100 GPa. The inset in (b) shows the enthalpy differences of $I4/m$ NeN$_{22}$ relative to the mixtures of $R\bar{3}m$ NeN$_{6}$, $P6_3/m$ NeN$_{10}$, or Neon and nitrogen.
NeN$_{6}$ is predicted to stabilize into a hexagonal structure with $R\bar{3}m$ symmetry [Fig. 2(a)]. In this structure, all nitrogen atoms have the equivalent 18$h$ Wyckoff position. More interestingly, a planar N$_6$ ring with a bond length of 1.32 Å at 100 GPa appears in the structure. These nitrogen hexagons are connected through six N–N bonds with a distance of 1.43 Å and further makeup of the nitrogen network. In contrast, Ne atoms reside in the center of the hexagonal nitrogen unit. Further electron localization function calculation of NeN$_{6}$ shows that each nitrogen has a pair of lone electrons, and the electron localization around each N atom is stronger than that of the N–N covalent bond [Fig. S2(a)].
cpl-39-5-056102-fig2.png
Fig. 2. Crystal structures of Ne–N compounds. (a) $R\bar{3}m$ NeN$_6$ at 100 GPa. (b) $P6_3/m$ NeN$_{10}$ at 100 GPa. (c) $I4/m$ NeN$_{22}$ at 100 GPa. Host N$_{20}$ consists of a sublattice with $I4/m$ symmetry. Guest Ne atoms constitute a sublattice with space group $I4/mmm$. Guest Ne and N$_2$ dimers are located in the channel of the host N$_{20}$ structure. (d) The host $I4/m$ N$_{20}$ in $I4/m$ NeN$_{22}$.
More N-rich NeN$_{10}$ has a hexagonal structure with space group $P6_3/m$ [Fig. 2(b)], in which N atoms have three inequivalent Wyckoff positions (2$d$, 6$h$, and 12$i$). Each nitrogen atom is located in a tetrahedron formed by three N atoms. Two kinds of nitrogen-nitrogen distances of 1.30 and 1.34 Å are found in the NeN$_{10}$ structure at 100 GPa, which are between the N–N single bond (1.45 Å) and N=N double bond (1.25 Å). Due to the different bond lengths, the N atoms constitute the highly distorted N$_{10}$ rings. Notably, each of the six N$_{10}$ rings contributes one bond with a bond length of 1.30 Å to form a regular hexagon (N$_6$) in the plane. Furthermore, the bonding feature of the N$_6$ is further supported by the ELF within the (001) plane (Fig. S2). It is noted that each N in N$_6$ hexagons have one lone pair of electrons, which reveals that the N$_6$ has six $\sigma$ bonds in the $sp^2$ hybridization state. In addition, some of the N atoms in NeN$_{10}$ show the $sp^3$ hybridizations or lone pair distribution [Fig. S3(a)]. Moreover, the Ne atoms are interspersed in the framework of N atoms. Such a structural character effectively increases the stability of the NeN$_{10}$ structure. NeN$_{22}$, having the highest N content among the predicted Ne–N phases, is a tetragonal host-guest structure with space group $I4/m$ [Fig. 2(c)]. $I4/m$ NeN$_{22}$ consists of $I4/mmm$ Ne and $I4/m$ N sublattices, in which guest atoms (Ne) occupy the 2$a$ position of the sublattice with $I4/mmm$ symmetry, whereas N atoms constituting guest N$_2$ and host N$_{20}$ occupy four inequivalent Wyckoff positions ($8h$, $8e$, $16i$, and $16i$) of N sublattice with space group $I4/m$ N$_{22}$ named t-N$_{22}$, Interestingly, the obtained host N$_{20}$ structure from NeN$_{22}$, termed t-N$_{20}$, still maintains the symmetry of $I4/m$ by removing both Ne and N$_{2}$. Notably, t-N$_{20}$ has a channel parallel to the $c$ crystallographic axis [Fig. 2(d)]. In the NeN$_{22}$, N$_2$ dimers are symmetrically equivalent. In addition, the bond length in the N$_2$ is about 1.10 Å, which is similar to that of a triple bond in $\epsilon$-N$_2$.[58,59] Each atom of N$_{20}$ bonded to the other three N atoms with the distance of 1.33–1.35 Å in the polyatomic network structure. The nearest neighboring Ne and N atoms have distance of approximately 2.08 Å, while the shortest distance between the N$_2$ dimer and the t-N$_{20}$ is about 2.20 Å. The exotic t-N$_{20}$ framework connects with the surface of irregular N$_{12}$ and N$_{10}$ rings. N$_{12}$ rings with channels parallel to the $c$-axis, while the bond of the N$_2$ dimers is also parallel to the $c$-axis. Such a structural character is conducive to the separation of Ne atoms and N$_2$ from the channel without destroying the N$_{22}$ frame structure. Because the experiments show that guests may be sufficiently removed to leave behind metastable empty clathrates,[14,61] guest-free Si,Ge-clathrates, and H$_2$O have indeed been obtained.[9,62,63] Based on the work reported previously, we can not only obtain t-N$_{22}$ by removing guest Ne, but also acquire t-N$_{20}$ via the removal of guest Ne and the N$_2$ dimer from the natural pores of NeN$_{22}$. We have optimized the pure tetragonal polymeric nitrogen structures t-N$_{22}$ and t-N$_{20}$ at 1 atm. The final lattice constants of t-N$_{22}$ and t-N$_{20}$ are $a = b = c = 6.0183$ Å and $a = b = c = 5.9487$ Å, respectively, which are smaller than the lattice constants ($a = b = c = 6.0869$ Å) of the NeN$_{22}$ at 1 atm. The lattice constants of t-N$_{22}$ and t-N$_{20}$ are only about 1% and 2% smaller than that of Ne$_{22}$, respectively. Therefore, the removal of the guest atom from NeN$_{22}$ results in a slight change in the lattice constant. We also observed the effect of pressure on the lattice by calculating the pressure-dependent lattice constants of NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ (Fig. S4). The results show that the lattice constants of NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ gradually decrease with increasing pressure. The lattice constants of t-N$_{22}$ and t-N$_{20}$ are smaller than that of NeN$_{22}$ at high pressure. The ELF shows that NeN$_{22}$ also has lone pairs [Fig. S3(b)]. Overall, they show increased polymerization characteristics with increasing N content. More structural details are listed in Table S1. These nitrogen-rich $P6_3/m$ NeN$_{10}$ and $I4/m$ NeN$_{22}$ with peculiar structures further motivate us to explore their mechanical properties. Based on the Born stability criteria,[64] the calculated elastic constants via the stress-strain approach[65] of hexagonal $P6_3/m$ NeN$_{10}$ and tetragonal $I4/m$ NeN$_{22}$ verify that they are mechanically stable at ambient pressure (Table S2). Furthermore, their bulk modulus $B$, shear modulus $G$, Young's modulus $E$, and Poisson's ratio $\nu$ are calculated using the Voigt–Reuss–Hill approximation.[66] As shown in Table S2, both $P6_3/m$ NeN$_{10}$ and $I4/m$ NeN$_{22}$ have large bulk modulus, shear modulus, Young's modulus, and low Poisson's ratio, indicating that they are stiff materials. Interestingly, based on Gao's model.[67] the Vickers hardness of $P6_3/m$ NeN$_{10}$ is estimated to be 31.3 GPa, which is larger than the high-hardness standard (30 GPa).[68] This result implies that NeN$_{10}$ is also a promising candidate of high-hardness materials. In contrast, the hardness of $I4/m$ NeN$_{22}$ (26.4 GPa) is slightly lower than that of $P6_3/m$ NeN$_{10}$. We analyzed the dynamic stabilities of NeN$_{10}$ and NeN$_{22}$ by calculating their phonon spectra at 1 atm [Figs. 3(a) and 3(b)]. Interestingly, there are no negative phonon frequencies below 0 THz in the respective Brillouin zones of NeN$_{10}$ and NeN$_{22}$, which confirms that they are dynamically stable under ambient pressure. Based on the analysis of the phonon density of states (PHDOS) of NeN$_{10}$ [Fig. S5(a)], we found that the phonon dispersion curve can be split into three groups: low-frequency acoustic modes (below 8 THz), low-frequency optic modes (8–24 THz), and high-frequency optic modes (24–42 THz). The acoustic modes primarily come from the contribution of vibrations of Ne atoms. The low-frequency optic vibrational modes are mainly contributed by the coupled vibrations between Ne and N atoms, while the high-frequency vibrational modes are dominated by N atoms. In contrast, the phonon modes corresponding to N atoms in NeN$_{22}$ dominate the whole frequency region compared to those of Ne atoms, which is closely related to the nitrogen framework. Notably, NeN$_{22}$ has an independent optical branch offered by N atoms at about 75 THz [Fig. S5(b)]. In addition, the absence of imaginary frequencies in the Brillouin zone indicates that $P6_3/m$ NeN$_{10}$ and $I4/m$ NeN$_{22}$ also exhibit good dynamic stability at 100 GPa (Fig. S6). NeN$_{6}$ becomes dynamically stable at 100 GPa [Fig. S7(a)]. However, it becomes unstable at 1 atm, so we will not discuss its property further. Meanwhile, we further remove the Ne atoms from the framework of $P6_3/m$ NeN$_{10}$ and $I4/m$ NeN$_{22}$ and explore the naked nitrogen properties. Moreover, the phonon dispersion curves show that the obtained nitrogen structures $P6_3/m$ N$_{10}$, t-N$_{22}$, and t-N$_{20}$ remain dynamically stable under ambient pressure [Fig. S6 in the Supporting Information, and Figs. 3(c) and 3(d)]. Surprisingly, they remain dynamically stable under ambient pressure, in which t-N$_{22}$ and t-N$_{20}$ with peculiar nitrogen structures are our focus.
cpl-39-5-056102-fig3.png
Fig. 3. (a)–(d) Phonon spectra of $P6_3/m$ NeN$_{10}$, $I4/m$ NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ at ambient pressure, where the horizontal red lines represent 0 THz. (e)–(g) Pair distribution functions of AIMD simulations of NeN$_{10}$, NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ at 300 K and pressure of 1 atm, wherein the vertical dashed lines represent the nearest or second shortest atomic distances of N–N, Ne–N, and Ne–Ne of the original structure. The terminal structures depicted in the inset graphics were obtained from the last step of molecular dynamics simulations.
To confirm the thermal stability of NeN$_{10}$, NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$, we performed molecular dynamics simulations at 1 atm and at different temperatures. As shown in Fig. S8, the total energies of these structures have no significant fluctuations with the evolution of time, indicating that they are in equilibrium at considered temperatures. To clearly reveal the efficiency of molecular dynamics simulations, the equilibrium structures were obtained from the last step of AIMD simulations. The radial distribution functions (RDFs) examine the thermal stability of NeN$_{10}$, NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ under ambient pressure and at 300 K, where the sharp peaks on the far left of each line represent the nearest N–N, Ne–N, and Ne–Ne distances, respectively [Figs. 3(e)–3(h)]. Generally, the closest distances between atoms of equilibrium structure have little change compared to the original structure, proving that this structure is thermally stable. For NeN$_{22}$, the first sharp peak of RDF is at approximately 1.09 Å, which matches well with the shortest N–N bond length of the N$_2$ dimer of the original structure (vertical dashed line). The second sharp peak representing the second shortest bond between nitrogen atoms is at 1.39 Å, which is consistent with the second shortest N–N bond length of the original structure. The first sharp peak of Ne–N is at approximately 2.31 Å, which agrees well with the shortest distance between Ne and N atoms of the original structure. Remarkably, the nearest N–N, Ne–N, and Ne–Ne distances have little change compared to those in the initial structures of NeN$_{10}$, NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$, which implies that they remain solid and keep thermal stability. As also can be seen from the insets in Figs. 3(e)–3(h), the terminal structures (NeN$_{10}$, NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$) from the last step of the AIMD simulations still retain their structural integrity. Furthermore, we performed the AIMD simulations at higher temperatures by adopting the initial structure. The AIMD simulations for NeN$_{10}$ at 1000 K and NeN$_{22}$ at 500 K [Figs. S9(a) and S9(b)] prove that they are still stable at higher temperatures. The above dynamic and thermal stability analyses of NeN$_{10}$ and NeN$_{22}$ indicate that they can be quenched to ambient conditions once synthesized at high pressure. In addition, we performed AIMD simulations of NeN$_{22}$ at a pressure of 76 GPa and a temperature of 300 K. As shown in Fig. S10(a), there is only a tiny difference in the simulated interatomic distance for the terminal structure compared to the original structure. The result shows that NeN$_{22}$ remains thermally stable at high pressure. In view of the above analysis, we prove that the ambient pressure polymerized nitrogen phases can be synthesized by removing the guest atoms from $I4/m$ NeN$_{22}$. The unique crystal structures in NeN$_{10}$ with N$_6$ and N$_{10}$ rings and NeN$_{22}$ with the N$_2$ dimers and N$_{20}$ framework further stimulate us to study their electronic properties. Strikingly, the calculated electronic bands and projected density of states (PDOS) of NeN$_{10}$ and NeN$_{22}$ at 1 atm reveal that they are semiconductors with large direct bandgaps of 2.8 and 3.0 eV, respectively (Fig. S11). As pressure increases up to 100 GPa, the increased band gaps of NeN$_{10}$ and NeN$_{22}$ become 3.8 and 4.6 eV, respectively [Figs. S12(a) and 4(a)]. In addition, NeN$_{22}$ was found to have a bandgap of 4.3 eV at an initial thermodynamically stable pressure of 76 GPa [Fig. S10(b)]. As illustrated in PDOS of Fig. S11, the obvious overlap between N $s$ and N $p$ orbitals exists in the valence band region, proving the strong coupling between N atoms and supporting the structural stability. Further, Bader charge analysis shows that the charge transfer from each Ne atom to N atoms in these two structures is less than $0.05|e|$ in NeN$_{10}$ and NeN$_{22}$ at 1 atm (Tables S3 and S4), which indicates that adding Ne has almost no effect on the electronic distribution of the N framework. Additionally, charge transfer could hardly be observed between the Ne and N atoms of NeN$_{10}$ and NeN$_{22}$ with further increasing pressures. However, for NeN$_{22}$, there are slightly large charge transfers from N$_{20}$ cages to N$_2$ dimers as pressure increases (Table S4), which indicates that the N atoms in NeN$_{22}$ can act as both cations and anions.
cpl-39-5-056102-fig4.png
Fig. 4. Electronic properties and the weak noncovalent interactions of $I4/m$ NeN$_{22}$ at 100 GPa. (a) Electronic band structures and (b) the minus projected crystal orbital Hamiltonian population (–pCOHP), where the horizontal dashed line represents the Fermi level. (c) The two-dimensional (2D) and (d) three-dimensional (3D) plots of RDG versus the electron density multiplied by the sign of the second Hessian eigenvalue ($\lambda _2$). The solid red line region in (c) represents the vdW interactions in the crystalline.
To investigate the reasons for the bonding characteristics of NeN$_{10}$ and NeN$_{22}$, we calculated their minus projected COHP (–pCOHP) at 100 GPa, as shown in Figs. 4(b) and S12(b). In general, the positive and negative –pCOHPs characterize the bonding and antibonding states, respectively. The –pCOHP for averaged nitrogen-nitrogen pair (N–N) [Fig. 4(b)] demonstrates that there is a bonding state between nitrogen atoms in the N$_2$ dimers, while the antibonding interactions between the shortest N–N of N$_{20}$ cage or N$_2$ dimers and N$_{20}$ cages are both negative in the energy range from $-6$ to 0 eV below the top of the valence bands. For NeN$_{10}$, the integrated COHP (ICOHP) values of Ne–N and N–N pairs are 0.01 and $-12.90$ eV/pair up to the Fermi level, respectively. For NeN$_{22}$, the ICOHP values of the N–N bond in N$_2$ dimer and the nearest N–N bond in N$_{20}$ up to the Fermi level are $-8.86$ and $-24.54$ eV/pair (Table S5), respectively, which shows that the triple bond in N$_2$ dimer is stronger than both the single and the double bond in N$_{20}$. The ICOHP values among N$_{20}$, Ne, and N$_2$ dimers are close to 0 eV/pair, further indicating that Ne and N$_2$ can be removed. Although the vdW interactions in nitrides bearing noble elements have been studied, there are no quantitative studies on the weak interactions in nitrides bearing noble elements. At the same time, due to the low electron density, the intricate weak noncovalent interactions (NCIs) cannot be identified via some analysis algorithms such as Bader charge transfer and ELF. Therefore, we introduce the reduced density gradient (RDG) to gain additional insight into the stable mechanism of the $P6_3/m$ NeN$_{10}$ and host-guest structure $I4/m$ NeN$_{22}$ at 100 GPa [Figs. S12(c) and 4(c)]. RDG is defined as $$ s = [2(3\pi^2)]^2| \Delta \rho |^{-4/3},~~ \tag {2} $$ where $\rho$ represents the electron density. To distinguish the different types of interactions, we multiplied RDG by the sign of the second Hessian eigenvalue [sign($\lambda _2$)] of $\Delta2\rho$. The low-density [sign($\lambda _2$)$\rho$ (arb. units)] and low-gradient [$s$ (arb. units)] spikes indicate the existence of weak interactions. The two-dimensional (2D) and related three-dimensional (3D) graphs of RDG can clearly show the NCI regions [Figs. 4(c), 4(d), S12(c), and S12(d)]. The areas surrounded by solid red lines in 2D graphs of RDG represent the vdW interactions in NeN$_{10}$ and NeN$_{22}$, corresponding to green contours plotted in 3D graphs of RDG. The cyan and red counters in 3D graphs of RDG display attractive and repulsive interactions, respectively. As seen in Fig. S12(d), the attractive interaction is stronger than the repulsive one around the Ne atoms in NeN$_{10}$. For NeN$_{22}$, button-like red contours are located around the Ne atoms and the N$_2$ dimers, indicating that the repulsive interaction is stronger than the attractive interaction. The results are consistent with the –pCOHP, also indicating that guest atoms can be removed in NeN$_{22}$. The decomposition enthalpies of $P6_3/m$ NeN$_{10}$ and $I4/m$ NeN$_{22}$ relative to Ne and nitrogen at ambient pressure are 1.61 and 1.64 eV/atom, respectively, indicating that they are potential high-energy-density materials. Thus, the energy density and explosive performance of NeN$_{10}$ and NeN$_{22}$ are further studied, in which the energy of nitrogen molecule is adopted.[58,59] NeN$_{10}$ and NeN$_{22}$ can be detonated in the following ways: NeN$_{10}$ (solid) $\rightarrow $ Ne (gaseous) + 5N$_2$ (gaseous), NeN$_{22}$ (solid) $\rightarrow $ Ne (gaseous) + 11N$_2$ (gaseous). Further calculations show that the energy densities ($E_{\rm d}$) of NeN$_{10}$ with density of 3.24 g/cm$^3$ and NeN$_{22}$ with a density of 3.17 g/cm$^3$ are estimated to be approximately 11.1 and 11.5 kJ/g, respectively, which are significantly larger than trinitrotoluene (TNT, 4.3 kJ/g) and 1,3,5,7-tetrazoctane (HMX, 5.7 kJ/g).[69] More interestingly, t-N$_{22}$ and t-N$_{20}$ exhibit high-energy densities of 11.6 and 12.0 kJ/g, respectively, which are higher than those of all reported polynitrogen materials. Additionally, as shown in Table 1, we also estimate the explosive performance including detonation velocity ($V_{\rm d}$) and pressure ($P_{\rm d}$) of $P6_3/m$ NeN$_{10}$, $I4/m$ NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ through the Kamlet–Jacobs empirical equation.[70] Its validity has been widely confirmed.[71–75] Using these equations, we also calculated detonation velocity and pressure for TNT and HMX, where the monoclinic $P2_1/c$ TNT and $P2_1/c$ HMX are adopted.[76,77] The differences between the calculated and experimental values for TNT and HMX are within acceptable limits (Table 1), indicating that our calculation methods are applicable. The Kamlet–Jacobs empirical equations are as follows: $$ V_{\rm d}=1.01(NM^{0.5}E_{\rm d}^{0.5})^{0.5}(1+1.30\rho),~~ \tag {3} $$ $$ P_{\rm d}=15.58\rho ^2NM^{0.5}E_{\rm d}^{0.5}. ~~~~~~~~~~~~~~~~~ \tag {4} $$ Here, $N$, $M$, and $\rho$ represent moles of N$_2$ per gram of explosives (mol/g), the molar mass for N$_2$ gas (28 g/mol), and the density (g/cm$^3$), respectively. A large amount of N$_2$ is released when NeN$_{10}$ and NeN$_{22}$ explode, resulting in a huge $P_{\rm d}$ and detonation velocity. We found that NeN$_{10}$ and NeN$_{22}$ release a huge detonation velocity of about 3 times higher than that of TNT and an explosion pressure of about 14 times than that of TNT. Notably, the calculated $V_{\rm d}$ of t-N$_{22}$ and t-N$_{20}$ (22.82 and 22.09 km/s) are approximately 2 times higher than that of TNT (6.90 km/s) and twice the value of HMX (9.10 km/s).[69,70] $P6_3/m$ NeN$_{10}$, $I4/m$ NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ can be considered as candidates for high-energy-density materials.
Table 1. Calculated moles of dinitrogen gas per gram of explosives ($N$), density $\rho$, energy density $E_{\rm d}$, volumetric energy density $E_{\rm v}$, detonation velocity $V_{\rm d}$, and detonation pressure $P_{\rm d}$ of NeN$_{10}$, NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$. For comparison, experimental values for the known TNT and HMX explosives are also listed.[69,78] Herein, superscript expt represents the experimental data.
$N$ (mol/g) $\rho$ (g/cm$^3$) $E_{\rm d}$ (kJ/g) $E_{\rm v}$ (kJ/cm$^3$) $V_{\rm d}$ (km/s) $P_{\rm d}$ (kbar)
NeN$_{10}$ 0.0313 3.24 11.1 35.96 21.96 2848
NeN$_{22}$ 0.0335 3.17 11.5 36.45 22.55 2977
t-N$_{22}$ 0.0357 3.08 11.6 35.72 22.82 3014
t-N$_{20}$ 0.0357 2.92 12.0 35.04 22.09 2764
TNT 1.62 3.9 6.32 6.76 189
TNT$^{\rm expt}$ 1.64 4.3 7.05 6.90 190
HMX 1.90 3.4 6.46 10.1 470
HMX$^{\rm expt}$ 1.90 5.7 10.83 9.10 393
In summary, to obtain high-energy-density Ne-containing nitrides, we have systematically studied Ne–N systems under high pressure by exploiting the first-principles swarm-intelligence structure search and calculated the convex hull of the Ne–N systems at 1 atm, 50 GPa, and 100 GPa. Strikingly, three previously unknown thermodynamically stable Ne–N phases are determined: $R\bar{3}m$ NeN$_{6}$, $P6_3/m$ NeN$_{10}$, and $I4/m$ NeN$_{22}$. Introducing Ne atoms into a pure nitrogen system can greatly reduce the synthesis pressure to form single and double N bonds compared to the synthesis with pure nitrogen. The predicted structures exhibit various forms of nitrogen: molecular N$_2$, N$_6$ ring, N$_{10}$ ring, and N$_{20}$. Interestingly, the reduced density gradient exhibits the weak non-covalent interactions between the Ne and N atoms, which stabilize the guest atoms within the host framework. In particular, NeN$_{10}$ and NeN$_{22}$ are dynamically and mechanically stable under ambient pressure. Based on the unique structure of $I4/m$ NeN$_{22}$ and weak interactions between host and guest, we propose to remove Ne or Ne and N$_2$ dimers in NeN$_{22}$ from the natural channels of the structure, and the unique pure tetragonal polymeric nitrogen structures t-N$_{22}$ and t-N$_{20}$ are obtained. Furthermore, the nitrogen framework in NeN$_{22}$ remains dynamically stable under ambient pressure after the removal of the Ne atom or Ne and N$_2$. The AIMD calculations suggest that NeN$_{10}$ and NeN$_{22}$ are thermally stable up to 1000 and 500 K under ambient pressure, respectively. More importantly, these results indicate that they are potentially quenchable to ambient conditions. The estimated energy density of NeN$_{10}$, NeN$_{22}$, t-N$_{22}$, or t-N$_{20}$ is more than 2 times larger than that of TNT. In addition, the detonation velocity and the detonation pressures of NeN$_{10}$, NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ are significantly larger than those of TNT and HMX. The results demonstrate that $P6_3/m$ NeN$_{10}$, $I4/m$ NeN$_{22}$, t-N$_{22}$, and t-N$_{20}$ are promising high-energy-density materials. Our work provides insights into the formation and properties of Ne–N compounds and deepens the understanding of the evolution of planets. Acknowledgments. This work was supported by the National Key Research and Development Program of China (Grant No. 2021YFA1400400), the Fundamental Research Funds for the Central Universities (Grant No. 020414380185), the Natural Science Foundation of Jiangsu Province (Grant No. BK20200007), the National Natural Science Foundation of China (Grant Nos. 12074181, 11834006, and 11704062), the Fok Ying-Tong Education Foundation of China (Grant No. 161006), and the Fund from Jilin Province (Grant No. JJKH20221152KJ). References THE INTERIORS OF GIANT PLANETS: Models and Outstanding QuestionsContribution of climatic changes in mean and variability to monthly temperature and precipitation extremesA stable compound of helium and sodium at high pressureHelium-Iron Compounds at Terapascal PressuresRare Helium-Bearing Compound FeO 2 He Stabilized at Deep-Earth ConditionsPrediction of pressure-induced stabilization of noble-gas-atom compounds with alkali oxides and alkali sulfidesReactivity of He with ionic compounds under high pressureReactivity of Xenon with Ice at Planetary ConditionsFormation and properties of ice XVI obtained by emptying a type sII clathrate hydrateStable structures of He and H 2 O at high pressureMultiple superionic states in helium–water compoundsVibrational line broadening in the mixed solid N 2 – Kr :   A high-pressure Raman study of the phase diagramHighly repulsive interaction in novel inclusion D2 –N2 compound at high pressure: Raman and x-ray evidenceThermodynamic Stability and Growth of Guest-Free Clathrate Hydrates: A Low-Density Crystal Phase of WaterStable xenon nitride at high pressuresProperties and Promise of Catenated Nitrogen Systems As High-Energy-Density MaterialsPolymeric nitrogenSingle-bonded cubic form of nitrogenNovel High Pressure Structures of Polymeric NitrogenCagelike Diamondoid Nitrogen at High PressuresStable All-Nitrogen Metallic Salt at Terapascal PressuresSingle-bonded allotrope of nitrogen predicted at high pressureNitrogen in black phosphorus structureHigh-Pressure Polymeric Nitrogen Allotrope with the Black Phosphorus StructureMetal azides under pressure: An emerging class of high energy density materialsHigh pressure X-ray diffraction study of potassium azidePressure-induced stable BeN 4 as a high-energy density materialModerate Pressure Stabilized Pentazolate Cyclo-N5– Anion in Zn(N5 )2 SaltCrystalline LiN5 Predicted from First-Principles as a Possible High-Energy MaterialPressure-stabilized GdN6 with an armchair–antiarmchair structure as a high energy density materialA high-pressure van der Waals compound in solid nitrogen-helium mixturesRoute to high-energy density polymeric nitrogen t-N via He−N compoundsHelium-nitrogen mixtures at high pressure ( N 2 ) 6 Ne 7 : A High Pressure van der Waals Insertion CompoundCrystal structure prediction via particle-swarm optimizationCALYPSO: A method for crystal structure predictionSubstitutional Alloy of Bi and Te at High PressurePredicted Novel High-Pressure Phases of LithiumCaesium in high oxidation states and as a p-block elementHexagonal BC2 N with Remarkably High HardnessGeneralized Gradient Approximation Made SimpleEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setProjector augmented-wave method"Special points for Brillouin-zone integrations"—a replyFirst-Principles Determination of the Soft Mode in Cubic ZrO 2 First principles phonon calculations in materials scienceA consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-PuEffect of the damping function in dispersion corrected density functional theoryCrystal Structure and Pair Potentials: A Molecular-Dynamics StudyA simple measure of electron localization in atomic and molecular systemsCrystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculationsLOBSTER: A tool to extract chemical bonding from plane-wave based DFTRevealing Noncovalent InteractionsCritic2: A program for real-space analysis of quantum chemical interactions in solidsVMD: Visual molecular dynamicsHigh-pressure phases of solid nitrogen by Raman and infrared spectroscopyHigh-Pressure Phases of NitrogenFirst-principle study of solid neon under high compressionMobile Bjerrum defects: A criterion for ice‐like crystal growthLow-density framework form of crystalline silicon with a wide optical band gapA guest-free germanium clathrateCrystal structures and elastic properties of superhard Ir N 2 and Ir N 3 from first principlesSymmetry-general least-squares extraction of elastic data for strained materials from ab initio calculations of stressThe Elastic Behaviour of a Crystalline AggregateTheoretical model of intrinsic hardnessChemistry of Detonations. III. Evaluation of the Simplified Calculational Method for Chapman‐Jouguet Detonation Pressures on the Basis of Available Experimental Information3,4,5-Trinitropyrazole-Based Energetic SaltsDerivatives of 1,5-Diamino-1 H -tetrazole: A New Family of Energetic Heterocyclic-Based SaltsA deep neural network surrogate modeling benchmark for temperature field prediction of heat source layoutStrategies for Achieving Balance between Detonation Performance and Crystal Stability of High-Energy-Density MaterialsPolymorphism in 2-4-6 TrinitrotolueneA study of the crystal structure of β-cyclotetramethylene tetranitramine by neutron diffractionPredictions on High-Power Trivalent Metal Pentazolate Salts
[1] Guillot T 2005 Annu. Rev. Earth Planet. Sci. 33 493
[2] Vogt M, Trieloff M, Ott U, Hopp J, and Schwarz W H 2021 Commun. Earth Environ. 2 1
[3] Dong X, Oganov A R, Goncharov A F et al. 2017 Nat. Chem. 9 440
[4] Monserrat B, Martinez-Canales M, Needs R J, and Pickard C J 2018 Phys. Rev. Lett. 121 015301
[5] Zhang J, Lv J, Li H, Feng X, Lu C, Redfern S A, Liu H, Chen C, and Ma Y 2018 Phys. Rev. Lett. 121 255703
[6] Gao H, Sun J, Pickard C J, and Needs R J 2019 Phys. Rev. Mater. 3 015002
[7] Liu Z, Botana J, Hermann A, Valdez S, Zurek E, Yan D, Lin H Q, and Miao M S 2018 Nat. Commun. 9 951
[8] Sanloup C, Bonev S A, Hochlaf M, and Casely H E M 2013 Phys. Rev. Lett. 110 265501
[9] Falenty A, Hansen T C, and Kuhs W F 2014 Nature 516 231
[10] Liu H, Yao Y, and Klug D D 2015 Phys. Rev. B 91 014102
[11] Liu C, Gao H, Wang Y, Needs R J, Pickard C J, Sun J, Wang H T, and Xing D 2019 Nat. Phys. 15 1065
[12] Lotz H and Schouten J 2001 Phys. Rev. B 64 184101
[13] Kim M and Yoo C S 2011 J. Chem. Phys. 134 044519
[14] Jacobson L C, Hujo W, and Molinero V 2009 J. Phys. Chem. B 113 10298
[15] Peng F, Wang Y, Wang H, Zhang Y, and Ma Y 2015 Phys. Rev. B 92 094104
[16]Cotton F A, Wilkinson G, Murillo C A, Bochmann M, and Grimes R 1988 Advanced Inorganic Chemistry 6 edn (New York: Wiley)
[17] O'Sullivan O T O and Zdilla M J 2020 Chem. Rev. 120 5682
[18]Stierstorfer J and Klapotke T M 2010 Annu. Rev. Earth Planet. 33 493
[19] Mailhiot C, Yang L, and McMahan A 1992 Phys. Rev. B 46 14419
[20] Eremets M I, Gavriliuk A G, Trojan I A, Dzivenko D A, and Boehler R 2004 Nat. Mater. 3 558
[21] Ma Y, Oganov A R, Li Z, Xie Y, and Kotakoski J 2009 Phys. Rev. Lett. 102 065501
[22] Wang X, Wang Y, Miao M, Zhong X, Lv J, Cui T, Li J, Chen L, Pickard C J, and Ma Y 2012 Phys. Rev. Lett. 109 175502
[23] Sun J, Martinez-Canales M, Klug D D, Pickard C J, and Needs R J 2013 Phys. Rev. Lett. 111 175502
[24] Adeleke A A, Greschner M J, Majumdar A, Wan B, Liu H, Li Z, Gou H, and Yao Y 2017 Phys. Rev. B 96 224104
[25] Ji C, Adeleke A A, Yang L, Wan B, Gou H, Yao Y, Li B, Meng Y, Smith J S, Prakapenka V B et al. 2020 Sci. Adv. 6 eaba9206
[26] Laniel D, Winkler B, Fedotenko T, Pakhomova A, Chariton S, Milman V, Prakapenka V, Dubrovinsky L, and Dubrovinskaia N 2020 Phys. Rev. Lett. 124 216001
[27] Vaitheeswaran G and Babu K R 2012 J. Chem. Sci. 124 1391
[28] Ji C, Zhang F, Hou D, Zhu H, Wu J, Chyu M C, Levitas V I, and Ma Y 2011 J. Phys. Chem. Solids 72 736
[29] Zhang S, Zhao Z, Liu L, and Yang G 2017 J. Power Sources 365 155
[30] Liu Z, Li D, Tian F, Duan D, Li H, and Cui T 2020 Inorg. Chem. 59 8002
[31] Peng F, Yao Y, Liu H, and Ma Y 2015 J. Phys. Chem. Lett. 6 2363
[32] Liu L, Wang D, Zhang S, and Zhang H 2021 J. Mater. Chem. A 9 16751
[33] Vos D W, Finger L, Hemley R, Hu J, Mao H, and Schouten J 1992 Nature 358 46
[34] Li Y, Feng X, Liu H, Hao J, Redfern S A, Lei W, Liu D, and Ma Y 2018 Nat. Commun. 9 722
[35] Hou J, Weng X J, Oganov A R, Shao X, Gao G, Dong X, Wang H T, Tian Y, and Zhou X F 2021 Phys. Rev. B 103 L060102
[36] Plisson T, Weck G, and Loubeyre P 2014 Phys. Rev. Lett. 113 025702
[37] Wang Y, Lv J, Zhu L, and Ma Y 2010 Phys. Rev. B 82 094116
[38] Wang Y, Lv J, Zhu L, and Ma Y 2012 Comput. Phys. Commun. 183 2063
[39] Zhu L, Wang H, Wang Y, Lv J, Ma Y, Cui Q, Ma Y, and Zou G 2011 Phys. Rev. Lett. 106 145501
[40] Lv J, Wang Y, Zhu L, and Ma Y 2011 Phys. Rev. Lett. 106 015503
[41] Miao M S 2013 Nat. Chem. 5 846
[42] Liu L, Zhao Z, Yu T, Zhang S, Lin J, and Yang G 2018 J. Phys. Chem. C 122 6801
[43] Perdew J P, Burke K, and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[44] Kresse G and Furthmuller J 1996 Phys. Rev. B 54 11169
[45] Blochl P E 1994 Phys. Rev. B 50 17953
[46] Pack J D and Monkhorst H J 1977 Phys. Rev. B 16 1748
[47] Parlinski K, Li Z, and Kawazoe Y 1997 Phys. Rev. Lett. 78 4063
[48] Togo A and Tanaka I 2015 Scr. Mater. 108 1
[49] Grimme S, Antony J, Ehrlich S, and Krieg H 2010 J. Chem. Phys. 132 154104
[50] Grimme S, Ehrlich S, and Goerigk L 2011 J. Comput. Chem. 32 1456
[51] Parrinello M and Rahman A 1980 Phys. Rev. Lett. 45 1196
[52] Becke A D and Edgecombe K E 1990 J. Chem. Phys. 92 5397
[53] Dronskowski R and Blochl P E 1993 J. Chem. Phys. 97 8617
[54] Maintz S, Deringer V L, Tchougreeff A L, and Dronskowski R 2016 J. Comput. Chem. 37 1030
[55] Mori-Sanchez H, Contreras J, Cohen A J, and Yang W 2010 J. Am. Chem. Soc. 132 6498
[56] Otero-de-la-Roza A, Johnson E R, and Luaña V 2014 Comput. Phys. Commun. 185 1007
[57] Humphrey W, Dalke A, and Schulten K 1996 J. Mol. Graphics 14 33
[58] Bini L R, Ulivi L, Kreutz J, and Jodl H J 2000 J. Chem. Phys. 112 8522
[59] Pickard C J and Needs R 2009 Phys. Rev. Lett. 102 125702
[60] He Y G, Tang X Z, and Pu Y K 2010 Physica B 405 4335
[61] Wooldridge P J, Richardson H H, and Devlin J P 1987 J. Chem. Phys. 87 4126
[62] Gryko J, McMillan P F, Marzke R F, Ramachandran G K, Patton D, Deb S K, and Sankey O F 2000 Phys. Rev. B 62 R7707
[63] Guloy A M and Ramlau R 2006 Nature 443 320
[64] Wu Z J, Zhao E J, Xiang H P, Hao X F, Liu X J, and Meng J 2007 Phys. Rev. B 76 054115
[65] Page Y L and Saxe P 2002 Phys. Rev. B 65 104104
[66] Hill R 1952 Proc. Phys. Soc. Sect. A 65 349
[67] Gao F 2006 Phys. Rev. B 73 132104
[68]Gale W F and Totemeier T C 2003 Smithells Metals Reference Book (Amsterdam: Elsevier)
[69]Dobratz and Brigitta M 1985 OSTI.GOV/Technical Report: LLNL Explosives Handbook: Properties of Chemical Explosives and Explosives and Explosive Simulants (CA: Lawrence Livermore National Lab)
[70] Kamlet M J and Dickinson C 1968 J. Chem. Phys. 48 43
[71] Zhang Y, Guo Y, Joo Y H, Parrish D A, and Shreeve J M 2010 Chem. - Eur. J. 16 10778
[72] Galvez-Ruiz J C, Holl G, Karaghiosoff K, Klapotke T M et al. 2005 Inorg. Chem. 44 4237
[73]Klapotke T M 2019 Chemistry of High-Energy Materials (Boston: de Gruyter)
[74] Yuan J, Xia K, Wu J, and Sun J 2021 Sci. Chin.: Phys. Mech. Astron. 64 1
[75] Li C, Li H, Zong H H, Huang Y, Gozin M, Sun C Q, and Zhang L 2020 iScience 23 100944
[76] Vrcelj R M, Sherwood J N, Kennedy A R, Gallagher H G, and Gelbrich T 2003 Cryst. Growth & Des. 3 1027
[77] Choi C S and Boutin H P 1970 Acta Crystallogr. B 26 1235
[78] Xia K, Yuan J, Zheng X, Liu C, Gao H, Wu Q, and Sun J 2019 J. Phys. Chem. Lett. 10 6166